Subgroups — C₂₃×#61161 #19208787

Order 5888.

2378 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3332	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3330	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3308	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3306	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3298	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3294	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3092	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3055	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3006	C₂	1	2	yes	maximal, complemented
15	C₄×C₂₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₂₃×#417	C₂	1	2	yes	maximal, complemented
18	C₂²×#41×C₂₃	—	2	1	no	—
19	C₂²×#41×C₂₃	C₂²	1	2	yes	—
20	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
22	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	complemented
23	C₂₃×#550	C₂²	1	1	yes	characteristic, complemented
24	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
25	C₂₃×#548	C₂²	1	2	yes	complemented
26	C₂₃×#547	—	2	1	no	—
27	C₂₃×#547	—	2	2	no	—
28	C₂₃×#547	—	2	1	no	—
29	C₂₃×#547	—	2	1	no	—
30	C₂₃×#547	C₂²	1	2	yes	—
31	C₂₃×#547	C₂²	1	1	yes	characteristic, complemented
32	C₂₃×#547	C₂²	1	4	yes	complemented
33	C₂₃×#547	C₂²	1	2	yes	complemented
34	C₂₃×#546	—	2	2	no	—
35	C₂₃×#546	C₂²	1	2	yes	complemented
36	D₄²×C₂₃	—	2	1	no	—
37	D₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#532	—	2	1	no	—
39	C₂₃×#532	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₂₃×#525	—	2	2	no	—
42	C₂₃×#525	C₂²	1	2	yes	—
43	C₂×C₂₃×#123	—	2	2	no	—
44	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
45	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
46	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₂₃	—	2	1	no	—
48	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
51	C₂₃×#489	C₂²	1	4	yes	complemented
52	C₂₃×#487	C₂²	1	2	yes	complemented
53	C₂₃×#486	C₂²	1	2	yes	complemented
54	C₂₃×#484	C₂²	1	4	yes	complemented
55	C₂₃×#483	C₂²	1	4	yes	complemented
56	C₂₃×#481	C₂²	1	4	yes	complemented
57	C₂₃×#480	C₂²	1	4	yes	complemented
58	C₂₃×#477	C₂²	1	2	yes	complemented
59	C₂₃×#476	C₂²	1	2	yes	complemented
60	C₂₃×#475	C₂²	1	2	yes	complemented
61	C₂₃×#474	C₂²	1	2	yes	complemented
62	C₂₃×#469	C₂²	1	4	yes	complemented
63	C₂₃×#468	C₂²	1	4	yes	complemented
64	C₂₃×#466	C₂²	1	4	yes	complemented
65	C₂₃×#465	C₂²	1	4	yes	complemented
66	C₂₃×#463	C₂²	1	4	yes	complemented
67	C₂₃×#461	C₂²	1	2	yes	complemented
68	C₂₃×#459	C₂²	1	2	yes	complemented
69	C₂₃×#449	C₂²	1	4	yes	complemented
70	C₂₃×#449	C₂²	1	4	yes	complemented
71	C₂₃×#448	C₂²	1	4	yes	complemented
72	C₂₃×#447	C₂²	1	4	yes	complemented
73	C₂₃×#442	C₂²	1	2	yes	complemented
74	C₂₃×#440	C₂²	1	2	yes	complemented
75	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
76	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
77	C₂₃×#436	C₂²	1	2	yes	complemented
78	C₂₃×#435	C₂²	1	4	yes	complemented
79	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
80	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
81	C₂₃×#428	C₂²	1	2	yes	complemented
82	C₂₃×#423	C₂²	1	1	yes	characteristic, complemented
83	C₂₃×#418	C₂²	1	1	yes	characteristic, complemented
84	C₂₃×#417	C₂²	1	1	yes	characteristic
85	C₂₃×#417	C₂²	1	2	yes	—
86	C₂₃×#417	C₂²	1	2	yes	complemented
87	C₂₃×#417	C₂²	1	2	yes	complemented
88	C₂₃×#417	C₂²	1	4	yes	complemented
89	C₂₃×#417	C₂²	1	4	yes	complemented
90	C₂₃×#417	C₂²	1	2	yes	complemented
91	C₂×C₂₃×#103	C₂²	1	4	yes	complemented
92	C₂×C₂₃×#102	C₂²	1	4	yes	complemented
93	C₂₃×#407	C₂²	1	2	yes	complemented
94	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
95	C₂×#41×C₂₃	—	2	2	no	—
96	C₂×#41×C₂₃	—	2	4	no	—
97	C₂×#41×C₂₃	—	2	2	no	—
98	C₂×#41×C₂₃	—	2	2	no	—
99	C₂×#41×C₂₃	—	2	2	no	—
100	C₂×#41×C₂₃	—	2	8	no	—
101	C₂×#41×C₂₃	—	4	4	no	—
102	C₂×#41×C₂₃	—	4	8	no	—
103	C₂×#41×C₂₃	C₂³	1	2	yes	—
104	C₂×#41×C₂₃	C₂³	1	2	yes	—
105	C₂×#41×C₂₃	C₂³	1	2	yes	—
106	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
107	C₂²×Q₈×C₂₃	—	2	1	no	—
108	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
109	C₂²×D₄×C₂₃	—	2	2	no	—
110	C₂²×D₄×C₂₃	—	2	2	no	—
111	C₂²×D₄×C₂₃	—	2	1	no	—
112	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
113	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
115	C₂³×C₄×C₂₃	—	2	2	no	—
116	C₂³×C₄×C₂₃	—	2	1	no	—
117	C₂³×C₄×C₂₃	—	2	2	no	—
118	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
119	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
120	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
121	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
122	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
123	C₂×D₈×C₂₃	C₂³	1	2	yes	—
