Subgroups — C₂₃×#34476 #19182102

Order 5888.

2736 conjugacy classes of subgroups.

The subgroup lattice has 1144 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	C₂₃×#2377	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2376	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2361	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2358	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2342	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2341	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2335	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2326	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2324	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2324	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2321	C₂	1	2	yes	maximal, complemented
18	C₂₃×#2319	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2315	C₂	1	2	yes	maximal, complemented
20	C₂₃×#2311	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₂₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
25	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₂₃×#546	C₄	1	16	yes	complemented
27	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#123	C₂²	1	2	yes	—
29	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#121	C₂²	1	2	yes	—
32	C₂×C₂₃×#120	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
41	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₂₃×#117	C₂²	1	2	yes	complemented
43	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
46	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
47	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
48	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
49	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
50	C₂₃×#391	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#391	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#390	C₂²	1	1	yes	characteristic
53	C₂₃×#390	C₂²	1	1	yes	characteristic
54	C₂₃×#390	C₂²	1	2	yes	—
55	C₂₃×#390	C₂²	1	1	yes	characteristic
56	C₂₃×#390	C₂²	1	1	yes	characteristic
57	C₂₃×#390	C₂²	1	2	yes	—
58	C₂₃×#390	C₂²	1	1	yes	characteristic
59	C₂₃×#390	C₂²	1	1	yes	characteristic
60	C₂₃×#390	C₂²	1	2	yes	complemented
61	C₂₃×#390	C₂²	1	2	yes	complemented
62	C₂₃×#390	C₂²	1	2	yes	complemented
63	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
64	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
65	C₂₃×#389	C₂²	1	2	yes	complemented
66	C₂₃×#389	C₂²	1	2	yes	complemented
67	C₂₃×#388	C₂²	1	1	yes	characteristic, complemented
68	C₂₃×#388	C₂²	1	1	yes	characteristic, complemented
69	C₂₃×#388	C₂²	1	2	yes	complemented
70	C₂₃×#388	C₂²	1	2	yes	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×#388	C₂²	1	2	yes	complemented
79	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
80	C₂₃×#387	C₂²	1	1	yes	characteristic, complemented
81	C₂₃×#387	C₂²	1	2	yes	complemented
82	C₂₃×#387	C₂²	1	2	yes	complemented
83	C₂₃×#386	C₂²	1	1	yes	characteristic
84	C₂₃×#386	C₂²	1	1	yes	characteristic
85	C₂₃×#386	C₂²	1	2	yes	—
86	C₂₃×#386	C₂²	1	2	yes	—
87	C₂₃×#386	C₂²	1	2	yes	complemented
88	C₂₃×#386	C₂²	1	2	yes	complemented
89	C₂₃×#386	C₂²	1	2	yes	complemented
90	C₂₃×#386	C₂²	1	2	yes	complemented
91	C₂₃×#385	C₂²	1	1	yes	characteristic
92	C₂₃×#385	C₂²	1	1	yes	characteristic
93	C₂₃×#385	C₂²	1	2	yes	—
94	C₂₃×#385	C₂²	1	2	yes	—
95	C₂₃×#385	C₂²	1	2	yes	—
96	C₂₃×#385	C₂²	1	2	yes	complemented
97	C₂₃×#385	C₂²	1	2	yes	complemented
98	C₂₃×#385	C₂²	1	2	yes	complemented
99	C₂₃×#385	C₂²	1	2	yes	complemented
100	C₂₃×#385	C₂²	1	2	yes	complemented
101	C₂₃×#385	C₂²	1	2	yes	complemented
102	C₂₃×#384	C₂²	1	1	yes	characteristic, complemented
103	C₂₃×#381	C₂²	1	2	yes	complemented
104	C₂₃×#380	C₂²	1	1	yes	characteristic
105	C₂₃×#380	C₂²	1	2	yes	complemented
106	C₂₃×#380	C₂²	1	2	yes	complemented
107	C₂₃×#380	C₂²	1	2	yes	complemented
108	C₂₃×#380	C₂²	1	2	yes	complemented
109	C₂₃×#380	C₂²	1	2	yes	complemented
110	C₂₃×#380	C₂²	1	1	yes	characteristic, complemented
111	C₂₃×#379	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
114	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
115	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
122	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
123	C₂₃×#376	C₂²	1	1	yes	characteristic, complemented
124	C₂⁵×C₂₃	C₂³	1	2	yes	—
125	C₂×#41×C₂₃	—	4	2	no	—
126	C₂×#41×C₂₃	—	4	2	no	—
127	C₂×#41×C₂₃	C₂×C₄	1	8	yes	complemented
128	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₂₃	—	4	2	no	—
130	C₂²×D₄×C₂₃	—	4	2	no	—
131	C₂²×D₄×C₂₃	C₂×C₄	1	8	yes	complemented
132	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
136	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
137	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
138	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
142	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
144	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
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×#124	C₂×C₄	1	8	yes	complemented
149	C₂₃×#123	C₂×C₄	1	16	yes	complemented
150	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
151	C₂₃×#121	C₂×C₄	1	8	yes	complemented
152	C₂₃×#121	C₂×C₄	1	16	yes	complemented
153	C₂₃×#120	C₂×C₄	1	16	yes	complemented
154	C₄×Q₈×C₂₃	—	4	2	no	—
155	C₄×Q₈×C₂₃	—	4	2	no	—
156	C₄×D₄×C₂₃	—	4	4	no	—
157	C₄×D₄×C₂₃	—	4	2	no	—
158	C₄×D₄×C₂₃	—	4	2	no	—
159	C₄×D₄×C₂₃	—	4	4	no	—
