Subgroups — C₂₃×#61095 #19208721

Order 5888.

2790 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#577	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3497	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3287	C₂	1	2	yes	maximal, complemented
5	D₄×SD₁₆×C₂₃	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3278	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3274	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3271	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3265	C₂	1	4	yes	maximal, complemented
10	C₂₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3062	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3012	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3010	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	complemented
19	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	2	yes	—
20	C₂₃×#577	—	2	16	no	—
21	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#137	C₂²	1	4	yes	complemented
23	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
24	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
25	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
26	C₂×C₂₃×#135	C₂²	1	2	yes	—
27	C₂×C₂₃×#135	C₂²	1	4	yes	complemented
28	C₂²×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
29	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
30	C₂×C₂₃×#131	C₂²	1	2	yes	complemented
31	C₂₃×#550	—	2	1	no	—
32	C₂₃×#550	C₂²	1	2	yes	—
33	C₂₃×#550	C₂²	1	2	yes	—
34	C₂₃×#550	C₂²	1	2	yes	complemented
35	D₄×Q₈×C₂₃	—	2	1	no	—
36	D₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
37	C₂₃×#548	—	2	2	no	—
38	C₂₃×#548	C₂²	1	4	yes	complemented
39	D₄²×C₂₃	—	2	2	no	—
40	D₄²×C₂₃	—	2	2	no	—
41	D₄²×C₂₃	C₂²	1	2	yes	—
42	D₄²×C₂₃	C₂²	1	2	yes	—
43	C₂₃×#537	—	2	2	no	—
44	C₂₃×#537	C₂²	1	2	yes	complemented
45	C₂₃×#535	—	2	2	no	—
46	C₂₃×#535	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, complemented
51	C₂×C₂₃×#127	—	2	1	no	—
52	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
53	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
54	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
55	C₂₃×#496	C₂²	1	4	yes	complemented
56	C₂₃×#493	C₂²	1	2	yes	complemented
57	C₂₃×#492	C₂²	1	2	yes	complemented
58	C₂₃×#469	C₂²	1	4	yes	complemented
59	C₂₃×#468	C₂²	1	4	yes	complemented
60	C₂₃×#466	C₂²	1	4	yes	complemented
61	C₂₃×#465	C₂²	1	4	yes	complemented
62	C₂₃×#464	C₂²	1	2	yes	complemented
63	C₂₃×#463	C₂²	1	2	yes	complemented
64	C₂₃×#462	C₂²	1	1	yes	characteristic, complemented
65	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#460	C₂²	1	4	yes	complemented
67	C₂₃×#460	C₂²	1	2	yes	complemented
68	C₂₃×#460	C₂²	1	2	yes	complemented
69	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
70	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
71	C₂₃×#452	C₂²	1	4	yes	complemented
72	C₂₃×#450	C₂²	1	4	yes	complemented
73	C₂₃×#449	C₂²	1	4	yes	complemented
74	C₂₃×#449	C₂²	1	4	yes	complemented
75	C₂₃×#449	C₂²	1	4	yes	complemented
76	C₂₃×#448	C₂²	1	4	yes	complemented
77	C₂₃×#448	C₂²	1	4	yes	complemented
78	C₂₃×#447	C₂²	1	4	yes	complemented
79	C₂₃×#441	C₂²	1	2	yes	complemented
80	C₂₃×#440	C₂²	1	2	yes	complemented
81	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
82	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
83	C₂₃×#436	C₂²	1	2	yes	complemented
84	C₂₃×#435	C₂²	1	4	yes	complemented
85	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
86	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
88	C₂₃×#419	C₂²	1	1	yes	characteristic, complemented
89	C₂₃×#417	C₂²	1	1	yes	characteristic
90	C₂₃×#416	C₂²	1	2	yes	complemented
91	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
92	C₂₃×#408	C₂²	1	2	yes	complemented
93	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
94	C₂₃×2₋¹⁺⁴	—	2	8	no	—
95	C₂₃×2₋¹⁺⁴	—	4	4	no	—
96	C₂₃×H(5,𝔽₂)	—	2	8	no	—
97	C₂₃×H(5,𝔽₂)	—	4	4	no	—
98	C₂×#41×C₂₃	—	2	2	no	—
99	C₂×#41×C₂₃	—	2	2	no	—
100	C₂×#41×C₂₃	—	2	4	no	—
101	C₂×#41×C₂₃	C₂³	1	2	yes	—
102	C₂×#41×C₂₃	C₂³	1	4	yes	—
103	C₂×#41×C₂₃	C₂³	1	4	yes	—
104	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
105	C₂×#41×C₂₃	C₂³	1	2	yes	—
106	C₂²×Q₈×C₂₃	—	2	2	no	—
107	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
108	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₂₃	—	2	2	no	—
110	C₂²×D₄×C₂₃	—	2	4	no	—
111	C₂²×D₄×C₂₃	—	2	2	no	—
112	C₂²×D₄×C₂₃	—	2	2	no	—
113	C₂²×D₄×C₂₃	—	2	1	no	—
