Subgroups — C₂₃×#60814 #19208440

Order 5888.

2026 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3225	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3223	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3218	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3215	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3211	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3209	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3156	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3137	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3046	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3044	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3004	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3002	C₂	1	1	yes	maximal, characteristic
16	C₂×C₂₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
19	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×#137	C₂²	1	2	yes	—
21	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
22	C₂×C₂₃×#135	C₂²	1	2	yes	—
23	C₂²×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
24	C₂₃×#556	—	2	1	no	—
25	C₂₃×#554	—	2	1	no	—
26	C₂₃×#552	—	2	2	no	—
27	C₂₃×#552	—	2	1	no	—
28	C₂₃×#552	—	2	1	no	—
29	C₂₃×#551	—	2	2	no	—
30	C₂₃×#544	C₂²	1	1	yes	characteristic, complemented
31	C₂₃×#542	C₂²	1	2	yes	complemented
32	C₂₃×#541	C₂²	1	2	yes	complemented
33	C₂₃×#536	—	2	1	no	—
34	C₂₃×#536	—	2	2	no	—
35	C₂₃×#536	—	2	1	no	—
36	C₂₃×#536	C₂²	1	4	yes	—
37	C₂₃×#536	C₂²	1	2	yes	—
38	C₂₃×#536	C₂²	1	2	yes	—
39	C₂₃×#536	C₂²	1	1	yes	characteristic, complemented
40	C₂₃×#533	C₂²	1	2	yes	—
41	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
42	C₂₃×#529	C₂²	1	2	yes	—
43	C₂×C₂₃×#124	C₂²	1	2	yes	—
44	C₂₃×#525	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×#123	—	2	2	no	—
46	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
47	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
48	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
49	C₂₃×#520	C₂²	1	1	yes	characteristic, complemented
50	C₂₃×#519	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
52	C₂₃×#497	C₂²	1	4	yes	complemented
53	C₂₃×#497	C₂²	1	4	yes	complemented
54	C₂₃×#495	C₂²	1	4	yes	complemented
55	C₂₃×#494	C₂²	1	4	yes	complemented
56	C₂₃×#491	C₂²	1	4	yes	complemented
57	C₂₃×#489	C₂²	1	4	yes	complemented
58	C₂₃×#488	C₂²	1	4	yes	complemented
59	C₂₃×#487	C₂²	1	4	yes	complemented
60	C₂₃×#464	C₂²	1	4	yes	complemented
61	C₂₃×#464	C₂²	1	4	yes	complemented
62	C₂₃×#464	C₂²	1	4	yes	complemented
63	C₂₃×#463	C₂²	1	4	yes	complemented
64	C₂₃×#462	C₂²	1	4	yes	complemented
65	C₂₃×#462	C₂²	1	4	yes	complemented
66	C₂₃×#462	C₂²	1	4	yes	complemented
67	C₂₃×#461	C₂²	1	4	yes	complemented
68	C₂₃×#452	C₂²	1	2	yes	—
69	C₂₃×#452	C₂²	1	4	yes	—
70	C₂₃×#451	C₂²	1	1	yes	characteristic
71	C₂₃×#451	C₂²	1	2	yes	—
72	C₂₃×#451	C₂²	1	2	yes	—
73	C₂₃×#451	C₂²	1	2	yes	—
74	C₂₃×#451	C₂²	1	2	yes	—
75	C₂₃×#451	C₂²	1	2	yes	complemented
76	C₂₃×#451	C₂²	1	4	yes	complemented
77	C₂₃×#450	C₂²	1	2	yes	—
78	C₂₃×#450	C₂²	1	1	yes	characteristic
79	C₂₃×#449	C₂²	1	2	yes	—
80	C₂₃×#448	C₂²	1	2	yes	—
81	C₂₃×#448	C₂²	1	1	yes	characteristic
82	C₂₃×#448	C₂²	1	2	yes	complemented
83	C₂₃×#447	C₂²	1	1	yes	characteristic
84	C₂₃×#433	C₂²	1	4	yes	complemented
85	C₂₃×#432	C₂²	1	2	yes	—
86	C₂₃×#431	C₂²	1	2	yes	—
87	C₂₃×#424	C₂²	1	2	yes	complemented
88	C₂₃×#419	C₂²	1	2	yes	complemented
89	C₂₃×#417	C₂²	1	2	yes	—
90	C₂₃×#416	C₂²	1	2	yes	—
91	C₂×C₂₃×#103	C₂²	1	2	yes	complemented
92	C₂₃×#407	C₂²	1	1	yes	characteristic
93	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
94	C₂₃×#405	C₂²	1	2	yes	complemented
95	C₂×#41×C₂₃	—	2	1	no	—
96	C₂×#41×C₂₃	—	2	1	no	—
97	C₂×#41×C₂₃	—	4	4	no	—
98	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
99	C₂×#41×C₂₃	C₂³	1	2	yes	—
100	C₂×#41×C₂₃	C₂³	1	2	yes	—
101	C₂²×Q₈×C₂₃	—	2	1	no	—
102	C₂²×Q₈×C₂₃	—	2	1	no	—
103	C₂²×Q₈×C₂₃	—	2	1	no	—
104	C₂²×Q₈×C₂₃	—	4	4	no	—
105	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
106	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
107	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
108	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