124	C₂×D₈×C₂₃	C₂³	1	4	yes	—
125	C₂×M₁₆×C₂₃	—	4	4	no	—
126	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
127	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
128	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
129	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
130	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
131	C₂₃×C₄⋊Q₈	—	2	1	no	—
132	C₂₃×C₄⋊Q₈	—	2	1	no	—
133	C₂₃×C₄⋊Q₈	—	2	1	no	—
134	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
135	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₂₃×#127	—	2	1	no	—
138	C₂₃×#127	C₂³	1	1	yes	characteristic
139	C₂₃×#124	—	2	2	no	—
140	C₂₃×#124	C₂³	1	2	yes	—
141	C₂₃×#123	—	2	2	no	—
142	C₂₃×#123	—	2	2	no	—
143	C₂₃×#123	—	2	4	no	—
144	C₂₃×#123	—	2	4	no	—
145	C₂₃×#123	—	2	4	no	—
146	C₂₃×#123	—	2	4	no	—
147	C₂₃×#123	—	2	2	no	—
148	C₂₃×C₂²⋊Q₈	—	2	2	no	—
149	C₂₃×C₂²⋊Q₈	—	2	2	no	—
150	C₂₃×C₂²⋊Q₈	—	2	4	no	—
151	C₂₃×C₂²⋊Q₈	—	2	2	no	—
152	C₂₃×C₂²⋊Q₈	—	2	2	no	—
153	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
154	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
155	C₂₃×#121	—	2	1	no	—
156	C₂₃×#121	—	2	2	no	—
157	C₂₃×#121	—	2	2	no	—
158	C₂₃×#121	—	2	2	no	—
159	C₂₃×#121	—	2	1	no	—
160	C₂₃×#121	—	2	1	no	—
161	C₂₃×#121	—	2	1	no	—
162	C₂₃×#121	—	2	2	no	—
163	C₂₃×#121	—	2	2	no	—
164	C₂₃×#121	C₂³	1	4	yes	—
165	C₂₃×#121	C₂³	1	4	yes	—
166	C₂₃×#121	C₂³	1	2	yes	—
167	C₂₃×#121	C₂³	1	2	yes	—
168	C₂₃×#120	—	2	2	no	—
169	C₂₃×#120	—	2	2	no	—
170	C₂₃×#120	—	2	2	no	—
171	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
172	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₂₃	—	2	1	no	—
174	C₄×D₄×C₂₃	—	2	1	no	—
175	C₄×D₄×C₂₃	—	2	2	no	—
176	C₄×D₄×C₂₃	—	2	1	no	—
177	C₄×D₄×C₂₃	—	2	2	no	—
178	C₄×D₄×C₂₃	—	2	1	no	—
179	C₄×D₄×C₂₃	—	2	2	no	—
180	C₄×D₄×C₂₃	—	2	1	no	—
181	C₄×D₄×C₂₃	—	2	1	no	—
182	C₄×D₄×C₂₃	—	2	1	no	—
183	C₄×D₄×C₂₃	—	2	1	no	—
184	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
185	C₄×D₄×C₂₃	D₄	1	2	yes	—
186	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
187	C₄×D₄×C₂₃	C₂³	1	2	yes	—
188	C₄×D₄×C₂₃	C₂³	1	2	yes	—
189	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
192	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
193	C₄×D₄×C₂₃	C₂³	1	2	yes	—
194	C₂₃×#117	—	2	1	no	—
195	C₂₃×#117	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
197	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
198	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
199	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
200	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
201	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
203	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
204	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
205	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
207	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
208	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
209	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
210	C₂×C₄²×C₂₃	—	2	1	no	—
211	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
212	C₂₃×#107	C₂³	1	2	yes	—
213	C₂₃×#107	C₂³	1	4	yes	—
214	C₂₃×#106	C₂³	1	2	yes	—
215	C₂₃×#106	C₂³	1	4	yes	—
216	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
217	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
218	C₂₃×#103	C₂³	1	2	yes	—
219	C₂₃×#103	C₂³	1	4	yes	—
220	C₂₃×#103	C₂³	1	4	yes	—
221	C₂₃×#103	C₂³	1	4	yes	—
222	C₂₃×#103	C₂³	1	4	yes	—
223	C₂₃×#102	C₂³	1	2	yes	—
224	C₂₃×#102	C₂³	1	4	yes	—
225	C₂₃×#102	C₂³	1	4	yes	—
226	C₂₃×#102	C₂³	1	4	yes	—
227	C₂₃×#102	C₂³	1	4	yes	—
228	C₂₃×#102	C₂³	1	2	yes	—
229	C₂₃×#102	C₂³	1	2	yes	—
230	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
231	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
232	C₂₃×#97	C₂³	1	2	yes	—
233	C₄×C₈×C₂₃	C₂³	1	2	yes	—
234	C₂⁴×C₂₃	—	2	1	no	—
235	C₂⁴×C₂₃	—	2	2	no	—
236	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
237	#41×C₂₃	—	2	2	no	—
238	#41×C₂₃	—	2	4	no	—
239	#41×C₂₃	—	2	4	no	—
240	#41×C₂₃	—	2	4	no	—
241	#41×C₂₃	—	2	4	no	—
242	#41×C₂₃	—	4	8	no	—
243	#41×C₂₃	—	4	2	no	—
244	#41×C₂₃	—	4	2	no	—
245	#41×C₂₃	—	4	8	no	—
246	#41×C₂₃	—	4	16	no	—
247	#41×C₂₃	—	4	8	no	—
248	#41×C₂₃	—	4	8	no	—
249	#41×C₂₃	#41	1	4	yes	complemented
250	C₂×Q₈×C₂₃	—	2	2	no	—
251	C₂×Q₈×C₂₃	—	2	2	no	—
252	C₂×Q₈×C₂₃	—	2	2	no	—
253	C₂×Q₈×C₂₃	—	2	4	no	—
254	C₂×Q₈×C₂₃	—	4	2	no	—
255	C₂×Q₈×C₂₃	—	4	4	no	—
256	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
257	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
258	C₂×D₄×C₂₃	—	2	1	no	—
259	C₂×D₄×C₂₃	—	2	4	no	—
260	C₂×D₄×C₂₃	—	2	4	no	—
261	C₂×D₄×C₂₃	—	2	2	no	—
262	C₂×D₄×C₂₃	—	2	2	no	—
263	C₂×D₄×C₂₃	—	2	2	no	—
264	C₂×D₄×C₂₃	—	2	2	no	—
