Subgroups — C₄×C₂₃×#538 #19181717

Order 5888.

2650 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#538	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2337	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2335	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2334	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2333	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2329	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2325	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2321	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2318	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2312	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₂₃×#126	C₂	1	2	yes	maximal, complemented
12	C₄×C₂₃×#124	C₂	1	2	yes	maximal, complemented
13	C₄×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂₃×#123	C₂	1	2	yes	maximal, complemented
15	C₄×C₂₃×#121	C₂	1	2	yes	maximal, complemented
16	C₄×C₂₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₂₃×#120	C₂	1	2	yes	maximal, complemented
18	C₄²×D₄×C₂₃	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂₃×#538	C₄	1	16	yes	direct product factor
22	C₂×C₂₃×#126	C₂²	1	2	yes	—
23	C₂×C₂₃×#124	C₂²	1	2	yes	—
24	C₂×C₂₃×#123	C₂²	1	2	yes	—
25	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#121	C₂²	1	2	yes	—
28	C₂×C₂₃×#120	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₂₃	C₂²	1	2	yes	complemented
41	C₂₃×#391	C₂²	1	1	yes	characteristic, complemented
42	C₂₃×#391	C₂²	1	2	yes	complemented
43	C₂₃×#390	C₂²	1	2	yes	—
44	C₂₃×#390	C₂²	1	2	yes	—
45	C₂₃×#390	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#389	C₂²	1	2	yes	complemented
47	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
48	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#388	C₂²	1	2	yes	—
50	C₂₃×#388	C₂²	1	2	yes	—
51	C₂₃×#388	C₂²	1	2	yes	—
52	C₂₃×#388	C₂²	1	2	yes	—
53	C₂₃×#388	C₂²	1	2	yes	—
54	C₂₃×#388	C₂²	1	2	yes	—
55	C₂₃×#388	C₂²	1	2	yes	—
56	C₂₃×#388	C₂²	1	2	yes	—
57	C₂₃×#388	C₂²	1	2	yes	complemented
58	C₂₃×#388	C₂²	1	2	yes	complemented
59	C₂₃×#388	C₂²	1	2	yes	complemented
60	C₂₃×#388	C₂²	1	2	yes	complemented
61	C₂₃×#387	C₂²	1	2	yes	complemented
62	C₂₃×#387	C₂²	1	2	yes	complemented
63	C₂₃×#387	C₂²	1	2	yes	complemented
64	C₂₃×#387	C₂²	1	2	yes	complemented
65	C₂₃×#387	C₂²	1	2	yes	complemented
66	C₂₃×#387	C₂²	1	2	yes	complemented
67	C₂₃×#386	C₂²	1	2	yes	—
68	C₂₃×#386	C₂²	1	2	yes	—
69	C₂₃×#386	C₂²	1	2	yes	—
70	C₂₃×#386	C₂²	1	2	yes	—
71	C₂₃×#386	C₂²	1	2	yes	—
72	C₂₃×#386	C₂²	1	2	yes	—
73	C₂₃×#386	C₂²	1	2	yes	complemented
74	C₂₃×#385	C₂²	1	2	yes	—
75	C₂₃×#385	C₂²	1	2	yes	—
76	C₂₃×#385	C₂²	1	2	yes	—
77	C₂₃×#385	C₂²	1	2	yes	—
78	C₂₃×#385	C₂²	1	2	yes	complemented
79	C₂₃×#383	C₂²	1	2	yes	complemented
80	C₂₃×#382	C₂²	1	2	yes	complemented
81	C₂₃×#381	C₂²	1	2	yes	complemented
82	C₂₃×#380	C₂²	1	1	yes	characteristic
83	C₂₃×#380	C₂²	1	1	yes	characteristic
84	C₂₃×#380	C₂²	1	2	yes	complemented
85	C₂₃×#379	C₂²	1	2	yes	—
86	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
87	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
88	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
89	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
90	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
91	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
92	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
93	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
94	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
95	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
103	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
105	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
106	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
107	C₄³×C₂₃	C₂²	1	2	yes	complemented
108	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
113	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₂₃	—	2	4	no	—
115	C₂³×C₄×C₂₃	—	4	2	no	—
116	C₂³×C₄×C₂₃	—	4	2	no	—
117	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
118	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
119	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
122	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
124	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
127	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
128	C₂₃×#126	C₂×C₄	1	16	yes	complemented
