Subgroups — C₂₃×#60752 #19208378

Order 5888.

2362 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3197	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3196	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3194	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3191	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3190	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3188	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3095	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3094	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3093	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3056	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3055	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3005	C₂	1	2	yes	maximal, complemented
17	C₂×C₂₃×#407	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
20	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
22	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
23	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	complemented
24	C₂₃×#525	—	2	1	no	—
25	C₂₃×#525	—	2	1	no	—
26	C₂₃×#525	—	2	1	no	—
27	C₂₃×#525	—	2	1	no	—
28	C₂₃×#525	—	2	1	no	—
29	C₂₃×#525	—	2	1	no	—
30	C₂₃×#525	—	2	1	no	—
31	C₂₃×#525	—	2	1	no	—
32	C₂₃×#525	C₂²	1	2	yes	—
33	C₂₃×#525	C₂²	1	2	yes	—
34	C₂₃×#525	C₂²	1	2	yes	—
35	C₂₃×#525	C₂²	1	2	yes	—
36	C₂₃×#525	C₂²	1	2	yes	complemented
37	C₂₃×#525	C₂²	1	2	yes	complemented
38	C₂₃×#525	C₂²	1	2	yes	complemented
39	C₂₃×#525	C₂²	1	2	yes	complemented
40	C₂×C₂₃×#123	—	2	1	no	—
41	C₂×C₂₃×#123	—	2	1	no	—
42	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₂₃×#120	—	2	1	no	—
51	C₂×C₂₃×#120	—	2	1	no	—
52	C₂×C₄×D₄×C₂₃	—	2	1	no	—
53	C₂×C₄×D₄×C₂₃	—	2	1	no	—
54	C₂×C₄×D₄×C₂₃	—	2	1	no	—
55	C₂×C₄×D₄×C₂₃	—	2	1	no	—
56	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
57	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
58	C₂₃×#485	C₂²	1	4	yes	complemented
59	C₂₃×#485	C₂²	1	4	yes	complemented
60	C₂₃×#485	C₂²	1	4	yes	complemented
61	C₂₃×#484	C₂²	1	2	yes	complemented
62	C₂₃×#483	C₂²	1	2	yes	complemented
63	C₂₃×#482	C₂²	1	4	yes	complemented
64	C₂₃×#482	C₂²	1	4	yes	complemented
65	C₂₃×#482	C₂²	1	4	yes	complemented
66	C₂₃×#481	C₂²	1	2	yes	complemented
67	C₂₃×#480	C₂²	1	2	yes	complemented
68	C₂₃×#470	C₂²	1	4	yes	complemented
69	C₂₃×#469	C₂²	1	4	yes	complemented
70	C₂₃×#468	C₂²	1	4	yes	complemented
71	C₂₃×#468	C₂²	1	4	yes	complemented
72	C₂₃×#467	C₂²	1	4	yes	complemented
73	C₂₃×#466	C₂²	1	4	yes	complemented
74	C₂₃×#465	C₂²	1	4	yes	complemented
75	C₂₃×#465	C₂²	1	4	yes	complemented
76	C₂₃×#452	C₂²	1	4	yes	complemented
77	C₂₃×#452	C₂²	1	4	yes	complemented
78	C₂₃×#452	C₂²	1	4	yes	complemented
79	C₂₃×#451	C₂²	1	2	yes	complemented
80	C₂₃×#450	C₂²	1	2	yes	complemented
81	C₂₃×#449	C₂²	1	4	yes	complemented
82	C₂₃×#449	C₂²	1	4	yes	complemented
83	C₂₃×#449	C₂²	1	4	yes	complemented
84	C₂₃×#448	C₂²	1	2	yes	complemented
85	C₂₃×#447	C₂²	1	2	yes	complemented
86	C₂₃×#428	C₂²	1	2	yes	complemented
87	C₂₃×#428	C₂²	1	2	yes	complemented
88	C₂₃×#419	C₂²	1	2	yes	complemented
89	C₂₃×#418	C₂²	1	2	yes	complemented
90	C₂₃×#417	C₂²	1	2	yes	complemented
91	C₂₃×#417	C₂²	1	2	yes	complemented
92	C₂₃×#407	C₂²	1	1	yes	characteristic
93	C₂₃×#407	C₂²	1	1	yes	characteristic
94	C₂₃×#407	C₂²	1	2	yes	complemented
95	C₂₃×#407	C₂²	1	2	yes	complemented
96	C₂₃×#407	C₂²	1	2	yes	complemented
97	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
98	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
99	C₂⁵×C₂₃	D₄	1	1	yes	characteristic
100	C₂×#41×C₂₃	—	2	1	no	—
101	C₂×#41×C₂₃	—	2	1	no	—
102	C₂×#41×C₂₃	—	2	1	no	—
103	C₂×#41×C₂₃	—	2	1	no	—
104	C₂×#41×C₂₃	—	4	4	no	—
105	C₂×#41×C₂₃	—	4	4	no	—
106	C₂×#41×C₂₃	C₂³	1	2	yes	—
107	C₂×#41×C₂₃	C₂³	1	2	yes	—
108	C₂×#41×C₂₃	C₂³	1	2	yes	—
109	C₂×#41×C₂₃	C₂³	1	2	yes	—
110	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₂₃	—	2	1	no	—
113	C₂²×D₄×C₂₃	—	2	1	no	—
114	C₂²×D₄×C₂₃	—	2	1	no	—
115	C₂²×D₄×C₂₃	—	2	1	no	—
116	C₂²×D₄×C₂₃	—	2	1	no	—
117	C₂²×D₄×C₂₃	—	2	1	no	—
118	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
119	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₂₃	—	2	1	no	—
121	C₂³×C₄×C₂₃	—	2	1	no	—
122	C₂³×C₄×C₂₃	—	4	4	no	—
123	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
124	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
125	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
126	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
127	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
128	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
129	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
130	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
137	C₂₃×#137	—	4	4	no	—
138	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
139	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	complemented
140	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	complemented
141	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	complemented
142	C₂×D₈×C₂₃	C₂³	1	4	yes	complemented
143	C₂×M₁₆×C₂₃	—	4	4	no	—