114	C₂²×D₄×C₂₃	—	2	1	no	—
115	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
116	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
117	C₂₃×#137	—	2	16	no	—
118	C₂₃×#137	D₄	1	8	yes	complemented
119	C₂₃×AGL(1,ℤ/8)	—	2	16	no	—
120	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
121	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
122	C₂₃×#135	—	2	8	no	—
123	C₂₃×#135	—	2	16	no	—
124	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
125	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₂₃	—	2	8	no	—
127	C₂×SD₁₆×C₂₃	—	2	16	no	—
128	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₂₃	C₂³	1	4	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×SD₁₆×C₂₃	C₂³	1	4	yes	—
134	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
135	C₂×D₈×C₂₃	C₂³	1	2	yes	—
136	C₂×D₈×C₂₃	C₂³	1	4	yes	—
137	C₂×D₈×C₂₃	C₂³	1	4	yes	—
138	C₂₃×#131	—	2	8	no	—
139	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
140	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
141	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
143	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
144	C₂₃×C₄⋊Q₈	—	2	2	no	—
145	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
146	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
147	C₂₃×#127	—	2	2	no	—
148	C₂₃×#127	—	2	2	no	—
149	C₂₃×#127	—	2	2	no	—
150	C₂₃×#127	—	2	2	no	—
151	C₂₃×#127	—	2	1	no	—
152	C₂₃×#127	—	2	1	no	—
153	C₂₃×#127	D₄	1	1	yes	characteristic
154	C₂₃×#127	C₂³	1	2	yes	—
155	C₂₃×#127	C₂³	1	2	yes	—
156	C₂₃×#127	C₂³	1	1	yes	characteristic
157	C₂₃×#124	—	2	2	no	—
158	C₂₃×#124	—	2	4	no	—
159	C₂₃×#124	D₄	1	2	yes	—
160	C₂₃×#124	C₂³	1	2	yes	—
161	C₂₃×C₂²⋊Q₈	—	2	2	no	—
162	C₂₃×C₂²⋊Q₈	—	2	4	no	—
163	C₂₃×C₂²⋊Q₈	—	2	4	no	—
164	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
165	C₂₃×#121	—	2	2	no	—
166	C₂₃×#121	—	2	4	no	—
167	C₂₃×#121	—	2	4	no	—
168	C₂₃×#121	—	2	1	no	—
169	C₂₃×#121	—	2	1	no	—
170	C₂₃×#121	—	2	2	no	—
171	C₂₃×#121	—	2	2	no	—
172	C₂₃×#121	—	2	4	no	—
173	C₂₃×#121	—	2	4	no	—
174	C₂₃×#121	—	2	4	no	—
175	C₂₃×#121	D₄	1	2	yes	—
176	C₂₃×#121	D₄	1	2	yes	—
177	C₂₃×#121	C₂³	1	4	yes	—
178	C₂₃×#121	C₂³	1	4	yes	—
179	C₂₃×#121	C₂³	1	4	yes	—
180	C₂₃×#120	—	2	4	no	—
181	C₂₃×#120	—	2	4	no	—
182	C₂₃×#120	—	2	4	no	—
183	C₄×Q₈×C₂₃	—	2	1	no	—
184	C₄×Q₈×C₂₃	—	2	1	no	—
185	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
186	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
187	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
188	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₂₃	—	2	2	no	—
190	C₄×D₄×C₂₃	—	2	1	no	—
191	C₄×D₄×C₂₃	—	2	1	no	—
192	C₄×D₄×C₂₃	—	2	2	no	—
193	C₄×D₄×C₂₃	—	2	2	no	—
194	C₄×D₄×C₂₃	—	2	2	no	—
195	C₄×D₄×C₂₃	—	2	4	no	—
196	C₄×D₄×C₂₃	—	2	1	no	—
197	C₄×D₄×C₂₃	—	2	1	no	—
198	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
199	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
200	C₄×D₄×C₂₃	C₂³	1	2	yes	—
201	C₄×D₄×C₂₃	C₂³	1	2	yes	—
202	C₂₃×#117	—	2	1	no	—
203	C₂₃×#117	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊C₄×C₂₃	—	2	1	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	2	yes	—
215	C₂₃×#103	C₂³	1	2	yes	—
216	C₂₃×#103	C₂³	1	2	yes	—
217	C₂₃×#103	C₂³	1	2	yes	—
218	C₂₃×#103	C₂³	1	2	yes	—
219	C₂₃×#102	C₂³	1	4	yes	—
220	C₂₃×#102	C₂³	1	4	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	C₂⁴×C₂₃	—	2	4	no	—
229	C₂⁴×C₂₃	—	2	2	no	—
230	#41×C₂₃	—	2	4	no	—
231	#41×C₂₃	—	2	2	no	—
232	#41×C₂₃	—	2	4	no	—
233	#41×C₂₃	—	2	8	no	—
234	#41×C₂₃	—	2	8	no	—
235	#41×C₂₃	—	2	4	no	—
236	#41×C₂₃	—	2	4	no	—
237	#41×C₂₃	—	4	4	no	—
238	#41×C₂₃	—	4	4	no	—
239	#41×C₂₃	—	4	16	no	—
240	#41×C₂₃	—	4	8	no	—
241	#41×C₂₃	—	4	8	no	—
242	#41×C₂₃	C₂×D₄	1	4	yes	—
243	C₂×Q₈×C₂₃	—	2	1	no	—
244	C₂×Q₈×C₂₃	—	2	4	no	—
245	C₂×Q₈×C₂₃	—	2	2	no	—
246	C₂×Q₈×C₂₃	—	2	8	no	—
247	C₂×Q₈×C₂₃	—	4	4	no	—
248	C₂×Q₈×C₂₃	—	4	8	no	—
249	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
250	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	complemented
251	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
252	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
253	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
254	C₂×D₄×C₂₃	—	2	1	no	—
255	C₂×D₄×C₂₃	—	2	8	no	—
256	C₂×D₄×C₂₃	—	2	2	no	—
257	C₂×D₄×C₂₃	—	2	4	no	—
258	C₂×D₄×C₂₃	—	2	4	no	—
259	C₂×D₄×C₂₃	—	2	4	no	—
260	C₂×D₄×C₂₃	—	2	4	no	—
261	C₂×D₄×C₂₃	—	2	4	no	—