129	C₂₃×#124	C₂×C₄	1	16	yes	complemented
130	C₂₃×#123	C₂×C₄	1	16	yes	complemented
131	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
132	C₂₃×#121	C₂×C₄	1	16	yes	complemented
133	C₂₃×#121	C₂×C₄	1	8	yes	complemented
134	C₂₃×#120	C₂×C₄	1	16	yes	complemented
135	C₄×Q₈×C₂₃	—	4	2	no	—
136	C₄×D₄×C₂₃	—	2	8	no	—
137	C₄×D₄×C₂₃	—	2	8	no	—
138	C₄×D₄×C₂₃	—	4	4	no	—
139	C₄×D₄×C₂₃	—	4	4	no	—
140	C₄×D₄×C₂₃	—	4	2	no	—
141	C₄×D₄×C₂₃	C₂×C₄	1	16	yes	complemented
142	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
156	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
157	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	8	yes	complemented
158	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
179	C₂×C₄²×C₂₃	—	4	2	no	—
180	C₂×C₄²×C₂₃	—	4	2	no	—
181	C₂×C₄²×C₂₃	—	4	4	no	—
182	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
183	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
184	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
185	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
186	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
189	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
190	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
191	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
192	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
195	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
196	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
197	C₂₃×#95	C₂³	1	2	yes	—
198	C₂₃×#95	C₂³	1	2	yes	—
199	C₂₃×#95	C₂³	1	2	yes	—
200	C₂₃×#95	C₂³	1	2	yes	—
201	C₂₃×#95	C₂³	1	2	yes	—
202	C₂₃×#95	C₂³	1	2	yes	—
203	C₂₃×#95	C₂³	1	2	yes	—
204	C₂₃×#95	C₂³	1	2	yes	—
205	C₂₃×#95	C₂³	1	2	yes	—
206	C₂₃×#95	C₂³	1	2	yes	—
207	C₂₃×#95	C₂³	1	2	yes	—
208	C₂₃×#95	C₂³	1	2	yes	—
209	C₂₃×#95	C₂³	1	2	yes	—
210	C₂₃×#95	C₂³	1	2	yes	—
211	C₂₃×#95	C₂³	1	2	yes	—
212	C₂₃×#95	C₂³	1	2	yes	—
213	C₂₃×#95	C₂³	1	2	yes	—
214	C₂₃×#95	C₂³	1	2	yes	—
215	C₂₃×#95	C₂³	1	2	yes	—
216	C₂₃×#95	C₂³	1	2	yes	—
217	C₂⁴×C₂₃	—	2	2	no	—
218	C₂⁴×C₂₃	—	2	2	no	—
219	C₂⁴×C₂₃	—	4	1	no	—
220	C₂⁴×C₂₃	—	4	1	no	—
221	C₂⁴×C₂₃	—	4	1	no	—
222	C₂⁴×C₂₃	—	4	1	no	—
223	C₂⁴×C₂₃	C₂²×C₄	1	4	yes	—
224	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
225	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
226	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
227	C₂×Q₈×C₂₃	—	4	1	no	—
228	C₂×Q₈×C₂₃	—	4	1	no	—
229	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	complemented
230	C₂×D₄×C₂₃	—	2	4	no	—
231	C₂×D₄×C₂₃	—	2	4	no	—
232	C₂×D₄×C₂₃	—	4	2	no	—
233	C₂×D₄×C₂₃	—	4	1	no	—
234	C₂×D₄×C₂₃	—	4	2	no	—
235	C₂×D₄×C₂₃	—	4	2	no	—
236	C₂×D₄×C₂₃	—	4	2	no	—
237	C₂×D₄×C₂₃	—	4	1	no	—
238	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
239	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
240	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
241	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	complemented
242	C₂²×C₄×C₂₃	—	2	2	no	—
243	C₂²×C₄×C₂₃	—	2	2	no	—
244	C₂²×C₄×C₂₃	—	2	2	no	—
245	C₂²×C₄×C₂₃	—	2	2	no	—
246	C₂²×C₄×C₂₃	—	2	4	no	—
247	C₂²×C₄×C₂₃	—	2	4	no	—
248	C₂²×C₄×C₂₃	—	2	4	no	—
249	C₂²×C₄×C₂₃	—	2	4	no	—
250	C₂²×C₄×C₂₃	—	2	4	no	—
251	C₂²×C₄×C₂₃	—	2	4	no	—
252	C₂²×C₄×C₂₃	—	2	4	no	—
253	C₂²×C₄×C₂₃	—	2	4	no	—
254	C₂²×C₄×C₂₃	—	4	1	no	—
255	C₂²×C₄×C₂₃	—	4	1	no	—
256	C₂²×C₄×C₂₃	—	4	2	no	—
257	C₂²×C₄×C₂₃	—	4	2	no	—
258	C₂²×C₄×C₂₃	—	4	1	no	—
259	C₂²×C₄×C₂₃	—	4	1	no	—
260	C₂²×C₄×C₂₃	—	4	2	no	—
261	C₂²×C₄×C₂₃	—	4	2	no	—
262	C₂²×C₄×C₂₃	—	4	1	no	—
263	C₂²×C₄×C₂₃	—	4	1	no	—
264	C₂²×C₄×C₂₃	—	4	1	no	—
265	C₂²×C₄×C₂₃	—	4	1	no	—
266	C₂²×C₄×C₂₃	—	4	2	no	—
267	C₂²×C₄×C₂₃	—	4	2	no	—
268	C₂²×C₄×C₂₃	—	4	1	no	—
269	C₂²×C₄×C₂₃	—	4	1	no	—
270	C₂²×C₄×C₂₃	—	4	16	no	—
271	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
272	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
273	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	complemented
274	C₂²×C₄×C₂₃	#41	1	4	yes	—
275	C₂²×C₄×C₂₃	#41	1	4	yes	—
276	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
292	C₄⋊C₄×C₂₃	—	2	4	no	—
293	C₄⋊C₄×C₂₃	—	2	4	no	—
294	C₄⋊C₄×C₂₃	—	4	1	no	—
295	C₄⋊C₄×C₂₃	—	4	2	no	—
296	C₄⋊C₄×C₂₃	—	4	1	no	—
297	C₄⋊C₄×C₂₃	—	4	2	no	—
298	C₄⋊C₄×C₂₃	—	4	1	no	—
299	C₄⋊C₄×C₂₃	—	4	2	no	—
300	C₄⋊C₄×C₂₃	—	4	1	no	—
301	C₄⋊C₄×C₂₃	—	4	2	no	—
302	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	complemented
303	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	complemented
