Subgroups — C₂₃×#61030 #19208656

Order 5888.

2796 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#575	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×#41×C₂₃	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3271	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3270	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3269	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3268	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3267	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3266	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3265	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3264	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3150	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3054	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3050	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3035	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3002	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3002	C₂	1	2	yes	maximal, complemented
18	C₂₃×#2943	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₂₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₂₃	C₂²	1	2	yes	complemented
21	C₂²×#41×C₂₃	C₂²	1	2	yes	complemented
22	C₂₃×#575	—	2	8	no	—
23	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
24	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
25	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
26	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
27	C₂×C₂₃×#135	—	2	8	no	—
28	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
30	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
31	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
33	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
37	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
38	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
39	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
40	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
41	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
42	C₂₃×#550	C₂²	1	2	yes	complemented
43	D₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
44	C₂₃×#548	C₂²	1	2	yes	—
45	C₂₃×#548	C₂²	1	2	yes	complemented
46	C₂₃×#547	—	2	2	no	—
47	C₂₃×#547	C₂²	1	2	yes	complemented
48	C₂₃×#546	—	2	2	no	—
49	C₂₃×#546	—	2	2	no	—
50	C₂₃×#546	C₂²	1	2	yes	—
51	C₂₃×#546	C₂²	1	2	yes	complemented
52	D₄²×C₂₃	—	2	2	no	—
53	D₄²×C₂₃	C₂²	1	2	yes	complemented
54	C₂₃×#532	—	2	2	no	—
55	C₂₃×#532	C₂²	1	2	yes	complemented
56	C₂₃×#525	—	2	2	no	—
57	C₂₃×#525	—	2	2	no	—
58	C₂₃×#525	C₂²	1	2	yes	complemented
59	C₂₃×#525	C₂²	1	2	yes	complemented
60	C₄×#41×C₂₃	C₂²	1	2	yes	complemented
61	C₂×C₄×D₄×C₂₃	—	2	2	no	—
62	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
63	C₂₃×#497	C₂²	1	2	yes	complemented
64	C₂₃×#497	C₂²	1	2	yes	complemented
65	C₂₃×#496	C₂²	1	2	yes	complemented
66	C₂₃×#496	C₂²	1	2	yes	complemented
67	C₂₃×#470	C₂²	1	2	yes	complemented
68	C₂₃×#469	C₂²	1	2	yes	complemented
69	C₂₃×#468	C₂²	1	2	yes	complemented
70	C₂₃×#468	C₂²	1	2	yes	complemented
71	C₂₃×#467	C₂²	1	1	yes	characteristic, complemented
72	C₂₃×#467	C₂²	1	1	yes	characteristic, complemented
73	C₂₃×#466	C₂²	1	1	yes	characteristic, complemented
74	C₂₃×#466	C₂²	1	1	yes	characteristic, complemented
75	C₂₃×#465	C₂²	1	2	yes	complemented
76	C₂₃×#465	C₂²	1	2	yes	complemented
77	C₂₃×#464	C₂²	1	2	yes	complemented
78	C₂₃×#464	C₂²	1	2	yes	complemented
79	C₂₃×#463	C₂²	1	2	yes	complemented
80	C₂₃×#463	C₂²	1	2	yes	complemented
81	C₂₃×#462	C₂²	1	2	yes	complemented
82	C₂₃×#461	C₂²	1	2	yes	complemented
83	C₂₃×#460	C₂²	1	2	yes	complemented
84	C₂₃×#459	C₂²	1	2	yes	complemented
85	C₂₃×#452	C₂²	1	2	yes	complemented
86	C₂₃×#452	C₂²	1	2	yes	complemented
87	C₂₃×#452	C₂²	1	2	yes	complemented
88	C₂₃×#452	C₂²	1	2	yes	complemented
89	C₂₃×#451	C₂²	1	2	yes	complemented
90	C₂₃×#451	C₂²	1	2	yes	complemented
91	C₂₃×#450	C₂²	1	2	yes	complemented
92	C₂₃×#450	C₂²	1	2	yes	complemented
93	C₂₃×#449	C₂²	1	2	yes	complemented
94	C₂₃×#449	C₂²	1	2	yes	complemented
95	C₂₃×#449	C₂²	1	2	yes	complemented
96	C₂₃×#449	C₂²	1	2	yes	complemented
97	C₂₃×#448	C₂²	1	2	yes	complemented
98	C₂₃×#448	C₂²	1	2	yes	complemented
99	C₂₃×#447	C₂²	1	2	yes	complemented
100	C₂₃×#447	C₂²	1	2	yes	complemented
101	C₂₃×#442	C₂²	1	2	yes	complemented
102	C₂₃×#441	C₂²	1	2	yes	complemented
103	C₂₃×#440	C₂²	1	2	yes	complemented
104	C₂₃×#440	C₂²	1	2	yes	complemented
105	C₂₃×#435	C₂²	1	2	yes	complemented
106	C₂₃×#435	C₂²	1	2	yes	complemented
107	C₂₃×#435	C₂²	1	2	yes	complemented
108	C₂₃×#435	C₂²	1	2	yes	complemented
109	C₂₃×#427	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
111	C₂₃×#416	C₂²	1	2	yes	complemented
112	C₂₃×#416	C₂²	1	2	yes	complemented
113	C₂₃×#416	C₂²	1	2	yes	complemented
114	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
116	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
117	C₂×#41×C₂₃	—	2	2	no	—
118	C₂×#41×C₂₃	—	2	2	no	—
119	C₂×#41×C₂₃	—	2	2	no	—
120	C₂×#41×C₂₃	—	2	2	no	—
121	C₂×#41×C₂₃	—	2	8	no	—
122	C₂×#41×C₂₃	—	2	8	no	—
123	C₂×#41×C₂₃	—	4	4	no	—
124	C₂×#41×C₂₃	—	4	4	no	—
125	C₂×#41×C₂₃	C₂³	1	2	yes	—
126	C₂×#41×C₂₃	C₂³	1	2	yes	—
127	C₂×#41×C₂₃	C₂³	1	2	yes	—
128	C₂×#41×C₂₃	C₂³	1	2	yes	—
129	C₂×#41×C₂₃	C₂³	1	2	yes	—
130	C₂×#41×C₂₃	C₂³	1	2	yes	—
131	C₂×#41×C₂₃	C₂³	1	2	yes	—
132	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
133	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
134	C₂²×D₄×C₂₃	—	2	2	no	—
135	C₂²×D₄×C₂₃	—	2	2	no	—
136	C₂²×D₄×C₂₃	—	2	2	no	—
137	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
138	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
