Subgroups — C₂₃×#61097 #19208723

Order 5888.

2654 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#578	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3497	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×Q₁₆×C₂₃	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3284	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3278	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3276	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3270	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3269	C₂	1	4	yes	maximal, complemented
10	C₂₃×#3152	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3063	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3013	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3011	C₂	1	2	yes	maximal, complemented
16	C₄×C₂₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2935	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	2	yes	—
19	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	2	yes	—
20	C₂₃×#578	—	2	16	no	—
21	C₂×C₂₃×#137	C₂²	1	4	yes	—
22	C₂×C₂₃×#137	C₂²	1	4	yes	—
23	C₂×C₂₃×#137	C₂²	1	2	yes	—
24	C₂×C₂₃×#137	C₂²	1	2	yes	—
25	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#135	C₂²	1	2	yes	—
27	C₂×C₂₃×#135	C₂²	1	4	yes	—
28	C₂²×Q₁₆×C₂₃	C₂²	1	2	yes	—
29	C₂²×Q₁₆×C₂₃	C₂²	1	4	yes	—
30	C₂×C₂₃×#131	C₂²	1	2	yes	—
31	C₂₃×#550	—	2	1	no	—
32	C₂₃×#550	C₂²	1	2	yes	—
33	D₄×Q₈×C₂₃	—	2	1	no	—
34	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
35	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
36	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
37	C₂₃×#548	—	2	2	no	—
38	C₂₃×#548	C₂²	1	4	yes	—
39	C₂₃×#547	—	2	2	no	—
40	C₂₃×#547	—	2	2	no	—
41	C₂₃×#547	C₂²	1	2	yes	—
42	C₂₃×#547	C₂²	1	2	yes	—
43	C₂₃×#537	—	2	2	no	—
44	C₂₃×#537	C₂²	1	2	yes	—
45	C₂₃×#536	—	2	2	no	—
46	C₂₃×#536	C₂²	1	2	yes	—
47	C₂₃×#532	—	2	1	no	—
48	C₂₃×#532	—	2	2	no	—
49	C₂₃×#532	C₂²	1	1	yes	characteristic
50	C₂₃×#532	C₂²	1	1	yes	characteristic
51	C₂×C₂₃×C₄⋊Q₈	—	2	1	no	—
52	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
53	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
54	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
55	C₂₃×#497	C₂²	1	4	yes	—
56	C₂₃×#494	C₂²	1	2	yes	—
57	C₂₃×#492	C₂²	1	2	yes	—
58	C₂₃×#470	C₂²	1	4	yes	—
59	C₂₃×#468	C₂²	1	4	yes	—
60	C₂₃×#467	C₂²	1	4	yes	—
61	C₂₃×#465	C₂²	1	4	yes	—
62	C₂₃×#464	C₂²	1	2	yes	—
63	C₂₃×#463	C₂²	1	2	yes	—
64	C₂₃×#462	C₂²	1	4	yes	—
65	C₂₃×#462	C₂²	1	2	yes	—
66	C₂₃×#462	C₂²	1	2	yes	—
67	C₂₃×#462	C₂²	1	1	yes	characteristic
68	C₂₃×#461	C₂²	1	1	yes	characteristic
69	C₂₃×#460	C₂²	1	1	yes	characteristic
70	C₂₃×#459	C₂²	1	1	yes	characteristic
71	C₂₃×#452	C₂²	1	4	yes	—
72	C₂₃×#452	C₂²	1	4	yes	—
73	C₂₃×#452	C₂²	1	4	yes	—
74	C₂₃×#451	C₂²	1	4	yes	—
75	C₂₃×#451	C₂²	1	4	yes	—
76	C₂₃×#451	C₂²	1	4	yes	—
77	C₂₃×#449	C₂²	1	4	yes	—
78	C₂₃×#448	C₂²	1	4	yes	—
79	C₂₃×#441	C₂²	1	2	yes	—
80	C₂₃×#440	C₂²	1	2	yes	—
81	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
82	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
83	C₂₃×#436	C₂²	1	2	yes	—
84	C₂₃×#435	C₂²	1	4	yes	—
85	C₈×D₄×C₂₃	C₂²	1	2	yes	—
86	C₂₃×#428	C₂²	1	1	yes	characteristic
87	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
88	C₂₃×#419	C₂²	1	1	yes	characteristic
89	C₂₃×#417	C₂²	1	1	yes	characteristic
90	C₂₃×#416	C₂²	1	2	yes	—
91	C₂×C₂₃×#103	C₂²	1	2	yes	—
92	C₂₃×#408	C₂²	1	2	yes	—
93	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
94	C₂₃×2₋¹⁺⁴	—	2	8	no	—
95	C₂₃×2₋¹⁺⁴	—	2	8	no	—
96	C₂₃×2₋¹⁺⁴	—	4	4	no	—
97	C₂₃×2₋¹⁺⁴	—	4	4	no	—
98	C₂×#41×C₂₃	—	2	4	no	—
99	C₂×#41×C₂₃	—	2	2	no	—
100	C₂×#41×C₂₃	—	2	2	no	—
101	C₂×#41×C₂₃	—	2	4	no	—
102	C₂×#41×C₂₃	C₂³	1	2	yes	—
103	C₂×#41×C₂₃	C₂³	1	4	yes	—
104	C₂×#41×C₂₃	C₂³	1	4	yes	—
105	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
106	C₂×#41×C₂₃	C₂³	1	2	yes	—
107	C₂²×Q₈×C₂₃	—	2	2	no	—
108	C₂²×Q₈×C₂₃	—	2	2	no	—
