Subgroups — C₄×C₂₃×#546 #19181783

Order 5888.

3720 conjugacy classes of subgroups.

The subgroup lattice has 1210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#546	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2364	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2359	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2358	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2349	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2342	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2339	C₂	1	1	yes	maximal, characteristic, complemented
14	D₄×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₂₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₂₃×#123	C₂	1	2	yes	maximal, complemented
18	C₄×C₂₃×#121	C₂	1	2	yes	maximal, complemented
19	C₄×C₂₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₂₃×#120	C₂	1	2	yes	maximal, complemented
21	C₄²×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄²×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×C₂²⋊C₄×C₂₃	C₂	1	2	yes	maximal, complemented
24	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
25	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₂⁴×C₄×C₂₃	C₂²	1	2	yes	—
27	C₂₃×#546	C₄	1	16	yes	direct product factor
28	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#123	C₂²	1	2	yes	—
30	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#121	C₂²	1	2	yes	—
33	C₂×C₂₃×#120	C₂²	1	2	yes	—
34	C₄×#41×C₂₃	—	2	8	no	—
35	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄×D₄×C₂₃	—	2	8	no	—
38	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
51	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
52	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
53	C₂×C₂₃×#117	C₂²	1	2	yes	complemented
54	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
55	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
56	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
57	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
58	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
59	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
60	C₂²×C₄²×C₂₃	C₂²	1	2	yes	complemented
61	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
62	C₂²×C₄²×C₂₃	C₂²	1	2	yes	complemented
63	C₂₃×#391	C₂²	1	1	yes	characteristic, complemented
64	C₂₃×#391	C₂²	1	1	yes	characteristic, complemented
65	C₂₃×#390	C₂²	1	1	yes	characteristic
66	C₂₃×#390	C₂²	1	1	yes	characteristic
67	C₂₃×#390	C₂²	1	2	yes	complemented
68	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
69	C₂₃×#389	C₂²	1	2	yes	complemented
70	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
71	C₂₃×#388	C₂²	1	2	yes	complemented
72	C₂₃×#388	C₂²	1	2	yes	complemented
73	C₂₃×#388	C₂²	1	2	yes	complemented
74	C₂₃×#388	C₂²	1	2	yes	complemented
75	C₂₃×#388	C₂²	1	2	yes	complemented
76	C₂₃×#388	C₂²	1	2	yes	complemented
77	C₂₃×#388	C₂²	1	2	yes	complemented
78	C₂₃×#387	C₂²	1	2	yes	complemented
79	C₂₃×#387	C₂²	1	2	yes	complemented
80	C₂₃×#387	C₂²	1	2	yes	complemented
81	C₂₃×#386	C₂²	1	2	yes	—
82	C₂₃×#386	C₂²	1	2	yes	—
83	C₂₃×#386	C₂²	1	2	yes	—
84	C₂₃×#386	C₂²	1	2	yes	complemented
85	C₂₃×#386	C₂²	1	2	yes	complemented
86	C₂₃×#386	C₂²	1	2	yes	complemented
87	C₂₃×#386	C₂²	1	2	yes	complemented
88	C₂₃×#385	C₂²	1	2	yes	—
89	C₂₃×#385	C₂²	1	2	yes	—
90	C₂₃×#385	C₂²	1	2	yes	complemented
91	C₂₃×#385	C₂²	1	2	yes	complemented
92	C₂₃×#385	C₂²	1	2	yes	complemented
93	C₂₃×#382	C₂²	1	1	yes	characteristic, complemented
94	C₂₃×#381	C₂²	1	2	yes	complemented
95	C₂₃×#380	C₂²	1	1	yes	characteristic
96	C₂₃×#380	C₂²	1	1	yes	characteristic, complemented
97	C₂₃×#380	C₂²	1	2	yes	complemented
98	C₂₃×#379	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
104	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
105	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
106	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
107	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
108	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
109	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
110	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
111	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
112	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
113	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
114	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
115	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
116	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
117	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
120	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
121	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
123	C₂×C₂₃×#95	C₂²	1	2	yes	complemented
124	C₂×C₂₃×#95	C₂²	1	2	yes	complemented
125	C₄³×C₂₃	C₂²	1	1	yes	characteristic, complemented
126	C₂⁵×C₂₃	C₂³	1	2	yes	—
127	C₂×#41×C₂₃	—	2	4	no	—
128	C₂×#41×C₂₃	—	2	4	no	—
129	C₂×#41×C₂₃	C₂×C₄	1	8	yes	complemented
130	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₂₃	—	2	4	no	—
132	C₂²×D₄×C₂₃	—	2	4	no	—
133	C₂²×D₄×C₂₃	C₂×C₄	1	8	yes	complemented
134	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
135	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
138	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
139	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₂₃	—	2	8	no	—
141	C₂³×C₄×C₂₃	—	2	8	no	—
142	C₂³×C₄×C₂₃	—	4	4	no	—
143	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
144	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
146	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
147	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
148	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
149	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
150	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
151	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
152	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
153	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
154	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
155	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
156	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
157	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
158	C₂₃×#124	C₂×C₄	1	8	yes	complemented
159	C₂₃×#123	C₂×C₄	1	16	yes	complemented
160	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
161	C₂₃×#121	C₂×C₄	1	8	yes	complemented
