Subgroups — C₂₃×#60837 #19208463

Order 5888.

2008 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3461	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×#3216	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3212	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×#3039	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3013	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3011	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	2	yes	—
19	C₂×C₂₃×#137	C₂²	1	2	yes	—
20	C₂×C₂₃×#137	C₂²	1	2	yes	—
21	C₂×C₂₃×#135	C₂²	1	2	yes	—
22	C₂²×Q₁₆×C₂₃	C₂²	1	2	yes	—
23	D₄×Q₈×C₂₃	—	2	1	no	—
24	D₄×Q₈×C₂₃	—	2	1	no	—
25	C₂₃×#547	—	2	2	no	—
26	C₂₃×#547	—	2	1	no	—
27	C₂₃×#547	—	2	2	no	—
28	C₂₃×#547	—	2	1	no	—
29	C₂₃×#544	C₂²	1	1	yes	characteristic
30	C₂₃×#542	—	2	1	no	—
31	C₂₃×#542	C₂²	1	2	yes	—
32	C₂₃×#541	—	2	1	no	—
33	C₂₃×#541	C₂²	1	2	yes	—
34	C₂₃×#539	—	2	2	no	—
35	C₂₃×#537	C₂²	1	1	yes	characteristic
36	C₂₃×#536	C₂²	1	1	yes	characteristic
37	C₂₃×#536	C₂²	1	4	yes	—
38	C₂₃×#536	C₂²	1	2	yes	—
39	C₂₃×#536	C₂²	1	1	yes	characteristic
40	C₂₃×#533	—	2	1	no	—
41	C₂₃×#533	C₂²	1	2	yes	—
42	C₂₃×#532	C₂²	1	2	yes	—
43	C₂₃×#532	C₂²	1	1	yes	characteristic
44	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
45	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
46	C₂₃×#529	—	2	2	no	—
47	C₂₃×#529	—	2	1	no	—
48	C₂₃×#529	C₂²	1	2	yes	—
49	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
50	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
52	C₂₃×#497	C₂²	1	4	yes	—
53	C₂₃×#497	C₂²	1	4	yes	—
54	C₂₃×#495	C₂²	1	4	yes	—
55	C₂₃×#494	C₂²	1	4	yes	—
56	C₂₃×#491	C₂²	1	4	yes	—
57	C₂₃×#489	C₂²	1	4	yes	—
58	C₂₃×#488	C₂²	1	4	yes	—
59	C₂₃×#487	C₂²	1	4	yes	—
60	C₂₃×#464	C₂²	1	2	yes	—
61	C₂₃×#464	C₂²	1	4	yes	—
62	C₂₃×#463	C₂²	1	2	yes	—
63	C₂₃×#462	C₂²	1	1	yes	characteristic
64	C₂₃×#462	C₂²	1	2	yes	—
65	C₂₃×#462	C₂²	1	2	yes	—
66	C₂₃×#462	C₂²	1	2	yes	—
67	C₂₃×#462	C₂²	1	2	yes	—
68	C₂₃×#462	C₂²	1	2	yes	—
69	C₂₃×#462	C₂²	1	4	yes	—
70	C₂₃×#461	C₂²	1	2	yes	—
71	C₂₃×#461	C₂²	1	1	yes	characteristic
72	C₂₃×#461	C₂²	1	2	yes	—
73	C₂₃×#460	C₂²	1	2	yes	—
74	C₂₃×#460	C₂²	1	1	yes	characteristic
75	C₂₃×#459	C₂²	1	1	yes	characteristic
76	C₂₃×#452	C₂²	1	4	yes	—
77	C₂₃×#452	C₂²	1	4	yes	—
78	C₂₃×#452	C₂²	1	4	yes	—
79	C₂₃×#451	C₂²	1	4	yes	—
80	C₂₃×#451	C₂²	1	4	yes	—
81	C₂₃×#451	C₂²	1	4	yes	—
82	C₂₃×#449	C₂²	1	4	yes	—
83	C₂₃×#448	C₂²	1	4	yes	—
84	C₂₃×#433	C₂²	1	4	yes	—
85	C₂₃×#432	C₂²	1	2	yes	—
86	C₂₃×#431	C₂²	1	2	yes	—
87	C₂₃×#423	C₂²	1	1	yes	characteristic
88	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
89	C₂₃×#419	C₂²	1	2	yes	—
90	C₂₃×#417	C₂²	1	2	yes	—
91	C₂₃×#416	C₂²	1	2	yes	—
92	C₂×C₂₃×#103	C₂²	1	2	yes	—
93	C₂₃×#408	C₂²	1	2	yes	—
94	C₂₃×#405	C₂²	1	2	yes	—
95	C₂₃×2₋¹⁺⁴	—	4	4	no	—
96	C₂₃×2₋¹⁺⁴	—	4	4	no	—
97	C₂×#41×C₂₃	—	2	4	no	—
98	C₂×#41×C₂₃	—	2	2	no	—
99	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
100	C₂×#41×C₂₃	C₂³	1	2	yes	—
101	C₂×#41×C₂₃	C₂³	1	4	yes	—
102	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₂₃	—	2	2	no	—
104	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
105	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
106	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
107	C₂₃×#137	—	4	4	no	—
108	C₂₃×#137	—	4	4	no	—
109	C₂₃×#135	—	4	4	no	—
110	C₂×Q₁₆×C₂₃	—	4	4	no	—
111	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
112	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
113	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
114	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
115	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
116	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
117	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