144	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
145	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
146	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
147	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
148	C₂₃×#123	—	2	2	no	—
149	C₂₃×#123	—	2	2	no	—
150	C₂₃×#123	—	2	2	no	—
151	C₂₃×#123	—	2	2	no	—
152	C₂₃×#123	—	2	2	no	—
153	C₂₃×#123	—	2	2	no	—
154	C₂₃×#123	—	2	2	no	—
155	C₂₃×#123	—	2	2	no	—
156	C₂₃×C₂²⋊Q₈	—	2	1	no	—
157	C₂₃×C₂²⋊Q₈	—	2	1	no	—
158	C₂₃×C₂²⋊Q₈	—	2	1	no	—
159	C₂₃×C₂²⋊Q₈	—	2	1	no	—
160	C₂₃×C₂²⋊Q₈	—	2	1	no	—
161	C₂₃×C₂²⋊Q₈	—	2	1	no	—
162	C₂₃×C₂²⋊Q₈	—	2	1	no	—
163	C₂₃×C₂²⋊Q₈	—	2	1	no	—
164	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
165	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
166	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
167	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
168	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
169	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
170	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
171	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
172	C₂₃×#121	—	2	1	no	—
173	C₂₃×#121	—	2	1	no	—
174	C₂₃×#121	—	2	1	no	—
175	C₂₃×#121	—	2	1	no	—
176	C₂₃×#121	—	2	1	no	—
177	C₂₃×#121	—	2	1	no	—
178	C₂₃×#121	—	2	1	no	—
179	C₂₃×#121	—	2	1	no	—
180	C₂₃×#121	C₂³	1	2	yes	—
181	C₂₃×#121	C₂³	1	2	yes	—
182	C₂₃×#121	C₂³	1	2	yes	—
183	C₂₃×#121	C₂³	1	2	yes	—
184	C₂₃×#121	C₂³	1	2	yes	—
185	C₂₃×#121	C₂³	1	2	yes	—
186	C₂₃×#121	C₂³	1	2	yes	—
187	C₂₃×#121	C₂³	1	2	yes	—
188	C₂₃×#120	—	2	2	no	—
189	C₂₃×#120	—	2	2	no	—
190	C₂₃×#120	—	2	2	no	—
191	C₂₃×#120	—	2	2	no	—
192	C₂₃×#120	—	2	2	no	—
193	C₂₃×#120	—	2	2	no	—
194	C₂₃×#120	—	2	2	no	—
195	C₂₃×#120	—	2	2	no	—
196	C₄×D₄×C₂₃	—	2	2	no	—
197	C₄×D₄×C₂₃	—	2	2	no	—
198	C₄×D₄×C₂₃	—	2	2	no	—
199	C₄×D₄×C₂₃	—	2	2	no	—
200	C₄×D₄×C₂₃	—	2	2	no	—
201	C₄×D₄×C₂₃	—	2	2	no	—
202	C₄×D₄×C₂₃	—	2	2	no	—
203	C₄×D₄×C₂₃	—	2	2	no	—
204	C₄×D₄×C₂₃	—	2	2	no	—
205	C₄×D₄×C₂₃	—	2	2	no	—
206	C₄×D₄×C₂₃	—	2	2	no	—
207	C₄×D₄×C₂₃	—	2	2	no	—
208	C₄×D₄×C₂₃	—	2	2	no	—
209	C₄×D₄×C₂₃	—	2	2	no	—
210	C₄×D₄×C₂₃	—	2	2	no	—
211	C₄×D₄×C₂₃	—	2	2	no	—
212	C₂₃×#117	—	2	1	no	—
213	C₂₃×#117	—	2	1	no	—
214	C₂₃×#117	—	2	1	no	—
215	C₂₃×#117	—	2	1	no	—
216	C₂₃×#117	C₂³	1	2	yes	—
217	C₂₃×#117	C₂³	1	2	yes	—
218	C₂₃×#117	C₂³	1	2	yes	—
219	C₂₃×#117	C₂³	1	2	yes	—
220	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
221	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
222	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
223	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
224	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
228	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
229	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
230	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
231	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
232	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
233	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
234	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
235	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
236	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
237	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
238	C₂×C₄²×C₂₃	—	2	1	no	—
239	C₂×C₄²×C₂₃	—	2	1	no	—
240	C₂₃×#107	C₂³	1	4	yes	complemented
241	C₂₃×#107	C₂³	1	4	yes	complemented
242	C₂₃×#106	C₂³	1	4	yes	complemented
243	C₂₃×#106	C₂³	1	4	yes	complemented
244	C₂₃×#103	C₂³	1	4	yes	complemented
245	C₂₃×#103	C₂³	1	4	yes	complemented
246	C₂₃×#103	C₂³	1	4	yes	complemented
247	C₂₃×#103	C₂³	1	4	yes	complemented
248	C₂₃×#102	C₂³	1	4	yes	complemented
249	C₂₃×#102	C₂³	1	4	yes	complemented
250	C₂₃×#102	C₂³	1	4	yes	complemented
251	C₂₃×#102	C₂³	1	4	yes	complemented
252	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
253	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
254	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
255	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
256	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
257	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
258	C₂⁴×C₂₃	—	2	1	no	—
259	C₂⁴×C₂₃	—	2	1	no	—
260	C₂⁴×C₂₃	—	4	2	no	—
261	C₂⁴×C₂₃	—	4	2	no	—
262	C₂⁴×C₂₃	—	4	2	no	—
263	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
264	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
265	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
266	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
267	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
268	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
269	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
270	#41×C₂₃	—	2	4	no	—
271	#41×C₂₃	—	2	4	no	—
272	#41×C₂₃	—	4	2	no	—
273	#41×C₂₃	—	4	4	no	—
274	#41×C₂₃	—	4	4	no	—
275	#41×C₂₃	—	4	2	no	—
276	#41×C₂₃	—	4	4	no	—
277	#41×C₂₃	—	4	4	no	—
278	#41×C₂₃	—	4	4	no	—
279	#41×C₂₃	—	4	4	no	—
280	C₂×Q₈×C₂₃	—	2	1	no	—
281	C₂×Q₈×C₂₃	—	2	1	no	—
282	C₂×Q₈×C₂₃	—	2	4	no	—
283	C₂×Q₈×C₂₃	—	4	2	no	—
284	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
285	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