162	C₂₃×#121	C₂×C₄	1	16	yes	complemented
163	C₂₃×#120	C₂×C₄	1	16	yes	complemented
164	C₄×Q₈×C₂₃	—	2	4	no	—
165	C₄×Q₈×C₂₃	—	2	4	no	—
166	C₄×D₄×C₂₃	—	2	4	no	—
167	C₄×D₄×C₂₃	—	2	4	no	—
168	C₄×D₄×C₂₃	—	2	4	no	—
169	C₄×D₄×C₂₃	—	2	8	no	—
170	C₄×D₄×C₂₃	—	2	8	no	—
171	C₄×D₄×C₂₃	—	2	4	no	—
172	C₄×D₄×C₂₃	—	2	4	no	—
173	C₄×D₄×C₂₃	—	2	8	no	—
174	C₄×D₄×C₂₃	—	2	8	no	—
175	C₄×D₄×C₂₃	—	2	4	no	—
176	C₄×D₄×C₂₃	—	2	4	no	—
177	C₄×D₄×C₂₃	—	4	4	no	—
178	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	complemented
179	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	complemented
180	C₄×D₄×C₂₃	D₄	1	8	yes	complemented
181	C₂₃×#117	—	2	4	no	—
182	C₂₃×#117	—	2	8	no	—
183	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
184	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
199	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
200	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	16	yes	complemented
201	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₂₃	—	2	8	no	—
226	C₂×C₄²×C₂₃	—	2	4	no	—
227	C₂×C₄²×C₂₃	—	2	4	no	—
228	C₂×C₄²×C₂₃	—	4	4	no	—
229	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
232	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
233	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
238	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
239	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
240	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
241	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
242	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
243	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
244	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
245	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
246	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
247	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
248	C₂₃×#95	C₂³	1	1	yes	characteristic
249	C₂₃×#95	C₂³	1	1	yes	characteristic
250	C₂₃×#95	C₂³	1	2	yes	—
251	C₂₃×#95	C₂³	1	2	yes	—
252	C₂₃×#95	C₂³	1	2	yes	—
253	C₂₃×#95	C₂³	1	2	yes	—
254	C₂₃×#95	C₂³	1	2	yes	—
255	C₂₃×#95	C₂³	1	2	yes	—
256	C₂₃×#95	C₂³	1	1	yes	characteristic
257	C₂₃×#95	C₂³	1	1	yes	characteristic
258	C₂₃×#95	C₂³	1	1	yes	characteristic
259	C₂₃×#95	C₂³	1	1	yes	characteristic
260	C₂₃×#95	C₂³	1	2	yes	—
261	C₂₃×#95	C₂³	1	2	yes	—
262	C₂₃×#95	C₂³	1	2	yes	—
263	C₂₃×#95	C₂³	1	2	yes	—
264	C₂₃×#95	C₂³	1	2	yes	—
265	C₂₃×#95	C₂³	1	2	yes	—
266	C₂₃×#95	C₂³	1	2	yes	—
267	C₂⁴×C₂₃	—	2	4	no	—
268	C₂⁴×C₂₃	—	2	4	no	—
269	C₂⁴×C₂₃	—	2	4	no	—
270	C₂⁴×C₂₃	—	2	4	no	—
271	C₂⁴×C₂₃	—	4	2	no	—
272	C₂⁴×C₂₃	—	4	2	no	—
273	C₂⁴×C₂₃	C₂²×C₄	1	8	yes	—
274	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
275	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
276	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
277	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
278	#41×C₂₃	—	2	32	no	—
279	C₂×Q₈×C₂₃	—	2	2	no	—
280	C₂×Q₈×C₂₃	—	2	2	no	—
281	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	complemented
282	C₂×D₄×C₂₃	—	2	4	no	—
283	C₂×D₄×C₂₃	—	2	4	no	—
284	C₂×D₄×C₂₃	—	2	2	no	—
285	C₂×D₄×C₂₃	—	2	2	no	—
286	C₂×D₄×C₂₃	—	2	4	no	—
287	C₂×D₄×C₂₃	—	2	4	no	—
288	C₂×D₄×C₂₃	—	2	32	no	—
289	C₂×D₄×C₂₃	—	2	2	no	—
290	C₂×D₄×C₂₃	—	2	2	no	—
291	C₂×D₄×C₂₃	—	4	2	no	—
292	C₂×D₄×C₂₃	—	4	2	no	—
293	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
294	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
295	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
296	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
297	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	complemented
298	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	complemented
299	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
300	C₂×D₄×C₂₃	#41	1	4	yes	—
301	C₂²×C₄×C₂₃	—	2	4	no	—
302	C₂²×C₄×C₂₃	—	2	4	no	—
303	C₂²×C₄×C₂₃	—	2	2	no	—
304	C₂²×C₄×C₂₃	—	2	2	no	—
305	C₂²×C₄×C₂₃	—	2	2	no	—
306	C₂²×C₄×C₂₃	—	2	4	no	—
307	C₂²×C₄×C₂₃	—	2	2	no	—
308	C₂²×C₄×C₂₃	—	2	2	no	—
309	C₂²×C₄×C₂₃	—	2	4	no	—
310	C₂²×C₄×C₂₃	—	2	2	no	—
311	C₂²×C₄×C₂₃	—	2	4	no	—
312	C₂²×C₄×C₂₃	—	2	4	no	—
313	C₂²×C₄×C₂₃	—	2	4	no	—
314	C₂²×C₄×C₂₃	—	2	2	no	—
315	C₂²×C₄×C₂₃	—	2	4	no	—
316	C₂²×C₄×C₂₃	—	2	2	no	—
317	C₂²×C₄×C₂₃	—	2	2	no	—
318	C₂²×C₄×C₂₃	—	2	2	no	—
319	C₂²×C₄×C₂₃	—	2	4	no	—
320	C₂²×C₄×C₂₃	—	2	4	no	—
321	C₂²×C₄×C₂₃	—	2	4	no	—
322	C₂²×C₄×C₂₃	—	2	4	no	—
323	C₂²×C₄×C₂₃	—	2	4	no	—
324	C₂²×C₄×C₂₃	—	2	2	no	—
325	C₂²×C₄×C₂₃	—	2	2	no	—
326	C₂²×C₄×C₂₃	—	2	4	no	—
327	C₂²×C₄×C₂₃	—	2	4	no	—
328	C₂²×C₄×C₂₃	—	2	4	no	—
329	C₂²×C₄×C₂₃	—	2	2	no	—
330	C₂²×C₄×C₂₃	—	2	4	no	—
331	C₂²×C₄×C₂₃	—	4	2	no	—
332	C₂²×C₄×C₂₃	—	4	2	no	—
333	C₂²×C₄×C₂₃	—	4	2	no	—
334	C₂²×C₄×C₂₃	—	4	2	no	—
335	C₂²×C₄×C₂₃	—	4	2	no	—
336	C₂²×C₄×C₂₃	—	4	2	no	—
337	C₂²×C₄×C₂₃	—	4	1	no	—
338	C₂²×C₄×C₂₃	—	4	1	no	—
339	C₂²×C₄×C₂₃	—	4	2	no	—
340	C₂²×C₄×C₂₃	—	4	32	no	—
341	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
342	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	complemented
343	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	complemented
344	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	complemented
345	C₂²×C₄×C₂₃	C₂×D₄	1	8	yes	—
346	C₂²×C₄×C₂₃	#41	1	4	yes	complemented
347	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
352	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
353	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
357	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
358	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
361	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₂₃	—	2	4	no	—
367	C₄⋊C₄×C₂₃	—	2	2	no	—
368	C₄⋊C₄×C₂₃	—	2	4	no	—
369	C₄⋊C₄×C₂₃	—	2	4	no	—
370	C₄⋊C₄×C₂₃	—	2	2	no	—
371	C₄⋊C₄×C₂₃	—	2	2	no	—
372	C₄⋊C₄×C₂₃	—	2	2	no	—
373	C₄⋊C₄×C₂₃	—	2	2	no	—
374	C₄⋊C₄×C₂₃	—	4	2	no	—
375	C₄⋊C₄×C₂₃	—	4	2	no	—
376	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	complemented
377	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	complemented
378	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	complemented
379	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
380	C₂²⋊C₄×C₂₃	—	2	4	no	—
381	C₂²⋊C₄×C₂₃	—	2	4	no	—
382	C₂²⋊C₄×C₂₃	—	2	4	no	—
383	C₂²⋊C₄×C₂₃	—	2	4	no	—
384	C₂²⋊C₄×C₂₃	—	2	2	no	—
385	C₂²⋊C₄×C₂₃	—	2	4	no	—
386	C₂²⋊C₄×C₂₃	—	2	4	no	—
387	C₂²⋊C₄×C₂₃	—	2	4	no	—
388	C₂²⋊C₄×C₂₃	—	2	4	no	—
389	C₂²⋊C₄×C₂₃	—	2	4	no	—
390	C₂²⋊C₄×C₂₃	—	2	2	no	—
391	C₂²⋊C₄×C₂₃	—	2	2	no	—
392	C₂²⋊C₄×C₂₃	—	4	2	no	—