139	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
140	C₂³×C₄×C₂₃	—	2	2	no	—
141	C₂³×C₄×C₂₃	—	2	2	no	—
142	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
144	C₂₃×#137	—	2	8	no	—
145	C₂₃×#137	—	2	8	no	—
146	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
147	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
148	C₂₃×#135	—	2	8	no	—
149	C₂₃×#135	—	2	8	no	—
150	C₂₃×#135	—	2	4	no	—
151	C₂₃×#135	—	2	8	no	—
152	C₂₃×#135	—	2	4	no	—
153	C₂₃×#135	—	2	4	no	—
154	C₂₃×#135	—	2	4	no	—
155	C₂₃×#135	—	4	4	no	—
156	C₂₃×#135	D₄	1	8	yes	complemented
157	C₂×Q₁₆×C₂₃	—	2	4	no	—
158	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
159	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
160	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
161	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
162	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
163	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
164	C₂×SD₁₆×C₂₃	—	2	8	no	—
165	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
167	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
168	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
169	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
170	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
171	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
172	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
173	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
174	C₂×D₈×C₂₃	—	2	4	no	—
175	C₂×D₈×C₂₃	C₂³	1	2	yes	—
176	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
177	C₂×D₈×C₂₃	C₂³	1	2	yes	—
178	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
179	C₂×D₈×C₂₃	C₂³	1	2	yes	—
180	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
181	C₂×M₁₆×C₂₃	—	2	4	no	—
182	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
183	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
184	C₂²×C₈×C₂₃	—	2	4	no	—
185	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
186	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
187	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
188	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
189	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
190	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
191	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
192	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
193	C₂₃×C₄⋊Q₈	—	2	2	no	—
194	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
195	C₂₃×#127	—	2	2	no	—
196	C₂₃×#127	C₂³	1	2	yes	—
197	C₂₃×#124	—	2	2	no	—
198	C₂₃×#124	—	2	2	no	—
199	C₂₃×#124	C₂³	1	2	yes	—
200	C₂₃×#124	C₂³	1	2	yes	—
201	C₂₃×#123	—	2	2	no	—
202	C₂₃×#123	—	2	2	no	—
203	C₂₃×#123	—	2	2	no	—
204	C₂₃×#123	—	2	2	no	—
205	C₂₃×#123	—	2	2	no	—
206	C₂₃×#123	—	2	2	no	—
207	C₂₃×C₂²⋊Q₈	—	2	2	no	—
208	C₂₃×C₂²⋊Q₈	—	2	2	no	—
209	C₂₃×C₂²⋊Q₈	—	2	2	no	—
210	C₂₃×C₂²⋊Q₈	—	2	2	no	—
211	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₂₃×#121	—	2	2	no	—
216	C₂₃×#121	—	2	2	no	—
217	C₂₃×#121	—	2	2	no	—
218	C₂₃×#121	—	2	2	no	—
219	C₂₃×#121	—	2	2	no	—
220	C₂₃×#121	—	2	2	no	—
221	C₂₃×#121	—	2	2	no	—
222	C₂₃×#121	—	2	2	no	—
223	C₂₃×#121	—	2	2	no	—
224	C₂₃×#121	—	2	2	no	—
225	C₂₃×#121	C₂³	1	2	yes	—
226	C₂₃×#121	C₂³	1	2	yes	—
227	C₂₃×#121	C₂³	1	2	yes	—
228	C₂₃×#121	C₂³	1	2	yes	—
229	C₂₃×#120	—	2	2	no	—
230	C₂₃×#120	—	2	2	no	—
231	C₂₃×#120	—	2	2	no	—
232	C₂₃×#120	—	2	2	no	—
233	C₂₃×#120	—	2	2	no	—
234	C₂₃×#120	—	2	2	no	—
235	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
236	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
237	C₄×D₄×C₂₃	—	2	2	no	—
238	C₄×D₄×C₂₃	—	2	2	no	—
239	C₄×D₄×C₂₃	—	2	2	no	—
240	C₄×D₄×C₂₃	—	2	2	no	—
241	C₄×D₄×C₂₃	—	2	2	no	—
242	C₄×D₄×C₂₃	—	2	2	no	—
243	C₄×D₄×C₂₃	—	2	2	no	—
244	C₄×D₄×C₂₃	—	2	2	no	—
245	C₄×D₄×C₂₃	—	2	2	no	—
246	C₄×D₄×C₂₃	—	2	2	no	—
247	C₄×D₄×C₂₃	—	2	2	no	—
248	C₄×D₄×C₂₃	—	2	2	no	—
249	C₄×D₄×C₂₃	D₄	1	2	yes	—
250	C₄×D₄×C₂₃	D₄	1	2	yes	—
251	C₄×D₄×C₂₃	C₂³	1	2	yes	—
252	C₄×D₄×C₂₃	C₂³	1	2	yes	—
253	C₄×D₄×C₂₃	C₂³	1	2	yes	—
254	C₄×D₄×C₂₃	C₂³	1	2	yes	—
255	C₂₃×#117	—	2	2	no	—
256	C₂₃×#117	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
258	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
260	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
261	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
263	C₂×C₄²×C₂₃	—	2	2	no	—
264	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
265	C₂₃×#107	C₂³	1	1	yes	characteristic
266	C₂₃×#107	C₂³	1	1	yes	characteristic
267	C₂₃×#106	C₂³	1	2	yes	—
268	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
269	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
270	C₂₃×#103	C₂³	1	2	yes	—
271	C₂₃×#103	C₂³	1	2	yes	—
272	C₂₃×#103	C₂³	1	2	yes	—
273	C₂₃×#103	C₂³	1	2	yes	—
274	C₂₃×#103	C₂³	1	2	yes	—
275	C₂₃×#103	C₂³	1	2	yes	—
276	C₂₃×#102	C₂³	1	2	yes	—
277	C₂₃×#102	C₂³	1	2	yes	—
278	C₂₃×#102	C₂³	1	2	yes	—
279	C₂₃×#102	C₂³	1	2	yes	—
280	C₂₃×#102	C₂³	1	2	yes	—
281	C₂₃×#102	C₂³	1	2	yes	—
282	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
283	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
284	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
285	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
286	C₂₃×#97	C₂³	1	2	yes	—
287	C₂₃×#97	C₂³	1	2	yes	—
288	C₂⁴×C₂₃	—	2	2	no	—
289	C₂⁴×C₂₃	—	2	2	no	—
290	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
291	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
292	#41×C₂₃	—	2	4	no	—
293	#41×C₂₃	—	2	4	no	—
294	#41×C₂₃	—	2	4	no	—
295	#41×C₂₃	—	2	4	no	—
296	#41×C₂₃	—	2	4	no	—
297	#41×C₂₃	—	2	4	no	—
298	#41×C₂₃	—	2	4	no	—
299	#41×C₂₃	—	2	4	no	—