286	C₂×D₄×C₂₃	—	2	2	no	—
287	C₂×D₄×C₂₃	—	2	2	no	—
288	C₂×D₄×C₂₃	—	2	2	no	—
289	C₂×D₄×C₂₃	—	2	2	no	—
290	C₂×D₄×C₂₃	—	2	2	no	—
291	C₂×D₄×C₂₃	—	2	2	no	—
292	C₂×D₄×C₂₃	—	2	2	no	—
293	C₂×D₄×C₂₃	—	2	2	no	—
294	C₂×D₄×C₂₃	—	2	2	no	—
295	C₂×D₄×C₂₃	—	2	2	no	—
296	C₂×D₄×C₂₃	—	2	2	no	—
297	C₂×D₄×C₂₃	—	2	2	no	—
298	C₂×D₄×C₂₃	—	2	1	no	—
299	C₂×D₄×C₂₃	—	2	1	no	—
300	C₂×D₄×C₂₃	—	2	4	no	—
301	C₂×D₄×C₂₃	—	4	2	no	—
302	C₂×D₄×C₂₃	—	4	4	no	—
303	C₂×D₄×C₂₃	—	4	4	no	—
304	C₂×D₄×C₂₃	—	4	4	no	—
305	C₂×D₄×C₂₃	—	4	4	no	—
306	C₂×D₄×C₂₃	—	4	4	no	—
307	C₂×D₄×C₂₃	—	4	4	no	—
308	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
309	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₂₃	—	2	4	no	—
311	C₂²×C₄×C₂₃	—	2	4	no	—
312	C₂²×C₄×C₂₃	—	2	4	no	—
313	C₂²×C₄×C₂₃	—	2	1	no	—
314	C₂²×C₄×C₂₃	—	2	1	no	—
315	C₂²×C₄×C₂₃	—	2	1	no	—
316	C₂²×C₄×C₂₃	—	2	1	no	—
317	C₂²×C₄×C₂₃	—	2	1	no	—
318	C₂²×C₄×C₂₃	—	2	1	no	—
319	C₂²×C₄×C₂₃	—	2	2	no	—
320	C₂²×C₄×C₂₃	—	2	2	no	—
321	C₂²×C₄×C₂₃	—	2	2	no	—
322	C₂²×C₄×C₂₃	—	2	2	no	—
323	C₂²×C₄×C₂₃	—	4	2	no	—
324	C₂²×C₄×C₂₃	—	4	2	no	—
325	C₂²×C₄×C₂₃	—	4	2	no	—
326	C₂²×C₄×C₂₃	—	4	2	no	—
327	C₂²×C₄×C₂₃	—	4	2	no	—
328	C₂²×C₄×C₂₃	—	4	2	no	—
329	C₂²×C₄×C₂₃	—	4	2	no	—
330	C₂²×C₄×C₂₃	—	4	2	no	—
331	C₂²×C₄×C₂₃	—	4	2	no	—
332	C₂²×C₄×C₂₃	—	4	2	no	—
333	C₂²×C₄×C₂₃	—	4	2	no	—
334	C₂²×C₄×C₂₃	—	4	4	no	—
335	C₂²×C₄×C₂₃	—	4	4	no	—
336	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
337	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
338	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
339	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
340	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
344	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
345	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
346	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
353	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
364	Q₁₆×C₂₃	—	4	4	no	—
365	SD₁₆×C₂₃	—	4	4	no	—
366	SD₁₆×C₂₃	—	4	4	no	—
367	D₈×C₂₃	—	4	4	no	—
368	M₁₆×C₂₃	—	2	4	no	—
369	M₁₆×C₂₃	—	2	4	no	—
370	M₁₆×C₂₃	—	4	4	no	—
371	C₂×C₈×C₂₃	—	4	4	no	—
372	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
373	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
374	C₄⋊C₄×C₂₃	—	2	2	no	—
375	C₄⋊C₄×C₂₃	—	2	2	no	—
376	C₄⋊C₄×C₂₃	—	2	2	no	—
377	C₄⋊C₄×C₂₃	—	2	2	no	—
378	C₄⋊C₄×C₂₃	—	2	2	no	—
379	C₄⋊C₄×C₂₃	—	2	2	no	—
380	C₄⋊C₄×C₂₃	—	2	2	no	—
381	C₄⋊C₄×C₂₃	—	2	2	no	—
382	C₄⋊C₄×C₂₃	—	2	1	no	—
383	C₄⋊C₄×C₂₃	—	2	1	no	—
384	C₄⋊C₄×C₂₃	—	2	1	no	—
385	C₄⋊C₄×C₂₃	—	2	1	no	—
386	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
387	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
388	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
389	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
390	C₂²⋊C₄×C₂₃	—	2	2	no	—
391	C₂²⋊C₄×C₂₃	—	2	2	no	—
392	C₂²⋊C₄×C₂₃	—	2	2	no	—
393	C₂²⋊C₄×C₂₃	—	2	2	no	—
394	C₂²⋊C₄×C₂₃	—	2	2	no	—
395	C₂²⋊C₄×C₂₃	—	2	2	no	—
396	C₂²⋊C₄×C₂₃	—	2	2	no	—
397	C₂²⋊C₄×C₂₃	—	2	2	no	—
398	C₂²⋊C₄×C₂₃	—	2	2	no	—
399	C₂²⋊C₄×C₂₃	—	2	2	no	—
400	C₂²⋊C₄×C₂₃	—	2	2	no	—
401	C₂²⋊C₄×C₂₃	—	2	2	no	—
402	C₂²⋊C₄×C₂₃	—	2	2	no	—
403	C₂²⋊C₄×C₂₃	—	2	2	no	—
404	C₂²⋊C₄×C₂₃	—	2	2	no	—
405	C₂²⋊C₄×C₂₃	—	2	2	no	—
406	C₂²⋊C₄×C₂₃	—	2	2	no	—
407	C₂²⋊C₄×C₂₃	—	2	2	no	—
408	C₂²⋊C₄×C₂₃	—	2	2	no	—
409	C₂²⋊C₄×C₂₃	—	2	2	no	—
410	C₄²×C₂₃	—	2	2	no	—
411	C₄²×C₂₃	—	2	2	no	—
412	C₄²×C₂₃	—	2	2	no	—
413	C₄²×C₂₃	—	2	2	no	—
414	#60752	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
415	C₂³×C₂₃	—	2	2	no	—
416	C₂³×C₂₃	—	2	2	no	—
417	C₂³×C₂₃	—	2	2	no	—
418	C₂³×C₂₃	—	2	2	no	—
419	C₂³×C₂₃	—	2	2	no	—
420	C₂³×C₂₃	—	2	2	no	—
421	C₂³×C₂₃	—	2	2	no	—
422	C₂³×C₂₃	—	2	2	no	—
423	C₂³×C₂₃	—	2	2	no	—
424	C₂³×C₂₃	—	2	2	no	—
425	C₂³×C₂₃	—	2	2	no	—
426	C₂³×C₂₃	—	4	1	no	—
427	C₂³×C₂₃	—	4	1	no	—
428	C₂³×C₂₃	—	4	1	no	—
429	C₂³×C₂₃	—	4	1	no	—
430	C₂³×C₂₃	—	4	1	no	—
431	C₂³×C₂₃	—	4	1	no	—
432	C₂³×C₂₃	—	4	1	no	—
433	C₂³×C₂₃	—	4	1	no	—
434	C₂³×C₂₃	—	4	1	no	—
435	C₂³×C₂₃	—	4	1	no	—
436	C₂³×C₂₃	—	4	1	no	—
437	C₂³×C₂₃	—	4	1	no	—
438	C₂³×C₂₃	—	4	2	no	—
439	C₂³×C₂₃	—	4	2	no	—
440	C₂³×C₂₃	—	4	2	no	—
441	C₂³×C₂₃	—	4	2	no	—
442	C₂³×C₂₃	—	4	16	no	—
443	C₂³×C₂₃	—	4	2	no	—
444	C₂³×C₂₃	—	4	2	no	—
445	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
446	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
447	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
448	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
449	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
450	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
451	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
452	Q₈×C₂₃	—	2	2	no	—
453	Q₈×C₂₃	—	2	4	no	—
454	Q₈×C₂₃	—	2	2	no	—
455	Q₈×C₂₃	—	4	2	no	—
456	Q₈×C₂₃	—	4	2	no	—
457	D₄×C₂₃	—	2	2	no	—
458	D₄×C₂₃	—	2	4	no	—
459	D₄×C₂₃	—	2	2	no	—
460	D₄×C₂₃	—	4	2	no	—
461	D₄×C₂₃	—	4	4	no	—
462	D₄×C₂₃	—	4	4	no	—
463	D₄×C₂₃	—	4	4	no	—
464	D₄×C₂₃	—	4	4	no	—
465	D₄×C₂₃	—	4	4	no	—
466	D₄×C₂₃	—	4	4	no	—
467	D₄×C₂₃	—	4	4	no	—
468	D₄×C₂₃	—	4	4	no	—
469	D₄×C₂₃	—	4	4	no	—
470	D₄×C₂₃	—	4	4	no	—
471	D₄×C₂₃	—	4	4	no	—
472	D₄×C₂₃	—	4	4	no	—