160	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	complemented
161	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	complemented
162	C₂₃×#117	—	4	2	no	—
163	C₂₃×#117	—	4	4	no	—
164	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
165	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
166	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
186	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
187	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
188	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	16	yes	complemented
189	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
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	2	yes	—
207	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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×C₄²×C₂₃	—	4	2	no	—
219	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
222	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
225	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
226	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
227	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
228	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
231	C₂₃×#95	C₂³	1	1	yes	characteristic
232	C₂₃×#95	C₂³	1	1	yes	characteristic
233	C₂₃×#95	C₂³	1	1	yes	characteristic
234	C₂₃×#95	C₂³	1	1	yes	characteristic
235	C₂₃×#95	C₂³	1	2	yes	—
236	C₂₃×#95	C₂³	1	2	yes	—
237	C₂₃×#95	C₂³	1	2	yes	—
238	C₂₃×#95	C₂³	1	2	yes	—
239	C₂₃×#95	C₂³	1	1	yes	characteristic
240	C₂₃×#95	C₂³	1	1	yes	characteristic
241	C₂₃×#95	C₂³	1	1	yes	characteristic
242	C₂₃×#95	C₂³	1	1	yes	characteristic
243	C₂₃×#95	C₂³	1	1	yes	characteristic
244	C₂₃×#95	C₂³	1	2	yes	—
245	C₂₃×#95	C₂³	1	2	yes	—
246	C₂₃×#95	C₂³	1	2	yes	—
247	C₂₃×#95	C₂³	1	2	yes	—
248	C₂₃×#95	C₂³	1	2	yes	—
249	C₂₃×#95	C₂³	1	2	yes	—
250	C₂₃×#95	C₂³	1	2	yes	—
251	C₂₃×#95	C₂³	1	1	yes	characteristic
252	C₂⁴×C₂₃	—	2	4	no	—
253	C₂⁴×C₂₃	—	2	4	no	—
254	C₂⁴×C₂₃	—	4	2	no	—
255	C₂⁴×C₂₃	—	4	2	no	—
256	C₂⁴×C₂₃	—	4	2	no	—
257	C₂⁴×C₂₃	—	4	2	no	—
258	C₂⁴×C₂₃	C₂²×C₄	1	8	yes	—
259	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
260	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
261	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
262	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
263	#41×C₂₃	—	4	16	no	—
264	C₂×Q₈×C₂₃	—	2	2	no	—
265	C₂×Q₈×C₂₃	—	2	2	no	—
266	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
267	C₂×D₄×C₂₃	—	2	2	no	—
268	C₂×D₄×C₂₃	—	2	2	no	—
269	C₂×D₄×C₂₃	—	2	2	no	—
270	C₂×D₄×C₂₃	—	2	2	no	—
271	C₂×D₄×C₂₃	—	2	2	no	—
272	C₂×D₄×C₂₃	—	2	2	no	—
273	C₂×D₄×C₂₃	—	4	16	no	—
274	C₂×D₄×C₂₃	—	4	2	no	—
275	C₂×D₄×C₂₃	—	4	2	no	—
276	C₂×D₄×C₂₃	—	4	2	no	—
277	C₂×D₄×C₂₃	—	4	2	no	—
278	C₂×D₄×C₂₃	—	4	2	no	—
279	C₂×D₄×C₂₃	—	4	2	no	—
280	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
281	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
282	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
283	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
284	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
285	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
286	C₂²×C₄×C₂₃	—	2	2	no	—
287	C₂²×C₄×C₂₃	—	2	2	no	—
288	C₂²×C₄×C₂₃	—	2	2	no	—
289	C₂²×C₄×C₂₃	—	2	2	no	—
290	C₂²×C₄×C₂₃	—	2	2	no	—
291	C₂²×C₄×C₂₃	—	2	2	no	—
292	C₂²×C₄×C₂₃	—	2	4	no	—
293	C₂²×C₄×C₂₃	—	2	2	no	—
294	C₂²×C₄×C₂₃	—	4	1	no	—
295	C₂²×C₄×C₂₃	—	4	1	no	—
296	C₂²×C₄×C₂₃	—	4	2	no	—
297	C₂²×C₄×C₂₃	—	4	2	no	—
298	C₂²×C₄×C₂₃	—	4	1	no	—
299	C₂²×C₄×C₂₃	—	4	2	no	—
300	C₂²×C₄×C₂₃	—	4	2	no	—
301	C₂²×C₄×C₂₃	—	4	2	no	—
302	C₂²×C₄×C₂₃	—	4	2	no	—
303	C₂²×C₄×C₂₃	—	4	2	no	—
304	C₂²×C₄×C₂₃	—	4	2	no	—
305	C₂²×C₄×C₂₃	—	4	2	no	—
306	C₂²×C₄×C₂₃	—	4	2	no	—
307	C₂²×C₄×C₂₃	—	4	2	no	—
308	C₂²×C₄×C₂₃	—	4	2	no	—
309	C₂²×C₄×C₂₃	—	4	2	no	—
310	C₂²×C₄×C₂₃	—	4	2	no	—
311	C₂²×C₄×C₂₃	—	4	2	no	—
312	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
313	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
314	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
315	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
316	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
329	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
330	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
335	C₄⋊C₄×C₂₃	—	2	2	no	—
336	C₄⋊C₄×C₂₃	—	2	2	no	—
337	C₄⋊C₄×C₂₃	—	2	2	no	—
338	C₄⋊C₄×C₂₃	—	2	2	no	—
339	C₄⋊C₄×C₂₃	—	2	2	no	—
340	C₄⋊C₄×C₂₃	—	4	2	no	—
341	C₄⋊C₄×C₂₃	—	4	2	no	—
342	C₄⋊C₄×C₂₃	—	4	1	no	—
343	C₄⋊C₄×C₂₃	—	4	2	no	—
344	C₄⋊C₄×C₂₃	—	4	2	no	—
345	C₄⋊C₄×C₂₃	—	4	1	no	—
346	C₄⋊C₄×C₂₃	—	4	1	no	—
347	C₄⋊C₄×C₂₃	—	4	2	no	—
348	C₄⋊C₄×C₂₃	—	4	2	no	—
349	C₄⋊C₄×C₂₃	—	4	2	no	—
350	C₄⋊C₄×C₂₃	—	4	2	no	—
351	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
352	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
353	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
354	C₂²⋊C₄×C₂₃	—	2	2	no	—
355	C₂²⋊C₄×C₂₃	—	2	4	no	—
356	C₂²⋊C₄×C₂₃	—	2	2	no	—
357	C₂²⋊C₄×C₂₃	—	2	4	no	—
358	C₂²⋊C₄×C₂₃	—	2	4	no	—
359	C₂²⋊C₄×C₂₃	—	2	2	no	—
360	C₂²⋊C₄×C₂₃	—	4	2	no	—
361	C₂²⋊C₄×C₂₃	—	4	2	no	—
362	C₂²⋊C₄×C₂₃	—	4	2	no	—
363	C₂²⋊C₄×C₂₃	—	4	2	no	—
364	C₂²⋊C₄×C₂₃	—	4	2	no	—
365	C₂²⋊C₄×C₂₃	—	4	2	no	—
366	C₂²⋊C₄×C₂₃	—	4	2	no	—
367	C₂²⋊C₄×C₂₃	—	4	2	no	—
368	C₂²⋊C₄×C₂₃	—	4	2	no	—
369	C₂²⋊C₄×C₂₃	—	4	1	no	—
370	C₂²⋊C₄×C₂₃	—	4	1	no	—
371	C₂²⋊C₄×C₂₃	—	4	1	no	—
372	C₂²⋊C₄×C₂₃	—	4	2	no	—
373	C₂²⋊C₄×C₂₃	—	4	2	no	—
374	C₂²⋊C₄×C₂₃	—	4	2	no	—