300	#41×C₂₃	—	2	4	no	—
301	#41×C₂₃	—	4	8	no	—
302	#41×C₂₃	—	4	8	no	—
303	#41×C₂₃	—	4	2	no	—
304	#41×C₂₃	—	4	2	no	—
305	#41×C₂₃	—	4	2	no	—
306	#41×C₂₃	—	4	2	no	—
307	#41×C₂₃	—	4	8	no	—
308	#41×C₂₃	—	4	8	no	—
309	#41×C₂₃	C₂×D₄	1	8	yes	complemented
310	C₂×Q₈×C₂₃	—	2	2	no	—
311	C₂×Q₈×C₂₃	—	2	2	no	—
312	C₂×Q₈×C₂₃	—	2	4	no	—
313	C₂×Q₈×C₂₃	—	2	4	no	—
314	C₂×Q₈×C₂₃	—	4	2	no	—
315	C₂×Q₈×C₂₃	—	4	2	no	—
316	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
317	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
318	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
319	C₂×D₄×C₂₃	—	2	2	no	—
320	C₂×D₄×C₂₃	—	2	4	no	—
321	C₂×D₄×C₂₃	—	2	4	no	—
322	C₂×D₄×C₂₃	—	2	2	no	—
323	C₂×D₄×C₂₃	—	2	2	no	—
324	C₂×D₄×C₂₃	—	2	2	no	—
325	C₂×D₄×C₂₃	—	2	2	no	—
326	C₂×D₄×C₂₃	—	2	2	no	—
327	C₂×D₄×C₂₃	—	2	2	no	—
328	C₂×D₄×C₂₃	—	2	2	no	—
329	C₂×D₄×C₂₃	—	2	2	no	—
330	C₂×D₄×C₂₃	—	2	2	no	—
331	C₂×D₄×C₂₃	—	2	2	no	—
332	C₂×D₄×C₂₃	—	2	2	no	—
333	C₂×D₄×C₂₃	—	2	2	no	—
334	C₂×D₄×C₂₃	—	2	2	no	—
335	C₂×D₄×C₂₃	—	2	2	no	—
336	C₂×D₄×C₂₃	—	4	2	no	—
337	C₂×D₄×C₂₃	—	4	2	no	—
338	C₂×D₄×C₂₃	—	4	2	no	—
339	C₂×D₄×C₂₃	—	4	8	no	—
340	C₂×D₄×C₂₃	—	4	8	no	—
341	C₂×D₄×C₂₃	—	4	8	no	—
342	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
343	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
345	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
346	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
347	C₂²×C₄×C₂₃	—	2	2	no	—
348	C₂²×C₄×C₂₃	—	2	2	no	—
349	C₂²×C₄×C₂₃	—	2	2	no	—
350	C₂²×C₄×C₂₃	—	2	2	no	—
351	C₂²×C₄×C₂₃	—	2	2	no	—
352	C₂²×C₄×C₂₃	—	2	2	no	—
353	C₂²×C₄×C₂₃	—	2	2	no	—
354	C₂²×C₄×C₂₃	—	2	2	no	—
355	C₂²×C₄×C₂₃	—	2	2	no	—
356	C₂²×C₄×C₂₃	—	2	2	no	—
357	C₂²×C₄×C₂₃	—	2	2	no	—
358	C₂²×C₄×C₂₃	—	2	2	no	—
359	C₂²×C₄×C₂₃	—	2	2	no	—
360	C₂²×C₄×C₂₃	—	2	2	no	—
361	C₂²×C₄×C₂₃	—	2	2	no	—
362	C₂²×C₄×C₂₃	—	4	8	no	—
363	C₂²×C₄×C₂₃	—	4	8	no	—
364	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
368	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
374	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
375	Q₁₆×C₂₃	—	2	4	no	—
376	Q₁₆×C₂₃	—	2	4	no	—
377	Q₁₆×C₂₃	—	2	2	no	—
378	Q₁₆×C₂₃	—	2	2	no	—
379	Q₁₆×C₂₃	—	4	2	no	—
380	Q₁₆×C₂₃	C₂×D₄	1	4	yes	complemented
381	SD₁₆×C₂₃	—	2	4	no	—
382	SD₁₆×C₂₃	—	2	4	no	—
383	SD₁₆×C₂₃	—	2	4	no	—
384	SD₁₆×C₂₃	—	2	4	no	—
385	SD₁₆×C₂₃	—	2	4	no	—
386	SD₁₆×C₂₃	—	2	4	no	—
387	SD₁₆×C₂₃	—	4	2	no	—
388	SD₁₆×C₂₃	—	4	2	no	—
389	SD₁₆×C₂₃	C₂×D₄	1	8	yes	complemented
390	D₈×C₂₃	—	2	4	no	—
391	D₈×C₂₃	—	2	4	no	—
392	D₈×C₂₃	—	2	2	no	—
393	D₈×C₂₃	—	2	2	no	—
394	D₈×C₂₃	—	4	2	no	—
395	D₈×C₂₃	C₂×D₄	1	4	yes	complemented
396	M₁₆×C₂₃	—	2	4	no	—
397	M₁₆×C₂₃	—	2	4	no	—
398	C₂×C₈×C₂₃	—	2	2	no	—
399	C₂×C₈×C₂₃	—	2	2	no	—
400	C₂×C₈×C₂₃	—	2	2	no	—
401	C₂×C₈×C₂₃	—	2	2	no	—
402	C₂×C₈×C₂₃	—	2	2	no	—
403	C₂×C₈×C₂₃	—	2	2	no	—
404	C₂×C₈×C₂₃	—	2	2	no	—
405	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	complemented
406	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
407	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
408	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
409	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
410	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
411	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₂₃	—	2	2	no	—
413	C₄⋊C₄×C₂₃	—	2	2	no	—
414	C₄⋊C₄×C₂₃	—	2	2	no	—
415	C₄⋊C₄×C₂₃	—	2	2	no	—
416	C₄⋊C₄×C₂₃	—	2	2	no	—
417	C₄⋊C₄×C₂₃	—	2	2	no	—
418	C₄⋊C₄×C₂₃	—	2	2	no	—
419	C₄⋊C₄×C₂₃	—	2	2	no	—
420	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
422	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
423	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
424	C₂²⋊C₄×C₂₃	—	2	2	no	—
425	C₂²⋊C₄×C₂₃	—	2	2	no	—
426	C₂²⋊C₄×C₂₃	—	2	2	no	—
427	C₂²⋊C₄×C₂₃	—	2	2	no	—
428	C₂²⋊C₄×C₂₃	—	2	2	no	—
429	C₂²⋊C₄×C₂₃	—	2	2	no	—
430	C₂²⋊C₄×C₂₃	—	2	2	no	—
431	C₂²⋊C₄×C₂₃	—	2	2	no	—
432	C₂²⋊C₄×C₂₃	—	2	2	no	—
433	C₂²⋊C₄×C₂₃	—	2	2	no	—
434	C₂²⋊C₄×C₂₃	—	2	2	no	—
435	C₂²⋊C₄×C₂₃	—	2	2	no	—
436	C₂²⋊C₄×C₂₃	—	2	2	no	—
437	C₂²⋊C₄×C₂₃	—	2	2	no	—
438	C₂²⋊C₄×C₂₃	—	2	2	no	—
439	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
443	C₄²×C₂₃	—	2	2	no	—
444	C₄²×C₂₃	—	2	2	no	—
445	C₄²×C₂₃	—	2	2	no	—
446	C₄²×C₂₃	C₂×D₄	1	2	yes	—
447	C₄²×C₂₃	C₂⁴	1	2	yes	—
448	#61030	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
449	C₂³×C₂₃	—	2	2	no	—
450	C₂³×C₂₃	—	2	2	no	—
451	C₂³×C₂₃	—	2	2	no	—
452	C₂³×C₂₃	—	2	2	no	—
453	C₂³×C₂₃	—	2	2	no	—
454	C₂³×C₂₃	—	2	2	no	—
455	C₂³×C₂₃	—	4	1	no	—
456	C₂³×C₂₃	—	4	1	no	—
457	C₂³×C₂₃	—	4	1	no	—
458	C₂³×C₂₃	—	4	4	no	—
459	C₂³×C₂₃	—	4	4	no	—
460	C₂³×C₂₃	—	4	4	no	—
461	C₂³×C₂₃	—	4	4	no	—
462	C₂³×C₂₃	—	8	2	no	—
463	C₂³×C₂₃	—	8	2	no	—
464	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
465	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
466	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
467	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
468	Q₈×C₂₃	—	2	2	no	—
469	Q₈×C₂₃	—	2	2	no	—
470	Q₈×C₂₃	—	2	2	no	—
471	Q₈×C₂₃	—	2	2	no	—
472	Q₈×C₂₃	—	2	2	no	—
473	Q₈×C₂₃	—	4	4	no	—
474	Q₈×C₂₃	—	4	4	no	—
475	Q₈×C₂₃	C₂²×D₄	1	4	yes	—
476	D₄×C₂₃	—	2	8	no	—
477	D₄×C₂₃	—	2	4	no	—
478	D₄×C₂₃	—	2	2	no	—
479	D₄×C₂₃	—	2	2	no	—
480	D₄×C₂₃	—	2	2	no	—
481	D₄×C₂₃	—	2	2	no	—
482	D₄×C₂₃	—	2	2	no	—
483	D₄×C₂₃	—	4	2	no	—
484	D₄×C₂₃	—	4	4	no	—
485	D₄×C₂₃	—	4	4	no	—
486	D₄×C₂₃	—	4	4	no	—
487	D₄×C₂₃	—	4	4	no	—
488	D₄×C₂₃	—	4	4	no	—
489	D₄×C₂₃	—	4	4	no	—
490	D₄×C₂₃	—	4	4	no	—
491	D₄×C₂₃	—	4	4	no	—
492	D₄×C₂₃	—	4	4	no	—
493	D₄×C₂₃	—	4	4	no	—
494	D₄×C₂₃	—	4	4	no	—
495	D₄×C₂₃	—	8	2	no	—
496	D₄×C₂₃	—	8	2	no	—
497	D₄×C₂₃	—	8	2	no	—
498	D₄×C₂₃	C₂²×D₄	1	4	yes	—
499	C₂×C₄×C₂₃	—	2	2	no	—