304	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	complemented
305	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	complemented
306	C₂²⋊C₄×C₂₃	—	2	4	no	—
307	C₂²⋊C₄×C₂₃	—	2	4	no	—
308	C₂²⋊C₄×C₂₃	—	2	4	no	—
309	C₂²⋊C₄×C₂₃	—	2	4	no	—
310	C₂²⋊C₄×C₂₃	—	2	4	no	—
311	C₂²⋊C₄×C₂₃	—	2	4	no	—
312	C₂²⋊C₄×C₂₃	—	4	2	no	—
313	C₂²⋊C₄×C₂₃	—	4	2	no	—
314	C₂²⋊C₄×C₂₃	—	4	2	no	—
315	C₂²⋊C₄×C₂₃	—	4	2	no	—
316	C₂²⋊C₄×C₂₃	—	4	2	no	—
317	C₂²⋊C₄×C₂₃	—	4	2	no	—
318	C₂²⋊C₄×C₂₃	—	4	2	no	—
319	C₂²⋊C₄×C₂₃	—	4	2	no	—
320	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
321	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
322	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
323	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
324	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
325	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	complemented
326	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	complemented
327	C₄²×C₂₃	—	2	4	no	—
328	C₄²×C₂₃	—	2	4	no	—
329	C₄²×C₂₃	—	2	4	no	—
330	C₄²×C₂₃	—	2	2	no	—
331	C₄²×C₂₃	—	2	4	no	—
332	C₄²×C₂₃	—	2	2	no	—
333	C₄²×C₂₃	—	2	4	no	—
334	C₄²×C₂₃	—	4	2	no	—
335	C₄²×C₂₃	—	4	2	no	—
336	C₄²×C₂₃	—	4	2	no	—
337	C₄²×C₂₃	—	4	1	no	—
338	C₄²×C₂₃	—	4	1	no	—
339	C₄²×C₂₃	—	4	2	no	—
340	C₄²×C₂₃	—	4	2	no	—
341	C₄²×C₂₃	C₂²×C₄	1	8	yes	complemented
342	C₄×#538	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
343	C₂³×C₂₃	—	2	1	no	—
344	C₂³×C₂₃	—	2	1	no	—
345	C₂³×C₂₃	—	2	1	no	—
346	C₂³×C₂₃	—	2	1	no	—
347	C₂³×C₂₃	—	2	8	no	—
348	C₂³×C₂₃	—	2	2	no	—
349	C₂³×C₂₃	—	2	2	no	—
350	C₂³×C₂₃	—	2	2	no	—
351	C₂³×C₂₃	—	2	2	no	—
352	C₂³×C₂₃	—	2	2	no	—
353	C₂³×C₂₃	—	2	2	no	—
354	C₂³×C₂₃	—	2	2	no	—
355	C₂³×C₂₃	—	2	2	no	—
356	C₂³×C₂₃	—	2	2	no	—
357	C₂³×C₂₃	—	2	2	no	—
358	C₂³×C₂₃	—	2	2	no	—
359	C₂³×C₂₃	—	2	2	no	—
360	C₂³×C₂₃	—	4	4	no	—
361	C₂³×C₂₃	—	4	4	no	—
362	C₂³×C₂₃	—	4	4	no	—
363	C₂³×C₂₃	—	4	4	no	—
364	C₂³×C₂₃	—	4	4	no	—
365	C₂³×C₂₃	—	4	4	no	—
366	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
367	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
368	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
369	C₂³×C₂₃	C₂×#41	1	2	yes	—
370	C₂³×C₂₃	C₂×#41	1	2	yes	—
371	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
372	Q₈×C₂₃	—	4	4	no	—
373	D₄×C₂₃	—	2	16	no	—
374	D₄×C₂₃	—	4	8	no	—
375	D₄×C₂₃	—	4	8	no	—
376	D₄×C₂₃	—	4	4	no	—
377	C₂×C₄×C₂₃	—	2	2	no	—
378	C₂×C₄×C₂₃	—	2	2	no	—
379	C₂×C₄×C₂₃	—	2	2	no	—
380	C₂×C₄×C₂₃	—	2	2	no	—
381	C₂×C₄×C₂₃	—	2	2	no	—
382	C₂×C₄×C₂₃	—	2	1	no	—
383	C₂×C₄×C₂₃	—	2	1	no	—
384	C₂×C₄×C₂₃	—	2	2	no	—
385	C₂×C₄×C₂₃	—	2	1	no	—
386	C₂×C₄×C₂₃	—	2	1	no	—
387	C₂×C₄×C₂₃	—	2	2	no	—
388	C₂×C₄×C₂₃	—	2	2	no	—
389	C₂×C₄×C₂₃	—	2	2	no	—
390	C₂×C₄×C₂₃	—	2	1	no	—
391	C₂×C₄×C₂₃	—	2	2	no	—
392	C₂×C₄×C₂₃	—	2	1	no	—
393	C₂×C₄×C₂₃	—	2	8	no	—
394	C₂×C₄×C₂₃	—	2	2	no	—
395	C₂×C₄×C₂₃	—	2	2	no	—
396	C₂×C₄×C₂₃	—	2	1	no	—
397	C₂×C₄×C₂₃	—	2	1	no	—
398	C₂×C₄×C₂₃	—	2	2	no	—
399	C₂×C₄×C₂₃	—	2	2	no	—
400	C₂×C₄×C₂₃	—	2	2	no	—
401	C₂×C₄×C₂₃	—	2	2	no	—
402	C₂×C₄×C₂₃	—	2	1	no	—
403	C₂×C₄×C₂₃	—	2	1	no	—
404	C₂×C₄×C₂₃	—	2	2	no	—
405	C₂×C₄×C₂₃	—	2	2	no	—
406	C₂×C₄×C₂₃	—	2	2	no	—
407	C₂×C₄×C₂₃	—	2	2	no	—
408	C₂×C₄×C₂₃	—	2	2	no	—
409	C₂×C₄×C₂₃	—	2	2	no	—
410	C₂×C₄×C₂₃	—	2	2	no	—
411	C₂×C₄×C₂₃	—	2	2	no	—
412	C₂×C₄×C₂₃	—	2	1	no	—
413	C₂×C₄×C₂₃	—	2	2	no	—
414	C₂×C₄×C₂₃	—	2	1	no	—
415	C₂×C₄×C₂₃	—	4	4	no	—
416	C₂×C₄×C₂₃	—	4	4	no	—
417	C₂×C₄×C₂₃	—	4	8	no	—
418	C₂×C₄×C₂₃	—	4	4	no	—
419	C₂×C₄×C₂₃	—	4	8	no	—
420	C₂×C₄×C₂₃	—	4	8	no	—
421	C₂×C₄×C₂₃	—	4	4	no	—
422	C₂×C₄×C₂₃	—	4	4	no	—
423	C₂×C₄×C₂₃	—	4	8	no	—
424	C₂×C₄×C₂₃	—	4	8	no	—
425	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
426	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
427	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
428	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
429	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
430	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
431	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
432	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
433	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
434	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
435	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
436	C₂×#538	C₂×C₂₃	1	1	yes	characteristic
437	#2337	C₂×C₂₃	1	2	yes	complemented
438	#2335	C₂×C₂₃	1	2	yes	complemented