262	C₂×D₄×C₂₃	—	2	4	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	4	no	—
267	C₂×D₄×C₂₃	—	2	2	no	—
268	C₂×D₄×C₂₃	—	2	1	no	—
269	C₂×D₄×C₂₃	—	2	2	no	—
270	C₂×D₄×C₂₃	—	2	2	no	—
271	C₂×D₄×C₂₃	—	2	4	no	—
272	C₂×D₄×C₂₃	—	4	4	no	—
273	C₂×D₄×C₂₃	—	4	8	no	—
274	C₂×D₄×C₂₃	—	4	16	no	—
275	C₂×D₄×C₂₃	—	8	2	no	—
276	C₂×D₄×C₂₃	—	8	4	no	—
277	C₂×D₄×C₂₃	—	8	2	no	—
278	C₂×D₄×C₂₃	—	8	4	no	—
279	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
280	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
281	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
282	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
283	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
284	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
285	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₂₃	—	2	1	no	—
287	C₂²×C₄×C₂₃	—	2	1	no	—
288	C₂²×C₄×C₂₃	—	2	4	no	—
289	C₂²×C₄×C₂₃	—	2	1	no	—
290	C₂²×C₄×C₂₃	—	2	1	no	—
291	C₂²×C₄×C₂₃	—	2	1	no	—
292	C₂²×C₄×C₂₃	—	2	4	no	—
293	C₂²×C₄×C₂₃	—	2	4	no	—
294	C₂²×C₄×C₂₃	—	2	2	no	—
295	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
298	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
299	Q₁₆×C₂₃	—	2	4	no	—
300	Q₁₆×C₂₃	C₂×D₄	1	8	yes	complemented
301	SD₁₆×C₂₃	—	2	8	no	—
302	SD₁₆×C₂₃	—	2	8	no	—
303	SD₁₆×C₂₃	—	2	4	no	—
304	SD₁₆×C₂₃	—	2	4	no	—
305	SD₁₆×C₂₃	—	2	8	no	—
306	SD₁₆×C₂₃	—	4	4	no	—
307	SD₁₆×C₂₃	C₂×D₄	1	8	yes	complemented
308	D₈×C₂₃	—	2	4	no	—
309	D₈×C₂₃	—	2	8	no	—
310	D₈×C₂₃	—	4	4	no	—
311	M₁₆×C₂₃	—	2	2	no	—
312	M₁₆×C₂₃	—	2	8	no	—
313	M₁₆×C₂₃	C₂×D₄	1	4	yes	complemented
314	C₂×C₈×C₂₃	—	2	4	no	—
315	C₂×C₈×C₂₃	—	2	8	no	—
316	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
317	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
318	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
319	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
320	C₄⋊C₄×C₂₃	—	2	2	no	—
321	C₄⋊C₄×C₂₃	—	2	2	no	—
322	C₄⋊C₄×C₂₃	—	2	1	no	—
323	C₄⋊C₄×C₂₃	—	2	1	no	—
324	C₄⋊C₄×C₂₃	—	2	1	no	—
325	C₄⋊C₄×C₂₃	—	2	1	no	—
326	C₄⋊C₄×C₂₃	—	2	1	no	—
327	C₄⋊C₄×C₂₃	—	2	4	no	—
328	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
329	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
330	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
331	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
332	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
333	C₂²⋊C₄×C₂₃	—	2	1	no	—
334	C₂²⋊C₄×C₂₃	—	2	4	no	—
335	C₂²⋊C₄×C₂₃	—	2	1	no	—
336	C₂²⋊C₄×C₂₃	—	2	1	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	—	2	4	no	—
342	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
343	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
344	C₄²×C₂₃	—	2	1	no	—
345	C₄²×C₂₃	—	2	1	no	—
346	C₄²×C₂₃	—	2	1	no	—
347	C₄²×C₂₃	—	2	2	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	C₂⁴	1	1	yes	characteristic
352	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
353	#61095	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
354	C₂³×C₂₃	—	2	1	no	—
355	C₂³×C₂₃	—	2	2	no	—
356	C₂³×C₂₃	—	2	4	no	—
357	C₂³×C₂₃	—	4	8	no	—
358	C₂³×C₂₃	—	4	4	no	—
359	C₂³×C₂₃	—	8	2	no	—
360	C₂³×C₂₃	—	8	2	no	—
361	C₂³×C₂₃	—	8	4	no	—
362	C₂³×C₂₃	—	8	4	no	—
363	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
364	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
365	Q₈×C₂₃	—	2	4	no	—
366	Q₈×C₂₃	—	2	4	no	—
367	Q₈×C₂₃	—	2	2	no	—
368	Q₈×C₂₃	—	2	1	no	—
369	Q₈×C₂₃	—	2	2	no	—
370	Q₈×C₂₃	—	2	2	no	—
371	Q₈×C₂₃	—	4	8	no	—
372	Q₈×C₂₃	C₂²×D₄	1	4	yes	—
373	Q₈×C₂₃	C₂²×D₄	1	2	yes	—
374	D₄×C₂₃	—	2	4	no	—
375	D₄×C₂₃	—	2	8	no	—
376	D₄×C₂₃	—	2	4	no	—
377	D₄×C₂₃	—	2	4	no	—
378	D₄×C₂₃	—	2	2	no	—
379	D₄×C₂₃	—	2	4	no	—
380	D₄×C₂₃	—	2	1	no	—
381	D₄×C₂₃	—	2	2	no	—
382	D₄×C₂₃	—	2	4	no	—
383	D₄×C₂₃	—	4	2	no	—
384	D₄×C₂₃	—	4	8	no	—
385	D₄×C₂₃	—	4	8	no	—
386	D₄×C₂₃	—	4	8	no	—
387	D₄×C₂₃	—	4	4	no	—
388	D₄×C₂₃	—	4	4	no	—
389	D₄×C₂₃	—	4	4	no	—
390	D₄×C₂₃	—	4	2	no	—
391	D₄×C₂₃	—	4	4	no	—
392	D₄×C₂₃	—	8	1	no	—
393	D₄×C₂₃	—	8	2	no	—
394	D₄×C₂₃	—	8	2	no	—
395	D₄×C₂₃	—	8	4	no	—
396	D₄×C₂₃	—	8	4	no	—
397	D₄×C₂₃	—	8	4	no	—
398	D₄×C₂₃	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₂₃	—	2	4	no	—
400	C₂×C₄×C₂₃	—	2	1	no	—
401	C₂×C₄×C₂₃	—	2	2	no	—
402	C₂×C₄×C₂₃	—	2	4	no	—
403	C₂×C₄×C₂₃	—	2	2	no	—
404	C₂×C₄×C₂₃	—	2	4	no	—
405	C₂×C₄×C₂₃	—	2	4	no	—
406	C₂×C₄×C₂₃	—	2	1	no	—
407	C₂×C₄×C₂₃	—	2	1	no	—
408	C₂×C₄×C₂₃	—	2	2	no	—
409	C₂×C₄×C₂₃	—	2	2	no	—
410	C₂×C₄×C₂₃	—	4	1	no	—
411	C₂×C₄×C₂₃	—	4	8	no	—
412	C₂×C₄×C₂₃	—	4	8	no	—