109	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₂₃	—	2	1	no	—
111	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₂₃	—	2	1	no	—
113	C₂³×C₄×C₂₃	—	2	1	no	—
114	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
115	C₂₃×#137	—	4	4	no	—
116	C₂₃×#137	—	4	4	no	—
117	C₂₃×#135	—	4	4	no	—
118	C₂×Q₁₆×C₂₃	—	4	4	no	—
119	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
120	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
121	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
122	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
123	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
124	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
127	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
128	C₂×D₈×C₂₃	C₂³	1	2	yes	—
129	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
130	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
131	C₂₃×C₄⋊Q₈	—	2	1	no	—
132	C₂₃×C₄⋊Q₈	—	2	2	no	—
133	C₂₃×C₄⋊Q₈	—	2	2	no	—
134	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
135	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
136	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₂₃×#126	—	2	2	no	—
139	C₂₃×#126	—	2	2	no	—
140	C₂₃×#126	—	2	2	no	—
141	C₂₃×#126	—	2	2	no	—
142	C₂₃×#125	—	2	2	no	—
143	C₂₃×#125	—	2	1	no	—
144	C₂₃×#125	—	2	2	no	—
145	C₂₃×#125	—	2	2	no	—
146	C₂₃×#125	C₂³	1	2	yes	—
147	C₂₃×#124	—	2	2	no	—
148	C₂₃×#124	—	2	2	no	—
149	C₂₃×#124	—	2	2	no	—
150	C₂₃×#124	C₂³	1	4	yes	—
151	C₂₃×#124	C₂³	1	4	yes	—
152	C₂₃×#124	C₂³	1	2	yes	—
153	C₂₃×#123	—	2	2	no	—
154	C₂₃×#123	—	2	1	no	—
155	C₂₃×#123	—	2	2	no	—
156	C₂₃×#123	—	2	2	no	—
157	C₂₃×#123	—	2	4	no	—
158	C₂₃×#123	—	2	4	no	—
159	C₂₃×#123	—	2	4	no	—
160	C₂₃×#123	—	2	4	no	—
161	C₂₃×C₂²⋊Q₈	—	2	2	no	—
162	C₂₃×C₂²⋊Q₈	—	2	1	no	—
163	C₂₃×C₂²⋊Q₈	—	2	1	no	—
164	C₂₃×C₂²⋊Q₈	—	2	1	no	—
165	C₂₃×C₂²⋊Q₈	—	2	2	no	—
166	C₂₃×C₂²⋊Q₈	—	2	1	no	—
167	C₂₃×C₂²⋊Q₈	—	2	2	no	—
168	C₂₃×C₂²⋊Q₈	—	2	2	no	—
169	C₂₃×C₂²⋊Q₈	—	2	4	no	—
170	C₂₃×C₂²⋊Q₈	—	2	2	no	—
171	C₂₃×C₂²⋊Q₈	—	2	2	no	—
172	C₂₃×C₂²⋊Q₈	—	2	4	no	—
173	C₂₃×C₂²⋊Q₈	—	2	2	no	—
174	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
175	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
176	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
177	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
178	C₂₃×#121	C₂³	1	1	yes	characteristic
179	C₂₃×#121	C₂³	1	1	yes	characteristic
180	C₂₃×#120	—	2	1	no	—
181	C₄×Q₈×C₂₃	—	2	1	no	—
182	C₄×Q₈×C₂₃	—	2	1	no	—
183	C₄×Q₈×C₂₃	—	2	2	no	—
184	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
185	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
186	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
187	C₄×D₄×C₂₃	—	2	2	no	—
188	C₄×D₄×C₂₃	—	2	1	no	—
189	C₄×D₄×C₂₃	—	2	1	no	—
190	C₄×D₄×C₂₃	—	2	2	no	—
191	C₄×D₄×C₂₃	C₂³	1	2	yes	—
192	C₂₃×#117	—	2	2	no	—
193	C₂₃×#117	—	2	1	no	—
194	C₂₃×#117	—	2	2	no	—
195	C₂₃×#117	—	2	2	no	—
196	C₂₃×#117	D₄	1	1	yes	characteristic
197	C₂₃×#117	D₄	1	2	yes	—
198	C₂₃×#117	D₄	1	1	yes	characteristic
199	C₂₃×#117	C₂³	1	1	yes	characteristic
200	C₂₃×#117	C₂³	1	1	yes	characteristic
201	C₂₃×#117	C₂³	1	1	yes	characteristic
202	C₂₃×#117	C₂³	1	2	yes	—
203	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
204	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
205	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
206	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
207	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
208	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
209	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
211	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
212	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
213	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
214	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
215	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
216	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
217	C₂₃×#103	C₂³	1	4	yes	—
218	C₂₃×#103	C₂³	1	4	yes	—
219	C₂₃×#103	C₂³	1	2	yes	—
220	C₂₃×#103	C₂³	1	2	yes	—
221	C₂₃×#103	C₂³	1	4	yes	—
222	C₂₃×#103	C₂³	1	4	yes	—
223	C₂₃×#103	C₂³	1	4	yes	—
224	C₂₃×#102	C₂³	1	2	yes	—
225	C₂₃×#102	C₂³	1	2	yes	—
226	C₂₃×#102	C₂³	1	4	yes	—