473	D₄×C₂₃	—	4	2	no	—
474	C₂×C₄×C₂₃	—	2	2	no	—
475	C₂×C₄×C₂₃	—	2	2	no	—
476	C₂×C₄×C₂₃	—	2	2	no	—
477	C₂×C₄×C₂₃	—	2	2	no	—
478	C₂×C₄×C₂₃	—	2	2	no	—
479	C₂×C₄×C₂₃	—	2	2	no	—
480	C₂×C₄×C₂₃	—	2	2	no	—
481	C₂×C₄×C₂₃	—	2	2	no	—
482	C₂×C₄×C₂₃	—	2	2	no	—
483	C₂×C₄×C₂₃	—	2	2	no	—
484	C₂×C₄×C₂₃	—	2	2	no	—
485	C₂×C₄×C₂₃	—	2	2	no	—
486	C₂×C₄×C₂₃	—	2	2	no	—
487	C₂×C₄×C₂₃	—	2	2	no	—
488	C₂×C₄×C₂₃	—	2	2	no	—
489	C₂×C₄×C₂₃	—	2	2	no	—
490	C₂×C₄×C₂₃	—	2	2	no	—
491	C₂×C₄×C₂₃	—	2	2	no	—
492	C₂×C₄×C₂₃	—	2	2	no	—
493	C₂×C₄×C₂₃	—	2	2	no	—
494	C₂×C₄×C₂₃	—	2	2	no	—
495	C₂×C₄×C₂₃	—	4	1	no	—
496	C₂×C₄×C₂₃	—	4	1	no	—
497	C₂×C₄×C₂₃	—	4	1	no	—
498	C₂×C₄×C₂₃	—	4	1	no	—
499	C₂×C₄×C₂₃	—	4	1	no	—
500	C₂×C₄×C₂₃	—	4	1	no	—
501	C₂×C₄×C₂₃	—	4	1	no	—
502	C₂×C₄×C₂₃	—	4	1	no	—
503	C₂×C₄×C₂₃	—	4	1	no	—
504	C₂×C₄×C₂₃	—	4	1	no	—
505	C₂×C₄×C₂₃	—	4	1	no	—
506	C₂×C₄×C₂₃	—	4	1	no	—
507	C₂×C₄×C₂₃	—	4	4	no	—
508	C₂×C₄×C₂₃	—	4	4	no	—
509	C₂×C₄×C₂₃	—	4	4	no	—
510	C₂×C₄×C₂₃	—	4	2	no	—
511	C₂×C₄×C₂₃	—	4	2	no	—
512	C₂×C₄×C₂₃	—	4	2	no	—
513	C₂×C₄×C₂₃	—	4	2	no	—
514	C₂×C₄×C₂₃	—	4	2	no	—
515	C₂×C₄×C₂₃	—	4	2	no	—
516	C₂×C₄×C₂₃	—	4	4	no	—
517	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
525	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
526	C₈×C₂₃	—	2	4	no	—
527	C₈×C₂₃	—	2	4	no	—
528	C₂×#525	C₂×C₂₃	1	1	yes	characteristic, complemented
529	C₂×#525	C₂×C₂₃	1	1	yes	characteristic, complemented
530	#3197	C₂×C₂₃	1	4	yes	complemented
531	#3196	C₂×C₂₃	1	2	yes	complemented
532	#3194	C₂×C₂₃	1	2	yes	complemented
533	#3191	C₂×C₂₃	1	4	yes	complemented
534	#3190	C₂×C₂₃	1	2	yes	complemented
535	#3188	C₂×C₂₃	1	2	yes	complemented
536	#3095	C₂×C₂₃	1	1	yes	characteristic, complemented
537	#3094	C₂×C₂₃	1	1	yes	characteristic, complemented
538	#3093	C₂×C₂₃	1	2	yes	complemented
539	#3056	C₂×C₂₃	1	2	yes	complemented
540	#3055	C₂×C₂₃	1	2	yes	complemented
541	#3007	C₂×C₂₃	1	1	yes	characteristic, complemented
542	#3006	C₂×C₂₃	1	1	yes	characteristic, complemented
543	#3005	C₂×C₂₃	1	2	yes	complemented
544	C₂×#407	C₂×C₂₃	1	1	yes	characteristic, complemented
545	C₂²×C₂₃	—	2	1	no	—
546	C₂²×C₂₃	—	2	1	no	—
547	C₂²×C₂₃	—	2	1	no	—
548	C₂²×C₂₃	—	2	1	no	—
549	C₂²×C₂₃	—	2	1	no	—
550	C₂²×C₂₃	—	2	1	no	—
551	C₂²×C₂₃	—	2	1	no	—
552	C₂²×C₂₃	—	2	1	no	—
553	C₂²×C₂₃	—	2	1	no	—
554	C₂²×C₂₃	—	2	1	no	—
555	C₂²×C₂₃	—	2	1	no	—
556	C₂²×C₂₃	—	2	1	no	—
557	C₂²×C₂₃	—	2	1	no	—
558	C₂²×C₂₃	—	2	1	no	—
559	C₂²×C₂₃	—	2	1	no	—
560	C₂²×C₂₃	—	2	1	no	—
561	C₂²×C₂₃	—	2	1	no	—
562	C₂²×C₂₃	—	2	1	no	—
563	C₂²×C₂₃	—	4	4	no	—
564	C₂²×C₂₃	—	4	4	no	—
565	C₂²×C₂₃	—	4	4	no	—
566	C₂²×C₂₃	—	4	4	no	—
567	C₂²×C₂₃	—	4	4	no	—
568	C₂²×C₂₃	—	4	4	no	—
569	C₂²×C₂₃	—	4	4	no	—
570	C₂²×C₂₃	—	4	2	no	—
571	C₂²×C₂₃	—	4	2	no	—
572	C₂²×C₂₃	—	4	2	no	—
573	C₂²×C₂₃	—	4	2	no	—
574	C₂²×C₂₃	—	4	2	no	—
575	C₂²×C₂₃	—	4	2	no	—
576	C₂²×C₂₃	—	8	4	no	—
577	C₂²×C₂₃	—	8	4	no	—
578	C₂²×C₂₃	#534	1	2	yes	—
579	C₂²×C₂₃	#575	1	2	yes	—
580	C₂²×C₂₃	#575	1	2	yes	—
581	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
582	C₄×C₂₃	—	2	1	no	—
583	C₄×C₂₃	—	2	1	no	—
584	C₄×C₂₃	—	2	1	no	—
585	C₄×C₂₃	—	2	1	no	—
586	C₄×C₂₃	—	2	1	no	—
587	C₄×C₂₃	—	2	1	no	—
588	C₄×C₂₃	—	4	2	no	—
589	C₄×C₂₃	—	4	2	no	—
590	C₄×C₂₃	—	4	2	no	—
591	C₄×C₂₃	—	4	2	no	—
592	C₄×C₂₃	—	4	2	no	—
593	C₄×C₂₃	—	4	2	no	—
594	C₄×C₂₃	#534	1	2	yes	—
595	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
596	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
597	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic, complemented
598	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
599	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
600	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
601	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	complemented
602	#525	—	2	1	no	—
603	#525	—	2	1	no	—
604	#525	—	2	1	no	—
605	#525	—	2	1	no	—
606	#525	—	2	1	no	—
607	#525	—	2	1	no	—
608	#525	—	2	1	no	—
609	#525	—	2	1	no	—
610	#525	C₂²×C₂₃	1	2	yes	—
611	#525	C₂²×C₂₃	1	2	yes	—
612	#525	C₂²×C₂₃	1	2	yes	—
613	#525	C₂²×C₂₃	1	2	yes	—
614	#525	C₂²×C₂₃	1	2	yes	complemented
615	#525	C₂²×C₂₃	1	2	yes	complemented
616	#525	C₂²×C₂₃	1	2	yes	complemented
617	#525	C₂²×C₂₃	1	2	yes	complemented
618	C₂×#123	—	2	1	no	—
619	C₂×#123	—	2	1	no	—
620	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
621	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
622	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
623	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
624	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
625	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic, complemented
626	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic, complemented
627	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic, complemented
628	C₂×#120	—	2	1	no	—
629	C₂×#120	—	2	1	no	—
630	C₂×C₄×D₄	—	2	1	no	—
631	C₂×C₄×D₄	—	2	1	no	—
632	C₂×C₄×D₄	—	2	1	no	—
633	C₂×C₄×D₄	—	2	1	no	—
634	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
635	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic, complemented
636	#485	C₂²×C₂₃	1	4	yes	complemented