500	C₂×C₄×C₂₃	—	2	2	no	—
501	C₂×C₄×C₂₃	—	2	2	no	—
502	C₂×C₄×C₂₃	—	2	2	no	—
503	C₂×C₄×C₂₃	—	2	4	no	—
504	C₂×C₄×C₂₃	—	2	2	no	—
505	C₂×C₄×C₂₃	—	2	8	no	—
506	C₂×C₄×C₂₃	—	2	1	no	—
507	C₂×C₄×C₂₃	—	2	1	no	—
508	C₂×C₄×C₂₃	—	2	2	no	—
509	C₂×C₄×C₂₃	—	2	1	no	—
510	C₂×C₄×C₂₃	—	2	2	no	—
511	C₂×C₄×C₂₃	—	2	1	no	—
512	C₂×C₄×C₂₃	—	2	2	no	—
513	C₂×C₄×C₂₃	—	2	2	no	—
514	C₂×C₄×C₂₃	—	2	2	no	—
515	C₂×C₄×C₂₃	—	2	2	no	—
516	C₂×C₄×C₂₃	—	4	1	no	—
517	C₂×C₄×C₂₃	—	4	1	no	—
518	C₂×C₄×C₂₃	—	4	4	no	—
519	C₂×C₄×C₂₃	—	4	4	no	—
520	C₂×C₄×C₂₃	—	4	4	no	—
521	C₂×C₄×C₂₃	—	4	4	no	—
522	C₂×C₄×C₂₃	—	4	4	no	—
523	C₂×C₄×C₂₃	—	4	4	no	—
524	C₂×C₄×C₂₃	—	4	4	no	—
525	C₂×C₄×C₂₃	—	4	4	no	—
526	C₂×C₄×C₂₃	—	4	4	no	—
527	C₂×C₄×C₂₃	—	8	2	no	—
528	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
534	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
536	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
537	C₈×C₂₃	—	2	1	no	—
538	C₈×C₂₃	—	2	1	no	—
539	C₈×C₂₃	—	2	2	no	—
540	C₈×C₂₃	—	2	2	no	—
541	C₈×C₂₃	C₂²×D₄	1	2	yes	—
542	C₈×C₂₃	C₂²×D₄	1	2	yes	—
543	C₂×#575	C₂×C₂₃	1	1	yes	characteristic, complemented
544	C₂²×#135	C₂×C₂₃	1	1	yes	characteristic, complemented
545	D₄×#41	C₂×C₂₃	1	2	yes	complemented
546	#3271	C₂×C₂₃	1	2	yes	complemented
547	#3270	C₂×C₂₃	1	2	yes	complemented
548	#3269	C₂×C₂₃	1	2	yes	complemented
549	#3268	C₂×C₂₃	1	2	yes	complemented
550	#3267	C₂×C₂₃	1	2	yes	complemented
551	#3266	C₂×C₂₃	1	2	yes	complemented
552	#3265	C₂×C₂₃	1	2	yes	complemented
553	#3264	C₂×C₂₃	1	2	yes	complemented
554	#3150	C₂×C₂₃	1	1	yes	characteristic, complemented
555	#3054	C₂×C₂₃	1	1	yes	characteristic, complemented
556	#3050	C₂×C₂₃	1	1	yes	characteristic, complemented
557	#3035	C₂×C₂₃	1	2	yes	complemented
558	#3002	C₂×C₂₃	1	2	yes	complemented
559	#3002	C₂×C₂₃	1	2	yes	complemented
560	#2943	C₂×C₂₃	1	1	yes	characteristic, complemented
561	C₂×#435	C₂×C₂₃	1	1	yes	characteristic, complemented
562	C₂²×C₂₃	—	2	1	no	—
563	C₂²×C₂₃	—	2	1	no	—
564	C₂²×C₂₃	—	2	1	no	—
565	C₂²×C₂₃	—	2	1	no	—
566	C₂²×C₂₃	—	2	1	no	—
567	C₂²×C₂₃	—	2	2	no	—
568	C₂²×C₂₃	—	2	2	no	—
569	C₂²×C₂₃	—	2	1	no	—
570	C₂²×C₂₃	—	2	4	no	—
571	C₂²×C₂₃	—	2	2	no	—
572	C₂²×C₂₃	—	2	1	no	—
573	C₂²×C₂₃	—	4	4	no	—
574	C₂²×C₂₃	—	4	2	no	—
575	C₂²×C₂₃	—	4	2	no	—
576	C₂²×C₂₃	—	4	2	no	—
577	C₂²×C₂₃	—	4	2	no	—
578	C₂²×C₂₃	—	4	2	no	—
579	C₂²×C₂₃	—	4	2	no	—
580	C₂²×C₂₃	—	4	2	no	—
581	C₂²×C₂₃	—	4	2	no	—
582	C₂²×C₂₃	—	8	2	no	—
583	C₂²×C₂₃	—	8	8	no	—
584	C₂²×C₂₃	—	8	8	no	—
585	C₂²×C₂₃	D₄²	1	2	yes	—
586	C₂²×C₂₃	#575	1	2	yes	complemented
587	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
588	C₄×C₂₃	—	2	2	no	—
589	C₄×C₂₃	—	2	1	no	—
590	C₄×C₂₃	—	2	2	no	—
591	C₄×C₂₃	—	2	1	no	—
592	C₄×C₂₃	—	2	4	no	—
593	C₄×C₂₃	—	2	2	no	—
594	C₄×C₂₃	—	4	2	no	—
595	C₄×C₂₃	—	4	2	no	—
596	C₄×C₂₃	—	4	2	no	—
597	C₄×C₂₃	—	4	2	no	—
598	C₄×C₂₃	D₄²	1	2	yes	—
599	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
600	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
601	C₂²×#41	C₂²×C₂₃	1	2	yes	complemented
602	C₂²×#41	C₂²×C₂₃	1	2	yes	complemented
603	#575	—	2	8	no	—
604	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
605	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
606	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
607	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
608	C₂×#135	—	2	8	no	—
609	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
610	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic, complemented
611	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic, complemented
612	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
613	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
614	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic, complemented
615	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
616	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic, complemented
617	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
618	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
619	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
620	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
621	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
622	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
623	#550	C₂²×C₂₃	1	2	yes	complemented
624	D₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
625	#548	C₂²×C₂₃	1	2	yes	—
626	#548	C₂²×C₂₃	1	2	yes	complemented
627	#547	—	2	2	no	—
628	#547	C₂²×C₂₃	1	2	yes	complemented
629	#546	—	2	2	no	—
630	#546	—	2	2	no	—
631	#546	C₂²×C₂₃	1	2	yes	—
632	#546	C₂²×C₂₃	1	2	yes	complemented
633	D₄²	—	2	2	no	—
634	D₄²	C₂²×C₂₃	1	2	yes	complemented
635	#532	—	2	2	no	—
636	#532	C₂²×C₂₃	1	2	yes	complemented
637	#525	—	2	2	no	—
638	#525	—	2	2	no	—
639	#525	C₂²×C₂₃	1	2	yes	complemented
640	#525	C₂²×C₂₃	1	2	yes	complemented
641	C₄×#41	C₂²×C₂₃	1	2	yes	complemented
642	C₂×C₄×D₄	—	2	2	no	—
643	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
644	#497	C₂²×C₂₃	1	2	yes	complemented
645	#497	C₂²×C₂₃	1	2	yes	complemented
646	#496	C₂²×C₂₃	1	2	yes	complemented
647	#496	C₂²×C₂₃	1	2	yes	complemented
648	#470	C₂²×C₂₃	1	2	yes	complemented
649	#469	C₂²×C₂₃	1	2	yes	complemented
650	#468	C₂²×C₂₃	1	2	yes	complemented
651	#468	C₂²×C₂₃	1	2	yes	complemented
652	#467	C₂²×C₂₃	1	1	yes	characteristic, complemented
653	#467	C₂²×C₂₃	1	1	yes	characteristic, complemented
654	#466	C₂²×C₂₃	1	1	yes	characteristic, complemented
655	#466	C₂²×C₂₃	1	1	yes	characteristic, complemented
656	#465	C₂²×C₂₃	1	2	yes	complemented
657	#465	C₂²×C₂₃	1	2	yes	complemented
658	#464	C₂²×C₂₃	1	2	yes	complemented
659	#464	C₂²×C₂₃	1	2	yes	complemented
660	#463	C₂²×C₂₃	1	2	yes	complemented