265	C₂×D₄×C₂₃	—	2	4	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	1	no	—
270	C₂×D₄×C₂₃	—	2	2	no	—
271	C₂×D₄×C₂₃	—	2	1	no	—
272	C₂×D₄×C₂₃	—	2	2	no	—
273	C₂×D₄×C₂₃	—	2	2	no	—
274	C₂×D₄×C₂₃	—	4	2	no	—
275	C₂×D₄×C₂₃	—	4	8	no	—
276	C₂×D₄×C₂₃	—	4	8	no	—
277	C₂×D₄×C₂₃	—	4	4	no	—
278	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
279	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
280	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
281	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
282	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
283	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₂₃	—	2	1	no	—
285	C₂²×C₄×C₂₃	—	2	4	no	—
286	C₂²×C₄×C₂₃	—	2	4	no	—
287	C₂²×C₄×C₂₃	—	2	1	no	—
288	C₂²×C₄×C₂₃	—	2	2	no	—
289	C₂²×C₄×C₂₃	—	2	4	no	—
290	C₂²×C₄×C₂₃	—	2	4	no	—
291	C₂²×C₄×C₂₃	—	2	2	no	—
292	C₂²×C₄×C₂₃	—	2	1	no	—
293	C₂²×C₄×C₂₃	—	2	2	no	—
294	C₂²×C₄×C₂₃	—	2	2	no	—
295	C₂²×C₄×C₂₃	—	2	2	no	—
296	C₂²×C₄×C₂₃	—	2	2	no	—
297	C₂²×C₄×C₂₃	—	2	2	no	—
298	C₂²×C₄×C₂₃	—	2	1	no	—
299	C₂²×C₄×C₂₃	—	4	8	no	—
300	C₂²×C₄×C₂₃	—	4	4	no	—
301	C₂²×C₄×C₂₃	—	4	8	no	—
302	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
304	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
305	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
306	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
310	SD₁₆×C₂₃	—	2	4	no	—
311	SD₁₆×C₂₃	—	4	4	no	—
312	D₈×C₂₃	—	2	4	no	—
313	D₈×C₂₃	—	4	4	no	—
314	M₁₆×C₂₃	—	2	2	no	—
315	M₁₆×C₂₃	—	2	2	no	—
316	M₁₆×C₂₃	—	2	4	no	—
317	M₁₆×C₂₃	—	4	4	no	—
318	C₂×C₈×C₂₃	—	4	4	no	—
319	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
320	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
321	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
322	C₄⋊C₄×C₂₃	—	2	1	no	—
323	C₄⋊C₄×C₂₃	—	2	2	no	—
324	C₄⋊C₄×C₂₃	—	2	4	no	—
325	C₄⋊C₄×C₂₃	—	2	4	no	—
326	C₄⋊C₄×C₂₃	—	2	1	no	—
327	C₄⋊C₄×C₂₃	—	2	2	no	—
328	C₄⋊C₄×C₂₃	—	2	2	no	—
329	C₄⋊C₄×C₂₃	—	2	2	no	—
330	C₄⋊C₄×C₂₃	—	2	1	no	—
331	C₄⋊C₄×C₂₃	—	2	1	no	—
332	C₄⋊C₄×C₂₃	—	2	1	no	—
333	C₄⋊C₄×C₂₃	—	2	2	no	—
334	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
335	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
336	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
337	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
338	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
339	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
340	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
341	C₂²⋊C₄×C₂₃	—	2	2	no	—
342	C₂²⋊C₄×C₂₃	—	2	1	no	—
343	C₂²⋊C₄×C₂₃	—	2	2	no	—
344	C₂²⋊C₄×C₂₃	—	2	2	no	—
345	C₂²⋊C₄×C₂₃	—	2	2	no	—
346	C₂²⋊C₄×C₂₃	—	2	2	no	—
347	C₂²⋊C₄×C₂₃	—	2	2	no	—
348	C₂²⋊C₄×C₂₃	—	2	4	no	—
349	C₂²⋊C₄×C₂₃	—	2	4	no	—
350	C₂²⋊C₄×C₂₃	—	2	1	no	—
351	C₂²⋊C₄×C₂₃	—	2	1	no	—
352	C₂²⋊C₄×C₂₃	—	2	2	no	—
353	C₂²⋊C₄×C₂₃	—	2	2	no	—
354	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
355	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
356	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
357	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
358	C₄²×C₂₃	—	2	1	no	—
359	C₄²×C₂₃	—	2	1	no	—
360	C₄²×C₂₃	—	2	1	no	—
361	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
362	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
363	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
364	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
365	#61161	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
366	C₂³×C₂₃	—	2	4	no	—
367	C₂³×C₂₃	—	2	4	no	—
368	C₂³×C₂₃	—	2	1	no	—
369	C₂³×C₂₃	—	2	2	no	—
370	C₂³×C₂₃	—	2	2	no	—
371	C₂³×C₂₃	—	4	2	no	—
372	C₂³×C₂₃	—	4	4	no	—
373	C₂³×C₂₃	—	4	2	no	—
374	C₂³×C₂₃	—	4	2	no	—
375	C₂³×C₂₃	—	4	2	no	—
376	C₂³×C₂₃	—	4	4	no	—
377	C₂³×C₂₃	—	8	2	no	—
378	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
379	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
380	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
381	Q₈×C₂₃	—	2	1	no	—
382	Q₈×C₂₃	—	2	2	no	—
383	Q₈×C₂₃	—	2	2	no	—
384	Q₈×C₂₃	—	4	4	no	—
385	Q₈×C₂₃	—	4	4	no	—
386	Q₈×C₂₃	—	4	4	no	—
387	Q₈×C₂₃	C₂×#41	1	2	yes	complemented
388	D₄×C₂₃	—	2	4	no	—
389	D₄×C₂₃	—	2	4	no	—
390	D₄×C₂₃	—	2	2	no	—
391	D₄×C₂₃	—	2	2	no	—
392	D₄×C₂₃	—	2	2	no	—
393	D₄×C₂₃	—	2	1	no	—
394	D₄×C₂₃	—	2	2	no	—
395	D₄×C₂₃	—	2	2	no	—
396	D₄×C₂₃	—	4	4	no	—
397	D₄×C₂₃	—	4	4	no	—
398	D₄×C₂₃	—	4	4	no	—
399	D₄×C₂₃	—	4	8	no	—
400	D₄×C₂₃	—	4	4	no	—
401	D₄×C₂₃	—	4	4	no	—
402	D₄×C₂₃	—	4	8	no	—
403	D₄×C₂₃	—	4	2	no	—
404	D₄×C₂₃	—	4	2	no	—
405	D₄×C₂₃	—	8	1	no	—
406	D₄×C₂₃	—	8	2	no	—
407	D₄×C₂₃	AGL(1,ℤ/8)	1	4	yes	complemented
408	D₄×C₂₃	C₂×#41	1	2	yes	complemented
409	C₂×C₄×C₂₃	—	2	4	no	—
410	C₂×C₄×C₂₃	—	2	1	no	—
411	C₂×C₄×C₂₃	—	2	4	no	—
412	C₂×C₄×C₂₃	—	2	4	no	—
413	C₂×C₄×C₂₃	—	2	4	no	—