109	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
110	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
111	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
112	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
113	C₂₃×#137	—	2	16	no	—
114	C₂₃×#137	—	2	16	no	—
115	C₂₃×#137	—	2	8	no	—
116	C₂₃×#137	—	4	4	no	—
117	C₂₃×#137	D₄	1	8	yes	complemented
118	C₂₃×#135	—	2	8	no	—
119	C₂₃×#135	—	2	16	no	—
120	C₂×Q₁₆×C₂₃	—	2	8	no	—
121	C₂×Q₁₆×C₂₃	—	2	16	no	—
122	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
123	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
124	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
125	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
126	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
127	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
131	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
132	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
133	C₂×D₈×C₂₃	C₂³	1	2	yes	—
134	C₂₃×#131	—	2	8	no	—
135	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
136	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
137	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
138	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
139	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
140	C₂₃×C₄⋊Q₈	—	2	2	no	—
141	C₂₃×C₄⋊Q₈	—	2	2	no	—
142	C₂₃×C₄⋊Q₈	—	2	2	no	—
143	C₂₃×C₄⋊Q₈	—	2	2	no	—
144	C₂₃×C₄⋊Q₈	—	2	1	no	—
145	C₂₃×C₄⋊Q₈	—	2	1	no	—
146	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
147	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
148	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
149	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
150	C₂₃×#127	—	2	2	no	—
151	C₂₃×#127	D₄	1	1	yes	characteristic
152	C₂₃×#127	C₂³	1	1	yes	characteristic
153	C₂₃×#124	—	2	2	no	—
154	C₂₃×#124	—	2	4	no	—
155	C₂₃×#124	D₄	1	2	yes	—
156	C₂₃×#124	C₂³	1	2	yes	—
157	C₂₃×#123	—	2	4	no	—
158	C₂₃×#123	—	2	4	no	—
159	C₂₃×#123	—	2	4	no	—
160	C₂₃×C₂²⋊Q₈	—	2	2	no	—
161	C₂₃×C₂²⋊Q₈	—	2	4	no	—
162	C₂₃×C₂²⋊Q₈	—	2	4	no	—
163	C₂₃×C₂²⋊Q₈	—	2	4	no	—
164	C₂₃×C₂²⋊Q₈	—	2	4	no	—
165	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
166	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
167	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
168	C₂₃×#121	—	2	2	no	—
169	C₂₃×#121	—	2	2	no	—
170	C₂₃×#121	—	2	2	no	—
171	C₂₃×#121	—	2	4	no	—
172	C₂₃×#121	—	2	4	no	—
173	C₂₃×#121	—	2	1	no	—
174	C₂₃×#121	—	2	1	no	—
175	C₂₃×#121	—	2	4	no	—
176	C₂₃×#121	D₄	1	2	yes	—
177	C₂₃×#121	D₄	1	2	yes	—
178	C₂₃×#121	C₂³	1	4	yes	—
179	C₄×Q₈×C₂₃	—	2	1	no	—
180	C₄×Q₈×C₂₃	—	2	1	no	—
181	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
182	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
183	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
184	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
185	C₄×D₄×C₂₃	—	2	2	no	—
186	C₄×D₄×C₂₃	—	2	2	no	—
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	—	2	4	no	—
192	C₄×D₄×C₂₃	—	2	1	no	—
193	C₄×D₄×C₂₃	—	2	1	no	—
194	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
195	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
196	C₄×D₄×C₂₃	C₂³	1	2	yes	—
197	C₄×D₄×C₂₃	C₂³	1	2	yes	—
198	C₂₃×#117	—	2	1	no	—
199	C₂₃×#117	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
201	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
202	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
203	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
204	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
205	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₂₃	—	2	1	no	—
207	C₂×C₄²×C₂₃	—	2	1	no	—
208	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
209	C₂₃×#107	C₂³	1	2	yes	—
210	C₂₃×#106	C₂³	1	2	yes	—
211	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
212	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₂₃×#103	C₂³	1	4	yes	—