661	#463	C₂²×C₂₃	1	2	yes	complemented
662	#462	C₂²×C₂₃	1	2	yes	complemented
663	#461	C₂²×C₂₃	1	2	yes	complemented
664	#460	C₂²×C₂₃	1	2	yes	complemented
665	#459	C₂²×C₂₃	1	2	yes	complemented
666	#452	C₂²×C₂₃	1	2	yes	complemented
667	#452	C₂²×C₂₃	1	2	yes	complemented
668	#452	C₂²×C₂₃	1	2	yes	complemented
669	#452	C₂²×C₂₃	1	2	yes	complemented
670	#451	C₂²×C₂₃	1	2	yes	complemented
671	#451	C₂²×C₂₃	1	2	yes	complemented
672	#450	C₂²×C₂₃	1	2	yes	complemented
673	#450	C₂²×C₂₃	1	2	yes	complemented
674	#449	C₂²×C₂₃	1	2	yes	complemented
675	#449	C₂²×C₂₃	1	2	yes	complemented
676	#449	C₂²×C₂₃	1	2	yes	complemented
677	#449	C₂²×C₂₃	1	2	yes	complemented
678	#448	C₂²×C₂₃	1	2	yes	complemented
679	#448	C₂²×C₂₃	1	2	yes	complemented
680	#447	C₂²×C₂₃	1	2	yes	complemented
681	#447	C₂²×C₂₃	1	2	yes	complemented
682	#442	C₂²×C₂₃	1	2	yes	complemented
683	#441	C₂²×C₂₃	1	2	yes	complemented
684	#440	C₂²×C₂₃	1	2	yes	complemented
685	#440	C₂²×C₂₃	1	2	yes	complemented
686	#435	C₂²×C₂₃	1	2	yes	complemented
687	#435	C₂²×C₂₃	1	2	yes	complemented
688	#435	C₂²×C₂₃	1	2	yes	complemented
689	#435	C₂²×C₂₃	1	2	yes	complemented
690	#427	C₂²×C₂₃	1	1	yes	characteristic, complemented
691	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
692	#416	C₂²×C₂₃	1	2	yes	complemented
693	#416	C₂²×C₂₃	1	2	yes	complemented
694	#416	C₂²×C₂₃	1	2	yes	complemented
695	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
696	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
697	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
698	C₂×C₂₃	—	2	2	no	—
699	C₂×C₂₃	—	2	2	no	—
700	C₂×C₂₃	—	4	1	no	—
701	C₂×C₂₃	—	4	2	no	—
702	C₂×C₂₃	—	4	4	no	—
703	C₂×C₂₃	—	8	2	no	—
704	C₂×C₂₃	—	8	2	no	—
705	C₂×C₂₃	C₂×D₄²	1	1	yes	characteristic
706	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
707	C₂×C₂₃	#3584	1	1	yes	characteristic
708	C₂×#41	—	2	2	no	—
709	C₂×#41	—	2	2	no	—
710	C₂×#41	—	2	2	no	—
711	C₂×#41	—	2	2	no	—
712	C₂×#41	—	2	8	no	—
713	C₂×#41	—	2	8	no	—
714	C₂×#41	—	4	4	no	—
715	C₂×#41	—	4	4	no	—
716	C₂×#41	C₂³×C₂₃	1	2	yes	—
717	C₂×#41	C₂³×C₂₃	1	2	yes	—
718	C₂×#41	C₂³×C₂₃	1	2	yes	—
719	C₂×#41	C₂³×C₂₃	1	2	yes	—
720	C₂×#41	C₂³×C₂₃	1	2	yes	—
721	C₂×#41	C₂³×C₂₃	1	2	yes	—
722	C₂×#41	C₂³×C₂₃	1	2	yes	—
723	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
724	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
725	C₂²×D₄	—	2	2	no	—
726	C₂²×D₄	—	2	2	no	—
727	C₂²×D₄	—	2	2	no	—
728	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
729	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
730	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
731	C₂³×C₄	—	2	2	no	—
732	C₂³×C₄	—	2	2	no	—
733	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
734	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
735	#137	—	2	8	no	—
736	#137	—	2	8	no	—
737	AGL(1,ℤ/8)	—	2	8	no	—
738	AGL(1,ℤ/8)	—	2	8	no	—
739	#135	—	2	8	no	—
740	#135	—	2	8	no	—
741	#135	—	2	4	no	—
742	#135	—	2	8	no	—
743	#135	—	2	4	no	—
744	#135	—	2	4	no	—
745	#135	—	2	4	no	—
746	#135	—	4	4	no	—
747	#135	D₄×C₂₃	1	8	yes	complemented
748	C₂×Q₁₆	—	2	4	no	—
749	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
750	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
751	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
752	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
753	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
754	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
755	C₂×SD₁₆	—	2	8	no	—
756	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
757	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
758	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
759	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
760	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
761	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
762	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
763	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
764	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
765	C₂×D₈	—	2	4	no	—
766	C₂×D₈	C₂³×C₂₃	1	2	yes	—
767	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
768	C₂×D₈	C₂³×C₂₃	1	2	yes	—
769	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
770	C₂×D₈	C₂³×C₂₃	1	2	yes	—
771	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
772	C₂×M₁₆	—	2	4	no	—
773	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
774	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
775	C₂²×C₈	—	2	4	no	—
776	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
777	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
778	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
779	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
780	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
781	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
782	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
783	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
784	C₄⋊Q₈	—	2	2	no	—
785	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
786	#127	—	2	2	no	—
787	#127	C₂³×C₂₃	1	2	yes	—
788	#124	—	2	2	no	—
789	#124	—	2	2	no	—
790	#124	C₂³×C₂₃	1	2	yes	—
791	#124	C₂³×C₂₃	1	2	yes	—
792	#123	—	2	2	no	—
793	#123	—	2	2	no	—
794	#123	—	2	2	no	—
795	#123	—	2	2	no	—
796	#123	—	2	2	no	—
797	#123	—	2	2	no	—
798	C₂²⋊Q₈	—	2	2	no	—
799	C₂²⋊Q₈	—	2	2	no	—
800	C₂²⋊Q₈	—	2	2	no	—
801	C₂²⋊Q₈	—	2	2	no	—
802	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
803	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
804	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
805	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