227	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
228	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
229	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
230	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
231	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
232	C₂₃×#97	C₂³	1	4	yes	—
233	C₄×C₈×C₂₃	C₂³	1	4	yes	—
234	C₂⁴×C₂₃	—	2	1	no	—
235	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
236	#41×C₂₃	—	2	4	no	—
237	#41×C₂₃	—	2	4	no	—
238	#41×C₂₃	—	2	4	no	—
239	#41×C₂₃	—	4	2	no	—
240	#41×C₂₃	—	4	2	no	—
241	#41×C₂₃	—	4	4	no	—
242	#41×C₂₃	—	4	4	no	—
243	C₂×Q₈×C₂₃	—	2	1	no	—
244	C₂×Q₈×C₂₃	—	2	2	no	—
245	C₂×Q₈×C₂₃	—	2	2	no	—
246	C₂×Q₈×C₂₃	—	2	2	no	—
247	C₂×Q₈×C₂₃	—	2	1	no	—
248	C₂×Q₈×C₂₃	—	2	2	no	—
249	C₂×Q₈×C₂₃	—	2	4	no	—
250	C₂×Q₈×C₂₃	—	2	4	no	—
251	C₂×Q₈×C₂₃	—	2	4	no	—
252	C₂×Q₈×C₂₃	—	4	4	no	—
253	C₂×Q₈×C₂₃	—	4	4	no	—
254	C₂×Q₈×C₂₃	—	4	2	no	—
255	C₂×Q₈×C₂₃	—	4	4	no	—
256	C₂×Q₈×C₂₃	—	4	4	no	—
257	C₂×Q₈×C₂₃	—	4	4	no	—
258	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
259	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
260	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
261	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
262	C₂×D₄×C₂₃	—	2	1	no	—
263	C₂×D₄×C₂₃	—	2	1	no	—
264	C₂×D₄×C₂₃	—	2	2	no	—
265	C₂×D₄×C₂₃	—	2	2	no	—
266	C₂×D₄×C₂₃	—	2	1	no	—
267	C₂×D₄×C₂₃	—	2	1	no	—
268	C₂×D₄×C₂₃	—	4	2	no	—
269	C₂×D₄×C₂₃	—	4	4	no	—
270	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
271	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₂₃	—	2	4	no	—
273	C₂²×C₄×C₂₃	—	2	2	no	—
274	C₂²×C₄×C₂₃	—	2	1	no	—
275	C₂²×C₄×C₂₃	—	2	1	no	—
276	C₂²×C₄×C₂₃	—	2	2	no	—
277	C₂²×C₄×C₂₃	—	2	2	no	—
278	C₂²×C₄×C₂₃	—	2	1	no	—
279	C₂²×C₄×C₂₃	—	2	1	no	—
280	C₂²×C₄×C₂₃	—	2	2	no	—
281	C₂²×C₄×C₂₃	—	2	2	no	—
282	C₂²×C₄×C₂₃	—	2	2	no	—
283	C₂²×C₄×C₂₃	—	4	4	no	—
284	C₂²×C₄×C₂₃	—	4	4	no	—
285	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
286	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
290	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
293	Q₁₆×C₂₃	—	4	4	no	—
294	Q₁₆×C₂₃	—	4	4	no	—
295	Q₁₆×C₂₃	—	4	2	no	—
296	Q₁₆×C₂₃	—	4	4	no	—
297	Q₁₆×C₂₃	—	4	4	no	—
298	SD₁₆×C₂₃	—	4	2	no	—
299	SD₁₆×C₂₃	—	4	2	no	—
300	SD₁₆×C₂₃	—	4	4	no	—
301	SD₁₆×C₂₃	—	4	4	no	—
302	D₈×C₂₃	—	4	2	no	—
303	M₁₆×C₂₃	—	2	4	no	—
304	C₂×C₈×C₂₃	—	2	4	no	—
305	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
306	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
307	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
308	C₄⋊C₄×C₂₃	—	2	1	no	—
309	C₄⋊C₄×C₂₃	—	2	2	no	—
310	C₄⋊C₄×C₂₃	—	2	2	no	—
311	C₄⋊C₄×C₂₃	—	2	2	no	—
312	C₄⋊C₄×C₂₃	—	2	4	no	—
313	C₄⋊C₄×C₂₃	—	2	4	no	—
314	C₄⋊C₄×C₂₃	—	2	4	no	—
315	C₄⋊C₄×C₂₃	—	2	4	no	—
316	C₄⋊C₄×C₂₃	—	2	2	no	—
317	C₄⋊C₄×C₂₃	—	2	2	no	—
318	C₄⋊C₄×C₂₃	—	2	2	no	—
319	C₄⋊C₄×C₂₃	—	2	2	no	—
320	C₄⋊C₄×C₂₃	—	2	2	no	—
321	C₄⋊C₄×C₂₃	—	2	1	no	—
322	C₄⋊C₄×C₂₃	—	2	2	no	—
323	C₄⋊C₄×C₂₃	—	2	1	no	—
324	C₄⋊C₄×C₂₃	—	2	2	no	—
325	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
326	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
327	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
328	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
329	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
330	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
331	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
332	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
333	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
334	C₂²⋊C₄×C₂₃	—	2	2	no	—
335	C₂²⋊C₄×C₂₃	—	2	2	no	—
336	C₂²⋊C₄×C₂₃	—	2	1	no	—
337	C₂²⋊C₄×C₂₃	—	2	1	no	—
338	C₂²⋊C₄×C₂₃	—	2	1	no	—
339	C₂²⋊C₄×C₂₃	—	2	4	no	—
340	C₂²⋊C₄×C₂₃	—	2	4	no	—
341	C₂²⋊C₄×C₂₃	—	2	4	no	—
342	C₂²⋊C₄×C₂₃	—	2	4	no	—
343	C₂²⋊C₄×C₂₃	—	2	1	no	—
344	C₂²⋊C₄×C₂₃	—	2	2	no	—
345	C₂²⋊C₄×C₂₃	—	2	2	no	—
346	C₂²⋊C₄×C₂₃	—	2	1	no	—
347	C₂²⋊C₄×C₂₃	—	2	2	no	—
348	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
349	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
350	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
351	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
352	C₄²×C₂₃	—	2	2	no	—
353	C₄²×C₂₃	—	2	2	no	—
354	C₄²×C₂₃	—	2	2	no	—
355	C₄²×C₂₃	—	2	1	no	—