118	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
119	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
120	C₂×D₈×C₂₃	C₂³	1	2	yes	—
121	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
122	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
123	C₂₃×C₄⋊Q₈	—	2	1	no	—
124	C₂₃×C₄⋊Q₈	—	2	1	no	—
125	C₂₃×C₄⋊Q₈	—	2	1	no	—
126	C₂₃×C₄⋊Q₈	—	2	2	no	—
127	C₂₃×C₄⋊Q₈	—	2	1	no	—
128	C₂₃×C₄⋊Q₈	—	2	2	no	—
129	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
130	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
131	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
132	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
133	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
134	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
135	C₂₃×#127	C₂³	1	1	yes	characteristic
136	C₂₃×#126	—	2	2	no	—
137	C₂₃×#126	—	2	2	no	—
138	C₂₃×#126	—	2	2	no	—
139	C₂₃×#126	—	2	2	no	—
140	C₂₃×#125	—	2	2	no	—
141	C₂₃×#125	—	2	1	no	—
142	C₂₃×#125	—	2	2	no	—
143	C₂₃×#125	—	2	2	no	—
144	C₂₃×#125	C₂³	1	2	yes	—
145	C₂₃×#124	—	2	1	no	—
146	C₂₃×#124	—	2	2	no	—
147	C₂₃×#124	C₂³	1	2	yes	—
148	C₂₃×#124	C₂³	1	4	yes	—
149	C₂₃×#124	C₂³	1	2	yes	—
150	C₂₃×#123	—	2	2	no	—
151	C₂₃×#123	—	2	2	no	—
152	C₂₃×#123	—	2	4	no	—
153	C₂₃×#123	—	2	4	no	—
154	C₂₃×#123	—	2	4	no	—
155	C₂₃×#123	—	2	2	no	—
156	C₂₃×#123	—	2	2	no	—
157	C₂₃×C₂²⋊Q₈	—	2	1	no	—
158	C₂₃×C₂²⋊Q₈	—	2	2	no	—
159	C₂₃×C₂²⋊Q₈	—	2	4	no	—
160	C₂₃×C₂²⋊Q₈	—	2	2	no	—
161	C₂₃×C₂²⋊Q₈	—	2	2	no	—
162	C₂₃×C₂²⋊Q₈	—	2	4	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	2	no	—
167	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
168	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
169	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
170	C₂₃×#121	—	2	2	no	—
171	C₂₃×#121	—	2	1	no	—
172	C₂₃×#121	—	2	1	no	—
173	C₂₃×#121	—	2	2	no	—
174	C₂₃×#121	—	2	1	no	—
175	C₂₃×#121	—	2	2	no	—
176	C₂₃×#121	C₂³	1	2	yes	—
177	C₄×Q₈×C₂₃	—	2	1	no	—
178	C₄×Q₈×C₂₃	—	2	1	no	—
179	C₄×Q₈×C₂₃	—	2	2	no	—
180	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
181	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
182	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
183	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
184	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
185	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₂₃	—	2	1	no	—
187	C₄×D₄×C₂₃	—	2	1	no	—
188	C₄×D₄×C₂₃	—	2	2	no	—
189	C₄×D₄×C₂₃	—	2	1	no	—
190	C₄×D₄×C₂₃	—	2	2	no	—
191	C₄×D₄×C₂₃	—	2	1	no	—
192	C₄×D₄×C₂₃	—	2	2	no	—
193	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
194	C₄×D₄×C₂₃	D₄	1	2	yes	—
195	C₄×D₄×C₂₃	D₄	1	2	yes	—
196	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
197	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
198	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
199	C₂₃×#117	—	2	2	no	—
200	C₂₃×#117	—	2	1	no	—
201	C₂₃×#117	—	2	2	no	—
202	C₂₃×#117	C₂³	1	1	yes	characteristic
203	C₂₃×#117	C₂³	1	1	yes	characteristic
204	C₂₃×#117	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
206	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
207	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
208	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
209	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
210	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₂₃	—	2	1	no	—
212	C₂×C₄²×C₂₃	—	2	1	no	—
213	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
215	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
217	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
218	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
219	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
220	C₂₃×#103	C₂³	1	4	yes	—