806	#121	—	2	2	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	—	2	2	no	—
812	#121	—	2	2	no	—
813	#121	—	2	2	no	—
814	#121	—	2	2	no	—
815	#121	—	2	2	no	—
816	#121	C₂³×C₂₃	1	2	yes	—
817	#121	C₂³×C₂₃	1	2	yes	—
818	#121	C₂³×C₂₃	1	2	yes	—
819	#121	C₂³×C₂₃	1	2	yes	—
820	#120	—	2	2	no	—
821	#120	—	2	2	no	—
822	#120	—	2	2	no	—
823	#120	—	2	2	no	—
824	#120	—	2	2	no	—
825	#120	—	2	2	no	—
826	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
827	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	2	no	—
833	C₄×D₄	—	2	2	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	2	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	—	2	2	no	—
838	C₄×D₄	—	2	2	no	—
839	C₄×D₄	—	2	2	no	—
840	C₄×D₄	D₄×C₂₃	1	2	yes	—
841	C₄×D₄	D₄×C₂₃	1	2	yes	—
842	C₄×D₄	C₂³×C₂₃	1	2	yes	—
843	C₄×D₄	C₂³×C₂₃	1	2	yes	—
844	C₄×D₄	C₂³×C₂₃	1	2	yes	—
845	C₄×D₄	C₂³×C₂₃	1	2	yes	—
846	#117	—	2	2	no	—
847	#117	C₂³×C₂₃	1	2	yes	—
848	C₂×C₄⋊C₄	—	2	2	no	—
849	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
850	C₂×C₂²⋊C₄	—	2	2	no	—
851	C₂×C₂²⋊C₄	—	2	2	no	—
852	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
853	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
854	C₂×C₄²	—	2	2	no	—
855	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
856	#107	C₂³×C₂₃	1	1	yes	characteristic
857	#107	C₂³×C₂₃	1	1	yes	characteristic
858	#106	C₂³×C₂₃	1	2	yes	—
859	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
860	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
861	#103	C₂³×C₂₃	1	2	yes	—
862	#103	C₂³×C₂₃	1	2	yes	—
863	#103	C₂³×C₂₃	1	2	yes	—
864	#103	C₂³×C₂₃	1	2	yes	—
865	#103	C₂³×C₂₃	1	2	yes	—
866	#103	C₂³×C₂₃	1	2	yes	—
867	#102	C₂³×C₂₃	1	2	yes	—
868	#102	C₂³×C₂₃	1	2	yes	—
869	#102	C₂³×C₂₃	1	2	yes	—
870	#102	C₂³×C₂₃	1	2	yes	—
871	#102	C₂³×C₂₃	1	2	yes	—
872	#102	C₂³×C₂₃	1	2	yes	—
873	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
874	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
875	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
876	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
877	#97	C₂³×C₂₃	1	2	yes	—
878	#97	C₂³×C₂₃	1	2	yes	—
879	C₂₃	#61030	1	1	yes	characteristic, direct product factor, Sylow
880	C₂⁴	—	2	2	no	—
881	C₂⁴	—	2	2	no	—
882	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
883	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
884	#41	—	2	4	no	—
885	#41	—	2	4	no	—
886	#41	—	2	4	no	—
887	#41	—	2	4	no	—
888	#41	—	2	4	no	—
889	#41	—	2	4	no	—
890	#41	—	2	4	no	—
891	#41	—	2	4	no	—
892	#41	—	2	4	no	—
893	#41	—	4	8	no	—
894	#41	—	4	8	no	—
895	#41	—	4	2	no	—
896	#41	—	4	2	no	—
897	#41	—	4	2	no	—
898	#41	—	4	2	no	—
899	#41	—	4	8	no	—
900	#41	—	4	8	no	—
901	#41	C₂×D₄×C₂₃	1	8	yes	complemented
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	—	2	2	no	—
904	C₂×Q₈	—	2	4	no	—
905	C₂×Q₈	—	2	4	no	—
906	C₂×Q₈	—	4	2	no	—
907	C₂×Q₈	—	4	2	no	—
908	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
909	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
910	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	4	no	—
913	C₂×D₄	—	2	4	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	4	2	no	—
929	C₂×D₄	—	4	2	no	—
930	C₂×D₄	—	4	2	no	—
931	C₂×D₄	—	4	8	no	—
932	C₂×D₄	—	4	8	no	—
933	C₂×D₄	—	4	8	no	—
934	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
935	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
936	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
937	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
938	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	2	2	no	—
952	C₂²×C₄	—	2	2	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	4	8	no	—
955	C₂²×C₄	—	4	8	no	—
956	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
957	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
958	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
959	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
960	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
961	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
962	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
963	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
964	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
965	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
966	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
967	Q₁₆	—	2	4	no	—
968	Q₁₆	—	2	4	no	—
969	Q₁₆	—	2	2	no	—
970	Q₁₆	—	2	2	no	—
971	Q₁₆	—	4	2	no	—
972	Q₁₆	C₂×D₄×C₂₃	1	4	yes	complemented
973	SD₁₆	—	2	4	no	—
974	SD₁₆	—	2	4	no	—
975	SD₁₆	—	2	4	no	—
976	SD₁₆	—	2	4	no	—
977	SD₁₆	—	2	4	no	—
978	SD₁₆	—	2	4	no	—
979	SD₁₆	—	4	2	no	—
980	SD₁₆	—	4	2	no	—
981	SD₁₆	C₂×D₄×C₂₃	1	8	yes	complemented
982	D₈	—	2	4	no	—
983	D₈	—	2	4	no	—
984	D₈	—	2	2	no	—
985	D₈	—	2	2	no	—
986	D₈	—	4	2	no	—
987	D₈	C₂×D₄×C₂₃	1	4	yes	complemented
988	M₁₆	—	2	4	no	—
989	M₁₆	—	2	4	no	—
990	C₂×C₈	—	2	2	no	—
991	C₂×C₈	—	2	2	no	—
992	C₂×C₈	—	2	2	no	—
993	C₂×C₈	—	2	2	no	—
994	C₂×C₈	—	2	2	no	—
995	C₂×C₈	—	2	2	no	—
996	C₂×C₈	—	2	2	no	—
997	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	complemented
998	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
999	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1000	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1001	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1002	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1003	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	2	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	2	no	—
1011	C₄⋊C₄	—	2	2	no	—