356	C₄²×C₂₃	C₂×D₄	1	2	yes	—
357	C₄²×C₂₃	C₂×D₄	1	2	yes	—
358	C₄²×C₂₃	C₂⁴	1	2	yes	—
359	C₄²×C₂₃	C₂⁴	1	2	yes	—
360	#60814	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
361	C₂³×C₂₃	—	2	2	no	—
362	C₂³×C₂₃	—	2	2	no	—
363	C₂³×C₂₃	—	2	1	no	—
364	C₂³×C₂₃	—	2	2	no	—
365	C₂³×C₂₃	—	4	1	no	—
366	C₂³×C₂₃	—	4	2	no	—
367	C₂³×C₂₃	—	4	2	no	—
368	C₂³×C₂₃	—	4	2	no	—
369	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
370	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
371	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
372	Q₈×C₂₃	—	2	4	no	—
373	Q₈×C₂₃	—	2	2	no	—
374	Q₈×C₂₃	—	2	4	no	—
375	Q₈×C₂₃	—	2	2	no	—
376	Q₈×C₂₃	—	2	4	no	—
377	Q₈×C₂₃	—	2	2	no	—
378	Q₈×C₂₃	—	4	4	no	—
379	Q₈×C₂₃	—	4	4	no	—
380	Q₈×C₂₃	—	4	2	no	—
381	Q₈×C₂₃	—	4	2	no	—
382	Q₈×C₂₃	—	4	4	no	—
383	Q₈×C₂₃	—	8	2	no	—
384	D₄×C₂₃	—	2	2	no	—
385	D₄×C₂₃	—	2	2	no	—
386	D₄×C₂₃	—	2	2	no	—
387	D₄×C₂₃	—	4	2	no	—
388	D₄×C₂₃	—	4	4	no	—
389	D₄×C₂₃	—	4	4	no	—
390	D₄×C₂₃	—	4	2	no	—
391	D₄×C₂₃	—	4	2	no	—
392	D₄×C₂₃	—	8	1	no	—
393	C₂×C₄×C₂₃	—	2	2	no	—
394	C₂×C₄×C₂₃	—	2	4	no	—
395	C₂×C₄×C₂₃	—	2	2	no	—
396	C₂×C₄×C₂₃	—	2	2	no	—
397	C₂×C₄×C₂₃	—	2	2	no	—
398	C₂×C₄×C₂₃	—	2	2	no	—
399	C₂×C₄×C₂₃	—	2	1	no	—
400	C₂×C₄×C₂₃	—	2	1	no	—
401	C₂×C₄×C₂₃	—	2	2	no	—
402	C₂×C₄×C₂₃	—	2	1	no	—
403	C₂×C₄×C₂₃	—	2	2	no	—
404	C₂×C₄×C₂₃	—	2	4	no	—
405	C₂×C₄×C₂₃	—	2	2	no	—
406	C₂×C₄×C₂₃	—	4	2	no	—
407	C₂×C₄×C₂₃	—	4	4	no	—
408	C₂×C₄×C₂₃	—	4	2	no	—
409	C₂×C₄×C₂₃	—	4	4	no	—
410	C₂×C₄×C₂₃	—	4	4	no	—
411	C₂×C₄×C₂₃	—	4	4	no	—
412	C₂×C₄×C₂₃	—	4	2	no	—
413	C₂×C₄×C₂₃	—	4	4	no	—
414	C₂×C₄×C₂₃	—	4	2	no	—
415	C₂×C₄×C₂₃	—	8	2	no	—
416	C₂×C₄×C₂₃	—	8	1	no	—
417	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
421	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
422	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
425	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
426	C₈×C₂₃	—	2	2	no	—
427	C₈×C₂₃	—	2	2	no	—
428	C₈×C₂₃	—	2	4	no	—
429	#3495	C₂×C₂₃	1	1	yes	characteristic, complemented
430	C₂×#536	C₂×C₂₃	1	1	yes	characteristic, complemented
431	#3225	C₂×C₂₃	1	4	yes	complemented
432	#3223	C₂×C₂₃	1	4	yes	complemented
433	#3218	C₂×C₂₃	1	2	yes	complemented
434	#3215	C₂×C₂₃	1	2	yes	complemented
435	#3211	C₂×C₂₃	1	2	yes	complemented
436	#3209	C₂×C₂₃	1	2	yes	complemented
437	#3156	C₂×C₂₃	1	2	yes	complemented
438	#3137	C₂×C₂₃	1	2	yes	complemented
439	#3046	C₂×C₂₃	1	2	yes	complemented
440	#3044	C₂×C₂₃	1	2	yes	complemented
441	#3007	C₂×C₂₃	1	1	yes	characteristic, complemented
442	#3004	C₂×C₂₃	1	1	yes	characteristic, complemented
443	#3002	C₂×C₂₃	1	1	yes	characteristic
444	C₂×#451	C₂×C₂₃	1	1	yes	characteristic, complemented
445	#2924	C₂×C₂₃	1	1	yes	characteristic, complemented
446	C₂²×C₂₃	—	2	1	no	—
447	C₂²×C₂₃	—	2	1	no	—
448	C₂²×C₂₃	—	2	1	no	—
449	C₂²×C₂₃	—	2	1	no	—
450	C₂²×C₂₃	—	2	1	no	—
451	C₂²×C₂₃	—	2	1	no	—
452	C₂²×C₂₃	—	2	1	no	—
453	C₂²×C₂₃	—	4	4	no	—
454	C₂²×C₂₃	—	4	1	no	—
455	C₂²×C₂₃	—	4	2	no	—
456	C₂²×C₂₃	—	4	2	no	—
457	C₂²×C₂₃	—	4	1	no	—
458	C₂²×C₂₃	—	4	1	no	—
459	C₂²×C₂₃	—	4	2	no	—
460	C₂²×C₂₃	—	8	4	no	—
461	C₂²×C₂₃	#535	1	2	yes	—
462	C₂²×C₂₃	#578	1	2	yes	—
463	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
464	C₄×C₂₃	—	2	2	no	—
465	C₄×C₂₃	—	2	2	no	—
466	C₄×C₂₃	—	2	1	no	—
467	C₄×C₂₃	—	2	1	no	—
468	C₄×C₂₃	—	2	2	no	—
469	C₄×C₂₃	—	2	2	no	—
470	C₄×C₂₃	—	4	2	no	—
471	C₄×C₂₃	—	4	1	no	—
472	C₄×C₂₃	—	4	2	no	—
473	C₄×C₂₃	—	4	4	no	—
474	C₄×C₂₃	—	4	1	no	—
475	C₄×C₂₃	—	4	2	no	—
476	C₄×C₂₃	—	4	1	no	—
477	C₄×C₂₃	#535	1	2	yes	—
478	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
479	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
480	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
481	C₂×#137	C₂²×C₂₃	1	2	yes	—
482	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
483	C₂×#135	C₂²×C₂₃	1	2	yes	—
484	C₂²×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
485	#556	—	2	1	no	—
486	#554	—	2	1	no	—
487	#552	—	2	2	no	—
488	#552	—	2	1	no	—
489	#552	—	2	1	no	—
490	#551	—	2	2	no	—
491	#544	C₂²×C₂₃	1	1	yes	characteristic, complemented
492	#542	C₂²×C₂₃	1	2	yes	complemented
493	#541	C₂²×C₂₃	1	2	yes	complemented
494	#536	—	2	1	no	—
495	#536	—	2	2	no	—
496	#536	—	2	1	no	—