393	C₂²⋊C₄×C₂₃	—	4	2	no	—
394	C₂²⋊C₄×C₂₃	—	4	2	no	—
395	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
396	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
397	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	complemented
398	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	complemented
399	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	complemented
400	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	complemented
401	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	complemented
402	C₂²⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
403	C₂²⋊C₄×C₂₃	#41	1	4	yes	complemented
404	C₄²×C₂₃	—	2	2	no	—
405	C₄²×C₂₃	—	2	2	no	—
406	C₄²×C₂₃	—	2	4	no	—
407	C₄²×C₂₃	—	2	2	no	—
408	C₄²×C₂₃	—	2	2	no	—
409	C₄²×C₂₃	—	2	2	no	—
410	C₄²×C₂₃	—	2	4	no	—
411	C₄²×C₂₃	—	2	2	no	—
412	C₄²×C₂₃	—	2	4	no	—
413	C₄²×C₂₃	—	2	2	no	—
414	C₄²×C₂₃	—	2	2	no	—
415	C₄²×C₂₃	—	2	2	no	—
416	C₄²×C₂₃	—	2	2	no	—
417	C₄²×C₂₃	—	2	4	no	—
418	C₄²×C₂₃	—	4	2	no	—
419	C₄²×C₂₃	—	4	2	no	—
420	C₄²×C₂₃	—	4	1	no	—
421	C₄²×C₂₃	C₂²×C₄	1	4	yes	complemented
422	C₄²×C₂₃	C₂×D₄	1	4	yes	—
423	C₄×#546	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
424	C₂³×C₂₃	—	2	1	no	—
425	C₂³×C₂₃	—	2	2	no	—
426	C₂³×C₂₃	—	2	2	no	—
427	C₂³×C₂₃	—	2	1	no	—
428	C₂³×C₂₃	—	2	2	no	—
429	C₂³×C₂₃	—	2	1	no	—
430	C₂³×C₂₃	—	2	2	no	—
431	C₂³×C₂₃	—	2	1	no	—
432	C₂³×C₂₃	—	2	16	no	—
433	C₂³×C₂₃	—	2	16	no	—
434	C₂³×C₂₃	—	2	1	no	—
435	C₂³×C₂₃	—	2	2	no	—
436	C₂³×C₂₃	—	2	2	no	—
437	C₂³×C₂₃	—	2	1	no	—
438	C₂³×C₂₃	—	2	1	no	—
439	C₂³×C₂₃	—	2	2	no	—
440	C₂³×C₂₃	—	2	1	no	—
441	C₂³×C₂₃	—	2	2	no	—
442	C₂³×C₂₃	—	2	1	no	—
443	C₂³×C₂₃	—	2	2	no	—
444	C₂³×C₂₃	—	2	2	no	—
445	C₂³×C₂₃	—	2	1	no	—
446	C₂³×C₂₃	—	4	8	no	—
447	C₂³×C₂₃	—	4	8	no	—
448	C₂³×C₂₃	—	4	8	no	—
449	C₂³×C₂₃	—	4	8	no	—
450	C₂³×C₂₃	—	4	8	no	—
451	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
452	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
453	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
454	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
455	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
456	C₂³×C₂₃	C₂×#41	1	4	yes	—
457	C₂³×C₂₃	C₂×#41	1	2	yes	—
458	C₂³×C₂₃	C₂×#41	1	2	yes	—
459	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
460	Q₈×C₂₃	—	2	8	no	—
461	D₄×C₂₃	—	2	16	no	—
462	D₄×C₂₃	—	2	16	no	—
463	D₄×C₂₃	—	2	8	no	—
464	D₄×C₂₃	—	2	8	no	—
465	D₄×C₂₃	—	4	8	no	—
466	D₄×C₂₃	C₄×D₄	1	16	yes	complemented
467	C₂×C₄×C₂₃	—	2	16	no	—
468	C₂×C₄×C₂₃	—	2	1	no	—
469	C₂×C₄×C₂₃	—	2	1	no	—
470	C₂×C₄×C₂₃	—	2	1	no	—
471	C₂×C₄×C₂₃	—	2	2	no	—
472	C₂×C₄×C₂₃	—	2	1	no	—
473	C₂×C₄×C₂₃	—	2	1	no	—
474	C₂×C₄×C₂₃	—	2	1	no	—
475	C₂×C₄×C₂₃	—	2	1	no	—
476	C₂×C₄×C₂₃	—	2	1	no	—
477	C₂×C₄×C₂₃	—	2	1	no	—
478	C₂×C₄×C₂₃	—	2	2	no	—
479	C₂×C₄×C₂₃	—	2	1	no	—
480	C₂×C₄×C₂₃	—	2	2	no	—
481	C₂×C₄×C₂₃	—	2	1	no	—
482	C₂×C₄×C₂₃	—	2	1	no	—
483	C₂×C₄×C₂₃	—	2	2	no	—
484	C₂×C₄×C₂₃	—	2	2	no	—
485	C₂×C₄×C₂₃	—	2	1	no	—
486	C₂×C₄×C₂₃	—	2	1	no	—
487	C₂×C₄×C₂₃	—	2	1	no	—
488	C₂×C₄×C₂₃	—	2	2	no	—
489	C₂×C₄×C₂₃	—	2	1	no	—
490	C₂×C₄×C₂₃	—	2	8	no	—
491	C₂×C₄×C₂₃	—	2	8	no	—
492	C₂×C₄×C₂₃	—	2	8	no	—
493	C₂×C₄×C₂₃	—	2	16	no	—
494	C₂×C₄×C₂₃	—	2	1	no	—
495	C₂×C₄×C₂₃	—	2	1	no	—
496	C₂×C₄×C₂₃	—	2	2	no	—
497	C₂×C₄×C₂₃	—	2	2	no	—
498	C₂×C₄×C₂₃	—	2	1	no	—
499	C₂×C₄×C₂₃	—	2	1	no	—
500	C₂×C₄×C₂₃	—	2	2	no	—
501	C₂×C₄×C₂₃	—	2	2	no	—
502	C₂×C₄×C₂₃	—	2	1	no	—
503	C₂×C₄×C₂₃	—	2	1	no	—
504	C₂×C₄×C₂₃	—	2	2	no	—
505	C₂×C₄×C₂₃	—	2	2	no	—
506	C₂×C₄×C₂₃	—	2	2	no	—
507	C₂×C₄×C₂₃	—	2	1	no	—
508	C₂×C₄×C₂₃	—	2	2	no	—
509	C₂×C₄×C₂₃	—	2	1	no	—
510	C₂×C₄×C₂₃	—	2	2	no	—
511	C₂×C₄×C₂₃	—	2	1	no	—
512	C₂×C₄×C₂₃	—	4	8	no	—
513	C₂×C₄×C₂₃	—	4	4	no	—
514	C₂×C₄×C₂₃	—	4	8	no	—
515	C₂×C₄×C₂₃	—	4	8	no	—
516	C₂×C₄×C₂₃	—	4	4	no	—
517	C₂×C₄×C₂₃	—	4	8	no	—
518	C₂×C₄×C₂₃	—	4	8	no	—
519	C₂×C₄×C₂₃	—	4	8	no	—
520	C₂×C₄×C₂₃	—	4	4	no	—
521	C₂×C₄×C₂₃	—	4	8	no	—
522	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
523	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
524	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
525	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
526	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
527	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
528	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
529	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
531	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
533	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
534	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
535	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
536	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
537	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
538	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
539	C₂×#546	C₂×C₂₃	1	1	yes	characteristic
540	C₂×C₄×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
541	C₂²×C₄×D₄	C₂×C₂₃	1	1	yes	characteristic, complemented
542	#2367	C₂×C₂₃	1	1	yes	characteristic, complemented
543	#2364	C₂×C₂₃	1	2	yes	complemented
544	#2363	C₂×C₂₃	1	1	yes	characteristic, complemented
545	#2360	C₂×C₂₃	1	1	yes	characteristic, complemented
546	#2359	C₂×C₂₃	1	2	yes	complemented
547	#2358	C₂×C₂₃	1	2	yes	complemented
548	#2352	C₂×C₂₃	1	1	yes	characteristic, complemented
549	#2349	C₂×C₂₃	1	1	yes	characteristic, complemented
550	#2342	C₂×C₂₃	1	2	yes	complemented
551	#2339	C₂×C₂₃	1	1	yes	characteristic, complemented
552	D₄×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
553	C₄×#124	C₂×C₂₃	1	1	yes	characteristic, complemented
554	C₄×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
555	C₄×#123	C₂×C₂₃	1	2	yes	complemented
556	C₄×#121	C₂×C₂₃	1	2	yes	complemented
557	C₄×#121	C₂×C₂₃	1	1	yes	characteristic, complemented
558	C₄×#120	C₂×C₂₃	1	2	yes	complemented
559	C₄²×D₄	C₂×C₂₃	1	1	yes	characteristic, complemented
560	C₄²×D₄	C₂×C₂₃	1	1	yes	characteristic, complemented
561	C₂×C₄×C₂²⋊C₄	C₂×C₂₃	1	2	yes	complemented
562	C₂²×C₂₃	—	2	2	no	—
563	C₂²×C₂₃	—	2	4	no	—
564	C₂²×C₂₃	—	2	4	no	—
565	C₂²×C₂₃	—	2	2	no	—
566	C₂²×C₂₃	—	2	2	no	—
567	C₂²×C₂₃	—	2	4	no	—
568	C₂²×C₂₃	—	2	2	no	—
569	C₂²×C₂₃	—	2	4	no	—
570	C₂²×C₂₃	—	2	2	no	—
571	C₂²×C₂₃	—	2	4	no	—
572	C₂²×C₂₃	—	2	4	no	—
573	C₂²×C₂₃	—	2	2	no	—
574	C₂²×C₂₃	—	2	2	no	—
575	C₂²×C₂₃	—	2	4	no	—
576	C₂²×C₂₃	—	2	2	no	—
577	C₂²×C₂₃	—	2	4	no	—
578	C₂²×C₂₃	—	2	2	no	—
579	C₂²×C₂₃	—	2	4	no	—
580	C₂²×C₂₃	—	4	32	no	—
581	C₂²×C₂₃	—	4	2	no	—