215	C₂₃×#103	C₂³	1	4	yes	—
216	C₂₃×#103	C₂³	1	2	yes	—
217	C₂₃×#103	C₂³	1	2	yes	—
218	C₂₃×#103	C₂³	1	2	yes	—
219	C₂₃×#103	C₂³	1	2	yes	—
220	C₂₃×#103	C₂³	1	2	yes	—
221	C₂₃×#102	C₂³	1	2	yes	—
222	C₂₃×#102	C₂³	1	2	yes	—
223	C₂₃×#102	C₂³	1	2	yes	—
224	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
225	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₂₃×#97	C₂³	1	2	yes	—
227	C₄×C₈×C₂₃	C₂³	1	2	yes	—
228	#41×C₂₃	—	2	4	no	—
229	#41×C₂₃	—	2	2	no	—
230	#41×C₂₃	—	2	4	no	—
231	#41×C₂₃	—	2	8	no	—
232	#41×C₂₃	—	2	8	no	—
233	#41×C₂₃	—	2	4	no	—
234	#41×C₂₃	—	2	4	no	—
235	#41×C₂₃	—	4	4	no	—
236	#41×C₂₃	—	4	4	no	—
237	#41×C₂₃	—	4	16	no	—
238	#41×C₂₃	—	4	8	no	—
239	#41×C₂₃	—	4	16	no	—
240	#41×C₂₃	—	4	8	no	—
241	#41×C₂₃	C₂×D₄	1	4	yes	—
242	C₂×Q₈×C₂₃	—	2	1	no	—
243	C₂×Q₈×C₂₃	—	2	4	no	—
244	C₂×Q₈×C₂₃	—	2	4	no	—
245	C₂×Q₈×C₂₃	—	2	2	no	—
246	C₂×Q₈×C₂₃	—	2	2	no	—
247	C₂×Q₈×C₂₃	—	2	8	no	—
248	C₂×Q₈×C₂₃	—	2	8	no	—
249	C₂×Q₈×C₂₃	—	2	4	no	—
250	C₂×Q₈×C₂₃	—	2	4	no	—
251	C₂×Q₈×C₂₃	—	4	4	no	—
252	C₂×Q₈×C₂₃	—	4	4	no	—
253	C₂×Q₈×C₂₃	—	4	8	no	—
254	C₂×Q₈×C₂₃	—	4	8	no	—
255	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
256	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
257	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
258	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
259	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
260	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
261	C₂×D₄×C₂₃	—	2	1	no	—
262	C₂×D₄×C₂₃	—	2	2	no	—
263	C₂×D₄×C₂₃	—	2	4	no	—
264	C₂×D₄×C₂₃	—	2	4	no	—
265	C₂×D₄×C₂₃	—	2	4	no	—
266	C₂×D₄×C₂₃	—	2	1	no	—
267	C₂×D₄×C₂₃	—	2	1	no	—
268	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
269	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
270	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
271	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
272	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
273	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
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	4	no	—
278	C₂²×C₄×C₂₃	—	2	4	no	—
279	C₂²×C₄×C₂₃	—	2	1	no	—
280	C₂²×C₄×C₂₃	—	2	1	no	—
281	C₂²×C₄×C₂₃	—	2	1	no	—
282	C₂²×C₄×C₂₃	—	2	4	no	—
283	C₂²×C₄×C₂₃	—	2	4	no	—
284	C₂²×C₄×C₂₃	—	2	2	no	—
285	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
288	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
289	Q₁₆×C₂₃	—	2	4	no	—
290	Q₁₆×C₂₃	—	2	8	no	—
291	Q₁₆×C₂₃	—	2	8	no	—
292	Q₁₆×C₂₃	—	2	8	no	—
293	Q₁₆×C₂₃	—	4	4	no	—
294	Q₁₆×C₂₃	C₂×D₄	1	8	yes	—
295	SD₁₆×C₂₃	—	2	4	no	—
296	SD₁₆×C₂₃	—	2	4	no	—
297	SD₁₆×C₂₃	—	2	8	no	—
298	SD₁₆×C₂₃	—	4	4	no	—
299	SD₁₆×C₂₃	C₂×D₄	1	8	yes	—
300	D₈×C₂₃	—	2	4	no	—
301	M₁₆×C₂₃	—	2	2	no	—
302	M₁₆×C₂₃	—	2	8	no	—
303	M₁₆×C₂₃	C₂×D₄	1	4	yes	—
304	C₂×C₈×C₂₃	—	2	4	no	—
305	C₂×C₈×C₂₃	—	2	8	no	—
306	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
307	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
308	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
309	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
310	C₄⋊C₄×C₂₃	—	2	2	no	—
311	C₄⋊C₄×C₂₃	—	2	2	no	—
312	C₄⋊C₄×C₂₃	—	2	2	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	4	no	—
317	C₄⋊C₄×C₂₃	—	2	4	no	—
318	C₄⋊C₄×C₂₃	—	2	1	no	—
319	C₄⋊C₄×C₂₃	—	2	1	no	—
320	C₄⋊C₄×C₂₃	—	2	1	no	—
321	C₄⋊C₄×C₂₃	—	2	1	no	—
322	C₄⋊C₄×C₂₃	—	2	1	no	—
323	C₄⋊C₄×C₂₃	—	2	4	no	—
324	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
325	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
326	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
327	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
328	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
329	C₂²⋊C₄×C₂₃	—	2	1	no	—
330	C₂²⋊C₄×C₂₃	—	2	4	no	—
331	C₂²⋊C₄×C₂₃	—	2	4	no	—
332	C₂²⋊C₄×C₂₃	—	2	4	no	—
333	C₂²⋊C₄×C₂₃	—	2	1	no	—
334	C₂²⋊C₄×C₂₃	—	2	1	no	—
335	C₂²⋊C₄×C₂₃	—	2	2	no	—
336	C₂²⋊C₄×C₂₃	—	2	2	no	—
337	C₂²⋊C₄×C₂₃	—	2	4	no	—