497	#536	C₂²×C₂₃	1	2	yes	—
498	#536	C₂²×C₂₃	1	4	yes	—
499	#536	C₂²×C₂₃	1	2	yes	—
500	#536	C₂²×C₂₃	1	1	yes	characteristic, complemented
501	#533	C₂²×C₂₃	1	2	yes	—
502	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
503	#529	C₂²×C₂₃	1	2	yes	—
504	C₂×#124	C₂²×C₂₃	1	2	yes	—
505	#525	C₂²×C₂₃	1	1	yes	characteristic
506	C₂×#123	—	2	2	no	—
507	C₂×C₂²⋊Q₈	—	2	1	no	—
508	C₂×C₂²⋊Q₈	—	2	1	no	—
509	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
510	#520	C₂²×C₂₃	1	1	yes	characteristic, complemented
511	#519	C₂²×C₂₃	1	1	yes	characteristic, complemented
512	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
513	#497	C₂²×C₂₃	1	4	yes	complemented
514	#497	C₂²×C₂₃	1	4	yes	complemented
515	#495	C₂²×C₂₃	1	4	yes	complemented
516	#494	C₂²×C₂₃	1	4	yes	complemented
517	#491	C₂²×C₂₃	1	4	yes	complemented
518	#489	C₂²×C₂₃	1	4	yes	complemented
519	#488	C₂²×C₂₃	1	4	yes	complemented
520	#487	C₂²×C₂₃	1	4	yes	complemented
521	#464	C₂²×C₂₃	1	4	yes	complemented
522	#464	C₂²×C₂₃	1	4	yes	complemented
523	#464	C₂²×C₂₃	1	4	yes	complemented
524	#463	C₂²×C₂₃	1	4	yes	complemented
525	#462	C₂²×C₂₃	1	4	yes	complemented
526	#462	C₂²×C₂₃	1	4	yes	complemented
527	#462	C₂²×C₂₃	1	4	yes	complemented
528	#461	C₂²×C₂₃	1	4	yes	complemented
529	#452	C₂²×C₂₃	1	2	yes	—
530	#452	C₂²×C₂₃	1	4	yes	—
531	#451	C₂²×C₂₃	1	1	yes	characteristic
532	#451	C₂²×C₂₃	1	2	yes	—
533	#451	C₂²×C₂₃	1	2	yes	—
534	#451	C₂²×C₂₃	1	2	yes	—
535	#451	C₂²×C₂₃	1	2	yes	—
536	#451	C₂²×C₂₃	1	2	yes	complemented
537	#451	C₂²×C₂₃	1	4	yes	complemented
538	#450	C₂²×C₂₃	1	2	yes	—
539	#450	C₂²×C₂₃	1	1	yes	characteristic
540	#449	C₂²×C₂₃	1	2	yes	—
541	#448	C₂²×C₂₃	1	2	yes	—
542	#448	C₂²×C₂₃	1	1	yes	characteristic
543	#448	C₂²×C₂₃	1	2	yes	complemented
544	#447	C₂²×C₂₃	1	1	yes	characteristic
545	#433	C₂²×C₂₃	1	4	yes	complemented
546	#432	C₂²×C₂₃	1	2	yes	—
547	#431	C₂²×C₂₃	1	2	yes	—
548	#424	C₂²×C₂₃	1	2	yes	complemented
549	#419	C₂²×C₂₃	1	2	yes	complemented
550	#417	C₂²×C₂₃	1	2	yes	—
551	#416	C₂²×C₂₃	1	2	yes	—
552	C₂×#103	C₂²×C₂₃	1	2	yes	complemented
553	#407	C₂²×C₂₃	1	1	yes	characteristic
554	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
555	#405	C₂²×C₂₃	1	2	yes	complemented
556	C₂×C₂₃	—	2	2	no	—
557	C₂×C₂₃	—	2	2	no	—
558	C₂×C₂₃	—	4	1	no	—
559	C₂×C₂₃	—	8	1	no	—
560	C₂×C₂₃	—	8	2	no	—
561	C₂×C₂₃	C₂×#535	1	1	yes	characteristic
562	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
563	C₂×C₂₃	#3586	1	1	yes	characteristic
564	C₂×#41	—	2	1	no	—
565	C₂×#41	—	2	1	no	—
566	C₂×#41	—	4	4	no	—
567	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
568	C₂×#41	C₂³×C₂₃	1	2	yes	—
569	C₂×#41	C₂³×C₂₃	1	2	yes	—
570	C₂²×Q₈	—	2	1	no	—
571	C₂²×Q₈	—	2	1	no	—
572	C₂²×Q₈	—	2	1	no	—
573	C₂²×Q₈	—	4	4	no	—
574	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
575	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
576	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
577	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
578	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
579	C₂²×D₄	—	2	1	no	—
580	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
581	C₂³×C₄	—	2	1	no	—
582	C₂³×C₄	—	2	1	no	—
583	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
584	#137	—	4	4	no	—
585	#137	—	4	4	no	—
586	#135	—	4	4	no	—
587	C₂×Q₁₆	—	4	4	no	—
588	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
589	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
590	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
591	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
592	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
593	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
594	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
595	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
596	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
597	C₂×D₈	C₂³×C₂₃	1	2	yes	—
598	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
599	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
600	C₄⋊Q₈	—	2	1	no	—
601	C₄⋊Q₈	—	2	2	no	—
602	C₄⋊Q₈	—	2	2	no	—
603	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
604	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