413	C₂×C₄×C₂₃	—	4	8	no	—
414	C₂×C₄×C₂₃	—	4	2	no	—
415	C₂×C₄×C₂₃	—	4	4	no	—
416	C₂×C₄×C₂₃	—	4	2	no	—
417	C₂×C₄×C₂₃	—	8	1	no	—
418	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
422	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
424	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
426	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
427	C₈×C₂₃	—	2	2	no	—
428	C₈×C₂₃	—	2	2	no	—
429	C₈×C₂₃	—	2	2	no	—
430	C₈×C₂₃	C₂²×D₄	1	4	yes	—
431	C₂×#577	C₂×C₂₃	1	2	yes	complemented
432	#3498	C₂×C₂₃	1	1	yes	characteristic, complemented
433	#3497	C₂×C₂₃	1	1	yes	characteristic, complemented
434	#3287	C₂×C₂₃	1	2	yes	complemented
435	D₄×SD₁₆	C₂×C₂₃	1	2	yes	complemented
436	#3278	C₂×C₂₃	1	2	yes	complemented
437	#3274	C₂×C₂₃	1	2	yes	complemented
438	#3271	C₂×C₂₃	1	4	yes	complemented
439	#3265	C₂×C₂₃	1	4	yes	complemented
440	#3151	C₂×C₂₃	1	1	yes	characteristic, complemented
441	#3062	C₂×C₂₃	1	2	yes	complemented
442	#3035	C₂×C₂₃	1	1	yes	characteristic, complemented
443	C₂×#460	C₂×C₂₃	1	1	yes	characteristic, complemented
444	#3012	C₂×C₂₃	1	2	yes	complemented
445	#3010	C₂×C₂₃	1	2	yes	complemented
446	C₄×#137	C₂×C₂₃	1	1	yes	characteristic, complemented
447	#2935	C₂×C₂₃	1	1	yes	characteristic, complemented
448	C₂²×C₂₃	—	2	1	no	—
449	C₂²×C₂₃	—	2	1	no	—
450	C₂²×C₂₃	—	2	4	no	—
451	C₂²×C₂₃	—	2	4	no	—
452	C₂²×C₂₃	—	2	2	no	—
453	C₂²×C₂₃	—	2	4	no	—
454	C₂²×C₂₃	—	4	1	no	—
455	C₂²×C₂₃	—	4	1	no	—
456	C₂²×C₂₃	—	4	4	no	—
457	C₂²×C₂₃	—	4	2	no	—
458	C₂²×C₂₃	—	4	2	no	—
459	C₂²×C₂₃	—	4	4	no	—
460	C₂²×C₂₃	—	4	4	no	—
461	C₂²×C₂₃	—	4	2	no	—
462	C₂²×C₂₃	—	16	4	no	—
463	C₂²×C₂₃	—	16	8	no	—
464	C₂²×C₂₃	D₄²	1	2	yes	—
465	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
466	C₄×C₂₃	—	2	1	no	—
467	C₄×C₂₃	—	2	1	no	—
468	C₄×C₂₃	—	2	2	no	—
469	C₄×C₂₃	—	2	4	no	—
470	C₄×C₂₃	—	2	4	no	—
471	C₄×C₂₃	—	2	1	no	—
472	C₄×C₂₃	—	4	1	no	—
473	C₄×C₂₃	—	4	2	no	—
474	C₄×C₂₃	—	4	2	no	—
475	C₄×C₂₃	—	4	1	no	—
476	C₄×C₂₃	D₄²	1	2	yes	—
477	C₄×C₂₃	#577	1	2	yes	complemented
478	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
479	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
480	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	2	yes	complemented
481	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	2	yes	—
482	#577	—	2	16	no	—
483	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
484	C₂×#137	C₂²×C₂₃	1	4	yes	complemented
485	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
486	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	4	yes	complemented
487	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
488	C₂×#135	C₂²×C₂₃	1	2	yes	—
489	C₂×#135	C₂²×C₂₃	1	4	yes	complemented
490	C₂²×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
491	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
492	C₂×#131	C₂²×C₂₃	1	2	yes	complemented
493	#550	—	2	1	no	—
494	#550	C₂²×C₂₃	1	2	yes	—
495	#550	C₂²×C₂₃	1	2	yes	—
496	#550	C₂²×C₂₃	1	2	yes	complemented
497	D₄×Q₈	—	2	1	no	—
498	D₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
499	#548	—	2	2	no	—
500	#548	C₂²×C₂₃	1	4	yes	complemented
501	D₄²	—	2	2	no	—
502	D₄²	—	2	2	no	—
503	D₄²	C₂²×C₂₃	1	2	yes	—
504	D₄²	C₂²×C₂₃	1	2	yes	—
505	#537	—	2	2	no	—
506	#537	C₂²×C₂₃	1	2	yes	complemented
507	#535	—	2	2	no	—
508	#535	C₂²×C₂₃	1	2	yes	—
509	#532	—	2	1	no	—
510	#532	—	2	2	no	—
511	#532	C₂²×C₂₃	1	1	yes	characteristic
512	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
513	C₂×#127	—	2	1	no	—
514	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
515	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
516	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
517	#496	C₂²×C₂₃	1	4	yes	complemented
518	#493	C₂²×C₂₃	1	2	yes	complemented
519	#492	C₂²×C₂₃	1	2	yes	complemented
520	#469	C₂²×C₂₃	1	4	yes	complemented
521	#468	C₂²×C₂₃	1	4	yes	complemented
522	#466	C₂²×C₂₃	1	4	yes	complemented
523	#465	C₂²×C₂₃	1	4	yes	complemented
524	#464	C₂²×C₂₃	1	2	yes	complemented
525	#463	C₂²×C₂₃	1	2	yes	complemented
526	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
527	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
528	#460	C₂²×C₂₃	1	4	yes	complemented
529	#460	C₂²×C₂₃	1	2	yes	complemented
530	#460	C₂²×C₂₃	1	2	yes	complemented
531	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
532	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
533	#452	C₂²×C₂₃	1	4	yes	complemented