637	#485	C₂²×C₂₃	1	4	yes	complemented
638	#485	C₂²×C₂₃	1	4	yes	complemented
639	#484	C₂²×C₂₃	1	2	yes	complemented
640	#483	C₂²×C₂₃	1	2	yes	complemented
641	#482	C₂²×C₂₃	1	4	yes	complemented
642	#482	C₂²×C₂₃	1	4	yes	complemented
643	#482	C₂²×C₂₃	1	4	yes	complemented
644	#481	C₂²×C₂₃	1	2	yes	complemented
645	#480	C₂²×C₂₃	1	2	yes	complemented
646	#470	C₂²×C₂₃	1	4	yes	complemented
647	#469	C₂²×C₂₃	1	4	yes	complemented
648	#468	C₂²×C₂₃	1	4	yes	complemented
649	#468	C₂²×C₂₃	1	4	yes	complemented
650	#467	C₂²×C₂₃	1	4	yes	complemented
651	#466	C₂²×C₂₃	1	4	yes	complemented
652	#465	C₂²×C₂₃	1	4	yes	complemented
653	#465	C₂²×C₂₃	1	4	yes	complemented
654	#452	C₂²×C₂₃	1	4	yes	complemented
655	#452	C₂²×C₂₃	1	4	yes	complemented
656	#452	C₂²×C₂₃	1	4	yes	complemented
657	#451	C₂²×C₂₃	1	2	yes	complemented
658	#450	C₂²×C₂₃	1	2	yes	complemented
659	#449	C₂²×C₂₃	1	4	yes	complemented
660	#449	C₂²×C₂₃	1	4	yes	complemented
661	#449	C₂²×C₂₃	1	4	yes	complemented
662	#448	C₂²×C₂₃	1	2	yes	complemented
663	#447	C₂²×C₂₃	1	2	yes	complemented
664	#428	C₂²×C₂₃	1	2	yes	complemented
665	#428	C₂²×C₂₃	1	2	yes	complemented
666	#419	C₂²×C₂₃	1	2	yes	complemented
667	#418	C₂²×C₂₃	1	2	yes	complemented
668	#417	C₂²×C₂₃	1	2	yes	complemented
669	#417	C₂²×C₂₃	1	2	yes	complemented
670	#407	C₂²×C₂₃	1	1	yes	characteristic
671	#407	C₂²×C₂₃	1	1	yes	characteristic
672	#407	C₂²×C₂₃	1	2	yes	complemented
673	#407	C₂²×C₂₃	1	2	yes	complemented
674	#407	C₂²×C₂₃	1	2	yes	complemented
675	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
676	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
677	C₂×C₂₃	—	2	2	no	—
678	C₂×C₂₃	—	2	2	no	—
679	C₂×C₂₃	—	2	2	no	—
680	C₂×C₂₃	—	4	1	no	—
681	C₂×C₂₃	—	4	1	no	—
682	C₂×C₂₃	—	4	1	no	—
683	C₂×C₂₃	—	4	1	no	—
684	C₂×C₂₃	—	8	2	no	—
685	C₂×C₂₃	—	8	2	no	—
686	C₂×C₂₃	C₂×#534	1	1	yes	characteristic
687	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
688	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
689	C₂⁵	D₄×C₂₃	1	1	yes	characteristic
690	C₂×#41	—	2	1	no	—
691	C₂×#41	—	2	1	no	—
692	C₂×#41	—	2	1	no	—
693	C₂×#41	—	2	1	no	—
694	C₂×#41	—	4	4	no	—
695	C₂×#41	—	4	4	no	—
696	C₂×#41	C₂³×C₂₃	1	2	yes	—
697	C₂×#41	C₂³×C₂₃	1	2	yes	—
698	C₂×#41	C₂³×C₂₃	1	2	yes	—
699	C₂×#41	C₂³×C₂₃	1	2	yes	—
700	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
701	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
702	C₂²×D₄	—	2	1	no	—
703	C₂²×D₄	—	2	1	no	—
704	C₂²×D₄	—	2	1	no	—
705	C₂²×D₄	—	2	1	no	—
706	C₂²×D₄	—	2	1	no	—
707	C₂²×D₄	—	2	1	no	—
708	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
709	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
710	C₂³×C₄	—	2	1	no	—
711	C₂³×C₄	—	2	1	no	—
712	C₂³×C₄	—	4	4	no	—
713	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
714	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
715	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
716	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
717	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
718	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
719	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
720	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
721	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
722	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
723	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
724	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
725	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
726	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
727	#137	—	4	4	no	—
728	AGL(1,ℤ/8)	—	4	4	no	—
729	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	complemented
730	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	complemented
731	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	complemented
732	C₂×D₈	C₂³×C₂₃	1	4	yes	complemented
733	C₂×M₁₆	—	4	4	no	—
734	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
735	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
736	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
737	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	C₂²⋊Q₈	—	2	1	no	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	1	no	—
754	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
755	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
756	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
757	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
758	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
759	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
760	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
762	#121	—	2	1	no	—
763	#121	—	2	1	no	—
764	#121	—	2	1	no	—
765	#121	—	2	1	no	—
766	#121	—	2	1	no	—
767	#121	—	2	1	no	—
768	#121	—	2	1	no	—
769	#121	—	2	1	no	—
770	#121	C₂³×C₂₃	1	2	yes	—
771	#121	C₂³×C₂₃	1	2	yes	—
772	#121	C₂³×C₂₃	1	2	yes	—
773	#121	C₂³×C₂₃	1	2	yes	—
774	#121	C₂³×C₂₃	1	2	yes	—
775	#121	C₂³×C₂₃	1	2	yes	—
776	#121	C₂³×C₂₃	1	2	yes	—
777	#121	C₂³×C₂₃	1	2	yes	—
778	#120	—	2	2	no	—
779	#120	—	2	2	no	—
780	#120	—	2	2	no	—
781	#120	—	2	2	no	—