1012	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1013	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1014	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1015	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1032	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1033	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1034	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1035	C₄²	—	2	2	no	—
1036	C₄²	—	2	2	no	—
1037	C₄²	—	2	2	no	—
1038	C₄²	C₂×D₄×C₂₃	1	2	yes	—
1039	C₄²	C₂⁴×C₂₃	1	2	yes	—
1040	C₂³	—	2	2	no	—
1041	C₂³	—	2	2	no	—
1042	C₂³	—	2	2	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	2	2	no	—
1045	C₂³	—	2	2	no	—
1046	C₂³	—	4	1	no	—
1047	C₂³	—	4	1	no	—
1048	C₂³	—	4	1	no	—
1049	C₂³	—	4	4	no	—
1050	C₂³	—	4	4	no	—
1051	C₂³	—	4	4	no	—
1052	C₂³	—	4	4	no	—
1053	C₂³	—	8	2	no	—
1054	C₂³	—	8	2	no	—
1055	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1056	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1057	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1058	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1059	Q₈	—	2	2	no	—
1060	Q₈	—	2	2	no	—
1061	Q₈	—	2	2	no	—
1062	Q₈	—	2	2	no	—
1063	Q₈	—	2	2	no	—
1064	Q₈	—	4	4	no	—
1065	Q₈	—	4	4	no	—
1066	Q₈	C₂²×D₄×C₂₃	1	4	yes	—
1067	D₄	—	2	4	no	—
1068	D₄	—	2	8	no	—
1069	D₄	—	2	2	no	—
1070	D₄	—	2	2	no	—
1071	D₄	—	2	2	no	—
1072	D₄	—	2	2	no	—
1073	D₄	—	2	2	no	—
1074	D₄	—	4	2	no	—
1075	D₄	—	4	4	no	—
1076	D₄	—	4	4	no	—
1077	D₄	—	4	4	no	—
1078	D₄	—	4	4	no	—
1079	D₄	—	4	4	no	—
1080	D₄	—	4	4	no	—
1081	D₄	—	4	4	no	—
1082	D₄	—	4	4	no	—
1083	D₄	—	4	4	no	—
1084	D₄	—	4	4	no	—
1085	D₄	—	4	4	no	—
1086	D₄	—	8	2	no	—
1087	D₄	—	8	2	no	—
1088	D₄	—	8	2	no	—
1089	D₄	C₂²×D₄×C₂₃	1	4	yes	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	4	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	8	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	4	1	no	—
1108	C₂×C₄	—	4	1	no	—
1109	C₂×C₄	—	4	4	no	—
1110	C₂×C₄	—	4	4	no	—
1111	C₂×C₄	—	4	4	no	—
1112	C₂×C₄	—	4	4	no	—
1113	C₂×C₄	—	4	4	no	—
1114	C₂×C₄	—	4	4	no	—
1115	C₂×C₄	—	4	4	no	—
1116	C₂×C₄	—	4	4	no	—
1117	C₂×C₄	—	4	4	no	—
1118	C₂×C₄	—	8	2	no	—
1119	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1120	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1121	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1122	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1123	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1124	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1125	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1126	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1127	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1128	C₈	—	2	1	no	—
1129	C₈	—	2	1	no	—
1130	C₈	—	2	2	no	—
1131	C₈	—	2	2	no	—
1132	C₈	C₂²×D₄×C₂₃	1	2	yes	—
1133	C₈	C₂²×D₄×C₂₃	1	2	yes	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	1	no	—
1136	C₂²	—	2	1	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	2	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	4	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	1	no	—
1143	C₂²	—	2	1	no	—
1144	C₂²	—	2	2	no	—
1145	C₂²	—	4	4	no	—
1146	C₂²	—	4	2	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	4	2	no	—
1150	C₂²	—	4	2	no	—
1151	C₂²	—	4	2	no	—
1152	C₂²	—	4	2	no	—
1153	C₂²	—	4	2	no	—
1154	C₂²	—	8	2	no	—
1155	C₂²	—	8	8	no	—
1156	C₂²	—	8	8	no	—
1157	C₂²	D₄²×C₂₃	1	2	yes	—
1158	C₂²	C₂₃×#575	1	2	yes	complemented
1159	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1160	C₄	—	2	1	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	1	no	—
1163	C₄	—	2	4	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	2	2	no	—
1166	C₄	—	4	2	no	—
1167	C₄	—	4	2	no	—
1168	C₄	—	4	2	no	—
1169	C₄	—	4	2	no	—
1170	C₄	D₄²×C₂₃	1	2	yes	—
1171	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
1172	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1173	C₂	—	2	2	no	—
1174	C₂	—	2	2	no	—
1175	C₂	—	4	1	no	—
1176	C₂	—	4	2	no	—
1177	C₂	—	4	4	no	—
1178	C₂	—	8	2	no	—
1179	C₂	—	8	2	no	—
1180	C₂	C₂×D₄²×C₂₃	1	1	yes	characteristic
1181	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
1182	C₂	C₂₃×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#575	C₂	semidirect
2. C₂²×C₂₃×#135	C₂	semidirect
3. D₄×#41×C₂₃	C₂	semidirect
4. C₂₃×#3271	C₂	semidirect
5. C₂₃×#3270	C₂	semidirect
6. C₂₃×#3269	C₂	semidirect
7. C₂₃×#3268	C₂	semidirect
8. C₂₃×#3267	C₂	semidirect
9. C₂₃×#3266	C₂	semidirect
10. C₂₃×#3265	C₂	semidirect
11. C₂₃×#3264	C₂	semidirect
12. C₂₃×#3150	C₂	semidirect
13. C₂₃×#3054	C₂	semidirect
14. C₂₃×#3050	C₂	semidirect
15. C₂₃×#3035	C₂	semidirect
16. C₂₃×#3002	C₂	semidirect
17. C₂₃×#3002	C₂	semidirect
18. C₂₃×#2943	C₂	semidirect
19. C₂×C₂₃×#435	C₂	semidirect
20. C₂²×#41×C₂₃	C₂²	semidirect
21. C₂²×#41×C₂₃	C₂²	semidirect
23. C₂×C₂₃×#137	C₂²	semidirect
24. C₂×C₂₃×#137	C₂²	semidirect
25. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
29. C₂×C₂₃×#135	C₂²	semidirect
30. C₂×C₂₃×#135	C₂²	semidirect
31. C₂×C₂₃×#135	C₂²	semidirect
32. C₂×C₂₃×#135	C₂²	semidirect
33. C₂×C₂₃×#135	C₂²	semidirect
34. C₂×C₂₃×#135	C₂²	semidirect
35. C₂×C₂₃×#135	C₂²	semidirect
36. C₂×C₂₃×#135	C₂²	semidirect
37. C₂²×Q₁₆×C₂₃	C₂²	semidirect
38. C₂²×SD₁₆×C₂₃	C₂²	semidirect
39. C₂²×D₈×C₂₃	C₂²	semidirect
40. C₂²×M₁₆×C₂₃	C₂²	semidirect
41. C₂³×C₈×C₂₃	C₂²	semidirect
42. C₂₃×#550	C₂²	semidirect
43. D₄×Q₈×C₂₃	C₂²	semidirect
45. C₂₃×#548	C₂²	semidirect
47. C₂₃×#547	C₂²	semidirect
51. C₂₃×#546	C₂²	semidirect
53. D₄²×C₂₃	C₂²	semidirect
55. C₂₃×#532	C₂²	semidirect
58. C₂₃×#525	C₂²	semidirect
59. C₂₃×#525	C₂²	semidirect
60. C₄×#41×C₂₃	C₂²	semidirect
63. C₂₃×#497	C₂²	semidirect
64. C₂₃×#497	C₂²	semidirect
65. C₂₃×#496	C₂²	semidirect
66. C₂₃×#496	C₂²	semidirect
67. C₂₃×#470	C₂²	semidirect
68. C₂₃×#469	C₂²	semidirect