338	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
339	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
340	C₄²×C₂₃	—	2	1	no	—
341	C₄²×C₂₃	—	2	1	no	—
342	C₄²×C₂₃	—	2	1	no	—
343	C₄²×C₂₃	—	2	2	no	—
344	C₄²×C₂₃	—	2	2	no	—
345	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
346	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
347	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
348	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
349	#61097	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
350	C₂³×C₂₃	—	2	1	no	—
351	C₂³×C₂₃	—	2	2	no	—
352	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
353	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
354	Q₈×C₂₃	—	2	4	no	—
355	Q₈×C₂₃	—	2	4	no	—
356	Q₈×C₂₃	—	2	2	no	—
357	Q₈×C₂₃	—	2	1	no	—
358	Q₈×C₂₃	—	2	2	no	—
359	Q₈×C₂₃	—	2	4	no	—
360	Q₈×C₂₃	—	2	4	no	—
361	Q₈×C₂₃	—	2	2	no	—
362	Q₈×C₂₃	—	4	8	no	—
363	Q₈×C₂₃	—	4	8	no	—
364	Q₈×C₂₃	—	4	4	no	—
365	Q₈×C₂₃	C₂²×D₄	1	2	yes	—
366	Q₈×C₂₃	C₂²×D₄	1	4	yes	—
367	D₄×C₂₃	—	2	4	no	—
368	D₄×C₂₃	—	2	8	no	—
369	D₄×C₂₃	—	2	4	no	—
370	D₄×C₂₃	—	2	4	no	—
371	D₄×C₂₃	—	2	2	no	—
372	D₄×C₂₃	—	2	1	no	—
373	D₄×C₂₃	—	2	2	no	—
374	D₄×C₂₃	—	4	2	no	—
375	D₄×C₂₃	—	4	8	no	—
376	D₄×C₂₃	—	4	8	no	—
377	D₄×C₂₃	—	4	4	no	—
378	D₄×C₂₃	—	4	2	no	—
379	D₄×C₂₃	—	8	1	no	—
380	D₄×C₂₃	—	8	4	no	—
381	D₄×C₂₃	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₂₃	—	2	4	no	—
383	C₂×C₄×C₂₃	—	2	2	no	—
384	C₂×C₄×C₂₃	—	2	1	no	—
385	C₂×C₄×C₂₃	—	2	4	no	—
386	C₂×C₄×C₂₃	—	2	2	no	—
387	C₂×C₄×C₂₃	—	2	4	no	—
388	C₂×C₄×C₂₃	—	2	4	no	—
389	C₂×C₄×C₂₃	—	2	1	no	—
390	C₂×C₄×C₂₃	—	2	1	no	—
391	C₂×C₄×C₂₃	—	2	2	no	—
392	C₂×C₄×C₂₃	—	2	2	no	—
393	C₂×C₄×C₂₃	—	2	4	no	—
394	C₂×C₄×C₂₃	—	4	1	no	—
395	C₂×C₄×C₂₃	—	4	8	no	—
396	C₂×C₄×C₂₃	—	4	8	no	—
397	C₂×C₄×C₂₃	—	4	8	no	—
398	C₂×C₄×C₂₃	—	4	8	no	—
399	C₂×C₄×C₂₃	—	4	2	no	—
400	C₂×C₄×C₂₃	—	4	4	no	—
401	C₂×C₄×C₂₃	—	4	4	no	—
402	C₂×C₄×C₂₃	—	4	2	no	—
403	C₂×C₄×C₂₃	—	8	1	no	—
404	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
408	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
410	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
412	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
413	C₈×C₂₃	—	2	2	no	—
414	C₈×C₂₃	—	2	2	no	—
415	C₈×C₂₃	—	2	2	no	—
416	C₈×C₂₃	C₂²×D₄	1	4	yes	—
417	C₂×#578	C₂×C₂₃	1	2	yes	complemented
418	#3499	C₂×C₂₃	1	1	yes	characteristic, complemented
419	#3497	C₂×C₂₃	1	1	yes	characteristic, complemented
420	D₄×Q₁₆	C₂×C₂₃	1	2	yes	complemented
421	#3284	C₂×C₂₃	1	2	yes	complemented
422	#3278	C₂×C₂₃	1	2	yes	complemented
423	#3276	C₂×C₂₃	1	2	yes	complemented
424	#3270	C₂×C₂₃	1	4	yes	complemented
425	#3269	C₂×C₂₃	1	4	yes	complemented
426	#3152	C₂×C₂₃	1	1	yes	characteristic, complemented
427	#3063	C₂×C₂₃	1	2	yes	complemented
428	#3035	C₂×C₂₃	1	1	yes	characteristic, complemented
429	C₂×#462	C₂×C₂₃	1	1	yes	characteristic, complemented
430	#3013	C₂×C₂₃	1	2	yes	complemented
431	#3011	C₂×C₂₃	1	2	yes	complemented
432	C₄×#137	C₂×C₂₃	1	1	yes	characteristic, complemented
433	#2935	C₂×C₂₃	1	1	yes	characteristic, complemented
434	C₂²×C₂₃	—	2	1	no	—
435	C₂²×C₂₃	—	2	1	no	—
436	C₂²×C₂₃	—	2	4	no	—
437	C₂²×C₂₃	—	2	4	no	—
438	C₂²×C₂₃	—	2	2	no	—
439	C₂²×C₂₃	—	2	4	no	—
440	C₂²×C₂₃	—	4	1	no	—
441	C₂²×C₂₃	—	4	1	no	—
442	C₂²×C₂₃	—	4	2	no	—
443	C₂²×C₂₃	—	4	2	no	—
444	C₂²×C₂₃	—	4	2	no	—
445	C₂²×C₂₃	D₄²	1	2	yes	—
446	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
447	C₄×C₂₃	—	2	1	no	—
448	C₄×C₂₃	—	2	1	no	—
449	C₄×C₂₃	—	2	2	no	—
450	C₄×C₂₃	—	2	4	no	—
451	C₄×C₂₃	—	2	4	no	—
452	C₄×C₂₃	—	2	1	no	—
453	C₄×C₂₃	—	4	1	no	—
454	C₄×C₂₃	—	4	2	no	—
455	C₄×C₂₃	—	4	2	no	—
456	C₄×C₂₃	—	4	4	no	—
457	C₄×C₂₃	—	4	1	no	—
458	C₄×C₂₃	D₄²	1	2	yes	—
459	C₄×C₂₃	#578	1	2	yes	complemented
460	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
461	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
462	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	2	yes	—