582	C₂²×C₂₃	—	4	1	no	—
583	C₂²×C₂₃	—	4	1	no	—
584	C₂²×C₂₃	—	4	2	no	—
585	C₂²×C₂₃	—	4	1	no	—
586	C₂²×C₂₃	—	4	2	no	—
587	C₂²×C₂₃	—	4	1	no	—
588	C₂²×C₂₃	—	4	2	no	—
589	C₂²×C₂₃	C₂×C₄×D₄	1	8	yes	—
590	C₂²×C₂₃	C₄×#41	1	4	yes	complemented
591	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
592	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
593	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
594	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
595	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
596	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
597	C₂²×C₂₃	#585	1	1	yes	characteristic
598	C₄×C₂₃	—	2	2	no	—
599	C₄×C₂₃	—	2	2	no	—
600	C₄×C₂₃	—	2	4	no	—
601	C₄×C₂₃	—	2	2	no	—
602	C₄×C₂₃	—	2	2	no	—
603	C₄×C₂₃	—	2	4	no	—
604	C₄×C₂₃	—	2	2	no	—
605	C₄×C₂₃	—	2	4	no	—
606	C₄×C₂₃	—	2	2	no	—
607	C₄×C₂₃	—	2	2	no	—
608	C₄×C₂₃	—	2	2	no	—
609	C₄×C₂₃	—	4	1	no	—
610	C₄×C₂₃	—	4	2	no	—
611	C₄×C₂₃	—	4	1	no	—
612	C₄×C₂₃	—	4	2	no	—
613	C₄×C₂₃	—	4	1	no	—
614	C₄×C₂₃	—	4	2	no	—
615	C₄×C₂₃	C₂×C₄×D₄	1	4	yes	—
616	C₄×C₂₃	#546	1	4	yes	direct product factor
617	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
618	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
619	C₂⁴×C₄	C₂²×C₂₃	1	2	yes	—
620	#546	C₄×C₂₃	1	16	yes	direct product factor
621	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
622	C₂×#123	C₂²×C₂₃	1	2	yes	—
623	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
624	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
625	C₂×#121	C₂²×C₂₃	1	2	yes	—
626	C₂×#120	C₂²×C₂₃	1	2	yes	—
627	C₄×#41	—	2	8	no	—
628	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
629	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
630	C₂×C₄×D₄	—	2	8	no	—
631	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
632	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
633	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
634	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
635	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
636	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
637	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
638	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
639	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
640	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
641	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
642	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
643	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
644	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
645	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
646	C₂×#117	C₂²×C₂₃	1	2	yes	complemented
647	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic, complemented
648	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
649	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
650	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
651	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
652	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
653	C₂²×C₄²	C₂²×C₂₃	1	2	yes	complemented
654	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
655	C₂²×C₄²	C₂²×C₂₃	1	2	yes	complemented
656	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
657	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
658	#390	C₂²×C₂₃	1	1	yes	characteristic
659	#390	C₂²×C₂₃	1	1	yes	characteristic
660	#390	C₂²×C₂₃	1	2	yes	complemented
661	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
662	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
663	#389	C₂²×C₂₃	1	2	yes	complemented
664	#388	C₂²×C₂₃	1	2	yes	complemented
665	#388	C₂²×C₂₃	1	2	yes	complemented
666	#388	C₂²×C₂₃	1	2	yes	complemented
667	#388	C₂²×C₂₃	1	2	yes	complemented
668	#388	C₂²×C₂₃	1	2	yes	complemented
669	#388	C₂²×C₂₃	1	2	yes	complemented
670	#388	C₂²×C₂₃	1	2	yes	complemented
671	#387	C₂²×C₂₃	1	2	yes	complemented
672	#387	C₂²×C₂₃	1	2	yes	complemented
673	#387	C₂²×C₂₃	1	2	yes	complemented
674	#386	C₂²×C₂₃	1	2	yes	—
675	#386	C₂²×C₂₃	1	2	yes	—
676	#386	C₂²×C₂₃	1	2	yes	—
677	#386	C₂²×C₂₃	1	2	yes	complemented
678	#386	C₂²×C₂₃	1	2	yes	complemented
679	#386	C₂²×C₂₃	1	2	yes	complemented
680	#386	C₂²×C₂₃	1	2	yes	complemented
681	#385	C₂²×C₂₃	1	2	yes	—
682	#385	C₂²×C₂₃	1	2	yes	—
683	#385	C₂²×C₂₃	1	2	yes	complemented
684	#385	C₂²×C₂₃	1	2	yes	complemented
685	#385	C₂²×C₂₃	1	2	yes	complemented
686	#382	C₂²×C₂₃	1	1	yes	characteristic, complemented
687	#381	C₂²×C₂₃	1	2	yes	complemented
688	#380	C₂²×C₂₃	1	1	yes	characteristic
689	#380	C₂²×C₂₃	1	1	yes	characteristic, complemented
690	#380	C₂²×C₂₃	1	2	yes	complemented
691	#379	C₂²×C₂₃	1	2	yes	—
692	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
693	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
694	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
695	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
696	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
697	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
698	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
699	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
700	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
701	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
702	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
703	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
704	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
705	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
706	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
707	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
708	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
709	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
710	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
711	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
712	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
713	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
714	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
715	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
716	C₂×#95	C₂²×C₂₃	1	2	yes	complemented
717	C₂×#95	C₂²×C₂₃	1	2	yes	complemented
718	C₄³	C₂²×C₂₃	1	1	yes	characteristic, complemented
719	C₂×C₂₃	—	2	4	no	—
720	C₂×C₂₃	—	2	8	no	—
721	C₂×C₂₃	—	4	2	no	—
722	C₂×C₂₃	—	4	4	no	—
723	C₂×C₂₃	C₂²×C₄×D₄	1	1	yes	characteristic
724	C₂×C₂₃	C₂×C₄×#41	1	1	yes	characteristic