375	C₂²⋊C₄×C₂₃	—	4	2	no	—
376	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
377	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
378	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
379	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
380	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
381	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
382	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
383	C₄²×C₂₃	—	2	2	no	—
384	C₄²×C₂₃	—	2	2	no	—
385	C₄²×C₂₃	—	2	4	no	—
386	C₄²×C₂₃	—	2	2	no	—
387	C₄²×C₂₃	—	2	2	no	—
388	C₄²×C₂₃	—	4	1	no	—
389	C₄²×C₂₃	—	4	1	no	—
390	C₄²×C₂₃	—	4	2	no	—
391	C₄²×C₂₃	—	4	2	no	—
392	C₄²×C₂₃	—	4	2	no	—
393	C₄²×C₂₃	—	4	2	no	—
394	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
395	#34476	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
396	C₂³×C₂₃	—	2	1	no	—
397	C₂³×C₂₃	—	2	1	no	—
398	C₂³×C₂₃	—	2	1	no	—
399	C₂³×C₂₃	—	2	1	no	—
400	C₂³×C₂₃	—	2	2	no	—
401	C₂³×C₂₃	—	2	2	no	—
402	C₂³×C₂₃	—	2	1	no	—
403	C₂³×C₂₃	—	2	2	no	—
404	C₂³×C₂₃	—	2	1	no	—
405	C₂³×C₂₃	—	2	1	no	—
406	C₂³×C₂₃	—	2	2	no	—
407	C₂³×C₂₃	—	2	2	no	—
408	C₂³×C₂₃	—	2	2	no	—
409	C₂³×C₂₃	—	2	1	no	—
410	C₂³×C₂₃	—	2	2	no	—
411	C₂³×C₂₃	—	2	2	no	—
412	C₂³×C₂₃	—	2	1	no	—
413	C₂³×C₂₃	—	2	2	no	—
414	C₂³×C₂₃	—	2	2	no	—
415	C₂³×C₂₃	—	2	2	no	—
416	C₂³×C₂₃	—	2	1	no	—
417	C₂³×C₂₃	—	2	2	no	—
418	C₂³×C₂₃	—	2	16	no	—
419	C₂³×C₂₃	—	4	8	no	—
420	C₂³×C₂₃	—	4	8	no	—
421	C₂³×C₂₃	—	8	4	no	—
422	C₂³×C₂₃	—	8	4	no	—
423	C₂³×C₂₃	—	8	4	no	—
424	C₂³×C₂₃	—	8	4	no	—
425	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
426	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
427	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
428	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
429	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
430	C₂³×C₂₃	2₋¹⁺⁴	1	2	yes	—
431	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
432	Q₈×C₂₃	—	2	8	no	—
433	D₄×C₂₃	—	2	8	no	—
434	D₄×C₂₃	—	2	8	no	—
435	D₄×C₂₃	—	2	8	no	—
436	D₄×C₂₃	—	4	8	no	—
437	D₄×C₂₃	—	4	8	no	—
438	D₄×C₂₃	—	4	8	no	—
439	C₂×C₄×C₂₃	—	2	1	no	—
440	C₂×C₄×C₂₃	—	2	2	no	—
441	C₂×C₄×C₂₃	—	2	1	no	—
442	C₂×C₄×C₂₃	—	2	1	no	—
443	C₂×C₄×C₂₃	—	2	2	no	—
444	C₂×C₄×C₂₃	—	2	2	no	—
445	C₂×C₄×C₂₃	—	2	1	no	—
446	C₂×C₄×C₂₃	—	2	1	no	—
447	C₂×C₄×C₂₃	—	2	1	no	—
448	C₂×C₄×C₂₃	—	2	1	no	—
449	C₂×C₄×C₂₃	—	2	1	no	—
450	C₂×C₄×C₂₃	—	2	1	no	—
451	C₂×C₄×C₂₃	—	2	1	no	—
452	C₂×C₄×C₂₃	—	2	2	no	—
453	C₂×C₄×C₂₃	—	2	8	no	—
454	C₂×C₄×C₂₃	—	2	8	no	—
455	C₂×C₄×C₂₃	—	2	1	no	—
456	C₂×C₄×C₂₃	—	2	1	no	—
457	C₂×C₄×C₂₃	—	2	1	no	—
458	C₂×C₄×C₂₃	—	2	1	no	—
459	C₂×C₄×C₂₃	—	2	1	no	—
460	C₂×C₄×C₂₃	—	2	1	no	—
461	C₂×C₄×C₂₃	—	2	2	no	—
462	C₂×C₄×C₂₃	—	2	1	no	—
463	C₂×C₄×C₂₃	—	2	1	no	—
464	C₂×C₄×C₂₃	—	2	2	no	—
465	C₂×C₄×C₂₃	—	2	2	no	—
466	C₂×C₄×C₂₃	—	2	2	no	—
467	C₂×C₄×C₂₃	—	2	2	no	—
468	C₂×C₄×C₂₃	—	2	2	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	2	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	2	no	—
478	C₂×C₄×C₂₃	—	2	2	no	—
479	C₂×C₄×C₂₃	—	2	2	no	—
480	C₂×C₄×C₂₃	—	2	1	no	—
481	C₂×C₄×C₂₃	—	2	1	no	—
482	C₂×C₄×C₂₃	—	2	1	no	—
483	C₂×C₄×C₂₃	—	2	1	no	—
484	C₂×C₄×C₂₃	—	2	1	no	—
485	C₂×C₄×C₂₃	—	2	2	no	—
486	C₂×C₄×C₂₃	—	2	1	no	—
487	C₂×C₄×C₂₃	—	2	1	no	—
488	C₂×C₄×C₂₃	—	4	8	no	—
489	C₂×C₄×C₂₃	—	4	8	no	—
490	C₂×C₄×C₂₃	—	4	4	no	—
491	C₂×C₄×C₂₃	—	4	4	no	—
492	C₂×C₄×C₂₃	—	8	4	no	—
493	C₂×C₄×C₂₃	—	8	4	no	—
494	C₂×C₄×C₂₃	—	8	4	no	—
495	C₂×C₄×C₂₃	—	8	4	no	—
496	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
497	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
498	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
499	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
500	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
501	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
502	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
503	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
504	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
505	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
506	C₂×#546	C₂×C₂₃	1	1	yes	characteristic
507	#2377	C₂×C₂₃	1	2	yes	complemented
508	#2376	C₂×C₂₃	1	2	yes	complemented
509	#2367	C₂×C₂₃	1	1	yes	characteristic, complemented
510	#2361	C₂×C₂₃	1	1	yes	characteristic, complemented
511	#2360	C₂×C₂₃	1	1	yes	characteristic, complemented
512	#2358	C₂×C₂₃	1	2	yes	complemented
513	#2354	C₂×C₂₃	1	1	yes	characteristic, complemented
514	D₄×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
515	#2342	C₂×C₂₃	1	2	yes	complemented
516	#2341	C₂×C₂₃	1	1	yes	characteristic, complemented
517	D₄×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
518	#2335	C₂×C₂₃	1	2	yes	complemented
519	#2326	C₂×C₂₃	1	1	yes	characteristic, complemented
520	#2324	C₂×C₂₃	1	1	yes	characteristic, complemented
521	#2324	C₂×C₂₃	1	2	yes	complemented
522	#2321	C₂×C₂₃	1	2	yes	complemented
523	#2319	C₂×C₂₃	1	1	yes	characteristic, complemented
524	#2315	C₂×C₂₃	1	2	yes	complemented
525	#2311	C₂×C₂₃	1	1	yes	characteristic, complemented
526	C₄×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
527	C₂×#390	C₂×C₂₃	1	1	yes	characteristic, complemented
528	#2290	C₂×C₂₃	1	1	yes	characteristic, complemented
529	C₂²×C₂₃	—	2	2	no	—
530	C₂²×C₂₃	—	2	2	no	—
531	C₂²×C₂₃	—	2	2	no	—
532	C₂²×C₂₃	—	2	2	no	—
533	C₂²×C₂₃	—	2	2	no	—
534	C₂²×C₂₃	—	2	2	no	—
535	C₂²×C₂₃	—	2	2	no	—
536	C₂²×C₂₃	—	2	4	no	—
537	C₂²×C₂₃	—	2	4	no	—