69. C₂₃×#468	C₂²	semidirect
70. C₂₃×#468	C₂²	semidirect
71. C₂₃×#467	C₂²	semidirect
72. C₂₃×#467	C₂²	semidirect
73. C₂₃×#466	C₂²	semidirect
74. C₂₃×#466	C₂²	semidirect
75. C₂₃×#465	C₂²	semidirect
76. C₂₃×#465	C₂²	semidirect
77. C₂₃×#464	C₂²	semidirect
78. C₂₃×#464	C₂²	semidirect
79. C₂₃×#463	C₂²	semidirect
80. C₂₃×#463	C₂²	semidirect
81. C₂₃×#462	C₂²	semidirect
82. C₂₃×#461	C₂²	semidirect
83. C₂₃×#460	C₂²	semidirect
84. C₂₃×#459	C₂²	semidirect
85. C₂₃×#452	C₂²	semidirect
86. C₂₃×#452	C₂²	semidirect
87. C₂₃×#452	C₂²	semidirect
88. C₂₃×#452	C₂²	semidirect
89. C₂₃×#451	C₂²	semidirect
90. C₂₃×#451	C₂²	semidirect
91. C₂₃×#450	C₂²	semidirect
92. C₂₃×#450	C₂²	semidirect
93. C₂₃×#449	C₂²	semidirect
94. C₂₃×#449	C₂²	semidirect
95. C₂₃×#449	C₂²	semidirect
96. C₂₃×#449	C₂²	semidirect
97. C₂₃×#448	C₂²	semidirect
98. C₂₃×#448	C₂²	semidirect
99. C₂₃×#447	C₂²	semidirect
100. C₂₃×#447	C₂²	semidirect
101. C₂₃×#442	C₂²	semidirect
102. C₂₃×#441	C₂²	semidirect
103. C₂₃×#440	C₂²	semidirect
104. C₂₃×#440	C₂²	semidirect
105. C₂₃×#435	C₂²	semidirect
106. C₂₃×#435	C₂²	semidirect
107. C₂₃×#435	C₂²	semidirect
108. C₂₃×#435	C₂²	semidirect
109. C₂₃×#427	C₂²	semidirect
110. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
111. C₂₃×#416	C₂²	semidirect
112. C₂₃×#416	C₂²	semidirect
113. C₂₃×#416	C₂²	semidirect
114. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
115. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
116. C₂×C₂₃×#97	C₂²	semidirect
156. C₂₃×#135	D₄	semidirect
309. #41×C₂₃	C₂×D₄	semidirect
380. Q₁₆×C₂₃	C₂×D₄	semidirect
389. SD₁₆×C₂₃	C₂×D₄	semidirect
395. D₈×C₂₃	C₂×D₄	semidirect
405. C₂×C₈×C₂₃	C₂×D₄	semidirect
448. #61030	C₂₃	direct (N × H)
543. C₂×#575	C₂×C₂₃	semidirect
544. C₂²×#135	C₂×C₂₃	semidirect
545. D₄×#41	C₂×C₂₃	semidirect
546. #3271	C₂×C₂₃	semidirect
547. #3270	C₂×C₂₃	semidirect
548. #3269	C₂×C₂₃	semidirect
549. #3268	C₂×C₂₃	semidirect
550. #3267	C₂×C₂₃	semidirect
551. #3266	C₂×C₂₃	semidirect
552. #3265	C₂×C₂₃	semidirect
553. #3264	C₂×C₂₃	semidirect
554. #3150	C₂×C₂₃	semidirect
555. #3054	C₂×C₂₃	semidirect
556. #3050	C₂×C₂₃	semidirect
557. #3035	C₂×C₂₃	semidirect
558. #3002	C₂×C₂₃	semidirect
559. #3002	C₂×C₂₃	semidirect
560. #2943	C₂×C₂₃	semidirect
561. C₂×#435	C₂×C₂₃	semidirect
586. C₂²×C₂₃	#575	semidirect
601. C₂²×#41	C₂²×C₂₃	semidirect
602. C₂²×#41	C₂²×C₂₃	semidirect
604. C₂×#137	C₂²×C₂₃	semidirect
605. C₂×#137	C₂²×C₂₃	semidirect
606. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
607. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
610. C₂×#135	C₂²×C₂₃	semidirect
611. C₂×#135	C₂²×C₂₃	semidirect
612. C₂×#135	C₂²×C₂₃	semidirect
613. C₂×#135	C₂²×C₂₃	semidirect
614. C₂×#135	C₂²×C₂₃	semidirect
615. C₂×#135	C₂²×C₂₃	semidirect
616. C₂×#135	C₂²×C₂₃	semidirect
617. C₂×#135	C₂²×C₂₃	semidirect
618. C₂²×Q₁₆	C₂²×C₂₃	semidirect
619. C₂²×SD₁₆	C₂²×C₂₃	semidirect
620. C₂²×D₈	C₂²×C₂₃	semidirect
621. C₂²×M₁₆	C₂²×C₂₃	semidirect
622. C₂³×C₈	C₂²×C₂₃	semidirect
623. #550	C₂²×C₂₃	semidirect
624. D₄×Q₈	C₂²×C₂₃	semidirect
626. #548	C₂²×C₂₃	semidirect
628. #547	C₂²×C₂₃	semidirect
632. #546	C₂²×C₂₃	semidirect
634. D₄²	C₂²×C₂₃	semidirect
636. #532	C₂²×C₂₃	semidirect
639. #525	C₂²×C₂₃	semidirect
640. #525	C₂²×C₂₃	semidirect
641. C₄×#41	C₂²×C₂₃	semidirect
644. #497	C₂²×C₂₃	semidirect
645. #497	C₂²×C₂₃	semidirect
646. #496	C₂²×C₂₃	semidirect
647. #496	C₂²×C₂₃	semidirect
648. #470	C₂²×C₂₃	semidirect
649. #469	C₂²×C₂₃	semidirect
650. #468	C₂²×C₂₃	semidirect
651. #468	C₂²×C₂₃	semidirect
652. #467	C₂²×C₂₃	semidirect
653. #467	C₂²×C₂₃	semidirect
654. #466	C₂²×C₂₃	semidirect
655. #466	C₂²×C₂₃	semidirect
656. #465	C₂²×C₂₃	semidirect
657. #465	C₂²×C₂₃	semidirect
658. #464	C₂²×C₂₃	semidirect
659. #464	C₂²×C₂₃	semidirect
660. #463	C₂²×C₂₃	semidirect
661. #463	C₂²×C₂₃	semidirect
662. #462	C₂²×C₂₃	semidirect
663. #461	C₂²×C₂₃	semidirect
664. #460	C₂²×C₂₃	semidirect
665. #459	C₂²×C₂₃	semidirect
666. #452	C₂²×C₂₃	semidirect
667. #452	C₂²×C₂₃	semidirect
668. #452	C₂²×C₂₃	semidirect
669. #452	C₂²×C₂₃	semidirect
670. #451	C₂²×C₂₃	semidirect
671. #451	C₂²×C₂₃	semidirect
672. #450	C₂²×C₂₃	semidirect
673. #450	C₂²×C₂₃	semidirect
674. #449	C₂²×C₂₃	semidirect
675. #449	C₂²×C₂₃	semidirect
676. #449	C₂²×C₂₃	semidirect
677. #449	C₂²×C₂₃	semidirect
678. #448	C₂²×C₂₃	semidirect
679. #448	C₂²×C₂₃	semidirect
680. #447	C₂²×C₂₃	semidirect
681. #447	C₂²×C₂₃	semidirect
682. #442	C₂²×C₂₃	semidirect
683. #441	C₂²×C₂₃	semidirect
684. #440	C₂²×C₂₃	semidirect
685. #440	C₂²×C₂₃	semidirect
686. #435	C₂²×C₂₃	semidirect
687. #435	C₂²×C₂₃	semidirect
688. #435	C₂²×C₂₃	semidirect
689. #435	C₂²×C₂₃	semidirect
690. #427	C₂²×C₂₃	semidirect
691. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
692. #416	C₂²×C₂₃	semidirect
693. #416	C₂²×C₂₃	semidirect
694. #416	C₂²×C₂₃	semidirect
695. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
696. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
697. C₂×#97	C₂²×C₂₃	semidirect
747. #135	D₄×C₂₃	semidirect
879. C₂₃	#61030	direct (N × H)
901. #41	C₂×D₄×C₂₃	semidirect
972. Q₁₆	C₂×D₄×C₂₃	semidirect
981. SD₁₆	C₂×D₄×C₂₃	semidirect
987. D₈	C₂×D₄×C₂₃	semidirect
997. C₂×C₈	C₂×D₄×C₂₃	semidirect
1158. C₂²	C₂₃×#575	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#575	2
C₂²×C₂₃×#135	2
D₄×#41×C₂₃	2
C₂₃×#3271	2
C₂₃×#3270	2
C₂₃×#3269	2
C₂₃×#3268	2
C₂₃×#3267	2
C₂₃×#3266	2
C₂₃×#3265	2
C₂₃×#3264	2
C₂₃×#3150	2
C₂₃×#3054	2
C₂₃×#3050	2
C₂₃×#3035	2
C₂₃×#3002	2
C₂₃×#2943	2
C₂×C₂₃×#435	2
#61030	23

Subgroups — C23×#61030 #19208656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61030 #19208656