439	#2334	C₂×C₂₃	1	2	yes	complemented
440	#2333	C₂×C₂₃	1	2	yes	complemented
441	#2329	C₂×C₂₃	1	1	yes	characteristic, complemented
442	#2325	C₂×C₂₃	1	1	yes	characteristic, complemented
443	#2321	C₂×C₂₃	1	2	yes	complemented
444	#2318	C₂×C₂₃	1	2	yes	complemented
445	#2312	C₂×C₂₃	1	1	yes	characteristic, complemented
446	C₄×#126	C₂×C₂₃	1	2	yes	complemented
447	C₄×#124	C₂×C₂₃	1	2	yes	complemented
448	C₄×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
449	C₄×#123	C₂×C₂₃	1	2	yes	complemented
450	C₄×#121	C₂×C₂₃	1	2	yes	complemented
451	C₄×#121	C₂×C₂₃	1	1	yes	characteristic, complemented
452	C₄×#120	C₂×C₂₃	1	2	yes	complemented
453	C₄²×D₄	C₂×C₂₃	1	2	yes	complemented
454	C₂×C₄×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
455	C₂²×C₂₃	—	2	2	no	—
456	C₂²×C₂₃	—	2	2	no	—
457	C₂²×C₂₃	—	2	2	no	—
458	C₂²×C₂₃	—	2	2	no	—
459	C₂²×C₂₃	—	2	2	no	—
460	C₂²×C₂₃	—	2	2	no	—
461	C₂²×C₂₃	—	2	4	no	—
462	C₂²×C₂₃	—	2	4	no	—
463	C₂²×C₂₃	—	2	4	no	—
464	C₂²×C₂₃	—	2	4	no	—
465	C₂²×C₂₃	—	2	4	no	—
466	C₂²×C₂₃	—	2	4	no	—
467	C₂²×C₂₃	—	4	16	no	—
468	C₂²×C₂₃	—	4	2	no	—
469	C₂²×C₂₃	—	4	2	no	—
470	C₂²×C₂₃	—	4	2	no	—
471	C₂²×C₂₃	—	4	2	no	—
472	C₂²×C₂₃	—	4	2	no	—
473	C₂²×C₂₃	—	4	2	no	—
474	C₂²×C₂₃	—	4	2	no	—
475	C₂²×C₂₃	—	4	2	no	—
476	C₂²×C₂₃	C₄×#41	1	4	yes	—
477	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
478	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
479	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
480	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
481	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
482	C₂²×C₂₃	#585	1	1	yes	characteristic
483	C₂²×C₂₃	#585	1	1	yes	characteristic
484	C₄×C₂₃	—	2	4	no	—
485	C₄×C₂₃	—	2	4	no	—
486	C₄×C₂₃	—	2	2	no	—
487	C₄×C₂₃	—	2	4	no	—
488	C₄×C₂₃	—	2	2	no	—
489	C₄×C₂₃	—	2	4	no	—
490	C₄×C₂₃	—	2	2	no	—
491	C₄×C₂₃	—	2	4	no	—
492	C₄×C₂₃	—	4	2	no	—
493	C₄×C₂₃	—	4	2	no	—
494	C₄×C₂₃	—	4	2	no	—
495	C₄×C₂₃	—	4	2	no	—
496	C₄×C₂₃	—	4	2	no	—
497	C₄×C₂₃	—	4	1	no	—
498	C₄×C₂₃	—	4	1	no	—
499	C₄×C₂₃	#538	1	4	yes	direct product factor
500	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
501	#538	C₄×C₂₃	1	16	yes	direct product factor
502	C₂×#126	C₂²×C₂₃	1	2	yes	—
503	C₂×#124	C₂²×C₂₃	1	2	yes	—
504	C₂×#123	C₂²×C₂₃	1	2	yes	—
505	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
506	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
507	C₂×#121	C₂²×C₂₃	1	2	yes	—
508	C₂×#120	C₂²×C₂₃	1	2	yes	—
509	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
510	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
511	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
512	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
513	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
514	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
515	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
516	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
517	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
518	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
519	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
520	C₂²×C₄²	C₂²×C₂₃	1	2	yes	complemented
521	#391	C₂²×C₂₃	1	2	yes	complemented
522	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
523	#390	C₂²×C₂₃	1	2	yes	—
524	#390	C₂²×C₂₃	1	2	yes	—
525	#390	C₂²×C₂₃	1	1	yes	characteristic, complemented
526	#389	C₂²×C₂₃	1	2	yes	complemented
527	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
528	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
529	#388	C₂²×C₂₃	1	2	yes	—
530	#388	C₂²×C₂₃	1	2	yes	—
531	#388	C₂²×C₂₃	1	2	yes	—
532	#388	C₂²×C₂₃	1	2	yes	—
533	#388	C₂²×C₂₃	1	2	yes	—
534	#388	C₂²×C₂₃	1	2	yes	—
535	#388	C₂²×C₂₃	1	2	yes	—
536	#388	C₂²×C₂₃	1	2	yes	—
537	#388	C₂²×C₂₃	1	2	yes	complemented
538	#388	C₂²×C₂₃	1	2	yes	complemented
539	#388	C₂²×C₂₃	1	2	yes	complemented
540	#388	C₂²×C₂₃	1	2	yes	complemented
541	#387	C₂²×C₂₃	1	2	yes	complemented
542	#387	C₂²×C₂₃	1	2	yes	complemented
543	#387	C₂²×C₂₃	1	2	yes	complemented
544	#387	C₂²×C₂₃	1	2	yes	complemented
545	#387	C₂²×C₂₃	1	2	yes	complemented
546	#387	C₂²×C₂₃	1	2	yes	complemented
547	#386	C₂²×C₂₃	1	2	yes	—
548	#386	C₂²×C₂₃	1	2	yes	—
549	#386	C₂²×C₂₃	1	2	yes	—
550	#386	C₂²×C₂₃	1	2	yes	—
551	#386	C₂²×C₂₃	1	2	yes	—
552	#386	C₂²×C₂₃	1	2	yes	—
553	#386	C₂²×C₂₃	1	2	yes	complemented
554	#385	C₂²×C₂₃	1	2	yes	—
555	#385	C₂²×C₂₃	1	2	yes	—