221	C₂₃×#103	C₂³	1	4	yes	—
222	C₂₃×#103	C₂³	1	2	yes	—
223	C₂₃×#103	C₂³	1	2	yes	—
224	C₂₃×#103	C₂³	1	4	yes	—
225	C₂₃×#103	C₂³	1	4	yes	—
226	C₂₃×#103	C₂³	1	4	yes	—
227	C₂₃×#102	C₂³	1	2	yes	—
228	C₂₃×#102	C₂³	1	2	yes	—
229	C₂₃×#102	C₂³	1	4	yes	—
230	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
231	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
232	C₂₃×#97	C₂³	1	4	yes	—
233	C₄×C₈×C₂₃	C₂³	1	4	yes	—
234	#41×C₂₃	—	2	2	no	—
235	#41×C₂₃	—	2	2	no	—
236	#41×C₂₃	—	2	2	no	—
237	#41×C₂₃	—	2	4	no	—
238	#41×C₂₃	—	2	2	no	—
239	#41×C₂₃	—	2	4	no	—
240	#41×C₂₃	—	4	4	no	—
241	#41×C₂₃	—	4	4	no	—
242	#41×C₂₃	—	4	16	no	—
243	#41×C₂₃	—	4	8	no	—
244	C₂×Q₈×C₂₃	—	2	1	no	—
245	C₂×Q₈×C₂₃	—	2	4	no	—
246	C₂×Q₈×C₂₃	—	2	2	no	—
247	C₂×Q₈×C₂₃	—	2	2	no	—
248	C₂×Q₈×C₂₃	—	2	2	no	—
249	C₂×Q₈×C₂₃	—	2	4	no	—
250	C₂×Q₈×C₂₃	—	2	2	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	8	no	—
255	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
256	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
257	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
258	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
259	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
260	C₂×D₄×C₂₃	—	2	1	no	—
261	C₂×D₄×C₂₃	—	2	4	no	—
262	C₂×D₄×C₂₃	—	2	2	no	—
263	C₂×D₄×C₂₃	—	2	2	no	—
264	C₂×D₄×C₂₃	—	2	1	no	—
265	C₂×D₄×C₂₃	—	2	1	no	—
266	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
267	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
268	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
269	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₂₃	—	2	1	no	—
271	C₂²×C₄×C₂₃	—	2	4	no	—
272	C₂²×C₄×C₂₃	—	2	2	no	—
273	C₂²×C₄×C₂₃	—	2	1	no	—
274	C₂²×C₄×C₂₃	—	2	1	no	—
275	C₂²×C₄×C₂₃	—	2	1	no	—
276	C₂²×C₄×C₂₃	—	2	4	no	—
277	C₂²×C₄×C₂₃	—	2	2	no	—
278	C₂²×C₄×C₂₃	—	2	1	no	—
279	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
281	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
283	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
285	Q₁₆×C₂₃	—	4	4	no	—
286	Q₁₆×C₂₃	—	4	4	no	—
287	Q₁₆×C₂₃	—	4	2	no	—
288	Q₁₆×C₂₃	—	4	4	no	—
289	Q₁₆×C₂₃	—	4	4	no	—
290	SD₁₆×C₂₃	—	4	2	no	—
291	SD₁₆×C₂₃	—	4	2	no	—
292	SD₁₆×C₂₃	—	4	4	no	—
293	SD₁₆×C₂₃	—	4	4	no	—
294	D₈×C₂₃	—	4	2	no	—
295	M₁₆×C₂₃	—	2	4	no	—
296	C₂×C₈×C₂₃	—	2	4	no	—
297	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
298	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
299	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
300	C₄⋊C₄×C₂₃	—	2	2	no	—
301	C₄⋊C₄×C₂₃	—	2	1	no	—
302	C₄⋊C₄×C₂₃	—	2	2	no	—
303	C₄⋊C₄×C₂₃	—	2	1	no	—
304	C₄⋊C₄×C₂₃	—	2	2	no	—
305	C₄⋊C₄×C₂₃	—	2	2	no	—
306	C₄⋊C₄×C₂₃	—	2	2	no	—
307	C₄⋊C₄×C₂₃	—	2	2	no	—
308	C₄⋊C₄×C₂₃	—	2	4	no	—
309	C₄⋊C₄×C₂₃	—	2	4	no	—
310	C₄⋊C₄×C₂₃	—	2	1	no	—
311	C₄⋊C₄×C₂₃	—	2	1	no	—
312	C₄⋊C₄×C₂₃	—	2	1	no	—
313	C₄⋊C₄×C₂₃	—	2	2	no	—
314	C₄⋊C₄×C₂₃	—	2	2	no	—
315	C₄⋊C₄×C₂₃	—	2	2	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	C₂×D₄	1	2	yes	—
322	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
323	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
324	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
325	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
326	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
327	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
328	C₂²⋊C₄×C₂₃	—	2	2	no	—
329	C₂²⋊C₄×C₂₃	—	2	2	no	—
330	C₂²⋊C₄×C₂₃	—	2	1	no	—
331	C₂²⋊C₄×C₂₃	—	2	2	no	—
332	C₂²⋊C₄×C₂₃	—	2	1	no	—
333	C₂²⋊C₄×C₂₃	—	2	1	no	—
334	C₂²⋊C₄×C₂₃	—	2	2	no	—
335	C₂²⋊C₄×C₂₃	—	2	2	no	—
336	C₂²⋊C₄×C₂₃	—	2	2	no	—
337	C₂²⋊C₄×C₂₃	—	2	2	no	—
338	C₂²⋊C₄×C₂₃	—	2	4	no	—
339	C₂²⋊C₄×C₂₃	—	2	4	no	—
340	C₂²⋊C₄×C₂₃	—	2	2	no	—
341	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
342	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