782	#120	—	2	2	no	—
783	#120	—	2	2	no	—
784	#120	—	2	2	no	—
785	#120	—	2	2	no	—
786	C₄×D₄	—	2	2	no	—
787	C₄×D₄	—	2	2	no	—
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	2	no	—
802	#117	—	2	1	no	—
803	#117	—	2	1	no	—
804	#117	—	2	1	no	—
805	#117	—	2	1	no	—
806	#117	C₂³×C₂₃	1	2	yes	—
807	#117	C₂³×C₂₃	1	2	yes	—
808	#117	C₂³×C₂₃	1	2	yes	—
809	#117	C₂³×C₂₃	1	2	yes	—
810	C₂×C₄⋊C₄	—	2	1	no	—
811	C₂×C₄⋊C₄	—	2	1	no	—
812	C₂×C₄⋊C₄	—	2	1	no	—
813	C₂×C₄⋊C₄	—	2	1	no	—
814	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
815	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
816	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
817	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
818	C₂×C₂²⋊C₄	—	2	1	no	—
819	C₂×C₂²⋊C₄	—	2	1	no	—
820	C₂×C₂²⋊C₄	—	2	1	no	—
821	C₂×C₂²⋊C₄	—	2	1	no	—
822	C₂×C₂²⋊C₄	—	2	1	no	—
823	C₂×C₂²⋊C₄	—	2	1	no	—
824	C₂×C₂²⋊C₄	—	2	1	no	—
825	C₂×C₂²⋊C₄	—	2	1	no	—
826	C₂×C₂²⋊C₄	—	2	1	no	—
827	C₂×C₂²⋊C₄	—	2	1	no	—
828	C₂×C₄²	—	2	1	no	—
829	C₂×C₄²	—	2	1	no	—
830	#107	C₂³×C₂₃	1	4	yes	complemented
831	#107	C₂³×C₂₃	1	4	yes	complemented
832	#106	C₂³×C₂₃	1	4	yes	complemented
833	#106	C₂³×C₂₃	1	4	yes	complemented
834	#103	C₂³×C₂₃	1	4	yes	complemented
835	#103	C₂³×C₂₃	1	4	yes	complemented
836	#103	C₂³×C₂₃	1	4	yes	complemented
837	#103	C₂³×C₂₃	1	4	yes	complemented
838	#102	C₂³×C₂₃	1	4	yes	complemented
839	#102	C₂³×C₂₃	1	4	yes	complemented
840	#102	C₂³×C₂₃	1	4	yes	complemented
841	#102	C₂³×C₂₃	1	4	yes	complemented
842	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
843	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
844	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
845	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
846	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
847	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
848	C₂₃	#60752	1	1	yes	characteristic, direct product factor, Sylow
849	C₂⁴	—	2	1	no	—
850	C₂⁴	—	2	1	no	—
851	C₂⁴	—	4	2	no	—
852	C₂⁴	—	4	2	no	—
853	C₂⁴	—	4	2	no	—
854	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
855	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
856	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
857	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
858	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
859	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
860	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
861	#41	—	2	4	no	—
862	#41	—	2	4	no	—
863	#41	—	4	2	no	—
864	#41	—	4	4	no	—
865	#41	—	4	4	no	—
866	#41	—	4	2	no	—
867	#41	—	4	4	no	—
868	#41	—	4	4	no	—
869	#41	—	4	4	no	—
870	#41	—	4	4	no	—
871	C₂×Q₈	—	2	1	no	—
872	C₂×Q₈	—	2	1	no	—
873	C₂×Q₈	—	2	4	no	—
874	C₂×Q₈	—	4	2	no	—
875	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
876	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	2	2	no	—
880	C₂×D₄	—	2	2	no	—
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	2	2	no	—
885	C₂×D₄	—	2	2	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	—	2	2	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	1	no	—
890	C₂×D₄	—	2	1	no	—
891	C₂×D₄	—	2	4	no	—
892	C₂×D₄	—	4	2	no	—
893	C₂×D₄	—	4	4	no	—
894	C₂×D₄	—	4	4	no	—
895	C₂×D₄	—	4	4	no	—
896	C₂×D₄	—	4	4	no	—
897	C₂×D₄	—	4	4	no	—
898	C₂×D₄	—	4	4	no	—
899	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
900	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
901	C₂²×C₄	—	2	4	no	—
902	C₂²×C₄	—	2	4	no	—
903	C₂²×C₄	—	2	4	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	4	2	no	—
915	C₂²×C₄	—	4	2	no	—
916	C₂²×C₄	—	4	2	no	—
917	C₂²×C₄	—	4	2	no	—
918	C₂²×C₄	—	4	2	no	—
919	C₂²×C₄	—	4	2	no	—
920	C₂²×C₄	—	4	2	no	—
921	C₂²×C₄	—	4	2	no	—
922	C₂²×C₄	—	4	2	no	—
923	C₂²×C₄	—	4	2	no	—
924	C₂²×C₄	—	4	2	no	—
925	C₂²×C₄	—	4	4	no	—
926	C₂²×C₄	—	4	4	no	—
927	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
928	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
929	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
930	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
931	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
932	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
933	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
934	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
935	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
936	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
937	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
938	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
939	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
940	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
941	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
942	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
943	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
944	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
945	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
946	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
947	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
948	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