414	C₂×C₄×C₂₃	—	2	2	no	—
415	C₂×C₄×C₂₃	—	2	2	no	—
416	C₂×C₄×C₂₃	—	2	2	no	—
417	C₂×C₄×C₂₃	—	2	2	no	—
418	C₂×C₄×C₂₃	—	2	2	no	—
419	C₂×C₄×C₂₃	—	2	1	no	—
420	C₂×C₄×C₂₃	—	2	1	no	—
421	C₂×C₄×C₂₃	—	2	2	no	—
422	C₂×C₄×C₂₃	—	2	2	no	—
423	C₂×C₄×C₂₃	—	2	4	no	—
424	C₂×C₄×C₂₃	—	4	1	no	—
425	C₂×C₄×C₂₃	—	4	4	no	—
426	C₂×C₄×C₂₃	—	4	4	no	—
427	C₂×C₄×C₂₃	—	4	4	no	—
428	C₂×C₄×C₂₃	—	4	4	no	—
429	C₂×C₄×C₂₃	—	4	2	no	—
430	C₂×C₄×C₂₃	—	4	4	no	—
431	C₂×C₄×C₂₃	—	4	8	no	—
432	C₂×C₄×C₂₃	—	4	8	no	—
433	C₂×C₄×C₂₃	—	4	4	no	—
434	C₂×C₄×C₂₃	—	4	4	no	—
435	C₂×C₄×C₂₃	—	4	2	no	—
436	C₂×C₄×C₂₃	—	8	1	no	—
437	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
441	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
442	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
445	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
446	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
447	C₈×C₂₃	—	2	2	no	—
448	C₈×C₂₃	—	2	2	no	—
449	C₈×C₂₃	—	2	4	no	—
450	D₄×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
451	C₂×#547	C₂×C₂₃	1	1	yes	characteristic, complemented
452	#3332	C₂×C₂₃	1	2	yes	complemented
453	#3330	C₂×C₂₃	1	2	yes	complemented
454	#3308	C₂×C₂₃	1	4	yes	complemented
455	#3306	C₂×C₂₃	1	4	yes	complemented
456	#3298	C₂×C₂₃	1	2	yes	complemented
457	#3294	C₂×C₂₃	1	2	yes	complemented
458	#3141	C₂×C₂₃	1	1	yes	characteristic, complemented
459	#3092	C₂×C₂₃	1	2	yes	complemented
460	#3079	C₂×C₂₃	1	1	yes	characteristic, complemented
461	#3055	C₂×C₂₃	1	2	yes	complemented
462	#3036	C₂×C₂₃	1	1	yes	characteristic, complemented
463	#3006	C₂×C₂₃	1	2	yes	complemented
464	C₄×AGL(1,ℤ/8)	C₂×C₂₃	1	1	yes	characteristic, complemented
465	D₄×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
466	C₂×#417	C₂×C₂₃	1	2	yes	complemented
467	C₂²×C₂₃	—	2	1	no	—
468	C₂²×C₂₃	—	2	2	no	—
469	C₂²×C₂₃	—	2	2	no	—
470	C₂²×C₂₃	—	2	1	no	—
471	C₂²×C₂₃	—	2	2	no	—
472	C₂²×C₂₃	—	2	2	no	—
473	C₂²×C₂₃	—	2	2	no	—
474	C₂²×C₂₃	—	2	2	no	—
475	C₂²×C₂₃	—	4	8	no	—
476	C₂²×C₂₃	—	4	1	no	—
477	C₂²×C₂₃	—	4	1	no	—
478	C₂²×C₂₃	—	4	2	no	—
479	C₂²×C₂₃	—	4	2	no	—
480	C₂²×C₂₃	—	4	2	no	—
481	C₂²×C₂₃	—	4	2	no	—
482	C₂²×C₂₃	—	4	2	no	—
483	C₂²×C₂₃	—	4	2	no	—
484	C₂²×C₂₃	—	8	8	no	—
485	C₂²×C₂₃	—	8	4	no	—
486	C₂²×C₂₃	#546	1	2	yes	—
487	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
488	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
489	C₄×C₂₃	—	2	1	no	—
490	C₄×C₂₃	—	2	1	no	—
491	C₄×C₂₃	—	2	2	no	—
492	C₄×C₂₃	—	2	2	no	—
493	C₄×C₂₃	—	2	2	no	—
494	C₄×C₂₃	—	2	1	no	—
495	C₄×C₂₃	—	4	1	no	—
496	C₄×C₂₃	—	4	2	no	—
497	C₄×C₂₃	—	4	2	no	—
498	C₄×C₂₃	—	4	4	no	—
499	C₄×C₂₃	—	4	1	no	—
500	C₄×C₂₃	#546	1	2	yes	—
501	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
502	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
503	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
504	C₂²×#41	—	2	1	no	—
505	C₂²×#41	C₂²×C₂₃	1	2	yes	—
506	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
507	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
508	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	complemented
509	#550	C₂²×C₂₃	1	1	yes	characteristic, complemented
510	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
511	#548	C₂²×C₂₃	1	2	yes	complemented
512	#547	—	2	1	no	—
513	#547	—	2	2	no	—
514	#547	—	2	1	no	—
515	#547	—	2	1	no	—
516	#547	C₂²×C₂₃	1	2	yes	—
517	#547	C₂²×C₂₃	1	1	yes	characteristic, complemented
518	#547	C₂²×C₂₃	1	2	yes	complemented
519	#547	C₂²×C₂₃	1	4	yes	complemented
520	#546	—	2	2	no	—
521	#546	C₂²×C₂₃	1	2	yes	complemented
522	D₄²	—	2	1	no	—
523	D₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
524	#532	—	2	1	no	—
525	#532	C₂²×C₂₃	1	1	yes	characteristic
526	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
527	#525	—	2	2	no	—
528	#525	C₂²×C₂₃	1	2	yes	—
529	C₂×#123	—	2	2	no	—
530	C₂×C₂²⋊Q₈	—	2	1	no	—
531	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
532	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
533	C₂×C₄×D₄	—	2	1	no	—
534	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
535	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
536	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
537	#489	C₂²×C₂₃	1	4	yes	complemented
538	#487	C₂²×C₂₃	1	2	yes	complemented
539	#486	C₂²×C₂₃	1	2	yes	complemented
540	#484	C₂²×C₂₃	1	4	yes	complemented
541	#483	C₂²×C₂₃	1	4	yes	complemented
542	#481	C₂²×C₂₃	1	4	yes	complemented
543	#480	C₂²×C₂₃	1	4	yes	complemented
544	#477	C₂²×C₂₃	1	2	yes	complemented
545	#476	C₂²×C₂₃	1	2	yes	complemented
546	#475	C₂²×C₂₃	1	2	yes	complemented
547	#474	C₂²×C₂₃	1	2	yes	complemented
548	#469	C₂²×C₂₃	1	4	yes	complemented
549	#468	C₂²×C₂₃	1	4	yes	complemented
550	#466	C₂²×C₂₃	1	4	yes	complemented
551	#465	C₂²×C₂₃	1	4	yes	complemented