725	C₂×C₂₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
726	C₂×C₂₃	C₂×#546	1	1	yes	characteristic
727	C₂×C₂₃	D₄×#41	1	1	yes	characteristic
728	C₂×C₂₃	#3475	1	1	yes	characteristic
729	C₂×C₂₃	#3481	1	1	yes	characteristic
730	C₂⁵	C₂³×C₂₃	1	2	yes	—
731	C₂×#41	—	2	4	no	—
732	C₂×#41	—	2	4	no	—
733	C₂×#41	C₂×C₄×C₂₃	1	8	yes	complemented
734	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
735	C₂²×D₄	—	2	4	no	—
736	C₂²×D₄	—	2	4	no	—
737	C₂²×D₄	C₂×C₄×C₂₃	1	8	yes	complemented
738	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
739	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
740	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
741	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
742	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
743	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
744	C₂³×C₄	—	2	8	no	—
745	C₂³×C₄	—	2	8	no	—
746	C₂³×C₄	—	4	4	no	—
747	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
748	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
749	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
750	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
751	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
752	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
753	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
754	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
755	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
756	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
757	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
758	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
759	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
760	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
761	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
762	#124	C₂×C₄×C₂₃	1	8	yes	complemented
763	#123	C₂×C₄×C₂₃	1	16	yes	complemented
764	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
765	#121	C₂×C₄×C₂₃	1	8	yes	complemented
766	#121	C₂×C₄×C₂₃	1	16	yes	complemented
767	#120	C₂×C₄×C₂₃	1	16	yes	complemented
768	C₄×Q₈	—	2	4	no	—
769	C₄×Q₈	—	2	4	no	—
770	C₄×D₄	—	2	4	no	—
771	C₄×D₄	—	2	4	no	—
772	C₄×D₄	—	2	4	no	—
773	C₄×D₄	—	2	8	no	—
774	C₄×D₄	—	2	8	no	—
775	C₄×D₄	—	2	4	no	—
776	C₄×D₄	—	2	4	no	—
777	C₄×D₄	—	2	8	no	—
778	C₄×D₄	—	2	8	no	—
779	C₄×D₄	—	2	4	no	—
780	C₄×D₄	—	2	4	no	—
781	C₄×D₄	—	4	4	no	—
782	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	complemented
783	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	complemented
784	C₄×D₄	D₄×C₂₃	1	8	yes	complemented
785	#117	—	2	4	no	—
786	#117	—	2	8	no	—
787	C₂×C₄⋊C₄	—	2	4	no	—
788	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
789	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
790	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
791	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
792	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
793	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
794	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
795	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
796	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
797	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
798	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
799	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
800	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
801	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
802	C₂×C₂²⋊C₄	—	2	8	no	—
803	C₂×C₂²⋊C₄	—	2	8	no	—
804	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	16	yes	complemented
805	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
806	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
807	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
808	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
809	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
810	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
811	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
812	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
813	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
814	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
815	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
816	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
817	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
818	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
819	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
820	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
821	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
822	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
823	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
824	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
825	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
826	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
827	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
828	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
829	C₂×C₄²	—	2	8	no	—
830	C₂×C₄²	—	2	4	no	—
831	C₂×C₄²	—	2	4	no	—
832	C₂×C₄²	—	4	4	no	—
833	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
834	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
835	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
836	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
837	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
838	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
839	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
840	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
841	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
842	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
843	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
844	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
845	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
846	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
847	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
848	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
849	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
850	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
851	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
852	#95	C₂³×C₂₃	1	1	yes	characteristic
853	#95	C₂³×C₂₃	1	1	yes	characteristic
854	#95	C₂³×C₂₃	1	2	yes	—
855	#95	C₂³×C₂₃	1	2	yes	—
856	#95	C₂³×C₂₃	1	2	yes	—