605	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
606	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
607	#126	—	2	2	no	—
608	#126	—	2	2	no	—
609	#126	—	2	2	no	—
610	#126	—	2	2	no	—
611	#125	—	2	2	no	—
612	#125	—	2	2	no	—
613	#125	—	2	1	no	—
614	#125	—	2	2	no	—
615	#125	C₂³×C₂₃	1	2	yes	—
616	#124	—	2	2	no	—
617	#124	—	2	2	no	—
618	#124	—	2	2	no	—
619	#124	C₂³×C₂₃	1	4	yes	—
620	#124	C₂³×C₂₃	1	4	yes	—
621	#124	C₂³×C₂₃	1	2	yes	—
622	#123	—	2	1	no	—
623	#123	—	2	2	no	—
624	#123	—	2	4	no	—
625	#123	—	2	4	no	—
626	#123	—	2	4	no	—
627	#123	—	2	4	no	—
628	#123	—	2	2	no	—
629	#123	—	2	2	no	—
630	C₂²⋊Q₈	—	2	1	no	—
631	C₂²⋊Q₈	—	2	1	no	—
632	C₂²⋊Q₈	—	2	2	no	—
633	C₂²⋊Q₈	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	—	2	4	no	—
637	C₂²⋊Q₈	—	2	2	no	—
638	C₂²⋊Q₈	—	2	4	no	—
639	C₂²⋊Q₈	—	2	1	no	—
640	C₂²⋊Q₈	—	2	1	no	—
641	C₂²⋊Q₈	—	2	2	no	—
642	C₂²⋊Q₈	—	2	2	no	—
643	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
644	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
645	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
646	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
647	#121	C₂³×C₂₃	1	1	yes	characteristic
648	#121	C₂³×C₂₃	1	1	yes	characteristic
649	#120	—	2	1	no	—
650	C₄×Q₈	—	2	1	no	—
651	C₄×Q₈	—	2	1	no	—
652	C₄×Q₈	—	2	2	no	—
653	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
654	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
655	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
656	C₄×D₄	—	2	1	no	—
657	C₄×D₄	—	2	1	no	—
658	C₄×D₄	—	2	2	no	—
659	C₄×D₄	—	2	2	no	—
660	C₄×D₄	C₂³×C₂₃	1	2	yes	—
661	#117	—	2	2	no	—
662	#117	—	2	1	no	—
663	#117	—	2	2	no	—
664	#117	—	2	2	no	—
665	#117	D₄×C₂₃	1	1	yes	characteristic
666	#117	D₄×C₂₃	1	2	yes	—
667	#117	D₄×C₂₃	1	1	yes	characteristic
668	#117	C₂³×C₂₃	1	1	yes	characteristic
669	#117	C₂³×C₂₃	1	1	yes	characteristic
670	#117	C₂³×C₂₃	1	1	yes	characteristic
671	#117	C₂³×C₂₃	1	2	yes	—
672	C₂×C₄⋊C₄	—	2	2	no	—
673	C₂×C₄⋊C₄	—	2	2	no	—
674	C₂×C₄⋊C₄	—	2	1	no	—
675	C₂×C₄⋊C₄	—	2	1	no	—
676	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
677	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
678	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
679	C₂×C₂²⋊C₄	—	2	1	no	—
680	C₂×C₂²⋊C₄	—	2	2	no	—
681	C₂×C₂²⋊C₄	—	2	2	no	—
682	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
683	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
684	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
685	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
686	#103	C₂³×C₂₃	1	4	yes	—
687	#103	C₂³×C₂₃	1	4	yes	—
688	#103	C₂³×C₂₃	1	2	yes	—
689	#103	C₂³×C₂₃	1	2	yes	—
690	#103	C₂³×C₂₃	1	4	yes	—
691	#103	C₂³×C₂₃	1	4	yes	—
692	#103	C₂³×C₂₃	1	4	yes	—
693	#102	C₂³×C₂₃	1	2	yes	—
694	#102	C₂³×C₂₃	1	2	yes	—
695	#102	C₂³×C₂₃	1	4	yes	—
696	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
697	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
698	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
699	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
700	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
701	#97	C₂³×C₂₃	1	4	yes	—
702	C₄×C₈	C₂³×C₂₃	1	4	yes	—
703	C₂₃	#60814	1	1	yes	characteristic, direct product factor, Sylow
704	C₂⁴	—	2	1	no	—
705	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
706	#41	—	2	4	no	—
707	#41	—	2	4	no	—
708	#41	—	2	4	no	—
709	#41	—	4	2	no	—
710	#41	—	4	2	no	—
711	#41	—	4	4	no	—
712	#41	—	4	4	no	—
713	C₂×Q₈	—	2	1	no	—
714	C₂×Q₈	—	2	2	no	—
715	C₂×Q₈	—	2	2	no	—
716	C₂×Q₈	—	2	2	no	—
717	C₂×Q₈	—	2	1	no	—
718	C₂×Q₈	—	2	2	no	—
719	C₂×Q₈	—	2	4	no	—
720	C₂×Q₈	—	2	4	no	—
721	C₂×Q₈	—	2	4	no	—
722	C₂×Q₈	—	4	4	no	—
723	C₂×Q₈	—	4	4	no	—
724	C₂×Q₈	—	4	2	no	—
725	C₂×Q₈	—	4	4	no	—
726	C₂×Q₈	—	4	4	no	—
727	C₂×Q₈	—	4	4	no	—
728	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
729	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
730	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
731	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
732	C₂×D₄	—	2	1	no	—
733	C₂×D₄	—	2	1	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	1	no	—
737	C₂×D₄	—	2	1	no	—
738	C₂×D₄	—	4	2	no	—
739	C₂×D₄	—	4	4	no	—
740	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