534	#450	C₂²×C₂₃	1	4	yes	complemented
535	#449	C₂²×C₂₃	1	4	yes	complemented
536	#449	C₂²×C₂₃	1	4	yes	complemented
537	#449	C₂²×C₂₃	1	4	yes	complemented
538	#448	C₂²×C₂₃	1	4	yes	complemented
539	#448	C₂²×C₂₃	1	4	yes	complemented
540	#447	C₂²×C₂₃	1	4	yes	complemented
541	#441	C₂²×C₂₃	1	2	yes	complemented
542	#440	C₂²×C₂₃	1	2	yes	complemented
543	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
544	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
545	#436	C₂²×C₂₃	1	2	yes	complemented
546	#435	C₂²×C₂₃	1	4	yes	complemented
547	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
548	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
549	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
550	#419	C₂²×C₂₃	1	1	yes	characteristic, complemented
551	#417	C₂²×C₂₃	1	1	yes	characteristic
552	#416	C₂²×C₂₃	1	2	yes	complemented
553	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
554	#408	C₂²×C₂₃	1	2	yes	complemented
555	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
556	C₂×C₂₃	—	2	2	no	—
557	C₂×C₂₃	—	4	4	no	—
558	C₂×C₂₃	—	4	2	no	—
559	C₂×C₂₃	—	8	2	no	—
560	C₂×C₂₃	—	8	4	no	—
561	C₂×C₂₃	C₂×D₄²	1	1	yes	characteristic
562	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
563	C₂×C₂₃	#3585	1	1	yes	characteristic
564	2₋¹⁺⁴	—	2	8	no	—
565	2₋¹⁺⁴	—	4	4	no	—
566	H(5,𝔽₂)	—	2	8	no	—
567	H(5,𝔽₂)	—	4	4	no	—
568	C₂×#41	—	2	2	no	—
569	C₂×#41	—	2	4	no	—
570	C₂×#41	—	2	2	no	—
571	C₂×#41	C₂³×C₂₃	1	2	yes	—
572	C₂×#41	C₂³×C₂₃	1	4	yes	—
573	C₂×#41	C₂³×C₂₃	1	4	yes	—
574	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
575	C₂×#41	C₂³×C₂₃	1	2	yes	—
576	C₂²×Q₈	—	2	2	no	—
577	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
578	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
579	C₂²×D₄	—	2	2	no	—
580	C₂²×D₄	—	2	4	no	—
581	C₂²×D₄	—	2	2	no	—
582	C₂²×D₄	—	2	2	no	—
583	C₂²×D₄	—	2	1	no	—
584	C₂²×D₄	—	2	1	no	—
585	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
586	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
587	#137	—	2	16	no	—
588	#137	D₄×C₂₃	1	8	yes	complemented
589	AGL(1,ℤ/8)	—	2	16	no	—
590	AGL(1,ℤ/8)	—	2	8	no	—
591	AGL(1,ℤ/8)	—	4	4	no	—
592	#135	—	2	8	no	—
593	#135	—	2	16	no	—
594	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
595	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
596	C₂×SD₁₆	—	2	8	no	—
597	C₂×SD₁₆	—	2	16	no	—
598	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
599	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
600	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
601	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
602	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
603	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
604	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
605	C₂×D₈	C₂³×C₂₃	1	2	yes	—
606	C₂×D₈	C₂³×C₂₃	1	4	yes	—
607	C₂×D₈	C₂³×C₂₃	1	4	yes	—
608	#131	—	2	8	no	—
609	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
610	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
611	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
612	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
613	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
614	C₄⋊Q₈	—	2	2	no	—
615	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
616	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
617	#127	—	2	2	no	—
618	#127	—	2	2	no	—
619	#127	—	2	2	no	—
620	#127	—	2	2	no	—
621	#127	—	2	1	no	—
622	#127	—	2	1	no	—
623	#127	D₄×C₂₃	1	1	yes	characteristic
624	#127	C₂³×C₂₃	1	2	yes	—
625	#127	C₂³×C₂₃	1	2	yes	—
626	#127	C₂³×C₂₃	1	1	yes	characteristic
627	#124	—	2	2	no	—
628	#124	—	2	4	no	—
629	#124	D₄×C₂₃	1	2	yes	—
630	#124	C₂³×C₂₃	1	2	yes	—
631	C₂²⋊Q₈	—	2	2	no	—
632	C₂²⋊Q₈	—	2	4	no	—
633	C₂²⋊Q₈	—	2	4	no	—
634	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
635	#121	—	2	4	no	—
636	#121	—	2	4	no	—
637	#121	—	2	2	no	—
638	#121	—	2	1	no	—
639	#121	—	2	1	no	—
640	#121	—	2	2	no	—
641	#121	—	2	2	no	—
642	#121	—	2	4	no	—
643	#121	—	2	4	no	—
644	#121	—	2	4	no	—
645	#121	D₄×C₂₃	1	2	yes	—
646	#121	D₄×C₂₃	1	2	yes	—
647	#121	C₂³×C₂₃	1	4	yes	—
648	#121	C₂³×C₂₃	1	4	yes	—
649	#121	C₂³×C₂₃	1	4	yes	—
650	#120	—	2	4	no	—
651	#120	—	2	4	no	—
652	#120	—	2	4	no	—
653	C₄×Q₈	—	2	1	no	—
654	C₄×Q₈	—	2	1	no	—
655	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
656	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
657	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