343	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
344	C₄²×C₂₃	—	2	2	no	—
345	C₄²×C₂₃	—	2	1	no	—
346	C₄²×C₂₃	—	2	1	no	—
347	C₄²×C₂₃	—	2	1	no	—
348	C₄²×C₂₃	—	2	2	no	—
349	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
350	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
351	C₄²×C₂₃	C₂×D₄	1	2	yes	—
352	C₄²×C₂₃	C₂×D₄	1	2	yes	—
353	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
354	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
355	C₄²×C₂₃	C₂⁴	1	2	yes	—
356	#60837	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
357	C₂³×C₂₃	—	2	1	no	—
358	C₂³×C₂₃	—	2	2	no	—
359	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
360	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
361	Q₈×C₂₃	—	2	2	no	—
362	Q₈×C₂₃	—	2	2	no	—
363	Q₈×C₂₃	—	2	1	no	—
364	Q₈×C₂₃	—	2	4	no	—
365	Q₈×C₂₃	—	2	2	no	—
366	Q₈×C₂₃	—	2	2	no	—
367	Q₈×C₂₃	—	2	1	no	—
368	Q₈×C₂₃	—	2	4	no	—
369	Q₈×C₂₃	—	2	2	no	—
370	Q₈×C₂₃	—	4	8	no	—
371	Q₈×C₂₃	—	4	2	no	—
372	Q₈×C₂₃	—	4	4	no	—
373	Q₈×C₂₃	—	8	2	no	—
374	D₄×C₂₃	—	2	4	no	—
375	D₄×C₂₃	—	2	2	no	—
376	D₄×C₂₃	—	2	1	no	—
377	D₄×C₂₃	—	2	2	no	—
378	D₄×C₂₃	—	2	1	no	—
379	D₄×C₂₃	—	2	2	no	—
380	D₄×C₂₃	—	4	2	no	—
381	D₄×C₂₃	—	4	8	no	—
382	D₄×C₂₃	—	4	2	no	—
383	D₄×C₂₃	—	4	4	no	—
384	D₄×C₂₃	—	4	2	no	—
385	D₄×C₂₃	—	8	2	no	—
386	C₂×C₄×C₂₃	—	2	2	no	—
387	C₂×C₄×C₂₃	—	2	4	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	1	no	—
394	C₂×C₄×C₂₃	—	2	2	no	—
395	C₂×C₄×C₂₃	—	2	4	no	—
396	C₂×C₄×C₂₃	—	2	2	no	—
397	C₂×C₄×C₂₃	—	4	1	no	—
398	C₂×C₄×C₂₃	—	4	2	no	—
399	C₂×C₄×C₂₃	—	4	8	no	—
400	C₂×C₄×C₂₃	—	4	8	no	—
401	C₂×C₄×C₂₃	—	4	2	no	—
402	C₂×C₄×C₂₃	—	4	4	no	—
403	C₂×C₄×C₂₃	—	4	4	no	—
404	C₂×C₄×C₂₃	—	4	2	no	—
405	C₂×C₄×C₂₃	—	4	2	no	—
406	C₂×C₄×C₂₃	—	8	1	no	—
407	C₂×C₄×C₂₃	—	8	1	no	—
408	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
417	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
418	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
419	C₈×C₂₃	—	2	2	no	—
420	C₈×C₂₃	—	2	2	no	—
421	C₈×C₂₃	—	2	4	no	—
422	#3499	C₂×C₂₃	1	1	yes	characteristic, complemented
423	#3461	C₂×C₂₃	1	1	yes	characteristic, complemented
424	#3225	C₂×C₂₃	1	4	yes	complemented
425	#3223	C₂×C₂₃	1	4	yes	complemented
426	#3218	C₂×C₂₃	1	2	yes	complemented
427	#3216	C₂×C₂₃	1	2	yes	complemented
428	#3212	C₂×C₂₃	1	2	yes	complemented
429	#3209	C₂×C₂₃	1	2	yes	complemented
430	#3156	C₂×C₂₃	1	2	yes	complemented
431	#3137	C₂×C₂₃	1	2	yes	complemented
432	#3039	C₂×C₂₃	1	1	yes	characteristic, complemented
433	#3037	C₂×C₂₃	1	1	yes	characteristic, complemented
434	#3035	C₂×C₂₃	1	1	yes	characteristic, complemented
435	C₂×#462	C₂×C₂₃	1	1	yes	characteristic, complemented
436	#3013	C₂×C₂₃	1	2	yes	complemented
437	#3011	C₂×C₂₃	1	2	yes	complemented
438	#2925	C₂×C₂₃	1	1	yes	characteristic, complemented
439	C₂²×C₂₃	—	2	1	no	—
440	C₂²×C₂₃	—	2	1	no	—
441	C₂²×C₂₃	—	2	2	no	—
442	C₂²×C₂₃	—	2	2	no	—
443	C₂²×C₂₃	—	2	2	no	—
444	C₂²×C₂₃	—	4	1	no	—
445	C₂²×C₂₃	—	4	2	no	—
446	C₂²×C₂₃	—	4	2	no	—
447	C₂²×C₂₃	—	4	1	no	—
448	C₂²×C₂₃	—	4	1	no	—
449	C₂²×C₂₃	—	4	2	no	—
450	C₂²×C₂₃	#535	1	2	yes	—
451	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
452	C₄×C₂₃	—	2	1	no	—
453	C₄×C₂₃	—	2	1	no	—
454	C₄×C₂₃	—	2	2	no	—
455	C₄×C₂₃	—	2	2	no	—
456	C₄×C₂₃	—	2	1	no	—
457	C₄×C₂₃	—	2	2	no	—
458	C₄×C₂₃	—	4	2	no	—
459	C₄×C₂₃	—	4	1	no	—
460	C₄×C₂₃	—	4	4	no	—
461	C₄×C₂₃	—	4	2	no	—
462	C₄×C₂₃	—	4	1	no	—
463	C₄×C₂₃	—	4	2	no	—
464	C₄×C₂₃	—	4	1	no	—
465	C₄×C₂₃	#535	1	2	yes	—
466	C₄×C₂₃	#578	1	2	yes	—
467	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
468	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
469	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	2	yes	—
470	C₂×#137	C₂²×C₂₃	1	2	yes	—