552	#463	C₂²×C₂₃	1	4	yes	complemented
553	#461	C₂²×C₂₃	1	2	yes	complemented
554	#459	C₂²×C₂₃	1	2	yes	complemented
555	#449	C₂²×C₂₃	1	4	yes	complemented
556	#449	C₂²×C₂₃	1	4	yes	complemented
557	#448	C₂²×C₂₃	1	4	yes	complemented
558	#447	C₂²×C₂₃	1	4	yes	complemented
559	#442	C₂²×C₂₃	1	2	yes	complemented
560	#440	C₂²×C₂₃	1	2	yes	complemented
561	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
562	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
563	#436	C₂²×C₂₃	1	2	yes	complemented
564	#435	C₂²×C₂₃	1	4	yes	complemented
565	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
566	#428	C₂²×C₂₃	1	2	yes	complemented
567	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
568	#423	C₂²×C₂₃	1	1	yes	characteristic, complemented
569	#418	C₂²×C₂₃	1	1	yes	characteristic, complemented
570	#417	C₂²×C₂₃	1	2	yes	—
571	#417	C₂²×C₂₃	1	1	yes	characteristic
572	#417	C₂²×C₂₃	1	4	yes	complemented
573	#417	C₂²×C₂₃	1	4	yes	complemented
574	#417	C₂²×C₂₃	1	2	yes	complemented
575	#417	C₂²×C₂₃	1	2	yes	complemented
576	#417	C₂²×C₂₃	1	2	yes	complemented
577	C₂×#103	C₂²×C₂₃	1	4	yes	complemented
578	C₂×#102	C₂²×C₂₃	1	4	yes	complemented
579	#407	C₂²×C₂₃	1	2	yes	complemented
580	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
581	C₂×C₂₃	—	2	2	no	—
582	C₂×C₂₃	—	2	4	no	—
583	C₂×C₂₃	—	4	2	no	—
584	C₂×C₂₃	—	4	2	no	—
585	C₂×C₂₃	—	8	2	no	—
586	C₂×C₂₃	—	8	2	no	—
587	C₂×C₂₃	C₂×#546	1	1	yes	characteristic
588	C₂×C₂₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
589	C₂×C₂₃	#3586	1	1	yes	characteristic
590	C₂×#41	—	2	2	no	—
591	C₂×#41	—	2	4	no	—
592	C₂×#41	—	2	2	no	—
593	C₂×#41	—	2	2	no	—
594	C₂×#41	—	2	2	no	—
595	C₂×#41	—	2	8	no	—
596	C₂×#41	—	4	4	no	—
597	C₂×#41	—	4	8	no	—
598	C₂×#41	C₂³×C₂₃	1	2	yes	—
599	C₂×#41	C₂³×C₂₃	1	2	yes	—
600	C₂×#41	C₂³×C₂₃	1	2	yes	—
601	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
602	C₂²×Q₈	—	2	1	no	—
603	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
604	C₂²×D₄	—	2	2	no	—
605	C₂²×D₄	—	2	2	no	—
606	C₂²×D₄	—	2	1	no	—
607	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
608	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
609	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
610	C₂³×C₄	—	2	2	no	—
611	C₂³×C₄	—	2	2	no	—
612	C₂³×C₄	—	2	1	no	—
613	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
614	AGL(1,ℤ/8)	—	2	4	no	—
615	AGL(1,ℤ/8)	—	4	4	no	—
616	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
617	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
618	C₂×D₈	C₂³×C₂₃	1	2	yes	—
619	C₂×D₈	C₂³×C₂₃	1	4	yes	—
620	C₂×M₁₆	—	4	4	no	—
621	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
622	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
623	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
624	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
625	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
626	C₄⋊Q₈	—	2	1	no	—
627	C₄⋊Q₈	—	2	1	no	—
628	C₄⋊Q₈	—	2	1	no	—
629	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
630	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
631	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
632	#127	—	2	1	no	—
633	#127	C₂³×C₂₃	1	1	yes	characteristic
634	#124	—	2	2	no	—
635	#124	C₂³×C₂₃	1	2	yes	—
636	#123	—	2	2	no	—
637	#123	—	2	2	no	—
638	#123	—	2	4	no	—
639	#123	—	2	4	no	—
640	#123	—	2	4	no	—
641	#123	—	2	4	no	—
642	#123	—	2	2	no	—
643	C₂²⋊Q₈	—	2	2	no	—
644	C₂²⋊Q₈	—	2	2	no	—
645	C₂²⋊Q₈	—	2	4	no	—
646	C₂²⋊Q₈	—	2	2	no	—
647	C₂²⋊Q₈	—	2	2	no	—
648	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
649	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
650	#121	—	2	2	no	—
651	#121	—	2	1	no	—
652	#121	—	2	2	no	—
653	#121	—	2	2	no	—
654	#121	—	2	1	no	—
655	#121	—	2	1	no	—
656	#121	—	2	1	no	—
657	#121	—	2	2	no	—
658	#121	—	2	2	no	—
659	#121	C₂³×C₂₃	1	4	yes	—
660	#121	C₂³×C₂₃	1	4	yes	—
661	#121	C₂³×C₂₃	1	2	yes	—
662	#121	C₂³×C₂₃	1	2	yes	—
663	#120	—	2	2	no	—
664	#120	—	2	2	no	—
665	#120	—	2	2	no	—
666	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
667	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
668	C₄×D₄	—	2	1	no	—
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	—	2	1	no	—
671	C₄×D₄	—	2	1	no	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	1	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	1	no	—
676	C₄×D₄	—	2	1	no	—
677	C₄×D₄	—	2	1	no	—
678	C₄×D₄	—	2	1	no	—
679	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
680	C₄×D₄	D₄×C₂₃	1	2	yes	—
681	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
682	C₄×D₄	C₂³×C₂₃	1	2	yes	—
683	C₄×D₄	C₂³×C₂₃	1	2	yes	—
684	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
685	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