538	C₂²×C₂₃	—	2	2	no	—
539	C₂²×C₂₃	—	2	4	no	—
540	C₂²×C₂₃	—	2	4	no	—
541	C₂²×C₂₃	—	2	4	no	—
542	C₂²×C₂₃	—	2	2	no	—
543	C₂²×C₂₃	—	2	4	no	—
544	C₂²×C₂₃	—	4	1	no	—
545	C₂²×C₂₃	—	4	2	no	—
546	C₂²×C₂₃	—	4	2	no	—
547	C₂²×C₂₃	—	4	2	no	—
548	C₂²×C₂₃	—	4	1	no	—
549	C₂²×C₂₃	—	4	2	no	—
550	C₂²×C₂₃	—	4	1	no	—
551	C₂²×C₂₃	—	4	2	no	—
552	C₂²×C₂₃	—	4	2	no	—
553	C₂²×C₂₃	—	4	1	no	—
554	C₂²×C₂₃	—	4	2	no	—
555	C₂²×C₂₃	—	4	2	no	—
556	C₂²×C₂₃	—	8	16	no	—
557	C₂²×C₂₃	#520	1	4	yes	—
558	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
559	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
560	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
561	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
562	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
563	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
564	C₂²×C₂₃	#585	1	1	yes	characteristic
565	C₄×C₂₃	—	2	2	no	—
566	C₄×C₂₃	—	2	2	no	—
567	C₄×C₂₃	—	2	4	no	—
568	C₄×C₂₃	—	2	2	no	—
569	C₄×C₂₃	—	2	2	no	—
570	C₄×C₂₃	—	2	4	no	—
571	C₄×C₂₃	—	2	2	no	—
572	C₄×C₂₃	—	4	1	no	—
573	C₄×C₂₃	—	4	1	no	—
574	C₄×C₂₃	—	4	1	no	—
575	C₄×C₂₃	—	4	1	no	—
576	C₄×C₂₃	—	4	2	no	—
577	C₄×C₂₃	—	4	1	no	—
578	C₄×C₂₃	—	4	2	no	—
579	C₄×C₂₃	—	4	2	no	—
580	C₄×C₂₃	—	4	1	no	—
581	C₄×C₂₃	—	4	2	no	—
582	C₄×C₂₃	—	4	1	no	—
583	C₄×C₂₃	#518	1	4	yes	—
584	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
585	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
586	#546	C₄×C₂₃	1	16	yes	complemented
587	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
588	C₂×#123	C₂²×C₂₃	1	2	yes	—
589	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
590	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
591	C₂×#121	C₂²×C₂₃	1	2	yes	—
592	C₂×#120	C₂²×C₂₃	1	2	yes	—
593	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
594	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
595	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
596	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
597	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
598	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
599	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
600	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
601	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic, complemented
602	C₂×#117	C₂²×C₂₃	1	2	yes	complemented
603	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
604	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
605	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
606	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
607	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
608	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
609	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
610	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
611	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
612	#390	C₂²×C₂₃	1	1	yes	characteristic
613	#390	C₂²×C₂₃	1	1	yes	characteristic
614	#390	C₂²×C₂₃	1	1	yes	characteristic
615	#390	C₂²×C₂₃	1	1	yes	characteristic
616	#390	C₂²×C₂₃	1	2	yes	—
617	#390	C₂²×C₂₃	1	1	yes	characteristic
618	#390	C₂²×C₂₃	1	1	yes	characteristic
619	#390	C₂²×C₂₃	1	2	yes	—
620	#390	C₂²×C₂₃	1	2	yes	complemented
621	#390	C₂²×C₂₃	1	2	yes	complemented
622	#390	C₂²×C₂₃	1	2	yes	complemented
623	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
624	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
625	#389	C₂²×C₂₃	1	2	yes	complemented
626	#389	C₂²×C₂₃	1	2	yes	complemented
627	#388	C₂²×C₂₃	1	2	yes	complemented
628	#388	C₂²×C₂₃	1	2	yes	complemented
629	#388	C₂²×C₂₃	1	2	yes	complemented
630	#388	C₂²×C₂₃	1	2	yes	complemented
631	#388	C₂²×C₂₃	1	2	yes	complemented
632	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
633	#388	C₂²×C₂₃	1	2	yes	complemented
634	#388	C₂²×C₂₃	1	2	yes	complemented
635	#388	C₂²×C₂₃	1	2	yes	complemented
636	#388	C₂²×C₂₃	1	2	yes	complemented
637	#388	C₂²×C₂₃	1	2	yes	complemented
638	#388	C₂²×C₂₃	1	1	yes	characteristic, complemented
639	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
640	#387	C₂²×C₂₃	1	2	yes	complemented
641	#387	C₂²×C₂₃	1	1	yes	characteristic, complemented
642	#387	C₂²×C₂₃	1	2	yes	complemented
643	#386	C₂²×C₂₃	1	1	yes	characteristic
644	#386	C₂²×C₂₃	1	2	yes	—
645	#386	C₂²×C₂₃	1	2	yes	—
646	#386	C₂²×C₂₃	1	1	yes	characteristic
647	#386	C₂²×C₂₃	1	2	yes	complemented
648	#386	C₂²×C₂₃	1	2	yes	complemented
649	#386	C₂²×C₂₃	1	2	yes	complemented
650	#386	C₂²×C₂₃	1	2	yes	complemented
651	#385	C₂²×C₂₃	1	1	yes	characteristic
652	#385	C₂²×C₂₃	1	2	yes	—
653	#385	C₂²×C₂₃	1	2	yes	—
654	#385	C₂²×C₂₃	1	2	yes	—
655	#385	C₂²×C₂₃	1	1	yes	characteristic
656	#385	C₂²×C₂₃	1	2	yes	complemented
657	#385	C₂²×C₂₃	1	2	yes	complemented
658	#385	C₂²×C₂₃	1	2	yes	complemented
659	#385	C₂²×C₂₃	1	2	yes	complemented
660	#385	C₂²×C₂₃	1	2	yes	complemented
661	#385	C₂²×C₂₃	1	2	yes	complemented
662	#384	C₂²×C₂₃	1	1	yes	characteristic, complemented
663	#381	C₂²×C₂₃	1	2	yes	complemented
664	#380	C₂²×C₂₃	1	1	yes	characteristic
665	#380	C₂²×C₂₃	1	2	yes	complemented
666	#380	C₂²×C₂₃	1	2	yes	complemented
667	#380	C₂²×C₂₃	1	2	yes	complemented
668	#380	C₂²×C₂₃	1	2	yes	complemented
669	#380	C₂²×C₂₃	1	2	yes	complemented
670	#380	C₂²×C₂₃	1	1	yes	characteristic, complemented
671	#379	C₂²×C₂₃	1	2	yes	—
672	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
673	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