471	C₂×#137	C₂²×C₂₃	1	2	yes	—
472	C₂×#135	C₂²×C₂₃	1	2	yes	—
473	C₂²×Q₁₆	C₂²×C₂₃	1	2	yes	—
474	D₄×Q₈	—	2	1	no	—
475	D₄×Q₈	—	2	1	no	—
476	#547	—	2	2	no	—
477	#547	—	2	1	no	—
478	#547	—	2	2	no	—
479	#547	—	2	1	no	—
480	#544	C₂²×C₂₃	1	1	yes	characteristic
481	#542	—	2	1	no	—
482	#542	C₂²×C₂₃	1	2	yes	—
483	#541	—	2	1	no	—
484	#541	C₂²×C₂₃	1	2	yes	—
485	#539	—	2	2	no	—
486	#537	C₂²×C₂₃	1	1	yes	characteristic
487	#536	C₂²×C₂₃	1	2	yes	—
488	#536	C₂²×C₂₃	1	1	yes	characteristic
489	#536	C₂²×C₂₃	1	4	yes	—
490	#536	C₂²×C₂₃	1	1	yes	characteristic
491	#533	—	2	1	no	—
492	#533	C₂²×C₂₃	1	2	yes	—
493	#532	C₂²×C₂₃	1	2	yes	—
494	#532	C₂²×C₂₃	1	1	yes	characteristic
495	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
496	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
497	#529	—	2	2	no	—
498	#529	—	2	1	no	—
499	#529	C₂²×C₂₃	1	2	yes	—
500	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
501	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
502	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
503	#497	C₂²×C₂₃	1	4	yes	—
504	#497	C₂²×C₂₃	1	4	yes	—
505	#495	C₂²×C₂₃	1	4	yes	—
506	#494	C₂²×C₂₃	1	4	yes	—
507	#491	C₂²×C₂₃	1	4	yes	—
508	#489	C₂²×C₂₃	1	4	yes	—
509	#488	C₂²×C₂₃	1	4	yes	—
510	#487	C₂²×C₂₃	1	4	yes	—
511	#464	C₂²×C₂₃	1	2	yes	—
512	#464	C₂²×C₂₃	1	4	yes	—
513	#463	C₂²×C₂₃	1	2	yes	—
514	#462	C₂²×C₂₃	1	1	yes	characteristic
515	#462	C₂²×C₂₃	1	2	yes	—
516	#462	C₂²×C₂₃	1	2	yes	—
517	#462	C₂²×C₂₃	1	2	yes	—
518	#462	C₂²×C₂₃	1	2	yes	—
519	#462	C₂²×C₂₃	1	2	yes	—
520	#462	C₂²×C₂₃	1	4	yes	—
521	#461	C₂²×C₂₃	1	2	yes	—
522	#461	C₂²×C₂₃	1	1	yes	characteristic
523	#461	C₂²×C₂₃	1	2	yes	—
524	#460	C₂²×C₂₃	1	2	yes	—
525	#460	C₂²×C₂₃	1	1	yes	characteristic
526	#459	C₂²×C₂₃	1	1	yes	characteristic
527	#452	C₂²×C₂₃	1	4	yes	—
528	#452	C₂²×C₂₃	1	4	yes	—
529	#452	C₂²×C₂₃	1	4	yes	—
530	#451	C₂²×C₂₃	1	4	yes	—
531	#451	C₂²×C₂₃	1	4	yes	—
532	#451	C₂²×C₂₃	1	4	yes	—
533	#449	C₂²×C₂₃	1	4	yes	—
534	#448	C₂²×C₂₃	1	4	yes	—
535	#433	C₂²×C₂₃	1	4	yes	—
536	#432	C₂²×C₂₃	1	2	yes	—
537	#431	C₂²×C₂₃	1	2	yes	—
538	#423	C₂²×C₂₃	1	1	yes	characteristic
539	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
540	#419	C₂²×C₂₃	1	2	yes	—
541	#417	C₂²×C₂₃	1	2	yes	—
542	#416	C₂²×C₂₃	1	2	yes	—
543	C₂×#103	C₂²×C₂₃	1	2	yes	—
544	#408	C₂²×C₂₃	1	2	yes	—
545	#405	C₂²×C₂₃	1	2	yes	—
546	C₂×C₂₃	—	2	2	no	—
547	C₂×C₂₃	—	4	2	no	—
548	C₂×C₂₃	—	8	1	no	—
549	C₂×C₂₃	—	8	2	no	—
550	C₂×C₂₃	C₂×#535	1	1	yes	characteristic
551	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
552	C₂×C₂₃	#3586	1	1	yes	characteristic
553	2₋¹⁺⁴	—	4	4	no	—
554	2₋¹⁺⁴	—	4	4	no	—
555	C₂×#41	—	2	4	no	—
556	C₂×#41	—	2	2	no	—
557	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
558	C₂×#41	C₂³×C₂₃	1	2	yes	—
559	C₂×#41	C₂³×C₂₃	1	4	yes	—
560	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
561	C₂²×Q₈	—	2	2	no	—
562	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
563	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
564	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
565	#137	—	4	4	no	—
566	#137	—	4	4	no	—
567	#135	—	4	4	no	—
568	C₂×Q₁₆	—	4	4	no	—
569	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
570	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
571	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
572	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
573	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
574	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
575	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
576	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
577	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
578	C₂×D₈	C₂³×C₂₃	1	2	yes	—
579	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