463	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	2	yes	—
464	#578	—	2	16	no	—
465	C₂×#137	C₂²×C₂₃	1	2	yes	—
466	C₂×#137	C₂²×C₂₃	1	4	yes	—
467	C₂×#137	C₂²×C₂₃	1	4	yes	—
468	C₂×#137	C₂²×C₂₃	1	2	yes	—
469	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
470	C₂×#135	C₂²×C₂₃	1	2	yes	—
471	C₂×#135	C₂²×C₂₃	1	4	yes	—
472	C₂²×Q₁₆	C₂²×C₂₃	1	2	yes	—
473	C₂²×Q₁₆	C₂²×C₂₃	1	4	yes	—
474	C₂×#131	C₂²×C₂₃	1	2	yes	—
475	#550	—	2	1	no	—
476	#550	C₂²×C₂₃	1	2	yes	—
477	D₄×Q₈	—	2	1	no	—
478	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
479	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
480	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
481	#548	—	2	2	no	—
482	#548	C₂²×C₂₃	1	4	yes	—
483	#547	—	2	2	no	—
484	#547	—	2	2	no	—
485	#547	C₂²×C₂₃	1	2	yes	—
486	#547	C₂²×C₂₃	1	2	yes	—
487	#537	—	2	2	no	—
488	#537	C₂²×C₂₃	1	2	yes	—
489	#536	—	2	2	no	—
490	#536	C₂²×C₂₃	1	2	yes	—
491	#532	—	2	1	no	—
492	#532	—	2	2	no	—
493	#532	C₂²×C₂₃	1	1	yes	characteristic
494	#532	C₂²×C₂₃	1	1	yes	characteristic
495	C₂×C₄⋊Q₈	—	2	1	no	—
496	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
497	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
498	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
499	#497	C₂²×C₂₃	1	4	yes	—
500	#494	C₂²×C₂₃	1	2	yes	—
501	#492	C₂²×C₂₃	1	2	yes	—
502	#470	C₂²×C₂₃	1	4	yes	—
503	#468	C₂²×C₂₃	1	4	yes	—
504	#467	C₂²×C₂₃	1	4	yes	—
505	#465	C₂²×C₂₃	1	4	yes	—
506	#464	C₂²×C₂₃	1	2	yes	—
507	#463	C₂²×C₂₃	1	2	yes	—
508	#462	C₂²×C₂₃	1	4	yes	—
509	#462	C₂²×C₂₃	1	2	yes	—
510	#462	C₂²×C₂₃	1	2	yes	—
511	#462	C₂²×C₂₃	1	1	yes	characteristic
512	#461	C₂²×C₂₃	1	1	yes	characteristic
513	#460	C₂²×C₂₃	1	1	yes	characteristic
514	#459	C₂²×C₂₃	1	1	yes	characteristic
515	#452	C₂²×C₂₃	1	4	yes	—
516	#452	C₂²×C₂₃	1	4	yes	—
517	#452	C₂²×C₂₃	1	4	yes	—
518	#451	C₂²×C₂₃	1	4	yes	—
519	#451	C₂²×C₂₃	1	4	yes	—
520	#451	C₂²×C₂₃	1	4	yes	—
521	#449	C₂²×C₂₃	1	4	yes	—
522	#448	C₂²×C₂₃	1	4	yes	—
523	#441	C₂²×C₂₃	1	2	yes	—
524	#440	C₂²×C₂₃	1	2	yes	—
525	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
526	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
527	#436	C₂²×C₂₃	1	2	yes	—
528	#435	C₂²×C₂₃	1	4	yes	—
529	C₈×D₄	C₂²×C₂₃	1	2	yes	—
530	#428	C₂²×C₂₃	1	1	yes	characteristic
531	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
532	#419	C₂²×C₂₃	1	1	yes	characteristic
533	#417	C₂²×C₂₃	1	1	yes	characteristic
534	#416	C₂²×C₂₃	1	2	yes	—
535	C₂×#103	C₂²×C₂₃	1	2	yes	—
536	#408	C₂²×C₂₃	1	2	yes	—
537	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
538	C₂×C₂₃	—	2	2	no	—
539	C₂×C₂₃	—	4	4	no	—
540	C₂×C₂₃	—	4	2	no	—
541	C₂×C₂₃	—	8	2	no	—
542	C₂×C₂₃	C₂×D₄²	1	1	yes	characteristic
543	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
544	C₂×C₂₃	#3586	1	1	yes	characteristic
545	2₋¹⁺⁴	—	2	8	no	—
546	2₋¹⁺⁴	—	2	8	no	—
547	2₋¹⁺⁴	—	4	4	no	—
548	2₋¹⁺⁴	—	4	4	no	—
549	C₂×#41	—	2	2	no	—
550	C₂×#41	—	2	4	no	—
551	C₂×#41	—	2	4	no	—
552	C₂×#41	—	2	2	no	—
553	C₂×#41	C₂³×C₂₃	1	2	yes	—
554	C₂×#41	C₂³×C₂₃	1	4	yes	—
555	C₂×#41	C₂³×C₂₃	1	4	yes	—
556	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
557	C₂×#41	C₂³×C₂₃	1	2	yes	—
558	C₂²×Q₈	—	2	2	no	—
559	C₂²×Q₈	—	2	2	no	—
560	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
561	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
562	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
563	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
564	#137	—	2	16	no	—
565	#137	—	2	16	no	—
566	#137	—	2	8	no	—
567	#137	—	4	4	no	—
568	#137	D₄×C₂₃	1	8	yes	complemented
569	#135	—	2	8	no	—
570	#135	—	2	16	no	—
571	C₂×Q₁₆	—	2	8	no	—
572	C₂×Q₁₆	—	2	16	no	—
573	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
574	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
575	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
576	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