556	#385	C₂²×C₂₃	1	2	yes	—
557	#385	C₂²×C₂₃	1	2	yes	—
558	#385	C₂²×C₂₃	1	2	yes	complemented
559	#383	C₂²×C₂₃	1	2	yes	complemented
560	#382	C₂²×C₂₃	1	2	yes	complemented
561	#381	C₂²×C₂₃	1	2	yes	complemented
562	#380	C₂²×C₂₃	1	1	yes	characteristic
563	#380	C₂²×C₂₃	1	1	yes	characteristic
564	#380	C₂²×C₂₃	1	2	yes	complemented
565	#379	C₂²×C₂₃	1	2	yes	—
566	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
567	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
568	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
569	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
570	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
571	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
572	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
573	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
574	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
575	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
576	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
577	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
578	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
579	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
580	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
581	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
582	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
583	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
584	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
585	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
586	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
587	C₄³	C₂²×C₂₃	1	2	yes	complemented
588	C₂×C₂₃	—	2	4	no	—
589	C₂×C₂₃	—	4	4	no	—
590	C₂×C₂₃	—	4	4	no	—
591	C₂×C₂₃	C₂×C₄×#41	1	1	yes	characteristic
592	C₂×C₂₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
593	C₂×C₂₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
594	C₂×C₂₃	C₂×#538	1	1	yes	characteristic
595	C₂×C₂₃	#3455	1	1	yes	characteristic
596	C₂×C₂₃	#3459	1	1	yes	characteristic
597	C₂×C₂₃	#3460	1	1	yes	characteristic
598	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
599	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
600	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
601	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
602	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
603	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
604	C₂³×C₄	—	2	4	no	—
605	C₂³×C₄	—	4	2	no	—
606	C₂³×C₄	—	4	2	no	—
607	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
608	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
609	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
610	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
612	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
613	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
614	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
615	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
616	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
617	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
618	#126	C₂×C₄×C₂₃	1	16	yes	complemented
619	#124	C₂×C₄×C₂₃	1	16	yes	complemented
620	#123	C₂×C₄×C₂₃	1	16	yes	complemented
621	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
622	#121	C₂×C₄×C₂₃	1	16	yes	complemented
623	#121	C₂×C₄×C₂₃	1	8	yes	complemented
624	#120	C₂×C₄×C₂₃	1	16	yes	complemented
625	C₄×Q₈	—	4	2	no	—
626	C₄×D₄	—	2	8	no	—
627	C₄×D₄	—	2	8	no	—
628	C₄×D₄	—	4	4	no	—
629	C₄×D₄	—	4	4	no	—
630	C₄×D₄	—	4	2	no	—
631	C₄×D₄	C₂×C₄×C₂₃	1	16	yes	complemented
632	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
646	C₂×C₂²⋊C₄	—	2	4	no	—
647	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	8	yes	complemented
648	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
669	C₂×C₄²	—	4	2	no	—
670	C₂×C₄²	—	4	2	no	—
671	C₂×C₄²	—	4	4	no	—
672	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
673	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
674	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
675	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
676	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
678	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
679	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
680	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
681	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