580	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
581	C₄⋊Q₈	—	2	1	no	—
582	C₄⋊Q₈	—	2	1	no	—
583	C₄⋊Q₈	—	2	1	no	—
584	C₄⋊Q₈	—	2	2	no	—
585	C₄⋊Q₈	—	2	1	no	—
586	C₄⋊Q₈	—	2	2	no	—
587	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
588	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
589	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
590	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
591	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
592	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
593	#127	C₂³×C₂₃	1	1	yes	characteristic
594	#126	—	2	2	no	—
595	#126	—	2	2	no	—
596	#126	—	2	2	no	—
597	#126	—	2	2	no	—
598	#125	—	2	2	no	—
599	#125	—	2	1	no	—
600	#125	—	2	2	no	—
601	#125	—	2	2	no	—
602	#125	C₂³×C₂₃	1	2	yes	—
603	#124	—	2	1	no	—
604	#124	—	2	2	no	—
605	#124	C₂³×C₂₃	1	2	yes	—
606	#124	C₂³×C₂₃	1	2	yes	—
607	#124	C₂³×C₂₃	1	4	yes	—
608	#123	—	2	2	no	—
609	#123	—	2	2	no	—
610	#123	—	2	2	no	—
611	#123	—	2	2	no	—
612	#123	—	2	4	no	—
613	#123	—	2	4	no	—
614	#123	—	2	4	no	—
615	C₂²⋊Q₈	—	2	1	no	—
616	C₂²⋊Q₈	—	2	2	no	—
617	C₂²⋊Q₈	—	2	1	no	—
618	C₂²⋊Q₈	—	2	1	no	—
619	C₂²⋊Q₈	—	2	2	no	—
620	C₂²⋊Q₈	—	2	2	no	—
621	C₂²⋊Q₈	—	2	4	no	—
622	C₂²⋊Q₈	—	2	2	no	—
623	C₂²⋊Q₈	—	2	4	no	—
624	C₂²⋊Q₈	—	2	2	no	—
625	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
626	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
627	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
628	#121	—	2	2	no	—
629	#121	—	2	1	no	—
630	#121	—	2	1	no	—
631	#121	—	2	2	no	—
632	#121	—	2	1	no	—
633	#121	—	2	2	no	—
634	#121	C₂³×C₂₃	1	2	yes	—
635	C₄×Q₈	—	2	1	no	—
636	C₄×Q₈	—	2	1	no	—
637	C₄×Q₈	—	2	2	no	—
638	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
639	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
640	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
641	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
642	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
643	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
644	C₄×D₄	—	2	1	no	—
645	C₄×D₄	—	2	1	no	—
646	C₄×D₄	—	2	2	no	—
647	C₄×D₄	—	2	1	no	—
648	C₄×D₄	—	2	2	no	—
649	C₄×D₄	—	2	1	no	—
650	C₄×D₄	—	2	2	no	—
651	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
652	C₄×D₄	D₄×C₂₃	1	2	yes	—
653	C₄×D₄	D₄×C₂₃	1	2	yes	—
654	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
655	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
656	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
657	#117	—	2	2	no	—
658	#117	—	2	1	no	—
659	#117	—	2	2	no	—
660	#117	C₂³×C₂₃	1	1	yes	characteristic
661	#117	C₂³×C₂₃	1	1	yes	characteristic
662	#117	C₂³×C₂₃	1	2	yes	—
663	C₂×C₄⋊C₄	—	2	1	no	—
664	C₂×C₄⋊C₄	—	2	1	no	—
665	C₂×C₄⋊C₄	—	2	2	no	—
666	C₂×C₄⋊C₄	—	2	1	no	—
667	C₂×C₄⋊C₄	—	2	2	no	—
668	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
669	C₂×C₄²	—	2	1	no	—
670	C₂×C₄²	—	2	1	no	—
671	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
672	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
673	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
674	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
675	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
676	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
677	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
678	#103	C₂³×C₂₃	1	4	yes	—
679	#103	C₂³×C₂₃	1	4	yes	—
680	#103	C₂³×C₂₃	1	2	yes	—
681	#103	C₂³×C₂₃	1	2	yes	—
682	#103	C₂³×C₂₃	1	4	yes	—
683	#103	C₂³×C₂₃	1	4	yes	—
684	#103	C₂³×C₂₃	1	4	yes	—
685	#102	C₂³×C₂₃	1	2	yes	—
686	#102	C₂³×C₂₃	1	2	yes	—
687	#102	C₂³×C₂₃	1	4	yes	—
688	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
689	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
690	#97	C₂³×C₂₃	1	4	yes	—