857	#95	C₂³×C₂₃	1	2	yes	—
858	#95	C₂³×C₂₃	1	2	yes	—
859	#95	C₂³×C₂₃	1	2	yes	—
860	#95	C₂³×C₂₃	1	1	yes	characteristic
861	#95	C₂³×C₂₃	1	1	yes	characteristic
862	#95	C₂³×C₂₃	1	1	yes	characteristic
863	#95	C₂³×C₂₃	1	1	yes	characteristic
864	#95	C₂³×C₂₃	1	2	yes	—
865	#95	C₂³×C₂₃	1	2	yes	—
866	#95	C₂³×C₂₃	1	2	yes	—
867	#95	C₂³×C₂₃	1	2	yes	—
868	#95	C₂³×C₂₃	1	2	yes	—
869	#95	C₂³×C₂₃	1	2	yes	—
870	#95	C₂³×C₂₃	1	2	yes	—
871	C₂₃	C₄×#546	1	1	yes	characteristic, direct product factor, Sylow
872	C₂⁴	—	2	4	no	—
873	C₂⁴	—	2	4	no	—
874	C₂⁴	—	2	4	no	—
875	C₂⁴	—	2	4	no	—
876	C₂⁴	—	4	2	no	—
877	C₂⁴	—	4	2	no	—
878	C₂⁴	C₂²×C₄×C₂₃	1	8	yes	—
879	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
880	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
881	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
882	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
883	#41	—	2	32	no	—
884	C₂×Q₈	—	2	2	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	complemented
887	C₂×D₄	—	2	4	no	—
888	C₂×D₄	—	2	4	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	4	no	—
892	C₂×D₄	—	2	4	no	—
893	C₂×D₄	—	2	32	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	4	2	no	—
897	C₂×D₄	—	4	2	no	—
898	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
899	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
900	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
901	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
902	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	complemented
903	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	complemented
904	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
905	C₂×D₄	#41×C₂₃	1	4	yes	—
906	C₂²×C₄	—	2	4	no	—
907	C₂²×C₄	—	2	4	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	4	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	4	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	4	no	—
917	C₂²×C₄	—	2	4	no	—
918	C₂²×C₄	—	2	4	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	4	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	4	no	—
925	C₂²×C₄	—	2	4	no	—
926	C₂²×C₄	—	2	4	no	—
927	C₂²×C₄	—	2	4	no	—
928	C₂²×C₄	—	2	4	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	4	no	—
932	C₂²×C₄	—	2	4	no	—
933	C₂²×C₄	—	2	4	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	4	no	—
936	C₂²×C₄	—	4	2	no	—
937	C₂²×C₄	—	4	2	no	—
938	C₂²×C₄	—	4	2	no	—
939	C₂²×C₄	—	4	2	no	—
940	C₂²×C₄	—	4	2	no	—
941	C₂²×C₄	—	4	2	no	—
942	C₂²×C₄	—	4	1	no	—
943	C₂²×C₄	—	4	1	no	—
944	C₂²×C₄	—	4	2	no	—
945	C₂²×C₄	—	4	32	no	—
946	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
947	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	complemented
948	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	complemented
949	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	complemented
950	C₂²×C₄	C₂×D₄×C₂₃	1	8	yes	—
951	C₂²×C₄	#41×C₂₃	1	4	yes	complemented
952	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
953	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
954	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
955	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
956	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
957	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
958	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
959	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
960	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
961	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
962	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
963	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
964	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
965	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
966	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
967	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
968	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
969	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
970	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
971	C₄⋊C₄	—	2	4	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	4	no	—
974	C₄⋊C₄	—	2	4	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	4	2	no	—
980	C₄⋊C₄	—	4	2	no	—
981	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	complemented
982	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	complemented
983	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	complemented
984	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
985	C₂²⋊C₄	—	2	4	no	—
986	C₂²⋊C₄	—	2	4	no	—
987	C₂²⋊C₄	—	2	4	no	—
988	C₂²⋊C₄	—	2	4	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	4	no	—
991	C₂²⋊C₄	—	2	4	no	—
992	C₂²⋊C₄	—	2	4	no	—
993	C₂²⋊C₄	—	2	4	no	—
994	C₂²⋊C₄	—	2	4	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	4	2	no	—
998	C₂²⋊C₄	—	4	2	no	—
999	C₂²⋊C₄	—	4	2	no	—
1000	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
1001	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
1002	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	complemented
1003	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	complemented
1004	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	complemented
1005	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	complemented
1006	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	complemented
1007	C₂²⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
1008	C₂²⋊C₄	#41×C₂₃	1	4	yes	complemented
1009	C₄²	—	2	2	no	—
1010	C₄²	—	2	2	no	—
1011	C₄²	—	2	4	no	—
1012	C₄²	—	2	2	no	—
1013	C₄²	—	2	2	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	4	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	4	no	—
1018	C₄²	—	2	2	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	—	2	2	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	4	no	—
1023	C₄²	—	4	2	no	—
1024	C₄²	—	4	2	no	—
1025	C₄²	—	4	1	no	—
1026	C₄²	C₂²×C₄×C₂₃	1	4	yes	complemented
1027	C₄²	C₂×D₄×C₂₃	1	4	yes	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	2	no	—
1030	C₂³	—	2	2	no	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	2	no	—
1033	C₂³	—	2	1	no	—
1034	C₂³	—	2	2	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	1	no	—
1037	C₂³	—	2	2	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	2	no	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	2	1	no	—
1045	C₂³	—	2	2	no	—
1046	C₂³	—	2	2	no	—
1047	C₂³	—	2	1	no	—
1048	C₂³	—	2	16	no	—