682	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
684	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
685	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
686	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
687	#95	C₂³×C₂₃	1	2	yes	—
688	#95	C₂³×C₂₃	1	2	yes	—
689	#95	C₂³×C₂₃	1	2	yes	—
690	#95	C₂³×C₂₃	1	2	yes	—
691	#95	C₂³×C₂₃	1	2	yes	—
692	#95	C₂³×C₂₃	1	2	yes	—
693	#95	C₂³×C₂₃	1	2	yes	—
694	#95	C₂³×C₂₃	1	2	yes	—
695	#95	C₂³×C₂₃	1	2	yes	—
696	#95	C₂³×C₂₃	1	2	yes	—
697	#95	C₂³×C₂₃	1	2	yes	—
698	#95	C₂³×C₂₃	1	2	yes	—
699	#95	C₂³×C₂₃	1	2	yes	—
700	#95	C₂³×C₂₃	1	2	yes	—
701	#95	C₂³×C₂₃	1	2	yes	—
702	#95	C₂³×C₂₃	1	2	yes	—
703	#95	C₂³×C₂₃	1	2	yes	—
704	#95	C₂³×C₂₃	1	2	yes	—
705	#95	C₂³×C₂₃	1	2	yes	—
706	#95	C₂³×C₂₃	1	2	yes	—
707	C₂₃	C₄×#538	1	1	yes	characteristic, direct product factor, Sylow
708	C₂⁴	—	2	2	no	—
709	C₂⁴	—	2	2	no	—
710	C₂⁴	—	4	1	no	—
711	C₂⁴	—	4	1	no	—
712	C₂⁴	—	4	1	no	—
713	C₂⁴	—	4	1	no	—
714	C₂⁴	C₂²×C₄×C₂₃	1	4	yes	—
715	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
716	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
717	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
718	C₂×Q₈	—	4	1	no	—
719	C₂×Q₈	—	4	1	no	—
720	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	complemented
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	4	2	no	—
724	C₂×D₄	—	4	1	no	—
725	C₂×D₄	—	4	2	no	—
726	C₂×D₄	—	4	2	no	—
727	C₂×D₄	—	4	2	no	—
728	C₂×D₄	—	4	1	no	—
729	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
730	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
731	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
732	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	complemented
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	4	no	—
738	C₂²×C₄	—	2	4	no	—
739	C₂²×C₄	—	2	4	no	—
740	C₂²×C₄	—	2	4	no	—
741	C₂²×C₄	—	2	4	no	—
742	C₂²×C₄	—	2	4	no	—
743	C₂²×C₄	—	2	4	no	—
744	C₂²×C₄	—	2	4	no	—
745	C₂²×C₄	—	4	1	no	—
746	C₂²×C₄	—	4	1	no	—
747	C₂²×C₄	—	4	2	no	—
748	C₂²×C₄	—	4	2	no	—
749	C₂²×C₄	—	4	1	no	—
750	C₂²×C₄	—	4	1	no	—
751	C₂²×C₄	—	4	2	no	—
752	C₂²×C₄	—	4	2	no	—
753	C₂²×C₄	—	4	1	no	—
754	C₂²×C₄	—	4	1	no	—
755	C₂²×C₄	—	4	1	no	—
756	C₂²×C₄	—	4	1	no	—
757	C₂²×C₄	—	4	2	no	—
758	C₂²×C₄	—	4	2	no	—
759	C₂²×C₄	—	4	1	no	—
760	C₂²×C₄	—	4	1	no	—
761	C₂²×C₄	—	4	16	no	—
762	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
763	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
764	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	complemented
765	C₂²×C₄	#41×C₂₃	1	4	yes	—
766	C₂²×C₄	#41×C₂₃	1	4	yes	—
767	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
777	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
781	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
783	C₄⋊C₄	—	2	4	no	—
784	C₄⋊C₄	—	2	4	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₄⋊C₄	—	4	1	no	—
787	C₄⋊C₄	—	4	2	no	—
788	C₄⋊C₄	—	4	1	no	—
789	C₄⋊C₄	—	4	2	no	—
790	C₄⋊C₄	—	4	1	no	—
791	C₄⋊C₄	—	4	2	no	—
792	C₄⋊C₄	—	4	1	no	—
793	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	complemented
794	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	complemented
795	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	complemented
796	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	complemented
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	4	2	no	—
804	C₂²⋊C₄	—	4	2	no	—
805	C₂²⋊C₄	—	4	2	no	—
806	C₂²⋊C₄	—	4	2	no	—
807	C₂²⋊C₄	—	4	2	no	—
808	C₂²⋊C₄	—	4	2	no	—
809	C₂²⋊C₄	—	4	2	no	—
810	C₂²⋊C₄	—	4	2	no	—
811	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
812	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
813	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
814	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
815	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
816	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	complemented
817	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	complemented
818	C₄²	—	2	4	no	—
819	C₄²	—	2	4	no	—
820	C₄²	—	2	4	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	4	no	—
823	C₄²	—	2	2	no	—
824	C₄²	—	2	4	no	—
825	C₄²	—	4	2	no	—
826	C₄²	—	4	2	no	—
827	C₄²	—	4	2	no	—
828	C₄²	—	4	1	no	—
829	C₄²	—	4	1	no	—
830	C₄²	—	4	2	no	—
831	C₄²	—	4	2	no	—
832	C₄²	C₂²×C₄×C₂₃	1	8	yes	complemented
833	C₂³	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	1	no	—