577	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
578	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
579	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
580	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
581	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
582	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
583	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
584	C₂×D₈	C₂³×C₂₃	1	2	yes	—
585	#131	—	2	8	no	—
586	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
587	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
588	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
589	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
590	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
591	C₄⋊Q₈	—	2	2	no	—
592	C₄⋊Q₈	—	2	2	no	—
593	C₄⋊Q₈	—	2	2	no	—
594	C₄⋊Q₈	—	2	2	no	—
595	C₄⋊Q₈	—	2	1	no	—
596	C₄⋊Q₈	—	2	1	no	—
597	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
598	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
599	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
600	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
601	#127	—	2	2	no	—
602	#127	D₄×C₂₃	1	1	yes	characteristic
603	#127	C₂³×C₂₃	1	1	yes	characteristic
604	#124	—	2	2	no	—
605	#124	—	2	4	no	—
606	#124	D₄×C₂₃	1	2	yes	—
607	#124	C₂³×C₂₃	1	2	yes	—
608	#123	—	2	4	no	—
609	#123	—	2	4	no	—
610	#123	—	2	4	no	—
611	C₂²⋊Q₈	—	2	2	no	—
612	C₂²⋊Q₈	—	2	4	no	—
613	C₂²⋊Q₈	—	2	4	no	—
614	C₂²⋊Q₈	—	2	4	no	—
615	C₂²⋊Q₈	—	2	4	no	—
616	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
617	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
618	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
619	#121	—	2	4	no	—
620	#121	—	2	2	no	—
621	#121	—	2	2	no	—
622	#121	—	2	4	no	—
623	#121	—	2	2	no	—
624	#121	—	2	1	no	—
625	#121	—	2	1	no	—
626	#121	—	2	4	no	—
627	#121	D₄×C₂₃	1	2	yes	—
628	#121	D₄×C₂₃	1	2	yes	—
629	#121	C₂³×C₂₃	1	4	yes	—
630	C₄×Q₈	—	2	1	no	—
631	C₄×Q₈	—	2	1	no	—
632	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
633	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
634	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
635	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	—	2	2	no	—
639	C₄×D₄	—	2	1	no	—
640	C₄×D₄	—	2	1	no	—
641	C₄×D₄	—	2	2	no	—
642	C₄×D₄	—	2	4	no	—
643	C₄×D₄	—	2	1	no	—
644	C₄×D₄	—	2	1	no	—
645	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
646	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
647	C₄×D₄	C₂³×C₂₃	1	2	yes	—
648	C₄×D₄	C₂³×C₂₃	1	2	yes	—
649	#117	—	2	1	no	—
650	#117	C₂³×C₂₃	1	1	yes	characteristic
651	C₂×C₄⋊C₄	—	2	1	no	—
652	C₂×C₄⋊C₄	—	2	1	no	—
653	C₂×C₄⋊C₄	—	2	1	no	—
654	C₂×C₄⋊C₄	—	2	2	no	—
655	C₂×C₄⋊C₄	—	2	2	no	—
656	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
657	C₂×C₄²	—	2	1	no	—
658	C₂×C₄²	—	2	1	no	—
659	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
660	#107	C₂³×C₂₃	1	2	yes	—
661	#106	C₂³×C₂₃	1	2	yes	—
662	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
663	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
664	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
665	#103	C₂³×C₂₃	1	4	yes	—
666	#103	C₂³×C₂₃	1	4	yes	—
667	#103	C₂³×C₂₃	1	2	yes	—
668	#103	C₂³×C₂₃	1	2	yes	—
669	#103	C₂³×C₂₃	1	2	yes	—
670	#103	C₂³×C₂₃	1	2	yes	—
671	#103	C₂³×C₂₃	1	2	yes	—
672	#102	C₂³×C₂₃	1	2	yes	—
673	#102	C₂³×C₂₃	1	2	yes	—
674	#102	C₂³×C₂₃	1	2	yes	—
675	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
676	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
677	#97	C₂³×C₂₃	1	2	yes	—
678	C₄×C₈	C₂³×C₂₃	1	2	yes	—
679	C₂₃	#61097	1	1	yes	characteristic, direct product factor, Sylow
680	#41	—	2	4	no	—
681	#41	—	2	4	no	—
682	#41	—	2	2	no	—
683	#41	—	2	8	no	—
684	#41	—	2	8	no	—
685	#41	—	2	4	no	—
686	#41	—	2	4	no	—
687	#41	—	4	4	no	—
688	#41	—	4	4	no	—
689	#41	—	4	16	no	—
690	#41	—	4	8	no	—
691	#41	—	4	16	no	—