686	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
687	C₄×D₄	C₂³×C₂₃	1	2	yes	—
688	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
689	#117	—	2	1	no	—
690	#117	C₂³×C₂₃	1	1	yes	characteristic
691	C₂×C₄⋊C₄	—	2	2	no	—
692	C₂×C₄⋊C₄	—	2	2	no	—
693	C₂×C₄⋊C₄	—	2	2	no	—
694	C₂×C₄⋊C₄	—	2	1	no	—
695	C₂×C₄⋊C₄	—	2	1	no	—
696	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
697	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
698	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
699	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
700	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
701	C₂×C₂²⋊C₄	—	2	1	no	—
702	C₂×C₂²⋊C₄	—	2	2	no	—
703	C₂×C₂²⋊C₄	—	2	2	no	—
704	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
705	C₂×C₄²	—	2	1	no	—
706	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
707	#107	C₂³×C₂₃	1	2	yes	—
708	#107	C₂³×C₂₃	1	4	yes	—
709	#106	C₂³×C₂₃	1	2	yes	—
710	#106	C₂³×C₂₃	1	4	yes	—
711	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
712	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
713	#103	C₂³×C₂₃	1	2	yes	—
714	#103	C₂³×C₂₃	1	4	yes	—
715	#103	C₂³×C₂₃	1	4	yes	—
716	#103	C₂³×C₂₃	1	4	yes	—
717	#103	C₂³×C₂₃	1	4	yes	—
718	#102	C₂³×C₂₃	1	2	yes	—
719	#102	C₂³×C₂₃	1	4	yes	—
720	#102	C₂³×C₂₃	1	4	yes	—
721	#102	C₂³×C₂₃	1	4	yes	—
722	#102	C₂³×C₂₃	1	4	yes	—
723	#102	C₂³×C₂₃	1	2	yes	—
724	#102	C₂³×C₂₃	1	2	yes	—
725	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
726	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
727	#97	C₂³×C₂₃	1	2	yes	—
728	C₄×C₈	C₂³×C₂₃	1	2	yes	—
729	C₂₃	#61161	1	1	yes	characteristic, direct product factor, Sylow
730	C₂⁴	—	2	1	no	—
731	C₂⁴	—	2	2	no	—
732	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
733	#41	—	2	2	no	—
734	#41	—	2	4	no	—
735	#41	—	2	4	no	—
736	#41	—	2	4	no	—
737	#41	—	2	4	no	—
738	#41	—	4	8	no	—
739	#41	—	4	2	no	—
740	#41	—	4	2	no	—
741	#41	—	4	8	no	—
742	#41	—	4	16	no	—
743	#41	—	4	8	no	—
744	#41	—	4	8	no	—
745	#41	#41×C₂₃	1	4	yes	complemented
746	C₂×Q₈	—	2	2	no	—
747	C₂×Q₈	—	2	2	no	—
748	C₂×Q₈	—	2	2	no	—
749	C₂×Q₈	—	2	4	no	—
750	C₂×Q₈	—	4	2	no	—
751	C₂×Q₈	—	4	4	no	—
752	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
753	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
754	C₂×D₄	—	2	1	no	—
755	C₂×D₄	—	2	4	no	—
756	C₂×D₄	—	2	4	no	—
757	C₂×D₄	—	2	2	no	—
758	C₂×D₄	—	2	2	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	4	no	—
762	C₂×D₄	—	2	4	no	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	2	1	no	—
765	C₂×D₄	—	2	1	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	2	1	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	4	2	no	—
771	C₂×D₄	—	4	8	no	—
772	C₂×D₄	—	4	8	no	—
773	C₂×D₄	—	4	4	no	—
774	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
775	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
776	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
777	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
778	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
779	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
780	C₂²×C₄	—	2	1	no	—
781	C₂²×C₄	—	2	4	no	—
782	C₂²×C₄	—	2	4	no	—
783	C₂²×C₄	—	2	1	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	4	no	—
786	C₂²×C₄	—	2	4	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	1	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	1	no	—
795	C₂²×C₄	—	4	8	no	—
796	C₂²×C₄	—	4	4	no	—
797	C₂²×C₄	—	4	8	no	—
798	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
799	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
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	1	yes	characteristic
803	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
804	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
805	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
806	SD₁₆	—	2	4	no	—
807	SD₁₆	—	4	4	no	—
808	D₈	—	2	4	no	—
809	D₈	—	4	4	no	—
810	M₁₆	—	2	2	no	—
811	M₁₆	—	2	2	no	—
812	M₁₆	—	2	4	no	—
813	M₁₆	—	4	4	no	—
814	C₂×C₈	—	4	4	no	—
815	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
816	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
817	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
818	C₄⋊C₄	—	2	1	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	4	no	—
821	C₄⋊C₄	—	2	4	no	—
822	C₄⋊C₄	—	2	1	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	1	no	—
827	C₄⋊C₄	—	2	1	no	—
828	C₄⋊C₄	—	2	1	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
831	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
832	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
833	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
834	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