836	C₂³	—	2	1	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	2	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	8	no	—
850	C₂³	—	4	4	no	—
851	C₂³	—	4	4	no	—
852	C₂³	—	4	4	no	—
853	C₂³	—	4	4	no	—
854	C₂³	—	4	4	no	—
855	C₂³	—	4	4	no	—
856	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
857	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
858	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
859	C₂³	C₂×#41×C₂₃	1	2	yes	—
860	C₂³	C₂×#41×C₂₃	1	2	yes	—
861	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
862	Q₈	—	4	4	no	—
863	D₄	—	2	16	no	—
864	D₄	—	4	8	no	—
865	D₄	—	4	8	no	—
866	D₄	—	4	4	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	8	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	4	4	no	—
906	C₂×C₄	—	4	4	no	—
907	C₂×C₄	—	4	8	no	—
908	C₂×C₄	—	4	4	no	—
909	C₂×C₄	—	4	8	no	—
910	C₂×C₄	—	4	8	no	—
911	C₂×C₄	—	4	4	no	—
912	C₂×C₄	—	4	4	no	—
913	C₂×C₄	—	4	8	no	—
914	C₂×C₄	—	4	8	no	—
915	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
916	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
917	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
918	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
919	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
920	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
921	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
922	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
923	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
924	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
925	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
926	C₂²	—	2	2	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	2	no	—
931	C₂²	—	2	2	no	—
932	C₂²	—	2	4	no	—
933	C₂²	—	2	4	no	—
934	C₂²	—	2	4	no	—
935	C₂²	—	2	4	no	—
936	C₂²	—	2	4	no	—
937	C₂²	—	2	4	no	—
938	C₂²	—	4	16	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	2	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	C₄×#41×C₂₃	1	4	yes	—
948	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
949	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
950	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
951	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
952	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
953	C₂²	C₂₃×#585	1	1	yes	characteristic
954	C₂²	C₂₃×#585	1	1	yes	characteristic
955	C₄	—	2	4	no	—
956	C₄	—	2	4	no	—
957	C₄	—	2	2	no	—
958	C₄	—	2	4	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	4	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	4	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	1	no	—
968	C₄	—	4	1	no	—
969	C₄	—	4	2	no	—
970	C₄	C₂₃×#538	1	4	yes	direct product factor
971	C₂	—	2	4	no	—
972	C₂	—	4	4	no	—
973	C₂	—	4	4	no	—
974	C₂	C₂×C₄×#41×C₂₃	1	1	yes	characteristic
975	C₂	C₄×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
976	C₂	C₄×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
977	C₂	C₂×C₂₃×#538	1	1	yes	characteristic
978	C₂	C₂₃×#3455	1	1	yes	characteristic
979	C₂	C₂₃×#3459	1	1	yes	characteristic
980	C₂	C₂₃×#3460	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×#538	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. C₂₃×#2337	C₂	semidirect
3. C₂₃×#2335	C₂	semidirect
4. C₂₃×#2334	C₂	semidirect
5. C₂₃×#2333	C₂	semidirect
6. C₂₃×#2329	C₂	semidirect
7. C₂₃×#2325	C₂	semidirect
8. C₂₃×#2321	C₂	semidirect
9. C₂₃×#2318	C₂	semidirect
10. C₂₃×#2312	C₂	semidirect
11. C₄×C₂₃×#126	C₂	semidirect
12. C₄×C₂₃×#124	C₂	semidirect
13. C₄×C₂₃×C₂²⋊Q₈	C₂	semidirect
14. C₄×C₂₃×#123	C₂	semidirect
15. C₄×C₂₃×#121	C₂	semidirect
16. C₄×C₂₃×#121	C₂	semidirect
17. C₄×C₂₃×#120	C₂	semidirect
18. C₄²×D₄×C₂₃	C₂	semidirect
19. C₂×C₄×C₂²⋊C₄×C₂₃	C₂	semidirect
21. C₂₃×#538	C₄	direct (N × H)
29. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
35. C₂×C₄×D₄×C₂₃	C₂²	semidirect
40. C₂²×C₄²×C₂₃	C₂²	semidirect
41. C₂₃×#391	C₂²	semidirect
42. C₂₃×#391	C₂²	semidirect
45. C₂₃×#390	C₂²	semidirect
46. C₂₃×#389	C₂²	semidirect
47. C₂₃×#389	C₂²	semidirect
48. C₂₃×#389	C₂²	semidirect
57. C₂₃×#388	C₂²	semidirect
58. C₂₃×#388	C₂²	semidirect
59. C₂₃×#388	C₂²	semidirect
60. C₂₃×#388	C₂²	semidirect
61. C₂₃×#387	C₂²	semidirect
62. C₂₃×#387	C₂²	semidirect
63. C₂₃×#387	C₂²	semidirect
64. C₂₃×#387	C₂²	semidirect
65. C₂₃×#387	C₂²	semidirect
66. C₂₃×#387	C₂²	semidirect
73. C₂₃×#386	C₂²	semidirect
78. C₂₃×#385	C₂²	semidirect
79. C₂₃×#383	C₂²	semidirect