949	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
950	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
951	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
952	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
953	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
954	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
955	Q₁₆	—	4	4	no	—
956	SD₁₆	—	4	4	no	—
957	SD₁₆	—	4	4	no	—
958	D₈	—	4	4	no	—
959	M₁₆	—	2	4	no	—
960	M₁₆	—	2	4	no	—
961	M₁₆	—	4	4	no	—
962	C₂×C₈	—	4	4	no	—
963	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
964	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
978	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
979	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
980	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	2	no	—
1005	C₂³	—	2	2	no	—
1006	C₂³	—	2	2	no	—
1007	C₂³	—	2	2	no	—
1008	C₂³	—	2	2	no	—
1009	C₂³	—	2	2	no	—
1010	C₂³	—	2	2	no	—
1011	C₂³	—	2	2	no	—
1012	C₂³	—	2	2	no	—
1013	C₂³	—	2	2	no	—
1014	C₂³	—	2	2	no	—
1015	C₂³	—	2	2	no	—
1016	C₂³	—	4	1	no	—
1017	C₂³	—	4	1	no	—
1018	C₂³	—	4	1	no	—
1019	C₂³	—	4	1	no	—
1020	C₂³	—	4	1	no	—
1021	C₂³	—	4	1	no	—
1022	C₂³	—	4	1	no	—
1023	C₂³	—	4	1	no	—
1024	C₂³	—	4	1	no	—
1025	C₂³	—	4	1	no	—
1026	C₂³	—	4	1	no	—
1027	C₂³	—	4	1	no	—
1028	C₂³	—	4	2	no	—
1029	C₂³	—	4	2	no	—
1030	C₂³	—	4	2	no	—
1031	C₂³	—	4	2	no	—
1032	C₂³	—	4	16	no	—
1033	C₂³	—	4	2	no	—
1034	C₂³	—	4	2	no	—
1035	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1036	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1037	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1038	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1039	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1040	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1041	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1042	Q₈	—	2	2	no	—
1043	Q₈	—	2	4	no	—
1044	Q₈	—	2	2	no	—
1045	Q₈	—	4	2	no	—
1046	Q₈	—	4	2	no	—
1047	D₄	—	2	2	no	—
1048	D₄	—	2	4	no	—
1049	D₄	—	2	2	no	—
1050	D₄	—	4	2	no	—
1051	D₄	—	4	4	no	—
1052	D₄	—	4	4	no	—
1053	D₄	—	4	4	no	—
1054	D₄	—	4	4	no	—
1055	D₄	—	4	4	no	—
1056	D₄	—	4	4	no	—
1057	D₄	—	4	4	no	—
1058	D₄	—	4	4	no	—
1059	D₄	—	4	4	no	—
1060	D₄	—	4	4	no	—
1061	D₄	—	4	4	no	—
1062	D₄	—	4	4	no	—
1063	D₄	—	4	2	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	4	1	no	—
1086	C₂×C₄	—	4	1	no	—
1087	C₂×C₄	—	4	1	no	—
1088	C₂×C₄	—	4	1	no	—
1089	C₂×C₄	—	4	1	no	—
1090	C₂×C₄	—	4	1	no	—
1091	C₂×C₄	—	4	1	no	—
1092	C₂×C₄	—	4	1	no	—
1093	C₂×C₄	—	4	1	no	—
1094	C₂×C₄	—	4	1	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	1	no	—
1097	C₂×C₄	—	4	4	no	—
1098	C₂×C₄	—	4	4	no	—
1099	C₂×C₄	—	4	4	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	4	2	no	—
1102	C₂×C₄	—	4	2	no	—
1103	C₂×C₄	—	4	2	no	—
1104	C₂×C₄	—	4	2	no	—
1105	C₂×C₄	—	4	2	no	—
1106	C₂×C₄	—	4	4	no	—
1107	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1108	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1109	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1110	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1111	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1112	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1113	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1114	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
1115	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1116	C₈	—	2	4	no	—
1117	C₈	—	2	4	no	—
1118	C₂²	—	2	1	no	—
1119	C₂²	—	2	1	no	—
1120	C₂²	—	2	1	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	1	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	1	no	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	2	1	no	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	1	no	—
1136	C₂²	—	4	4	no	—
1137	C₂²	—	4	4	no	—
1138	C₂²	—	4	4	no	—
1139	C₂²	—	4	4	no	—
1140	C₂²	—	4	4	no	—
1141	C₂²	—	4	4	no	—
1142	C₂²	—	4	4	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	4	2	no	—
1146	C₂²	—	4	2	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	8	4	no	—
1150	C₂²	—	8	4	no	—
1151	C₂²	C₂₃×#534	1	2	yes	—
1152	C₂²	C₂₃×#575	1	2	yes	—
1153	C₂²	C₂₃×#575	1	2	yes	—
1154	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1155	C₄	—	2	1	no	—
1156	C₄	—	2	1	no	—
1157	C₄	—	2	1	no	—
1158	C₄	—	2	1	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	1	no	—
1161	C₄	—	4	2	no	—
1162	C₄	—	4	2	no	—
1163	C₄	—	4	2	no	—
1164	C₄	—	4	2	no	—
1165	C₄	—	4	2	no	—
1166	C₄	—	4	2	no	—
1167	C₄	C₂₃×#534	1	2	yes	—
1168	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
1169	C₂	—	2	2	no	—
1170	C₂	—	2	2	no	—
1171	C₂	—	2	2	no	—
1172	C₂	—	4	1	no	—
1173	C₂	—	4	1	no	—
1174	C₂	—	4	1	no	—
1175	C₂	—	4	1	no	—
1176	C₂	—	8	2	no	—
1177	C₂	—	8	2	no	—
1178	C₂	C₂×C₂₃×#534	1	1	yes	characteristic
1179	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
1180	C₂	C₂×C₂₃×#575	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 ◁ C₂⁴×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#525	C₂	semidirect
2. C₂×C₂₃×#525	C₂	semidirect
3. C₂₃×#3197	C₂	semidirect
4. C₂₃×#3196	C₂	semidirect
5. C₂₃×#3194	C₂	semidirect