658	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
659	C₄×D₄	—	2	2	no	—
660	C₄×D₄	—	2	1	no	—
661	C₄×D₄	—	2	1	no	—
662	C₄×D₄	—	2	2	no	—
663	C₄×D₄	—	2	2	no	—
664	C₄×D₄	—	2	2	no	—
665	C₄×D₄	—	2	4	no	—
666	C₄×D₄	—	2	1	no	—
667	C₄×D₄	—	2	1	no	—
668	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
669	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
670	C₄×D₄	C₂³×C₂₃	1	2	yes	—
671	C₄×D₄	C₂³×C₂₃	1	2	yes	—
672	#117	—	2	1	no	—
673	#117	C₂³×C₂₃	1	1	yes	characteristic
674	C₂×C₄⋊C₄	—	2	1	no	—
675	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
676	C₂×C₄²	—	2	1	no	—
677	C₂×C₄²	—	2	1	no	—
678	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
679	#107	C₂³×C₂₃	1	2	yes	—
680	#106	C₂³×C₂₃	1	2	yes	—
681	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
682	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
683	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
684	#103	C₂³×C₂₃	1	2	yes	—
685	#103	C₂³×C₂₃	1	2	yes	—
686	#103	C₂³×C₂₃	1	2	yes	—
687	#103	C₂³×C₂₃	1	2	yes	—
688	#103	C₂³×C₂₃	1	2	yes	—
689	#102	C₂³×C₂₃	1	4	yes	—
690	#102	C₂³×C₂₃	1	4	yes	—
691	#102	C₂³×C₂₃	1	2	yes	—
692	#102	C₂³×C₂₃	1	2	yes	—
693	#102	C₂³×C₂₃	1	2	yes	—
694	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
695	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
696	#97	C₂³×C₂₃	1	2	yes	—
697	C₄×C₈	C₂³×C₂₃	1	2	yes	—
698	C₂₃	#61095	1	1	yes	characteristic, direct product factor, Sylow
699	C₂⁴	—	2	4	no	—
700	C₂⁴	—	2	2	no	—
701	#41	—	2	4	no	—
702	#41	—	2	2	no	—
703	#41	—	2	4	no	—
704	#41	—	2	8	no	—
705	#41	—	2	8	no	—
706	#41	—	2	4	no	—
707	#41	—	2	4	no	—
708	#41	—	4	4	no	—
709	#41	—	4	4	no	—
710	#41	—	4	16	no	—
711	#41	—	4	8	no	—
712	#41	—	4	8	no	—
713	#41	C₂×D₄×C₂₃	1	4	yes	—
714	C₂×Q₈	—	2	1	no	—
715	C₂×Q₈	—	2	4	no	—
716	C₂×Q₈	—	2	2	no	—
717	C₂×Q₈	—	2	8	no	—
718	C₂×Q₈	—	4	4	no	—
719	C₂×Q₈	—	4	8	no	—
720	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
721	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	complemented
722	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
723	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
724	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	8	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	2	4	no	—
731	C₂×D₄	—	2	4	no	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	2	4	no	—
734	C₂×D₄	—	2	1	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	2	no	—
737	C₂×D₄	—	2	4	no	—
738	C₂×D₄	—	2	2	no	—
739	C₂×D₄	—	2	1	no	—
740	C₂×D₄	—	2	2	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	2	4	no	—
743	C₂×D₄	—	4	4	no	—
744	C₂×D₄	—	4	8	no	—
745	C₂×D₄	—	4	16	no	—
746	C₂×D₄	—	8	2	no	—
747	C₂×D₄	—	8	4	no	—
748	C₂×D₄	—	8	2	no	—
749	C₂×D₄	—	8	4	no	—
750	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
751	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
752	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
753	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
754	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
755	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
756	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
757	C₂²×C₄	—	2	1	no	—
758	C₂²×C₄	—	2	1	no	—
759	C₂²×C₄	—	2	4	no	—
760	C₂²×C₄	—	2	1	no	—
761	C₂²×C₄	—	2	1	no	—
762	C₂²×C₄	—	2	1	no	—
763	C₂²×C₄	—	2	4	no	—
764	C₂²×C₄	—	2	4	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
767	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
769	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
770	Q₁₆	—	2	4	no	—
771	Q₁₆	C₂×D₄×C₂₃	1	8	yes	complemented
772	SD₁₆	—	2	8	no	—
773	SD₁₆	—	2	8	no	—
774	SD₁₆	—	2	4	no	—
775	SD₁₆	—	2	4	no	—
776	SD₁₆	—	2	8	no	—
777	SD₁₆	—	4	4	no	—
778	SD₁₆	C₂×D₄×C₂₃	1	8	yes	complemented
779	D₈	—	2	4	no	—
780	D₈	—	2	8	no	—
781	D₈	—	4	4	no	—
782	M₁₆	—	2	2	no	—
783	M₁₆	—	2	8	no	—
784	M₁₆	C₂×D₄×C₂₃	1	4	yes	complemented
785	C₂×C₈	—	2	4	no	—
786	C₂×C₈	—	2	8	no	—
787	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
788	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
789	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
790	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	1	no	—
794	C₄⋊C₄	—	2	1	no	—
795	C₄⋊C₄	—	2	1	no	—
796	C₄⋊C₄	—	2	1	no	—
797	C₄⋊C₄	—	2	1	no	—
798	C₄⋊C₄	—	2	4	no	—
799	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
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	1	no	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	2	1	no	—