692	#41	—	4	8	no	—
693	#41	C₂×D₄×C₂₃	1	4	yes	—
694	C₂×Q₈	—	2	1	no	—
695	C₂×Q₈	—	2	4	no	—
696	C₂×Q₈	—	2	4	no	—
697	C₂×Q₈	—	2	2	no	—
698	C₂×Q₈	—	2	2	no	—
699	C₂×Q₈	—	2	8	no	—
700	C₂×Q₈	—	2	8	no	—
701	C₂×Q₈	—	2	4	no	—
702	C₂×Q₈	—	2	4	no	—
703	C₂×Q₈	—	4	4	no	—
704	C₂×Q₈	—	4	4	no	—
705	C₂×Q₈	—	4	8	no	—
706	C₂×Q₈	—	4	8	no	—
707	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
708	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
709	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
710	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
711	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
712	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
713	C₂×D₄	—	2	1	no	—
714	C₂×D₄	—	2	2	no	—
715	C₂×D₄	—	2	4	no	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	2	4	no	—
718	C₂×D₄	—	2	1	no	—
719	C₂×D₄	—	2	1	no	—
720	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
721	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
722	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
723	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
724	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
725	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
726	C₂²×C₄	—	2	1	no	—
727	C₂²×C₄	—	2	1	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	4	no	—
730	C₂²×C₄	—	2	4	no	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	4	no	—
735	C₂²×C₄	—	2	4	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
738	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
740	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
741	Q₁₆	—	2	4	no	—
742	Q₁₆	—	2	8	no	—
743	Q₁₆	—	2	8	no	—
744	Q₁₆	—	2	8	no	—
745	Q₁₆	—	4	4	no	—
746	Q₁₆	C₂×D₄×C₂₃	1	8	yes	—
747	SD₁₆	—	2	4	no	—
748	SD₁₆	—	2	4	no	—
749	SD₁₆	—	2	8	no	—
750	SD₁₆	—	4	4	no	—
751	SD₁₆	C₂×D₄×C₂₃	1	8	yes	—
752	D₈	—	2	4	no	—
753	M₁₆	—	2	2	no	—
754	M₁₆	—	2	8	no	—
755	M₁₆	C₂×D₄×C₂₃	1	4	yes	—
756	C₂×C₈	—	2	4	no	—
757	C₂×C₈	—	2	8	no	—
758	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
759	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
760	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
761	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
762	C₄⋊C₄	—	2	2	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	2	no	—
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	2	4	no	—
770	C₄⋊C₄	—	2	1	no	—
771	C₄⋊C₄	—	2	1	no	—
772	C₄⋊C₄	—	2	1	no	—
773	C₄⋊C₄	—	2	1	no	—
774	C₄⋊C₄	—	2	1	no	—
775	C₄⋊C₄	—	2	4	no	—
776	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
777	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
778	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
779	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
780	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
781	C₂²⋊C₄	—	2	1	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	4	no	—
784	C₂²⋊C₄	—	2	4	no	—
785	C₂²⋊C₄	—	2	1	no	—
786	C₂²⋊C₄	—	2	1	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	4	no	—
790	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
791	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
792	C₄²	—	2	1	no	—
793	C₄²	—	2	1	no	—
794	C₄²	—	2	1	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	2	no	—
797	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
798	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
799	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
800	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
801	C₂³	—	2	1	no	—
802	C₂³	—	2	2	no	—
803	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
804	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
805	Q₈	—	2	2	no	—
806	Q₈	—	2	1	no	—
807	Q₈	—	2	4	no	—
808	Q₈	—	2	4	no	—
809	Q₈	—	2	2	no	—
810	Q₈	—	2	4	no	—
811	Q₈	—	2	4	no	—
812	Q₈	—	2	2	no	—
813	Q₈	—	4	8	no	—
814	Q₈	—	4	8	no	—
815	Q₈	—	4	4	no	—
816	Q₈	C₂²×D₄×C₂₃	1	2	yes	—
817	Q₈	C₂²×D₄×C₂₃	1	4	yes	—