674	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
675	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
676	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
677	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
678	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
679	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
680	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
681	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
682	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
683	#376	C₂²×C₂₃	1	1	yes	characteristic, complemented
684	C₂×C₂₃	—	2	4	no	—
685	C₂×C₂₃	—	4	2	no	—
686	C₂×C₂₃	—	4	4	no	—
687	C₂×C₂₃	—	4	4	no	—
688	C₂×C₂₃	C₂×#518	1	1	yes	characteristic
689	C₂×C₂₃	C₂×#520	1	1	yes	characteristic
690	C₂×C₂₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
691	C₂×C₂₃	#3536	1	1	yes	characteristic
692	C₂×C₂₃	#3542	1	1	yes	characteristic
693	C₂×C₂₃	#3543	1	1	yes	characteristic
694	C₂×C₂₃	#3561	1	1	yes	characteristic
695	C₂⁵	C₂³×C₂₃	1	2	yes	—
696	C₂×#41	—	4	2	no	—
697	C₂×#41	—	4	2	no	—
698	C₂×#41	C₂×C₄×C₂₃	1	8	yes	complemented
699	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
700	C₂²×D₄	—	4	2	no	—
701	C₂²×D₄	—	4	2	no	—
702	C₂²×D₄	C₂×C₄×C₂₃	1	8	yes	complemented
703	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
704	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
705	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
706	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
707	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
708	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
709	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
710	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
711	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
712	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
713	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
714	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
715	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
716	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
717	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
718	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
719	#124	C₂×C₄×C₂₃	1	8	yes	complemented
720	#123	C₂×C₄×C₂₃	1	16	yes	complemented
721	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
722	#121	C₂×C₄×C₂₃	1	8	yes	complemented
723	#121	C₂×C₄×C₂₃	1	16	yes	complemented
724	#120	C₂×C₄×C₂₃	1	16	yes	complemented
725	C₄×Q₈	—	4	2	no	—
726	C₄×Q₈	—	4	2	no	—
727	C₄×D₄	—	4	4	no	—
728	C₄×D₄	—	4	2	no	—
729	C₄×D₄	—	4	2	no	—
730	C₄×D₄	—	4	4	no	—
731	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	complemented
732	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	complemented
733	#117	—	4	2	no	—
734	#117	—	4	4	no	—
735	C₂×C₄⋊C₄	—	4	2	no	—
736	C₂×C₄⋊C₄	—	4	2	no	—
737	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
738	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
739	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
740	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
741	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
742	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
743	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
744	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
745	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
746	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
747	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
748	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
749	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
750	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
751	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
752	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
753	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
754	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
755	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
756	C₂×C₂²⋊C₄	—	4	4	no	—
757	C₂×C₂²⋊C₄	—	4	4	no	—
758	C₂×C₂²⋊C₄	—	4	4	no	—
759	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	16	yes	complemented
760	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
761	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
762	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
765	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
766	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
767	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
768	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
769	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
776	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
777	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
780	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
781	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
782	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
783	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
784	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
785	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
786	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
787	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
788	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
789	C₂×C₄²	—	4	2	no	—
790	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