741	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
742	C₂²×C₄	—	2	4	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	1	no	—
745	C₂²×C₄	—	2	1	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	4	4	no	—
754	C₂²×C₄	—	4	4	no	—
755	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
756	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
757	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
758	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
759	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
763	Q₁₆	—	4	4	no	—
764	Q₁₆	—	4	4	no	—
765	Q₁₆	—	4	2	no	—
766	Q₁₆	—	4	4	no	—
767	Q₁₆	—	4	4	no	—
768	SD₁₆	—	4	2	no	—
769	SD₁₆	—	4	2	no	—
770	SD₁₆	—	4	4	no	—
771	SD₁₆	—	4	4	no	—
772	D₈	—	4	2	no	—
773	M₁₆	—	2	4	no	—
774	C₂×C₈	—	2	4	no	—
775	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
776	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
777	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
778	C₄⋊C₄	—	2	1	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	4	no	—
783	C₄⋊C₄	—	2	4	no	—
784	C₄⋊C₄	—	2	4	no	—
785	C₄⋊C₄	—	2	4	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	1	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	1	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
796	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
797	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
798	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
799	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
800	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
801	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
802	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
803	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	1	no	—
807	C₂²⋊C₄	—	2	1	no	—
808	C₂²⋊C₄	—	2	1	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	4	no	—
812	C₂²⋊C₄	—	2	4	no	—
813	C₂²⋊C₄	—	2	1	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	1	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
819	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
820	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
821	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
822	C₄²	—	2	2	no	—
823	C₄²	—	2	2	no	—
824	C₄²	—	2	2	no	—
825	C₄²	—	2	1	no	—
826	C₄²	C₂×D₄×C₂₃	1	2	yes	—
827	C₄²	C₂×D₄×C₂₃	1	2	yes	—
828	C₄²	C₂⁴×C₂₃	1	2	yes	—
829	C₄²	C₂⁴×C₂₃	1	2	yes	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	4	1	no	—
835	C₂³	—	4	2	no	—
836	C₂³	—	4	2	no	—
837	C₂³	—	4	2	no	—
838	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
839	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
840	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
841	Q₈	—	2	4	no	—
842	Q₈	—	2	2	no	—
843	Q₈	—	2	4	no	—
844	Q₈	—	2	2	no	—
845	Q₈	—	2	4	no	—
846	Q₈	—	2	2	no	—
847	Q₈	—	4	4	no	—
848	Q₈	—	4	4	no	—
849	Q₈	—	4	2	no	—
850	Q₈	—	4	4	no	—
851	Q₈	—	4	2	no	—
852	Q₈	—	8	2	no	—
853	D₄	—	2	2	no	—
854	D₄	—	2	2	no	—
855	D₄	—	2	2	no	—
856	D₄	—	4	2	no	—
857	D₄	—	4	4	no	—
858	D₄	—	4	2	no	—
859	D₄	—	4	4	no	—
860	D₄	—	4	2	no	—
861	D₄	—	8	1	no	—
862	C₂×C₄	—	2	4	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	4	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	4	2	no	—
876	C₂×C₄	—	4	4	no	—
877	C₂×C₄	—	4	2	no	—
878	C₂×C₄	—	4	4	no	—
879	C₂×C₄	—	4	4	no	—
880	C₂×C₄	—	4	4	no	—
881	C₂×C₄	—	4	2	no	—
882	C₂×C₄	—	4	4	no	—
883	C₂×C₄	—	4	2	no	—
884	C₂×C₄	—	8	2	no	—
885	C₂×C₄	—	8	1	no	—
886	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
887	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
888	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
889	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
890	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
891	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
892	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
893	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
894	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
895	C₈	—	2	2	no	—
896	C₈	—	2	2	no	—
897	C₈	—	2	4	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	2	1	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	4	4	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	1	no	—