835	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
836	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	1	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	4	no	—
845	C₂²⋊C₄	—	2	4	no	—
846	C₂²⋊C₄	—	2	1	no	—
847	C₂²⋊C₄	—	2	1	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
851	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
852	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
853	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
854	C₄²	—	2	1	no	—
855	C₄²	—	2	1	no	—
856	C₄²	—	2	1	no	—
857	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
858	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
859	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
860	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
861	C₂³	—	2	4	no	—
862	C₂³	—	2	1	no	—
863	C₂³	—	2	4	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	2	no	—
866	C₂³	—	4	2	no	—
867	C₂³	—	4	4	no	—
868	C₂³	—	4	2	no	—
869	C₂³	—	4	2	no	—
870	C₂³	—	4	4	no	—
871	C₂³	—	4	2	no	—
872	C₂³	—	8	2	no	—
873	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
874	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
875	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
876	Q₈	—	2	1	no	—
877	Q₈	—	2	2	no	—
878	Q₈	—	2	2	no	—
879	Q₈	—	4	4	no	—
880	Q₈	—	4	4	no	—
881	Q₈	—	4	4	no	—
882	Q₈	C₂×#41×C₂₃	1	2	yes	complemented
883	D₄	—	2	4	no	—
884	D₄	—	2	4	no	—
885	D₄	—	2	2	no	—
886	D₄	—	2	2	no	—
887	D₄	—	2	2	no	—
888	D₄	—	2	1	no	—
889	D₄	—	2	2	no	—
890	D₄	—	2	2	no	—
891	D₄	—	4	4	no	—
892	D₄	—	4	4	no	—
893	D₄	—	4	4	no	—
894	D₄	—	4	8	no	—
895	D₄	—	4	8	no	—
896	D₄	—	4	4	no	—
897	D₄	—	4	4	no	—
898	D₄	—	4	2	no	—
899	D₄	—	4	2	no	—
900	D₄	—	8	1	no	—
901	D₄	—	8	2	no	—
902	D₄	C₂₃×AGL(1,ℤ/8)	1	4	yes	complemented
903	D₄	C₂×#41×C₂₃	1	2	yes	complemented
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	4	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	4	no	—
912	C₂×C₄	—	2	4	no	—
913	C₂×C₄	—	2	4	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	4	no	—
919	C₂×C₄	—	4	1	no	—
920	C₂×C₄	—	4	4	no	—
921	C₂×C₄	—	4	4	no	—
922	C₂×C₄	—	4	4	no	—
923	C₂×C₄	—	4	4	no	—
924	C₂×C₄	—	4	2	no	—
925	C₂×C₄	—	4	4	no	—
926	C₂×C₄	—	4	8	no	—
927	C₂×C₄	—	4	8	no	—
928	C₂×C₄	—	4	4	no	—
929	C₂×C₄	—	4	2	no	—
930	C₂×C₄	—	4	4	no	—
931	C₂×C₄	—	8	1	no	—
932	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
933	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
934	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
935	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
936	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
937	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
938	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
939	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
940	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
941	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
942	C₈	—	2	2	no	—
943	C₈	—	2	2	no	—
944	C₈	—	2	4	no	—
945	C₂²	—	2	2	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	2	1	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	2	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	4	8	no	—
954	C₂²	—	4	1	no	—
955	C₂²	—	4	1	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	8	8	no	—
963	C₂²	—	8	4	no	—
964	C₂²	C₂₃×#546	1	2	yes	—
965	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	4	yes	—
966	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
967	C₄	—	2	2	no	—
968	C₄	—	2	2	no	—
969	C₄	—	2	2	no	—
970	C₄	—	2	1	no	—
971	C₄	—	2	1	no	—
972	C₄	—	2	1	no	—
973	C₄	—	4	2	no	—
974	C₄	—	4	2	no	—
975	C₄	—	4	4	no	—
976	C₄	—	4	1	no	—
977	C₄	—	4	1	no	—
978	C₄	C₂₃×#546	1	2	yes	—
979	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
980	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
981	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
982	C₂	—	2	2	no	—
983	C₂	—	2	4	no	—
984	C₂	—	4	2	no	—
985	C₂	—	4	2	no	—
986	C₂	—	8	2	no	—
987	C₂	—	8	2	no	—
988	C₂	C₂×C₂₃×#546	1	1	yes	characteristic
989	C₂	C₂²×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
990	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 ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. D₄×#41×C₂₃	C₂	semidirect
2. C₂×C₂₃×#547	C₂	semidirect
3. C₂₃×#3332	C₂	semidirect
4. C₂₃×#3330	C₂	semidirect
5. C₂₃×#3308	C₂	semidirect
6. C₂₃×#3306	C₂	semidirect
7. C₂₃×#3298	C₂	semidirect
8. C₂₃×#3294	C₂	semidirect
9. C₂₃×#3141	C₂	semidirect
10. C₂₃×#3092	C₂	semidirect
11. C₂₃×#3079	C₂	semidirect
12. C₂₃×#3055	C₂	semidirect
13. C₂₃×#3036	C₂	semidirect
14. C₂₃×#3006	C₂	semidirect
15. C₄×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
16. D₄×M₁₆×C₂₃	C₂	semidirect
17. C₂×C₂₃×#417	C₂	semidirect
21. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂²×M₁₆×C₂₃	C₂²	semidirect
23. C₂₃×#550	C₂²	semidirect
24. D₄×Q₈×C₂₃	C₂²	semidirect
25. C₂₃×#548	C₂²	semidirect
31. C₂₃×#547	C₂²	semidirect
32. C₂₃×#547	C₂²	semidirect
33. C₂₃×#547	C₂²	semidirect
35. C₂₃×#546	C₂²	semidirect
37. D₄²×C₂₃	C₂²	semidirect
40. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
45. C₂×C₂₃×#121	C₂²	semidirect
49. C₂×C₄×D₄×C₂₃	C₂²	semidirect
50. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
51. C₂₃×#489	C₂²	semidirect
52. C₂₃×#487	C₂²	semidirect
53. C₂₃×#486	C₂²	semidirect
54. C₂₃×#484	C₂²	semidirect
55. C₂₃×#483	C₂²	semidirect
56. C₂₃×#481	C₂²	semidirect
57. C₂₃×#480	C₂²	semidirect
58. C₂₃×#477	C₂²	semidirect
59. C₂₃×#476	C₂²	semidirect
60. C₂₃×#475	C₂²	semidirect
61. C₂₃×#474	C₂²	semidirect
62. C₂₃×#469	C₂²	semidirect
63. C₂₃×#468	C₂²	semidirect
64. C₂₃×#466	C₂²	semidirect
65. C₂₃×#465	C₂²	semidirect
66. C₂₃×#463	C₂²	semidirect
67. C₂₃×#461	C₂²	semidirect
68. C₂₃×#459	C₂²	semidirect
69. C₂₃×#449	C₂²	semidirect
70. C₂₃×#449	C₂²	semidirect
71. C₂₃×#448	C₂²	semidirect
72. C₂₃×#447	C₂²	semidirect
73. C₂₃×#442	C₂²	semidirect
74. C₂₃×#440	C₂²	semidirect
75. C₄×SD₁₆×C₂₃	C₂²	semidirect
76. C₄×D₈×C₂₃	C₂²	semidirect
77. C₂₃×#436	C₂²	semidirect
78. C₂₃×#435	C₂²	semidirect
79. C₈×D₄×C₂₃	C₂²	semidirect
80. C₂₃×#428	C₂²	semidirect
81. C₂₃×#428	C₂²	semidirect
82. C₂₃×#423	C₂²	semidirect
83. C₂₃×#418	C₂²	semidirect
86. C₂₃×#417	C₂²	semidirect
87. C₂₃×#417	C₂²	semidirect
88. C₂₃×#417	C₂²	semidirect
89. C₂₃×#417	C₂²	semidirect
90. C₂₃×#417	C₂²	semidirect
91. C₂×C₂₃×#103	C₂²	semidirect
92. C₂×C₂₃×#102	C₂²	semidirect
93. C₂₃×#407	C₂²	semidirect
94. C₄×M₁₆×C₂₃	C₂²	semidirect
249. #41×C₂₃	#41	semidirect
365. #61161	C₂₃	direct (N × H)
387. Q₈×C₂₃	C₂×#41	semidirect
407. D₄×C₂₃	AGL(1,ℤ/8)	semidirect
408. D₄×C₂₃	C₂×#41	semidirect
450. D₄×#41	C₂×C₂₃	semidirect
451. C₂×#547	C₂×C₂₃	semidirect
452. #3332	C₂×C₂₃	semidirect
453. #3330	C₂×C₂₃	semidirect
454. #3308	C₂×C₂₃	semidirect
455. #3306	C₂×C₂₃	semidirect
456. #3298	C₂×C₂₃	semidirect
457. #3294	C₂×C₂₃	semidirect
458. #3141	C₂×C₂₃	semidirect
459. #3092	C₂×C₂₃	semidirect
460. #3079	C₂×C₂₃	semidirect
461. #3055	C₂×C₂₃	semidirect
462. #3036	C₂×C₂₃	semidirect
463. #3006	C₂×C₂₃	semidirect
464. C₄×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
465. D₄×M₁₆	C₂×C₂₃	semidirect
466. C₂×#417	C₂×C₂₃	semidirect
507. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
508. C₂²×M₁₆	C₂²×C₂₃	semidirect
509. #550	C₂²×C₂₃	semidirect
510. D₄×Q₈	C₂²×C₂₃	semidirect
511. #548	C₂²×C₂₃	semidirect
517. #547	C₂²×C₂₃	semidirect
518. #547	C₂²×C₂₃	semidirect
519. #547	C₂²×C₂₃	semidirect
521. #546	C₂²×C₂₃	semidirect
523. D₄²	C₂²×C₂₃	semidirect
526. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
531. C₂×#121	C₂²×C₂₃	semidirect
535. C₂×C₄×D₄	C₂²×C₂₃	semidirect
536. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
537. #489	C₂²×C₂₃	semidirect
538. #487	C₂²×C₂₃	semidirect
539. #486	C₂²×C₂₃	semidirect
540. #484	C₂²×C₂₃	semidirect
541. #483	C₂²×C₂₃	semidirect
542. #481	C₂²×C₂₃	semidirect
543. #480	C₂²×C₂₃	semidirect
544. #477	C₂²×C₂₃	semidirect
545. #476	C₂²×C₂₃	semidirect
546. #475	C₂²×C₂₃	semidirect
547. #474	C₂²×C₂₃	semidirect
548. #469	C₂²×C₂₃	semidirect
549. #468	C₂²×C₂₃	semidirect
550. #466	C₂²×C₂₃	semidirect
551. #465	C₂²×C₂₃	semidirect
552. #463	C₂²×C₂₃	semidirect
553. #461	C₂²×C₂₃	semidirect
554. #459	C₂²×C₂₃	semidirect
555. #449	C₂²×C₂₃	semidirect
556. #449	C₂²×C₂₃	semidirect
557. #448	C₂²×C₂₃	semidirect
558. #447	C₂²×C₂₃	semidirect
559. #442	C₂²×C₂₃	semidirect
560. #440	C₂²×C₂₃	semidirect
561. C₄×SD₁₆	C₂²×C₂₃	semidirect
562. C₄×D₈	C₂²×C₂₃	semidirect
563. #436	C₂²×C₂₃	semidirect
564. #435	C₂²×C₂₃	semidirect
565. C₈×D₄	C₂²×C₂₃	semidirect
566. #428	C₂²×C₂₃	semidirect
567. #428	C₂²×C₂₃	semidirect
568. #423	C₂²×C₂₃	semidirect
569. #418	C₂²×C₂₃	semidirect
572. #417	C₂²×C₂₃	semidirect
573. #417	C₂²×C₂₃	semidirect
574. #417	C₂²×C₂₃	semidirect
575. #417	C₂²×C₂₃	semidirect
576. #417	C₂²×C₂₃	semidirect
577. C₂×#103	C₂²×C₂₃	semidirect
578. C₂×#102	C₂²×C₂₃	semidirect
579. #407	C₂²×C₂₃	semidirect
580. C₄×M₁₆	C₂²×C₂₃	semidirect
729. C₂₃	#61161	direct (N × H)
745. #41	#41×C₂₃	semidirect
882. Q₈	C₂×#41×C₂₃	semidirect
902. D₄	C₂₃×AGL(1,ℤ/8)	semidirect
903. D₄	C₂×#41×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
D₄×#41×C₂₃	2
C₂×C₂₃×#547	2
C₂₃×#3332	2
C₂₃×#3330	2
C₂₃×#3308	2
C₂₃×#3306	2
C₂₃×#3298	2
C₂₃×#3294	2
C₂₃×#3141	2
C₂₃×#3092	2
C₂₃×#3079	2
C₂₃×#3055	2
C₂₃×#3036	2
C₂₃×#3006	2
C₄×C₂₃×AGL(1,ℤ/8)	2
D₄×M₁₆×C₂₃	2
C₂×C₂₃×#417	2
#61161	23

Subgroups — C23×#61161 #19208787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61161 #19208787