791	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
792	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
793	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
794	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
795	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
796	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
797	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
798	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
799	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
800	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
801	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
802	#95	C₂³×C₂₃	1	1	yes	characteristic
803	#95	C₂³×C₂₃	1	1	yes	characteristic
804	#95	C₂³×C₂₃	1	1	yes	characteristic
805	#95	C₂³×C₂₃	1	1	yes	characteristic
806	#95	C₂³×C₂₃	1	2	yes	—
807	#95	C₂³×C₂₃	1	2	yes	—
808	#95	C₂³×C₂₃	1	2	yes	—
809	#95	C₂³×C₂₃	1	2	yes	—
810	#95	C₂³×C₂₃	1	1	yes	characteristic
811	#95	C₂³×C₂₃	1	1	yes	characteristic
812	#95	C₂³×C₂₃	1	1	yes	characteristic
813	#95	C₂³×C₂₃	1	1	yes	characteristic
814	#95	C₂³×C₂₃	1	1	yes	characteristic
815	#95	C₂³×C₂₃	1	2	yes	—
816	#95	C₂³×C₂₃	1	2	yes	—
817	#95	C₂³×C₂₃	1	2	yes	—
818	#95	C₂³×C₂₃	1	2	yes	—
819	#95	C₂³×C₂₃	1	2	yes	—
820	#95	C₂³×C₂₃	1	2	yes	—
821	#95	C₂³×C₂₃	1	2	yes	—
822	#95	C₂³×C₂₃	1	1	yes	characteristic
823	C₂₃	#34476	1	1	yes	characteristic, direct product factor, Sylow
824	C₂⁴	—	2	4	no	—
825	C₂⁴	—	2	4	no	—
826	C₂⁴	—	4	2	no	—
827	C₂⁴	—	4	2	no	—
828	C₂⁴	—	4	2	no	—
829	C₂⁴	—	4	2	no	—
830	C₂⁴	C₂²×C₄×C₂₃	1	8	yes	—
831	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
832	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
833	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
834	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
835	#41	—	4	16	no	—
836	C₂×Q₈	—	2	2	no	—
837	C₂×Q₈	—	2	2	no	—
838	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
839	C₂×D₄	—	2	2	no	—
840	C₂×D₄	—	2	2	no	—
841	C₂×D₄	—	2	2	no	—
842	C₂×D₄	—	2	2	no	—
843	C₂×D₄	—	2	2	no	—
844	C₂×D₄	—	2	2	no	—
845	C₂×D₄	—	4	16	no	—
846	C₂×D₄	—	4	2	no	—
847	C₂×D₄	—	4	2	no	—
848	C₂×D₄	—	4	2	no	—
849	C₂×D₄	—	4	2	no	—
850	C₂×D₄	—	4	2	no	—
851	C₂×D₄	—	4	2	no	—
852	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
853	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
854	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
855	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
856	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
857	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	2	no	—
863	C₂²×C₄	—	2	2	no	—
864	C₂²×C₄	—	2	4	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	4	1	no	—
867	C₂²×C₄	—	4	1	no	—
868	C₂²×C₄	—	4	2	no	—
869	C₂²×C₄	—	4	2	no	—
870	C₂²×C₄	—	4	2	no	—
871	C₂²×C₄	—	4	2	no	—
872	C₂²×C₄	—	4	1	no	—
873	C₂²×C₄	—	4	2	no	—
874	C₂²×C₄	—	4	2	no	—
875	C₂²×C₄	—	4	2	no	—
876	C₂²×C₄	—	4	2	no	—
877	C₂²×C₄	—	4	2	no	—
878	C₂²×C₄	—	4	2	no	—
879	C₂²×C₄	—	4	2	no	—
880	C₂²×C₄	—	4	2	no	—
881	C₂²×C₄	—	4	2	no	—
882	C₂²×C₄	—	4	2	no	—
883	C₂²×C₄	—	4	2	no	—
884	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
885	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
886	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
887	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
888	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
889	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
890	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
891	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
892	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
893	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
894	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
895	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
896	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
897	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
898	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
899	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
900	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
901	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
902	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
903	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
904	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
905	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
906	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	4	2	no	—
913	C₄⋊C₄	—	4	2	no	—
914	C₄⋊C₄	—	4	2	no	—
915	C₄⋊C₄	—	4	1	no	—
916	C₄⋊C₄	—	4	1	no	—
917	C₄⋊C₄	—	4	2	no	—
918	C₄⋊C₄	—	4	2	no	—
919	C₄⋊C₄	—	4	2	no	—
920	C₄⋊C₄	—	4	2	no	—
921	C₄⋊C₄	—	4	1	no	—
922	C₄⋊C₄	—	4	2	no	—
923	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
924	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
925	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	4	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	4	no	—
930	C₂²⋊C₄	—	2	4	no	—
931	C₂²⋊C₄	—	2	2	no	—
932	C₂²⋊C₄	—	4	2	no	—
933	C₂²⋊C₄	—	4	2	no	—
934	C₂²⋊C₄	—	4	2	no	—
935	C₂²⋊C₄	—	4	2	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	1	no	—
941	C₂²⋊C₄	—	4	1	no	—
942	C₂²⋊C₄	—	4	2	no	—
943	C₂²⋊C₄	—	4	2	no	—
944	C₂²⋊C₄	—	4	2	no	—
945	C₂²⋊C₄	—	4	2	no	—
946	C₂²⋊C₄	—	4	2	no	—
947	C₂²⋊C₄	—	4	1	no	—
948	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
949	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