691	C₄×C₈	C₂³×C₂₃	1	4	yes	—
692	C₂₃	#60837	1	1	yes	characteristic, direct product factor, Sylow
693	#41	—	2	2	no	—
694	#41	—	2	2	no	—
695	#41	—	2	2	no	—
696	#41	—	2	4	no	—
697	#41	—	2	2	no	—
698	#41	—	2	4	no	—
699	#41	—	4	4	no	—
700	#41	—	4	4	no	—
701	#41	—	4	16	no	—
702	#41	—	4	8	no	—
703	C₂×Q₈	—	2	1	no	—
704	C₂×Q₈	—	2	4	no	—
705	C₂×Q₈	—	2	2	no	—
706	C₂×Q₈	—	2	2	no	—
707	C₂×Q₈	—	2	2	no	—
708	C₂×Q₈	—	2	4	no	—
709	C₂×Q₈	—	2	2	no	—
710	C₂×Q₈	—	2	4	no	—
711	C₂×Q₈	—	4	4	no	—
712	C₂×Q₈	—	4	4	no	—
713	C₂×Q₈	—	4	8	no	—
714	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
715	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
716	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
717	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
718	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
719	C₂×D₄	—	2	1	no	—
720	C₂×D₄	—	2	4	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	1	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
726	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
727	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
728	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
729	C₂²×C₄	—	2	1	no	—
730	C₂²×C₄	—	2	4	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	1	no	—
735	C₂²×C₄	—	2	4	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	1	no	—
738	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
739	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
740	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
741	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
744	Q₁₆	—	4	4	no	—
745	Q₁₆	—	4	4	no	—
746	Q₁₆	—	4	2	no	—
747	Q₁₆	—	4	4	no	—
748	Q₁₆	—	4	4	no	—
749	SD₁₆	—	4	2	no	—
750	SD₁₆	—	4	2	no	—
751	SD₁₆	—	4	4	no	—
752	SD₁₆	—	4	4	no	—
753	D₈	—	4	2	no	—
754	M₁₆	—	2	4	no	—
755	C₂×C₈	—	2	4	no	—
756	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
757	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
758	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	1	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	1	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	4	no	—
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	2	1	no	—
770	C₄⋊C₄	—	2	1	no	—
771	C₄⋊C₄	—	2	1	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
781	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
782	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
783	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
784	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
785	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
786	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	1	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	1	no	—
792	C₂²⋊C₄	—	2	1	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
801	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
802	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
803	C₄²	—	2	2	no	—
804	C₄²	—	2	1	no	—
805	C₄²	—	2	1	no	—
806	C₄²	—	2	1	no	—
807	C₄²	—	2	2	no	—
808	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
809	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
810	C₄²	C₂×D₄×C₂₃	1	2	yes	—
811	C₄²	C₂×D₄×C₂₃	1	2	yes	—
812	C₄²	C₂⁴×C₂₃	1	2	yes	—
813	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
814	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
815	C₂³	—	2	1	no	—
816	C₂³	—	2	2	no	—
817	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
818	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
819	Q₈	—	2	2	no	—
820	Q₈	—	2	2	no	—
821	Q₈	—	2	1	no	—
822	Q₈	—	2	4	no	—
823	Q₈	—	2	2	no	—
824	Q₈	—	2	2	no	—
825	Q₈	—	2	1	no	—
826	Q₈	—	2	4	no	—
827	Q₈	—	2	2	no	—
828	Q₈	—	4	8	no	—
829	Q₈	—	4	4	no	—
830	Q₈	—	4	2	no	—
831	Q₈	—	8	2	no	—
832	D₄	—	2	4	no	—