807	C₂²⋊C₄	—	2	1	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	4	no	—
813	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
814	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
815	C₄²	—	2	1	no	—
816	C₄²	—	2	1	no	—
817	C₄²	—	2	1	no	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	2	no	—
820	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
821	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
822	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
823	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
824	C₂³	—	2	1	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	2	4	no	—
827	C₂³	—	4	8	no	—
828	C₂³	—	4	4	no	—
829	C₂³	—	8	2	no	—
830	C₂³	—	8	2	no	—
831	C₂³	—	8	4	no	—
832	C₂³	—	8	4	no	—
833	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
834	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
835	Q₈	—	2	2	no	—
836	Q₈	—	2	1	no	—
837	Q₈	—	2	4	no	—
838	Q₈	—	2	4	no	—
839	Q₈	—	2	2	no	—
840	Q₈	—	2	2	no	—
841	Q₈	—	4	8	no	—
842	Q₈	C₂²×D₄×C₂₃	1	4	yes	—
843	Q₈	C₂²×D₄×C₂₃	1	2	yes	—
844	D₄	—	2	4	no	—
845	D₄	—	2	8	no	—
846	D₄	—	2	4	no	—
847	D₄	—	2	2	no	—
848	D₄	—	2	4	no	—
849	D₄	—	2	1	no	—
850	D₄	—	2	2	no	—
851	D₄	—	2	4	no	—
852	D₄	—	2	4	no	—
853	D₄	—	4	2	no	—
854	D₄	—	4	8	no	—
855	D₄	—	4	8	no	—
856	D₄	—	4	8	no	—
857	D₄	—	4	4	no	—
858	D₄	—	4	4	no	—
859	D₄	—	4	4	no	—
860	D₄	—	4	2	no	—
861	D₄	—	4	4	no	—
862	D₄	—	8	2	no	—
863	D₄	—	8	2	no	—
864	D₄	—	8	1	no	—
865	D₄	—	8	4	no	—
866	D₄	—	8	4	no	—
867	D₄	—	8	4	no	—
868	D₄	C₂²×D₄×C₂₃	1	2	yes	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	4	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	4	no	—
874	C₂×C₄	—	2	4	no	—
875	C₂×C₄	—	2	4	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	8	no	—
882	C₂×C₄	—	4	8	no	—
883	C₂×C₄	—	4	8	no	—
884	C₂×C₄	—	4	2	no	—
885	C₂×C₄	—	4	2	no	—
886	C₂×C₄	—	4	4	no	—
887	C₂×C₄	—	8	1	no	—
888	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
889	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
890	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
891	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
892	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
893	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
894	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
895	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
896	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
897	C₈	—	2	2	no	—
898	C₈	—	2	2	no	—
899	C₈	—	2	2	no	—
900	C₈	C₂²×D₄×C₂₃	1	4	yes	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	4	no	—
904	C₂²	—	2	2	no	—
905	C₂²	—	2	4	no	—
906	C₂²	—	2	4	no	—
907	C₂²	—	4	1	no	—
908	C₂²	—	4	1	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	4	no	—
911	C₂²	—	4	4	no	—
912	C₂²	—	4	2	no	—
913	C₂²	—	4	4	no	—
914	C₂²	—	4	2	no	—
915	C₂²	—	16	4	no	—
916	C₂²	—	16	8	no	—
917	C₂²	D₄²×C₂₃	1	2	yes	—
918	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
919	C₄	—	2	2	no	—
920	C₄	—	2	4	no	—
921	C₄	—	2	4	no	—
922	C₄	—	2	1	no	—
923	C₄	—	2	1	no	—
924	C₄	—	2	1	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	1	no	—
927	C₄	—	4	1	no	—
928	C₄	—	4	2	no	—
929	C₄	D₄²×C₂₃	1	2	yes	—
930	C₄	C₂₃×#577	1	2	yes	complemented
931	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
932	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
933	C₂	—	2	2	no	—
934	C₂	—	4	4	no	—
935	C₂	—	4	2	no	—
936	C₂	—	8	4	no	—
937	C₂	—	8	2	no	—
938	C₂	C₂×D₄²×C₂₃	1	1	yes	characteristic
939	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
940	C₂	C₂₃×#3585	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×#577	C₂	semidirect
2. C₂₃×#3498	C₂	semidirect
3. C₂₃×#3497	C₂	semidirect
4. C₂₃×#3287	C₂	semidirect
5. D₄×SD₁₆×C₂₃	C₂	semidirect
6. C₂₃×#3278	C₂	semidirect
7. C₂₃×#3274	C₂	semidirect
8. C₂₃×#3271	C₂	semidirect
9. C₂₃×#3265	C₂	semidirect
10. C₂₃×#3151	C₂	semidirect
11. C₂₃×#3062	C₂	semidirect
12. C₂₃×#3035	C₂	semidirect
13. C₂×C₂₃×#460	C₂	semidirect
14. C₂₃×#3012	C₂	semidirect
15. C₂₃×#3010	C₂	semidirect
16. C₄×C₂₃×#137	C₂	semidirect
17. C₂₃×#2935	C₂	semidirect
18. C₂×C₂₃×2₋¹⁺⁴	C₂²	semidirect
22. C₂×C₂₃×#137	C₂²	semidirect
23. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
24. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
27. C₂×C₂₃×#135	C₂²	semidirect
28. C₂²×SD₁₆×C₂₃	C₂²	semidirect
29. C₂²×SD₁₆×C₂₃	C₂²	semidirect
30. C₂×C₂₃×#131	C₂²	semidirect