950	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
951	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
952	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
953	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
954	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	2	no	—
957	C₄²	—	2	4	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	2	2	no	—
960	C₄²	—	4	1	no	—
961	C₄²	—	4	1	no	—
962	C₄²	—	4	2	no	—
963	C₄²	—	4	2	no	—
964	C₄²	—	4	2	no	—
965	C₄²	—	4	2	no	—
966	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
967	C₂³	—	2	1	no	—
968	C₂³	—	2	1	no	—
969	C₂³	—	2	1	no	—
970	C₂³	—	2	1	no	—
971	C₂³	—	2	2	no	—
972	C₂³	—	2	2	no	—
973	C₂³	—	2	1	no	—
974	C₂³	—	2	2	no	—
975	C₂³	—	2	1	no	—
976	C₂³	—	2	1	no	—
977	C₂³	—	2	2	no	—
978	C₂³	—	2	2	no	—
979	C₂³	—	2	2	no	—
980	C₂³	—	2	1	no	—
981	C₂³	—	2	2	no	—
982	C₂³	—	2	2	no	—
983	C₂³	—	2	1	no	—
984	C₂³	—	2	2	no	—
985	C₂³	—	2	2	no	—
986	C₂³	—	2	2	no	—
987	C₂³	—	2	1	no	—
988	C₂³	—	2	2	no	—
989	C₂³	—	2	16	no	—
990	C₂³	—	4	8	no	—
991	C₂³	—	4	8	no	—
992	C₂³	—	8	4	no	—
993	C₂³	—	8	4	no	—
994	C₂³	—	8	4	no	—
995	C₂³	—	8	4	no	—
996	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
997	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
998	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
999	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
1000	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
1001	C₂³	C₂₃×2₋¹⁺⁴	1	2	yes	—
1002	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
1003	Q₈	—	2	8	no	—
1004	D₄	—	2	8	no	—
1005	D₄	—	2	8	no	—
1006	D₄	—	2	8	no	—
1007	D₄	—	4	8	no	—
1008	D₄	—	4	8	no	—
1009	D₄	—	4	8	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	8	no	—
1025	C₂×C₄	—	2	8	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	4	8	no	—
1060	C₂×C₄	—	4	8	no	—
1061	C₂×C₄	—	4	4	no	—
1062	C₂×C₄	—	4	4	no	—
1063	C₂×C₄	—	8	4	no	—
1064	C₂×C₄	—	8	4	no	—
1065	C₂×C₄	—	8	4	no	—
1066	C₂×C₄	—	8	4	no	—
1067	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1068	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1069	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
1070	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1071	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
1072	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1073	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1074	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1075	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1076	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1077	C₂²	—	2	2	no	—
1078	C₂²	—	2	2	no	—
1079	C₂²	—	2	2	no	—
1080	C₂²	—	2	2	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	2	no	—
1084	C₂²	—	2	4	no	—
1085	C₂²	—	2	4	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	2	4	no	—
1088	C₂²	—	2	4	no	—
1089	C₂²	—	2	4	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	2	4	no	—
1092	C₂²	—	4	2	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	2	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	2	no	—
1100	C₂²	—	4	2	no	—
1101	C₂²	—	4	2	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	8	16	no	—
1105	C₂²	C₂₃×#520	1	4	yes	—
1106	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
1107	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1108	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1109	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1110	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1111	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1112	C₂²	C₂₃×#585	1	1	yes	characteristic
1113	C₄	—	2	2	no	—
1114	C₄	—	2	2	no	—
1115	C₄	—	2	4	no	—
1116	C₄	—	2	2	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	4	no	—
1119	C₄	—	2	2	no	—
1120	C₄	—	4	1	no	—
1121	C₄	—	4	1	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	2	no	—
1126	C₄	—	4	2	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	2	no	—
1129	C₄	—	4	2	no	—
1130	C₄	—	4	1	no	—
1131	C₄	C₂₃×#518	1	4	yes	—
1132	C₂	—	2	4	no	—
1133	C₂	—	4	4	no	—
1134	C₂	—	4	4	no	—
1135	C₂	—	4	2	no	—
1136	C₂	C₂×C₂₃×#518	1	1	yes	characteristic
1137	C₂	C₂×C₂₃×#520	1	1	yes	characteristic
1138	C₂	C₄×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1139	C₂	C₂₃×#3536	1	1	yes	characteristic
1140	C₂	C₂₃×#3542	1	1	yes	characteristic
1141	C₂	C₂₃×#3543	1	1	yes	characteristic
1142	C₂	C₂₃×#3561	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2377	C₂	semidirect
3. C₂₃×#2376	C₂	semidirect
4. C₂₃×#2367	C₂	semidirect
5. C₂₃×#2361	C₂	semidirect
6. C₂₃×#2360	C₂	semidirect
7. C₂₃×#2358	C₂	semidirect
8. C₂₃×#2354	C₂	semidirect
9. D₄×C₄⋊C₄×C₂₃	C₂	semidirect
10. C₂₃×#2342	C₂	semidirect
11. C₂₃×#2341	C₂	semidirect
12. D₄×C₂²⋊C₄×C₂₃	C₂	semidirect
13. C₂₃×#2335	C₂	semidirect
14. C₂₃×#2326	C₂	semidirect
15. C₂₃×#2324	C₂	semidirect
16. C₂₃×#2324	C₂	semidirect
17. C₂₃×#2321	C₂	semidirect
18. C₂₃×#2319	C₂	semidirect
19. C₂₃×#2315	C₂	semidirect
20. C₂₃×#2311	C₂	semidirect
21. C₄×C₂₃×C₂²⋊Q₈	C₂	semidirect
22. C₂×C₂₃×#390	C₂	semidirect
23. C₂₃×#2290	C₂	semidirect
26. C₂₃×#546	C₄	semidirect
33. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
34. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
40. C₂×C₄×D₄×C₂₃	C₂²	semidirect
41. C₂×C₂₃×#117	C₂²	semidirect
42. C₂×C₂₃×#117	C₂²	semidirect
44. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
50. C₂₃×#391	C₂²	semidirect
51. C₂₃×#391	C₂²	semidirect