833	D₄	—	2	1	no	—
834	D₄	—	2	2	no	—
835	D₄	—	2	1	no	—
836	D₄	—	2	2	no	—
837	D₄	—	2	2	no	—
838	D₄	—	4	2	no	—
839	D₄	—	4	8	no	—
840	D₄	—	4	4	no	—
841	D₄	—	4	2	no	—
842	D₄	—	4	2	no	—
843	D₄	—	8	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	4	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	4	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	4	1	no	—
856	C₂×C₄	—	4	2	no	—
857	C₂×C₄	—	4	8	no	—
858	C₂×C₄	—	4	8	no	—
859	C₂×C₄	—	4	4	no	—
860	C₂×C₄	—	4	2	no	—
861	C₂×C₄	—	4	2	no	—
862	C₂×C₄	—	4	4	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	8	1	no	—
865	C₂×C₄	—	8	1	no	—
866	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
867	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
868	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
869	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
870	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
871	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
872	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
873	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
874	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
875	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
876	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
877	C₈	—	2	2	no	—
878	C₈	—	2	2	no	—
879	C₈	—	2	4	no	—
880	C₂²	—	2	1	no	—
881	C₂²	—	2	1	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	1	no	—
887	C₂²	—	4	1	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	4	1	no	—
890	C₂²	—	4	2	no	—
891	C₂²	C₂₃×#535	1	2	yes	—
892	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
893	C₄	—	2	2	no	—
894	C₄	—	2	1	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	1	no	—
897	C₄	—	2	1	no	—
898	C₄	—	2	2	no	—
899	C₄	—	4	4	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	1	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	1	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	1	no	—
906	C₄	C₂₃×#535	1	2	yes	—
907	C₄	C₂₃×#578	1	2	yes	—
908	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
909	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
910	C₂	—	2	2	no	—
911	C₂	—	4	2	no	—
912	C₂	—	8	2	no	—
913	C₂	—	8	1	no	—
914	C₂	C₂×C₂₃×#535	1	1	yes	characteristic
915	C₂	C₂×C₂₃×#578	1	1	yes	characteristic
916	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3499	C₂	semidirect
2. C₂₃×#3461	C₂	semidirect
3. C₂₃×#3225	C₂	semidirect
4. C₂₃×#3223	C₂	semidirect
5. C₂₃×#3218	C₂	semidirect
6. C₂₃×#3216	C₂	semidirect
7. C₂₃×#3212	C₂	semidirect
8. C₂₃×#3209	C₂	semidirect
9. C₂₃×#3156	C₂	semidirect
10. C₂₃×#3137	C₂	semidirect
11. C₂₃×#3039	C₂	semidirect
12. C₂₃×#3037	C₂	semidirect
13. C₂₃×#3035	C₂	semidirect
14. C₂×C₂₃×#462	C₂	semidirect
15. C₂₃×#3013	C₂	semidirect
16. C₂₃×#3011	C₂	semidirect
17. C₂₃×#2925	C₂	semidirect
356. #60837	C₂₃	direct (N × H)
422. #3499	C₂×C₂₃	semidirect
423. #3461	C₂×C₂₃	semidirect
424. #3225	C₂×C₂₃	semidirect
425. #3223	C₂×C₂₃	semidirect
426. #3218	C₂×C₂₃	semidirect
427. #3216	C₂×C₂₃	semidirect
428. #3212	C₂×C₂₃	semidirect
429. #3209	C₂×C₂₃	semidirect
430. #3156	C₂×C₂₃	semidirect
431. #3137	C₂×C₂₃	semidirect
432. #3039	C₂×C₂₃	semidirect
433. #3037	C₂×C₂₃	semidirect
434. #3035	C₂×C₂₃	semidirect
435. C₂×#462	C₂×C₂₃	semidirect
436. #3013	C₂×C₂₃	semidirect
437. #3011	C₂×C₂₃	semidirect
438. #2925	C₂×C₂₃	semidirect
692. C₂₃	#60837	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×#3499	2
C₂₃×#3461	2
C₂₃×#3225	2
C₂₃×#3223	2
C₂₃×#3218	2
C₂₃×#3216	2
C₂₃×#3212	2
C₂₃×#3209	2
C₂₃×#3156	2
C₂₃×#3137	2
C₂₃×#3039	2
C₂₃×#3037	2
C₂₃×#3035	2
C₂×C₂₃×#462	2
C₂₃×#3013	2
C₂₃×#3011	2
C₂₃×#2925	2
#60837	23

Subgroups — C23×#60837 #19208463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60837 #19208463