34. C₂₃×#550	C₂²	semidirect
36. D₄×Q₈×C₂₃	C₂²	semidirect
38. C₂₃×#548	C₂²	semidirect
44. C₂₃×#537	C₂²	semidirect
50. C₂₃×#532	C₂²	semidirect
54. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
55. C₂₃×#496	C₂²	semidirect
56. C₂₃×#493	C₂²	semidirect
57. C₂₃×#492	C₂²	semidirect
58. C₂₃×#469	C₂²	semidirect
59. C₂₃×#468	C₂²	semidirect
60. C₂₃×#466	C₂²	semidirect
61. C₂₃×#465	C₂²	semidirect
62. C₂₃×#464	C₂²	semidirect
63. C₂₃×#463	C₂²	semidirect
64. C₂₃×#462	C₂²	semidirect
65. C₂₃×#461	C₂²	semidirect
66. C₂₃×#460	C₂²	semidirect
67. C₂₃×#460	C₂²	semidirect
68. C₂₃×#460	C₂²	semidirect
69. C₂₃×#460	C₂²	semidirect
70. C₂₃×#459	C₂²	semidirect
71. C₂₃×#452	C₂²	semidirect
72. C₂₃×#450	C₂²	semidirect
73. C₂₃×#449	C₂²	semidirect
74. C₂₃×#449	C₂²	semidirect
75. C₂₃×#449	C₂²	semidirect
76. C₂₃×#448	C₂²	semidirect
77. C₂₃×#448	C₂²	semidirect
78. C₂₃×#447	C₂²	semidirect
79. C₂₃×#441	C₂²	semidirect
80. C₂₃×#440	C₂²	semidirect
81. C₄×Q₁₆×C₂₃	C₂²	semidirect
82. C₄×SD₁₆×C₂₃	C₂²	semidirect
83. C₂₃×#436	C₂²	semidirect
84. C₂₃×#435	C₂²	semidirect
85. C₈×D₄×C₂₃	C₂²	semidirect
86. C₂₃×#428	C₂²	semidirect
87. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
88. C₂₃×#419	C₂²	semidirect
90. C₂₃×#416	C₂²	semidirect
91. C₂×C₂₃×#102	C₂²	semidirect
92. C₂₃×#408	C₂²	semidirect
93. C₄×M₁₆×C₂₃	C₂²	semidirect
118. C₂₃×#137	D₄	semidirect
250. C₂×Q₈×C₂₃	C₂×D₄	semidirect
300. Q₁₆×C₂₃	C₂×D₄	semidirect
307. SD₁₆×C₂₃	C₂×D₄	semidirect
313. M₁₆×C₂₃	C₂×D₄	semidirect
353. #61095	C₂₃	direct (N × H)
431. C₂×#577	C₂×C₂₃	semidirect
432. #3498	C₂×C₂₃	semidirect
433. #3497	C₂×C₂₃	semidirect
434. #3287	C₂×C₂₃	semidirect
435. D₄×SD₁₆	C₂×C₂₃	semidirect
436. #3278	C₂×C₂₃	semidirect
437. #3274	C₂×C₂₃	semidirect
438. #3271	C₂×C₂₃	semidirect
439. #3265	C₂×C₂₃	semidirect
440. #3151	C₂×C₂₃	semidirect
441. #3062	C₂×C₂₃	semidirect
442. #3035	C₂×C₂₃	semidirect
443. C₂×#460	C₂×C₂₃	semidirect
444. #3012	C₂×C₂₃	semidirect
445. #3010	C₂×C₂₃	semidirect
446. C₄×#137	C₂×C₂₃	semidirect
447. #2935	C₂×C₂₃	semidirect
477. C₄×C₂₃	#577	semidirect
480. C₂×2₋¹⁺⁴	C₂²×C₂₃	semidirect
484. C₂×#137	C₂²×C₂₃	semidirect
485. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
486. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
487. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
489. C₂×#135	C₂²×C₂₃	semidirect
490. C₂²×SD₁₆	C₂²×C₂₃	semidirect
491. C₂²×SD₁₆	C₂²×C₂₃	semidirect
492. C₂×#131	C₂²×C₂₃	semidirect
496. #550	C₂²×C₂₃	semidirect
498. D₄×Q₈	C₂²×C₂₃	semidirect
500. #548	C₂²×C₂₃	semidirect
506. #537	C₂²×C₂₃	semidirect
512. #532	C₂²×C₂₃	semidirect
516. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
517. #496	C₂²×C₂₃	semidirect
518. #493	C₂²×C₂₃	semidirect
519. #492	C₂²×C₂₃	semidirect
520. #469	C₂²×C₂₃	semidirect
521. #468	C₂²×C₂₃	semidirect
522. #466	C₂²×C₂₃	semidirect
523. #465	C₂²×C₂₃	semidirect
524. #464	C₂²×C₂₃	semidirect
525. #463	C₂²×C₂₃	semidirect
526. #462	C₂²×C₂₃	semidirect
527. #461	C₂²×C₂₃	semidirect
528. #460	C₂²×C₂₃	semidirect
529. #460	C₂²×C₂₃	semidirect
530. #460	C₂²×C₂₃	semidirect
531. #460	C₂²×C₂₃	semidirect
532. #459	C₂²×C₂₃	semidirect
533. #452	C₂²×C₂₃	semidirect
534. #450	C₂²×C₂₃	semidirect
535. #449	C₂²×C₂₃	semidirect
536. #449	C₂²×C₂₃	semidirect
537. #449	C₂²×C₂₃	semidirect
538. #448	C₂²×C₂₃	semidirect
539. #448	C₂²×C₂₃	semidirect
540. #447	C₂²×C₂₃	semidirect
541. #441	C₂²×C₂₃	semidirect
542. #440	C₂²×C₂₃	semidirect
543. C₄×Q₁₆	C₂²×C₂₃	semidirect
544. C₄×SD₁₆	C₂²×C₂₃	semidirect
545. #436	C₂²×C₂₃	semidirect
546. #435	C₂²×C₂₃	semidirect
547. C₈×D₄	C₂²×C₂₃	semidirect
548. #428	C₂²×C₂₃	semidirect
549. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
550. #419	C₂²×C₂₃	semidirect
552. #416	C₂²×C₂₃	semidirect
553. C₂×#102	C₂²×C₂₃	semidirect
554. #408	C₂²×C₂₃	semidirect
555. C₄×M₁₆	C₂²×C₂₃	semidirect
588. #137	D₄×C₂₃	semidirect
698. C₂₃	#61095	direct (N × H)
721. C₂×Q₈	C₂×D₄×C₂₃	semidirect
771. Q₁₆	C₂×D₄×C₂₃	semidirect
778. SD₁₆	C₂×D₄×C₂₃	semidirect
784. M₁₆	C₂×D₄×C₂₃	semidirect
930. C₄	C₂₃×#577	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#577	2
C₂₃×#3498	2
C₂₃×#3497	2
C₂₃×#3287	2
D₄×SD₁₆×C₂₃	2
C₂₃×#3278	2
C₂₃×#3274	2
C₂₃×#3271	2
C₂₃×#3265	2
C₂₃×#3151	2
C₂₃×#3062	2
C₂₃×#3035	2
C₂×C₂₃×#460	2
C₂₃×#3012	2
C₂₃×#3010	2
C₄×C₂₃×#137	2
C₂₃×#2935	2
#61095	23

Subgroups — C23×#61095 #19208721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61095 #19208721