60. C₂₃×#390	C₂²	semidirect
61. C₂₃×#390	C₂²	semidirect
62. C₂₃×#390	C₂²	semidirect
63. C₂₃×#389	C₂²	semidirect
64. C₂₃×#389	C₂²	semidirect
65. C₂₃×#389	C₂²	semidirect
66. C₂₃×#389	C₂²	semidirect
67. C₂₃×#388	C₂²	semidirect
68. C₂₃×#388	C₂²	semidirect
69. C₂₃×#388	C₂²	semidirect
70. C₂₃×#388	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×#388	C₂²	semidirect
79. C₂₃×#387	C₂²	semidirect
80. C₂₃×#387	C₂²	semidirect
81. C₂₃×#387	C₂²	semidirect
82. C₂₃×#387	C₂²	semidirect
87. C₂₃×#386	C₂²	semidirect
88. C₂₃×#386	C₂²	semidirect
89. C₂₃×#386	C₂²	semidirect
90. C₂₃×#386	C₂²	semidirect
96. C₂₃×#385	C₂²	semidirect
97. C₂₃×#385	C₂²	semidirect
98. C₂₃×#385	C₂²	semidirect
99. C₂₃×#385	C₂²	semidirect
100. C₂₃×#385	C₂²	semidirect
101. C₂₃×#385	C₂²	semidirect
102. C₂₃×#384	C₂²	semidirect
103. C₂₃×#381	C₂²	semidirect
105. C₂₃×#380	C₂²	semidirect
106. C₂₃×#380	C₂²	semidirect
107. C₂₃×#380	C₂²	semidirect
108. C₂₃×#380	C₂²	semidirect
109. C₂₃×#380	C₂²	semidirect
110. C₂₃×#380	C₂²	semidirect
112. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
113. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
114. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
115. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
116. C₄×C₄⋊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. C₂₃×#376	C₂²	semidirect
127. C₂×#41×C₂₃	C₂×C₄	semidirect
131. C₂²×D₄×C₂₃	C₂×C₄	semidirect
148. C₂₃×#124	C₂×C₄	semidirect
149. C₂₃×#123	C₂×C₄	semidirect
150. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
151. C₂₃×#121	C₂×C₄	semidirect
152. C₂₃×#121	C₂×C₄	semidirect
153. C₂₃×#120	C₂×C₄	semidirect
160. C₄×D₄×C₂₃	C₂×C₄	semidirect
161. C₄×D₄×C₂₃	C₂×C₄	semidirect
188. C₂×C₂²⋊C₄×C₂₃	C₂×C₄	semidirect
395. #34476	C₂₃	direct (N × H)
507. #2377	C₂×C₂₃	semidirect
508. #2376	C₂×C₂₃	semidirect
509. #2367	C₂×C₂₃	semidirect
510. #2361	C₂×C₂₃	semidirect
511. #2360	C₂×C₂₃	semidirect
512. #2358	C₂×C₂₃	semidirect
513. #2354	C₂×C₂₃	semidirect
514. D₄×C₄⋊C₄	C₂×C₂₃	semidirect
515. #2342	C₂×C₂₃	semidirect
516. #2341	C₂×C₂₃	semidirect
517. D₄×C₂²⋊C₄	C₂×C₂₃	semidirect
518. #2335	C₂×C₂₃	semidirect
519. #2326	C₂×C₂₃	semidirect
520. #2324	C₂×C₂₃	semidirect
521. #2324	C₂×C₂₃	semidirect
522. #2321	C₂×C₂₃	semidirect
523. #2319	C₂×C₂₃	semidirect
524. #2315	C₂×C₂₃	semidirect
525. #2311	C₂×C₂₃	semidirect
526. C₄×C₂²⋊Q₈	C₂×C₂₃	semidirect
527. C₂×#390	C₂×C₂₃	semidirect
528. #2290	C₂×C₂₃	semidirect
586. #546	C₄×C₂₃	semidirect
593. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
594. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
600. C₂×C₄×D₄	C₂²×C₂₃	semidirect
601. C₂×#117	C₂²×C₂₃	semidirect
602. C₂×#117	C₂²×C₂₃	semidirect
604. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
610. #391	C₂²×C₂₃	semidirect
611. #391	C₂²×C₂₃	semidirect
620. #390	C₂²×C₂₃	semidirect
621. #390	C₂²×C₂₃	semidirect
622. #390	C₂²×C₂₃	semidirect
623. #389	C₂²×C₂₃	semidirect
624. #389	C₂²×C₂₃	semidirect
625. #389	C₂²×C₂₃	semidirect
626. #389	C₂²×C₂₃	semidirect
627. #388	C₂²×C₂₃	semidirect
628. #388	C₂²×C₂₃	semidirect
629. #388	C₂²×C₂₃	semidirect
630. #388	C₂²×C₂₃	semidirect
631. #388	C₂²×C₂₃	semidirect
632. #388	C₂²×C₂₃	semidirect
633. #388	C₂²×C₂₃	semidirect
634. #388	C₂²×C₂₃	semidirect
635. #388	C₂²×C₂₃	semidirect
636. #388	C₂²×C₂₃	semidirect
637. #388	C₂²×C₂₃	semidirect
638. #388	C₂²×C₂₃	semidirect
639. #387	C₂²×C₂₃	semidirect
640. #387	C₂²×C₂₃	semidirect
641. #387	C₂²×C₂₃	semidirect
642. #387	C₂²×C₂₃	semidirect
647. #386	C₂²×C₂₃	semidirect
648. #386	C₂²×C₂₃	semidirect
649. #386	C₂²×C₂₃	semidirect
650. #386	C₂²×C₂₃	semidirect
656. #385	C₂²×C₂₃	semidirect
657. #385	C₂²×C₂₃	semidirect
658. #385	C₂²×C₂₃	semidirect
659. #385	C₂²×C₂₃	semidirect
660. #385	C₂²×C₂₃	semidirect
661. #385	C₂²×C₂₃	semidirect
662. #384	C₂²×C₂₃	semidirect
663. #381	C₂²×C₂₃	semidirect
665. #380	C₂²×C₂₃	semidirect
666. #380	C₂²×C₂₃	semidirect
667. #380	C₂²×C₂₃	semidirect
668. #380	C₂²×C₂₃	semidirect
669. #380	C₂²×C₂₃	semidirect
670. #380	C₂²×C₂₃	semidirect
672. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
673. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
674. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
675. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
676. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
680. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
681. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
682. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
683. #376	C₂²×C₂₃	semidirect
698. C₂×#41	C₂×C₄×C₂₃	semidirect
702. C₂²×D₄	C₂×C₄×C₂₃	semidirect
719. #124	C₂×C₄×C₂₃	semidirect
720. #123	C₂×C₄×C₂₃	semidirect
721. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
722. #121	C₂×C₄×C₂₃	semidirect
723. #121	C₂×C₄×C₂₃	semidirect
724. #120	C₂×C₄×C₂₃	semidirect
731. C₄×D₄	C₂×C₄×C₂₃	semidirect
732. C₄×D₄	C₂×C₄×C₂₃	semidirect
759. C₂×C₂²⋊C₄	C₂×C₄×C₂₃	semidirect
823. C₂₃	#34476	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
C₂₃×#2377	2
C₂₃×#2376	2
C₂₃×#2367	2
C₂₃×#2361	2
C₂₃×#2360	2
C₂₃×#2358	2
C₂₃×#2354	2
D₄×C₄⋊C₄×C₂₃	2
C₂₃×#2342	2
C₂₃×#2341	2
D₄×C₂²⋊C₄×C₂₃	2
C₂₃×#2335	2
C₂₃×#2326	2
C₂₃×#2324	2
C₂₃×#2321	2
C₂₃×#2319	2
C₂₃×#2315	2
C₂₃×#2311	2
C₄×C₂₃×C₂²⋊Q₈	2
C₂×C₂₃×#390	2
C₂₃×#2290	2
#34476	23

Subgroups — C23×#34476 #19182102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34476 #19182102