80. C₂₃×#382	C₂²	semidirect
81. C₂₃×#381	C₂²	semidirect
84. C₂₃×#380	C₂²	semidirect
86. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
87. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
88. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
89. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
90. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
91. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
101. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
102. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
107. C₄³×C₂₃	C₂²	semidirect
128. C₂₃×#126	C₂×C₄	semidirect
129. C₂₃×#124	C₂×C₄	semidirect
130. C₂₃×#123	C₂×C₄	semidirect
131. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
132. C₂₃×#121	C₂×C₄	semidirect
133. C₂₃×#121	C₂×C₄	semidirect
134. C₂₃×#120	C₂×C₄	semidirect
141. C₄×D₄×C₂₃	C₂×C₄	semidirect
157. C₂×C₂²⋊C₄×C₂₃	C₂×C₄	semidirect
229. C₂×Q₈×C₂₃	C₂²×C₄	semidirect
241. C₂×D₄×C₂₃	C₂²×C₄	semidirect
273. C₂²×C₄×C₂₃	C₂²×C₄	semidirect
302. C₄⋊C₄×C₂₃	C₂²×C₄	semidirect
303. C₄⋊C₄×C₂₃	C₂²×C₄	semidirect
304. C₄⋊C₄×C₂₃	C₂²×C₄	semidirect
305. C₄⋊C₄×C₂₃	C₂²×C₄	semidirect
325. C₂²⋊C₄×C₂₃	C₂²×C₄	semidirect
326. C₂²⋊C₄×C₂₃	C₂²×C₄	semidirect
341. C₄²×C₂₃	C₂²×C₄	semidirect
342. C₄×#538	C₂₃	direct (N × H)
437. #2337	C₂×C₂₃	semidirect
438. #2335	C₂×C₂₃	semidirect
439. #2334	C₂×C₂₃	semidirect
440. #2333	C₂×C₂₃	semidirect
441. #2329	C₂×C₂₃	semidirect
442. #2325	C₂×C₂₃	semidirect
443. #2321	C₂×C₂₃	semidirect
444. #2318	C₂×C₂₃	semidirect
445. #2312	C₂×C₂₃	semidirect
446. C₄×#126	C₂×C₂₃	semidirect
447. C₄×#124	C₂×C₂₃	semidirect
448. C₄×C₂²⋊Q₈	C₂×C₂₃	semidirect
449. C₄×#123	C₂×C₂₃	semidirect
450. C₄×#121	C₂×C₂₃	semidirect
451. C₄×#121	C₂×C₂₃	semidirect
452. C₄×#120	C₂×C₂₃	semidirect
453. C₄²×D₄	C₂×C₂₃	semidirect
454. C₂×C₄×C₂²⋊C₄	C₂×C₂₃	semidirect
499. C₄×C₂₃	#538	direct (N × H)
501. #538	C₄×C₂₃	direct (N × H)
509. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
515. C₂×C₄×D₄	C₂²×C₂₃	semidirect
520. C₂²×C₄²	C₂²×C₂₃	semidirect
521. #391	C₂²×C₂₃	semidirect
522. #391	C₂²×C₂₃	semidirect
525. #390	C₂²×C₂₃	semidirect
526. #389	C₂²×C₂₃	semidirect
527. #389	C₂²×C₂₃	semidirect
528. #389	C₂²×C₂₃	semidirect
537. #388	C₂²×C₂₃	semidirect
538. #388	C₂²×C₂₃	semidirect
539. #388	C₂²×C₂₃	semidirect
540. #388	C₂²×C₂₃	semidirect
541. #387	C₂²×C₂₃	semidirect
542. #387	C₂²×C₂₃	semidirect
543. #387	C₂²×C₂₃	semidirect
544. #387	C₂²×C₂₃	semidirect
545. #387	C₂²×C₂₃	semidirect
546. #387	C₂²×C₂₃	semidirect
553. #386	C₂²×C₂₃	semidirect
558. #385	C₂²×C₂₃	semidirect
559. #383	C₂²×C₂₃	semidirect
560. #382	C₂²×C₂₃	semidirect
561. #381	C₂²×C₂₃	semidirect
564. #380	C₂²×C₂₃	semidirect
566. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
567. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
568. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
569. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
570. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
571. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
581. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
582. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
583. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
584. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
587. C₄³	C₂²×C₂₃	semidirect
618. #126	C₂×C₄×C₂₃	semidirect
619. #124	C₂×C₄×C₂₃	semidirect
620. #123	C₂×C₄×C₂₃	semidirect
621. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
622. #121	C₂×C₄×C₂₃	semidirect
623. #121	C₂×C₄×C₂₃	semidirect
624. #120	C₂×C₄×C₂₃	semidirect
631. C₄×D₄	C₂×C₄×C₂₃	semidirect
647. C₂×C₂²⋊C₄	C₂×C₄×C₂₃	semidirect
707. C₂₃	C₄×#538	direct (N × H)
720. C₂×Q₈	C₂²×C₄×C₂₃	semidirect
732. C₂×D₄	C₂²×C₄×C₂₃	semidirect
764. C₂²×C₄	C₂²×C₄×C₂₃	semidirect
793. C₄⋊C₄	C₂²×C₄×C₂₃	semidirect
794. C₄⋊C₄	C₂²×C₄×C₂₃	semidirect
795. C₄⋊C₄	C₂²×C₄×C₂₃	semidirect
796. C₄⋊C₄	C₂²×C₄×C₂₃	semidirect
816. C₂²⋊C₄	C₂²×C₄×C₂₃	semidirect
817. C₂²⋊C₄	C₂²×C₄×C₂₃	semidirect
832. C₄²	C₂²×C₄×C₂₃	semidirect
970. C₄	C₂₃×#538	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×#538	2
C₂₃×#2337	2
C₂₃×#2335	2
C₂₃×#2334	2
C₂₃×#2333	2
C₂₃×#2329	2
C₂₃×#2325	2
C₂₃×#2321	2
C₂₃×#2318	2
C₂₃×#2312	2
C₄×C₂₃×#126	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×#538	23

Subgroups — C4×C23×#538 #19181717

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂₃×#538 #19181717