818	D₄	—	2	4	no	—
819	D₄	—	2	8	no	—
820	D₄	—	2	4	no	—
821	D₄	—	2	2	no	—
822	D₄	—	2	1	no	—
823	D₄	—	2	2	no	—
824	D₄	—	2	4	no	—
825	D₄	—	4	2	no	—
826	D₄	—	4	8	no	—
827	D₄	—	4	8	no	—
828	D₄	—	4	4	no	—
829	D₄	—	4	2	no	—
830	D₄	—	8	1	no	—
831	D₄	—	8	4	no	—
832	D₄	C₂²×D₄×C₂₃	1	2	yes	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	4	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	4	no	—
838	C₂×C₄	—	2	4	no	—
839	C₂×C₄	—	2	4	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	4	no	—
845	C₂×C₄	—	4	1	no	—
846	C₂×C₄	—	4	8	no	—
847	C₂×C₄	—	4	8	no	—
848	C₂×C₄	—	4	8	no	—
849	C₂×C₄	—	4	8	no	—
850	C₂×C₄	—	4	2	no	—
851	C₂×C₄	—	4	4	no	—
852	C₂×C₄	—	4	2	no	—
853	C₂×C₄	—	4	4	no	—
854	C₂×C₄	—	8	1	no	—
855	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
856	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
857	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
858	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
859	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
860	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
861	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
862	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
863	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
864	C₈	—	2	2	no	—
865	C₈	—	2	2	no	—
866	C₈	—	2	2	no	—
867	C₈	C₂²×D₄×C₂₃	1	4	yes	—
868	C₂²	—	2	1	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	4	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	2	4	no	—
873	C₂²	—	2	4	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	4	1	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	D₄²×C₂₃	1	2	yes	—
880	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
881	C₄	—	2	2	no	—
882	C₄	—	2	4	no	—
883	C₄	—	2	4	no	—
884	C₄	—	2	1	no	—
885	C₄	—	2	1	no	—
886	C₄	—	2	1	no	—
887	C₄	—	4	2	no	—
888	C₄	—	4	4	no	—
889	C₄	—	4	1	no	—
890	C₄	—	4	1	no	—
891	C₄	—	4	2	no	—
892	C₄	D₄²×C₂₃	1	2	yes	—
893	C₄	C₂₃×#578	1	2	yes	complemented
894	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
895	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
896	C₂	—	2	2	no	—
897	C₂	—	4	4	no	—
898	C₂	—	4	2	no	—
899	C₂	—	8	2	no	—
900	C₂	C₂×D₄²×C₂₃	1	1	yes	characteristic
901	C₂	C₂×C₂₃×#578	1	1	yes	characteristic
902	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 ◁ C₂₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#578	C₂	semidirect
2. C₂₃×#3499	C₂	semidirect
3. C₂₃×#3497	C₂	semidirect
4. D₄×Q₁₆×C₂₃	C₂	semidirect
5. C₂₃×#3284	C₂	semidirect
6. C₂₃×#3278	C₂	semidirect
7. C₂₃×#3276	C₂	semidirect
8. C₂₃×#3270	C₂	semidirect
9. C₂₃×#3269	C₂	semidirect
10. C₂₃×#3152	C₂	semidirect
11. C₂₃×#3063	C₂	semidirect
12. C₂₃×#3035	C₂	semidirect
13. C₂×C₂₃×#462	C₂	semidirect
14. C₂₃×#3013	C₂	semidirect
15. C₂₃×#3011	C₂	semidirect
16. C₄×C₂₃×#137	C₂	semidirect
17. C₂₃×#2935	C₂	semidirect
117. C₂₃×#137	D₄	semidirect
349. #61097	C₂₃	direct (N × H)
417. C₂×#578	C₂×C₂₃	semidirect
418. #3499	C₂×C₂₃	semidirect
419. #3497	C₂×C₂₃	semidirect
420. D₄×Q₁₆	C₂×C₂₃	semidirect
421. #3284	C₂×C₂₃	semidirect
422. #3278	C₂×C₂₃	semidirect
423. #3276	C₂×C₂₃	semidirect
424. #3270	C₂×C₂₃	semidirect
425. #3269	C₂×C₂₃	semidirect
426. #3152	C₂×C₂₃	semidirect
427. #3063	C₂×C₂₃	semidirect
428. #3035	C₂×C₂₃	semidirect
429. C₂×#462	C₂×C₂₃	semidirect
430. #3013	C₂×C₂₃	semidirect
431. #3011	C₂×C₂₃	semidirect
432. C₄×#137	C₂×C₂₃	semidirect
433. #2935	C₂×C₂₃	semidirect
459. C₄×C₂₃	#578	semidirect
568. #137	D₄×C₂₃	semidirect
679. C₂₃	#61097	direct (N × H)
893. C₄	C₂₃×#578	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#578	2
C₂₃×#3499	2
C₂₃×#3497	2
D₄×Q₁₆×C₂₃	2
C₂₃×#3284	2
C₂₃×#3278	2
C₂₃×#3276	2
C₂₃×#3270	2
C₂₃×#3269	2
C₂₃×#3152	2
C₂₃×#3063	2
C₂₃×#3035	2
C₂×C₂₃×#462	2
C₂₃×#3013	2
C₂₃×#3011	2
C₄×C₂₃×#137	2
C₂₃×#2935	2
#61097	23

Subgroups — C23×#61097 #19208723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61097 #19208723