1049	C₂³	—	2	16	no	—
1050	C₂³	—	4	8	no	—
1051	C₂³	—	4	8	no	—
1052	C₂³	—	4	8	no	—
1053	C₂³	—	4	8	no	—
1054	C₂³	—	4	8	no	—
1055	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
1056	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
1057	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
1058	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
1059	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
1060	C₂³	C₂×#41×C₂₃	1	4	yes	—
1061	C₂³	C₂×#41×C₂₃	1	2	yes	—
1062	C₂³	C₂×#41×C₂₃	1	2	yes	—
1063	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
1064	Q₈	—	2	8	no	—
1065	D₄	—	2	16	no	—
1066	D₄	—	2	16	no	—
1067	D₄	—	2	8	no	—
1068	D₄	—	2	8	no	—
1069	D₄	—	4	8	no	—
1070	D₄	C₄×D₄×C₂₃	1	16	yes	complemented
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	16	no	—
1094	C₂×C₄	—	2	8	no	—
1095	C₂×C₄	—	2	8	no	—
1096	C₂×C₄	—	2	8	no	—
1097	C₂×C₄	—	2	16	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	4	8	no	—
1117	C₂×C₄	—	4	8	no	—
1118	C₂×C₄	—	4	4	no	—
1119	C₂×C₄	—	4	8	no	—
1120	C₂×C₄	—	4	8	no	—
1121	C₂×C₄	—	4	8	no	—
1122	C₂×C₄	—	4	4	no	—
1123	C₂×C₄	—	4	8	no	—
1124	C₂×C₄	—	4	8	no	—
1125	C₂×C₄	—	4	4	no	—
1126	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1127	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1128	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
1129	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1130	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
1131	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1132	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1133	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1134	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
1135	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1136	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1137	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1138	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1139	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1140	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1141	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1142	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	2	4	no	—
1145	C₂²	—	2	4	no	—
1146	C₂²	—	2	2	no	—
1147	C₂²	—	2	2	no	—
1148	C₂²	—	2	4	no	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	4	no	—
1151	C₂²	—	2	2	no	—
1152	C₂²	—	2	4	no	—
1153	C₂²	—	2	4	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	2	2	no	—
1156	C₂²	—	2	4	no	—
1157	C₂²	—	2	2	no	—
1158	C₂²	—	2	4	no	—
1159	C₂²	—	2	2	no	—
1160	C₂²	—	2	4	no	—
1161	C₂²	—	4	32	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	1	no	—
1165	C₂²	—	4	2	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	4	1	no	—
1168	C₂²	—	4	2	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	C₂×C₄×D₄×C₂₃	1	8	yes	—
1171	C₂²	C₄×#41×C₂₃	1	4	yes	complemented
1172	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
1173	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1174	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1175	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1176	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1177	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1178	C₂²	C₂₃×#585	1	1	yes	characteristic
1179	C₄	—	2	2	no	—
1180	C₄	—	2	2	no	—
1181	C₄	—	2	4	no	—
1182	C₄	—	2	2	no	—
1183	C₄	—	2	2	no	—
1184	C₄	—	2	4	no	—
1185	C₄	—	2	2	no	—
1186	C₄	—	2	4	no	—
1187	C₄	—	2	2	no	—
1188	C₄	—	2	2	no	—
1189	C₄	—	2	2	no	—
1190	C₄	—	4	2	no	—
1191	C₄	—	4	1	no	—
1192	C₄	—	4	1	no	—
1193	C₄	—	4	2	no	—
1194	C₄	—	4	1	no	—
1195	C₄	—	4	2	no	—
1196	C₄	C₂×C₄×D₄×C₂₃	1	4	yes	—
1197	C₄	C₂₃×#546	1	4	yes	direct product factor
1198	C₂	—	2	4	no	—
1199	C₂	—	2	8	no	—
1200	C₂	—	4	4	no	—
1201	C₂	—	4	2	no	—
1202	C₂	C₂²×C₄×D₄×C₂₃	1	1	yes	characteristic
1203	C₂	C₂×C₄×#41×C₂₃	1	1	yes	characteristic
1204	C₂	C₄×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1205	C₂	C₂×C₂₃×#546	1	1	yes	characteristic
1206	C₂	D₄×#41×C₂₃	1	1	yes	characteristic
1207	C₂	C₂₃×#3475	1	1	yes	characteristic
1208	C₂	C₂₃×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁵×C₂₃
socle	C₂³×C₂₃	C₂⁵
prime radical	C₂×C₂₃×#546	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₄×#41×C₂₃	C₂	semidirect
3. C₂²×C₄×D₄×C₂₃	C₂	semidirect
4. C₂₃×#2367	C₂	semidirect
5. C₂₃×#2364	C₂	semidirect
6. C₂₃×#2363	C₂	semidirect
7. C₂₃×#2360	C₂	semidirect
8. C₂₃×#2359	C₂	semidirect
9. C₂₃×#2358	C₂	semidirect
10. C₂₃×#2352	C₂	semidirect
11. C₂₃×#2349	C₂	semidirect
12. C₂₃×#2342	C₂	semidirect
13. C₂₃×#2339	C₂	semidirect
14. D₄×C₂²⋊C₄×C₂₃	C₂	semidirect
15. C₄×C₂₃×#124	C₂	semidirect
16. C₄×C₂₃×C₂²⋊Q₈	C₂	semidirect
17. C₄×C₂₃×#123	C₂	semidirect
18. C₄×C₂₃×#121	C₂	semidirect
19. C₄×C₂₃×#121	C₂	semidirect
20. C₄×C₂₃×#120	C₂	semidirect
21. C₄²×D₄×C₂₃	C₂	semidirect
22. C₄²×D₄×C₂₃	C₂	semidirect
23. C₂×C₄×C₂²⋊C₄×C₂₃	C₂	semidirect
27. C₂₃×#546	C₄	direct (N × H)
35. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
36. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
50. C₂×C₄×D₄×C₂₃	C₂²	semidirect
51. C₂×C₄×D₄×C₂₃	C₂²	semidirect
52. C₂×C₄×D₄×C₂₃	C₂²	semidirect
53. C₂×C₂₃×#117	C₂²	semidirect
54. C₂×C₂₃×#117	C₂²	semidirect
60. C₂²×C₄²×C₂₃	C₂²	semidirect
61. C₂²×C₄²×C₂₃	C₂²	semidirect
62. C₂²×C₄²×C₂₃	C₂²	semidirect
63. C₂₃×#391	C₂²	semidirect
64. C₂₃×#391	C₂²	semidirect
67. C₂₃×#390	C₂²	semidirect
68. C₂₃×#389	C₂²	semidirect
69. C₂₃×#389	C₂²	semidirect
70. C₂₃×#389	C₂²	semidirect
71. C₂₃×#388	C₂²	semidirect
72. C₂₃×#388	C₂²	semidirect
73. C₂₃×#388	C₂²	semidirect
74. C₂₃×#388	C₂²	semidirect
75. C₂₃×#388	C₂²	semidirect
76. C₂₃×#388	C₂²	semidirect
77. C₂₃×#388	C₂²	semidirect
78. C₂₃×#387	C₂²	semidirect
79. C₂₃×#387	C₂²	semidirect
80. C₂₃×#387	C₂²	semidirect
84. C₂₃×#386	C₂²	semidirect
85. C₂₃×#386	C₂²	semidirect
86. C₂₃×#386	C₂²	semidirect
87. C₂₃×#386	C₂²	semidirect
90. C₂₃×#385	C₂²	semidirect
91. C₂₃×#385	C₂²	semidirect
92. C₂₃×#385	C₂²	semidirect
93. C₂₃×#382	C₂²	semidirect
94. C₂₃×#381	C₂²	semidirect
96. C₂₃×#380	C₂²	semidirect
97. C₂₃×#380	C₂²	semidirect
99. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
100. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
101. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
102. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
103. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
104. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
105. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
112. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
113. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
114. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
115. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
116. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
117. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
118. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
119. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
123. C₂×C₂₃×#95	C₂²	semidirect
124. C₂×C₂₃×#95	C₂²	semidirect
125. C₄³×C₂₃	C₂²	semidirect
129. C₂×#41×C₂₃	C₂×C₄	semidirect
133. C₂²×D₄×C₂₃	C₂×C₄	semidirect
158. C₂₃×#124	C₂×C₄	semidirect
159. C₂₃×#123	C₂×C₄	semidirect
160. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
161. C₂₃×#121	C₂×C₄	semidirect
162. C₂₃×#121	C₂×C₄	semidirect
163. C₂₃×#120	C₂×C₄	semidirect
178. C₄×D₄×C₂₃	C₂×C₄	semidirect
179. C₄×D₄×C₂₃	C₂×C₄	semidirect
180. C₄×D₄×C₂₃	D₄	semidirect
200. C₂×C₂²⋊C₄×C₂₃	C₂×C₄	semidirect
281. C₂×Q₈×C₂₃	C₂²×C₄	semidirect
297. C₂×D₄×C₂₃	C₂²×C₄	semidirect
298. C₂×D₄×C₂₃	C₂²×C₄	semidirect
342. C₂²×C₄×C₂₃	C₂²×C₄	semidirect
343. C₂²×C₄×C₂₃	C₂²×C₄	semidirect
344. C₂²×C₄×C₂₃	C₂²×C₄	semidirect
346. C₂²×C₄×C₂₃	#41	semidirect
376. C₄⋊C₄×C₂₃	C₂²×C₄	semidirect
377. C₄⋊C₄×C₂₃	C₂²×C₄	semidirect
378. C₄⋊C₄×C₂₃	C₂²×C₄	semidirect
397. C₂²⋊C₄×C₂₃	C₂²×C₄	semidirect
398. C₂²⋊C₄×C₂₃	C₂²×C₄	semidirect
399. C₂²⋊C₄×C₂₃	C₂²×C₄	semidirect
400. C₂²⋊C₄×C₂₃	C₂²×C₄	semidirect
401. C₂²⋊C₄×C₂₃	C₂²×C₄	semidirect
403. C₂²⋊C₄×C₂₃	#41	semidirect
421. C₄²×C₂₃	C₂²×C₄	semidirect
423. C₄×#546	C₂₃	direct (N × H)
466. D₄×C₂₃	C₄×D₄	semidirect
540. C₂×C₄×#41	C₂×C₂₃	semidirect
541. C₂²×C₄×D₄	C₂×C₂₃	semidirect
542. #2367	C₂×C₂₃	semidirect
543. #2364	C₂×C₂₃	semidirect
544. #2363	C₂×C₂₃	semidirect
545. #2360	C₂×C₂₃	semidirect
546. #2359	C₂×C₂₃	semidirect
547. #2358	C₂×C₂₃	semidirect
548. #2352	C₂×C₂₃	semidirect
549. #2349	C₂×C₂₃	semidirect
550. #2342	C₂×C₂₃	semidirect
551. #2339	C₂×C₂₃	semidirect
552. D₄×C₂²⋊C₄	C₂×C₂₃	semidirect
553. C₄×#124	C₂×C₂₃	semidirect
554. C₄×C₂²⋊Q₈	C₂×C₂₃	semidirect
555. C₄×#123	C₂×C₂₃	semidirect
556. C₄×#121	C₂×C₂₃	semidirect
557. C₄×#121	C₂×C₂₃	semidirect
558. C₄×#120	C₂×C₂₃	semidirect
559. C₄²×D₄	C₂×C₂₃	semidirect
560. C₄²×D₄	C₂×C₂₃	semidirect
561. C₂×C₄×C₂²⋊C₄	C₂×C₂₃	semidirect
590. C₂²×C₂₃	C₄×#41	semidirect
616. C₄×C₂₃	#546	direct (N × H)
620. #546	C₄×C₂₃	direct (N × H)
628. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
629. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
643. C₂×C₄×D₄	C₂²×C₂₃	semidirect
644. C₂×C₄×D₄	C₂²×C₂₃	semidirect
645. C₂×C₄×D₄	C₂²×C₂₃	semidirect
646. C₂×#117	C₂²×C₂₃	semidirect
647. C₂×#117	C₂²×C₂₃	semidirect
653. C₂²×C₄²	C₂²×C₂₃	semidirect
654. C₂²×C₄²	C₂²×C₂₃	semidirect
655. C₂²×C₄²	C₂²×C₂₃	semidirect
656. #391	C₂²×C₂₃	semidirect
657. #391	C₂²×C₂₃	semidirect
660. #390	C₂²×C₂₃	semidirect
661. #389	C₂²×C₂₃	semidirect
662. #389	C₂²×C₂₃	semidirect
663. #389	C₂²×C₂₃	semidirect
664. #388	C₂²×C₂₃	semidirect
665. #388	C₂²×C₂₃	semidirect
666. #388	C₂²×C₂₃	semidirect
667. #388	C₂²×C₂₃	semidirect
668. #388	C₂²×C₂₃	semidirect
669. #388	C₂²×C₂₃	semidirect
670. #388	C₂²×C₂₃	semidirect
671. #387	C₂²×C₂₃	semidirect
672. #387	C₂²×C₂₃	semidirect
673. #387	C₂²×C₂₃	semidirect
677. #386	C₂²×C₂₃	semidirect
678. #386	C₂²×C₂₃	semidirect
679. #386	C₂²×C₂₃	semidirect
680. #386	C₂²×C₂₃	semidirect
683. #385	C₂²×C₂₃	semidirect
684. #385	C₂²×C₂₃	semidirect
685. #385	C₂²×C₂₃	semidirect
686. #382	C₂²×C₂₃	semidirect
687. #381	C₂²×C₂₃	semidirect
689. #380	C₂²×C₂₃	semidirect
690. #380	C₂²×C₂₃	semidirect
692. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
693. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
694. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
695. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
696. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
697. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
698. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
705. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
706. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
707. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
708. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
709. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
710. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
711. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
712. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
713. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
714. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
715. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
716. C₂×#95	C₂²×C₂₃	semidirect
717. C₂×#95	C₂²×C₂₃	semidirect
718. C₄³	C₂²×C₂₃	semidirect
733. C₂×#41	C₂×C₄×C₂₃	semidirect
737. C₂²×D₄	C₂×C₄×C₂₃	semidirect
762. #124	C₂×C₄×C₂₃	semidirect
763. #123	C₂×C₄×C₂₃	semidirect
764. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
765. #121	C₂×C₄×C₂₃	semidirect
766. #121	C₂×C₄×C₂₃	semidirect
767. #120	C₂×C₄×C₂₃	semidirect
782. C₄×D₄	C₂×C₄×C₂₃	semidirect
783. C₄×D₄	C₂×C₄×C₂₃	semidirect
784. C₄×D₄	D₄×C₂₃	semidirect
804. C₂×C₂²⋊C₄	C₂×C₄×C₂₃	semidirect
871. C₂₃	C₄×#546	direct (N × H)
886. C₂×Q₈	C₂²×C₄×C₂₃	semidirect
902. C₂×D₄	C₂²×C₄×C₂₃	semidirect
903. C₂×D₄	C₂²×C₄×C₂₃	semidirect
947. C₂²×C₄	C₂²×C₄×C₂₃	semidirect
948. C₂²×C₄	C₂²×C₄×C₂₃	semidirect
949. C₂²×C₄	C₂²×C₄×C₂₃	semidirect
951. C₂²×C₄	#41×C₂₃	semidirect
981. C₄⋊C₄	C₂²×C₄×C₂₃	semidirect
982. C₄⋊C₄	C₂²×C₄×C₂₃	semidirect
983. C₄⋊C₄	C₂²×C₄×C₂₃	semidirect
1002. C₂²⋊C₄	C₂²×C₄×C₂₃	semidirect
1003. C₂²⋊C₄	C₂²×C₄×C₂₃	semidirect
1004. C₂²⋊C₄	C₂²×C₄×C₂₃	semidirect
1005. C₂²⋊C₄	C₂²×C₄×C₂₃	semidirect
1006. C₂²⋊C₄	C₂²×C₄×C₂₃	semidirect
1008. C₂²⋊C₄	#41×C₂₃	semidirect
1026. C₄²	C₂²×C₄×C₂₃	semidirect
1070. D₄	C₄×D₄×C₂₃	semidirect
1171. C₂²	C₄×#41×C₂₃	semidirect
1197. C₄	C₂₃×#546	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₂₃×#546	2
C₂×C₄×#41×C₂₃	2
C₂²×C₄×D₄×C₂₃	2
C₂₃×#2367	2
C₂₃×#2364	2
C₂₃×#2363	2
C₂₃×#2360	2
C₂₃×#2359	2
C₂₃×#2358	2
C₂₃×#2352	2
C₂₃×#2349	2
C₂₃×#2342	2
C₂₃×#2339	2
D₄×C₂²⋊C₄×C₂₃	2
C₄×C₂₃×#124	2
C₄×C₂₃×C₂²⋊Q₈	2
C₄×C₂₃×#123	2
C₄×C₂₃×#121	2
C₄×C₂₃×#120	2
C₄²×D₄×C₂₃	2
C₂×C₄×C₂²⋊C₄×C₂₃	2
C₄×#546	23

Subgroups — C4×C23×#546 #19181783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂₃×#546 #19181783