908	C₂²	—	4	1	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	1	no	—
911	C₂²	—	4	2	no	—
912	C₂²	—	8	4	no	—
913	C₂²	C₂₃×#535	1	2	yes	—
914	C₂²	C₂₃×#578	1	2	yes	—
915	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
916	C₄	—	2	1	no	—
917	C₄	—	2	1	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	2	2	no	—
921	C₄	—	2	2	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	4	no	—
924	C₄	—	4	1	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	1	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	1	no	—
929	C₄	C₂₃×#535	1	2	yes	—
930	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
931	C₂	—	2	2	no	—
932	C₂	—	2	2	no	—
933	C₂	—	4	1	no	—
934	C₂	—	8	2	no	—
935	C₂	—	8	1	no	—
936	C₂	C₂×C₂₃×#535	1	1	yes	characteristic
937	C₂	C₂×C₂₃×#578	1	1	yes	characteristic
938	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3002	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3495	C₂	semidirect
2. C₂×C₂₃×#536	C₂	semidirect
3. C₂₃×#3225	C₂	semidirect
4. C₂₃×#3223	C₂	semidirect
5. C₂₃×#3218	C₂	semidirect
6. C₂₃×#3215	C₂	semidirect
7. C₂₃×#3211	C₂	semidirect
8. C₂₃×#3209	C₂	semidirect
9. C₂₃×#3156	C₂	semidirect
10. C₂₃×#3137	C₂	semidirect
11. C₂₃×#3046	C₂	semidirect
12. C₂₃×#3044	C₂	semidirect
13. C₂₃×#3007	C₂	semidirect
14. C₂₃×#3004	C₂	semidirect
16. C₂×C₂₃×#451	C₂	semidirect
17. C₂₃×#2924	C₂	semidirect
21. C₂×C₂₃×#137	C₂²	semidirect
23. C₂²×Q₁₆×C₂₃	C₂²	semidirect
30. C₂₃×#544	C₂²	semidirect
31. C₂₃×#542	C₂²	semidirect
32. C₂₃×#541	C₂²	semidirect
39. C₂₃×#536	C₂²	semidirect
49. C₂₃×#520	C₂²	semidirect
50. C₂₃×#519	C₂²	semidirect
52. C₂₃×#497	C₂²	semidirect
53. C₂₃×#497	C₂²	semidirect
54. C₂₃×#495	C₂²	semidirect
55. C₂₃×#494	C₂²	semidirect
56. C₂₃×#491	C₂²	semidirect
57. C₂₃×#489	C₂²	semidirect
58. C₂₃×#488	C₂²	semidirect
59. C₂₃×#487	C₂²	semidirect
60. C₂₃×#464	C₂²	semidirect
61. C₂₃×#464	C₂²	semidirect
62. C₂₃×#464	C₂²	semidirect
63. C₂₃×#463	C₂²	semidirect
64. C₂₃×#462	C₂²	semidirect
65. C₂₃×#462	C₂²	semidirect
66. C₂₃×#462	C₂²	semidirect
67. C₂₃×#461	C₂²	semidirect
75. C₂₃×#451	C₂²	semidirect
76. C₂₃×#451	C₂²	semidirect
82. C₂₃×#448	C₂²	semidirect
84. C₂₃×#433	C₂²	semidirect
87. C₂₃×#424	C₂²	semidirect
88. C₂₃×#419	C₂²	semidirect
91. C₂×C₂₃×#103	C₂²	semidirect
94. C₂₃×#405	C₂²	semidirect
360. #60814	C₂₃	direct (N × H)
429. #3495	C₂×C₂₃	semidirect
430. C₂×#536	C₂×C₂₃	semidirect
431. #3225	C₂×C₂₃	semidirect
432. #3223	C₂×C₂₃	semidirect
433. #3218	C₂×C₂₃	semidirect
434. #3215	C₂×C₂₃	semidirect
435. #3211	C₂×C₂₃	semidirect
436. #3209	C₂×C₂₃	semidirect
437. #3156	C₂×C₂₃	semidirect
438. #3137	C₂×C₂₃	semidirect
439. #3046	C₂×C₂₃	semidirect
440. #3044	C₂×C₂₃	semidirect
441. #3007	C₂×C₂₃	semidirect
442. #3004	C₂×C₂₃	semidirect
444. C₂×#451	C₂×C₂₃	semidirect
445. #2924	C₂×C₂₃	semidirect
482. C₂×#137	C₂²×C₂₃	semidirect
484. C₂²×Q₁₆	C₂²×C₂₃	semidirect
491. #544	C₂²×C₂₃	semidirect
492. #542	C₂²×C₂₃	semidirect
493. #541	C₂²×C₂₃	semidirect
500. #536	C₂²×C₂₃	semidirect
510. #520	C₂²×C₂₃	semidirect
511. #519	C₂²×C₂₃	semidirect
513. #497	C₂²×C₂₃	semidirect
514. #497	C₂²×C₂₃	semidirect
515. #495	C₂²×C₂₃	semidirect
516. #494	C₂²×C₂₃	semidirect
517. #491	C₂²×C₂₃	semidirect
518. #489	C₂²×C₂₃	semidirect
519. #488	C₂²×C₂₃	semidirect
520. #487	C₂²×C₂₃	semidirect
521. #464	C₂²×C₂₃	semidirect
522. #464	C₂²×C₂₃	semidirect
523. #464	C₂²×C₂₃	semidirect
524. #463	C₂²×C₂₃	semidirect
525. #462	C₂²×C₂₃	semidirect
526. #462	C₂²×C₂₃	semidirect
527. #462	C₂²×C₂₃	semidirect
528. #461	C₂²×C₂₃	semidirect
536. #451	C₂²×C₂₃	semidirect
537. #451	C₂²×C₂₃	semidirect
543. #448	C₂²×C₂₃	semidirect
545. #433	C₂²×C₂₃	semidirect
548. #424	C₂²×C₂₃	semidirect
549. #419	C₂²×C₂₃	semidirect
552. C₂×#103	C₂²×C₂₃	semidirect
555. #405	C₂²×C₂₃	semidirect
703. C₂₃	#60814	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3495	2
C₂×C₂₃×#536	2
C₂₃×#3225	2
C₂₃×#3223	2
C₂₃×#3218	2
C₂₃×#3215	2
C₂₃×#3211	2
C₂₃×#3209	2
C₂₃×#3156	2
C₂₃×#3137	2
C₂₃×#3046	2
C₂₃×#3044	2
C₂₃×#3007	2
C₂₃×#3004	2
C₂₃×#3002	2
C₂×C₂₃×#451	2
C₂₃×#2924	2
#60814	23

Subgroups — C23×#60814 #19208440

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60814 #19208440