6. C₂₃×#3191	C₂	semidirect
7. C₂₃×#3190	C₂	semidirect
8. C₂₃×#3188	C₂	semidirect
9. C₂₃×#3095	C₂	semidirect
10. C₂₃×#3094	C₂	semidirect
11. C₂₃×#3093	C₂	semidirect
12. C₂₃×#3056	C₂	semidirect
13. C₂₃×#3055	C₂	semidirect
14. C₂₃×#3007	C₂	semidirect
15. C₂₃×#3006	C₂	semidirect
16. C₂₃×#3005	C₂	semidirect
17. C₂×C₂₃×#407	C₂	semidirect
19. C₂²×#41×C₂₃	C₂²	semidirect
21. C₂×C₂₃×#137	C₂²	semidirect
22. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
23. C₂²×M₁₆×C₂₃	C₂²	semidirect
36. C₂₃×#525	C₂²	semidirect
37. C₂₃×#525	C₂²	semidirect
38. C₂₃×#525	C₂²	semidirect
39. C₂₃×#525	C₂²	semidirect
43. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
44. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
45. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
47. C₂×C₂₃×#121	C₂²	semidirect
48. C₂×C₂₃×#121	C₂²	semidirect
49. C₂×C₂₃×#121	C₂²	semidirect
57. C₂×C₂₃×#117	C₂²	semidirect
58. C₂₃×#485	C₂²	semidirect
59. C₂₃×#485	C₂²	semidirect
60. C₂₃×#485	C₂²	semidirect
61. C₂₃×#484	C₂²	semidirect
62. C₂₃×#483	C₂²	semidirect
63. C₂₃×#482	C₂²	semidirect
64. C₂₃×#482	C₂²	semidirect
65. C₂₃×#482	C₂²	semidirect
66. C₂₃×#481	C₂²	semidirect
67. C₂₃×#480	C₂²	semidirect
68. C₂₃×#470	C₂²	semidirect
69. C₂₃×#469	C₂²	semidirect
70. C₂₃×#468	C₂²	semidirect
71. C₂₃×#468	C₂²	semidirect
72. C₂₃×#467	C₂²	semidirect
73. C₂₃×#466	C₂²	semidirect
74. C₂₃×#465	C₂²	semidirect
75. C₂₃×#465	C₂²	semidirect
76. C₂₃×#452	C₂²	semidirect
77. C₂₃×#452	C₂²	semidirect
78. C₂₃×#452	C₂²	semidirect
79. C₂₃×#451	C₂²	semidirect
80. C₂₃×#450	C₂²	semidirect
81. C₂₃×#449	C₂²	semidirect
82. C₂₃×#449	C₂²	semidirect
83. C₂₃×#449	C₂²	semidirect
84. C₂₃×#448	C₂²	semidirect
85. C₂₃×#447	C₂²	semidirect
86. C₂₃×#428	C₂²	semidirect
87. C₂₃×#428	C₂²	semidirect
88. C₂₃×#419	C₂²	semidirect
89. C₂₃×#418	C₂²	semidirect
90. C₂₃×#417	C₂²	semidirect
91. C₂₃×#417	C₂²	semidirect
94. C₂₃×#407	C₂²	semidirect
95. C₂₃×#407	C₂²	semidirect
96. C₂₃×#407	C₂²	semidirect
97. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
98. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
139. C₂×Q₁₆×C₂₃	C₂³	semidirect
140. C₂×SD₁₆×C₂₃	C₂³	semidirect
141. C₂×SD₁₆×C₂₃	C₂³	semidirect
142. C₂×D₈×C₂₃	C₂³	semidirect
240. C₂₃×#107	C₂³	semidirect
241. C₂₃×#107	C₂³	semidirect
242. C₂₃×#106	C₂³	semidirect
243. C₂₃×#106	C₂³	semidirect
244. C₂₃×#103	C₂³	semidirect
245. C₂₃×#103	C₂³	semidirect
246. C₂₃×#103	C₂³	semidirect
247. C₂₃×#103	C₂³	semidirect
248. C₂₃×#102	C₂³	semidirect
249. C₂₃×#102	C₂³	semidirect
250. C₂₃×#102	C₂³	semidirect
251. C₂₃×#102	C₂³	semidirect
414. #60752	C₂₃	direct (N × H)
528. C₂×#525	C₂×C₂₃	semidirect
529. C₂×#525	C₂×C₂₃	semidirect
530. #3197	C₂×C₂₃	semidirect
531. #3196	C₂×C₂₃	semidirect
532. #3194	C₂×C₂₃	semidirect
533. #3191	C₂×C₂₃	semidirect
534. #3190	C₂×C₂₃	semidirect
535. #3188	C₂×C₂₃	semidirect
536. #3095	C₂×C₂₃	semidirect
537. #3094	C₂×C₂₃	semidirect
538. #3093	C₂×C₂₃	semidirect
539. #3056	C₂×C₂₃	semidirect
540. #3055	C₂×C₂₃	semidirect
541. #3007	C₂×C₂₃	semidirect
542. #3006	C₂×C₂₃	semidirect
543. #3005	C₂×C₂₃	semidirect
544. C₂×#407	C₂×C₂₃	semidirect
597. C₂²×#41	C₂²×C₂₃	semidirect
599. C₂×#137	C₂²×C₂₃	semidirect
600. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
601. C₂²×M₁₆	C₂²×C₂₃	semidirect
614. #525	C₂²×C₂₃	semidirect
615. #525	C₂²×C₂₃	semidirect
616. #525	C₂²×C₂₃	semidirect
617. #525	C₂²×C₂₃	semidirect
621. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
622. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
623. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
625. C₂×#121	C₂²×C₂₃	semidirect
626. C₂×#121	C₂²×C₂₃	semidirect
627. C₂×#121	C₂²×C₂₃	semidirect
635. C₂×#117	C₂²×C₂₃	semidirect
636. #485	C₂²×C₂₃	semidirect
637. #485	C₂²×C₂₃	semidirect
638. #485	C₂²×C₂₃	semidirect
639. #484	C₂²×C₂₃	semidirect
640. #483	C₂²×C₂₃	semidirect
641. #482	C₂²×C₂₃	semidirect
642. #482	C₂²×C₂₃	semidirect
643. #482	C₂²×C₂₃	semidirect
644. #481	C₂²×C₂₃	semidirect
645. #480	C₂²×C₂₃	semidirect
646. #470	C₂²×C₂₃	semidirect
647. #469	C₂²×C₂₃	semidirect
648. #468	C₂²×C₂₃	semidirect
649. #468	C₂²×C₂₃	semidirect
650. #467	C₂²×C₂₃	semidirect
651. #466	C₂²×C₂₃	semidirect
652. #465	C₂²×C₂₃	semidirect
653. #465	C₂²×C₂₃	semidirect
654. #452	C₂²×C₂₃	semidirect
655. #452	C₂²×C₂₃	semidirect
656. #452	C₂²×C₂₃	semidirect
657. #451	C₂²×C₂₃	semidirect
658. #450	C₂²×C₂₃	semidirect
659. #449	C₂²×C₂₃	semidirect
660. #449	C₂²×C₂₃	semidirect
661. #449	C₂²×C₂₃	semidirect
662. #448	C₂²×C₂₃	semidirect
663. #447	C₂²×C₂₃	semidirect
664. #428	C₂²×C₂₃	semidirect
665. #428	C₂²×C₂₃	semidirect
666. #419	C₂²×C₂₃	semidirect
667. #418	C₂²×C₂₃	semidirect
668. #417	C₂²×C₂₃	semidirect
669. #417	C₂²×C₂₃	semidirect
672. #407	C₂²×C₂₃	semidirect
673. #407	C₂²×C₂₃	semidirect
674. #407	C₂²×C₂₃	semidirect
675. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
676. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
729. C₂×Q₁₆	C₂³×C₂₃	semidirect
730. C₂×SD₁₆	C₂³×C₂₃	semidirect
731. C₂×SD₁₆	C₂³×C₂₃	semidirect
732. C₂×D₈	C₂³×C₂₃	semidirect
830. #107	C₂³×C₂₃	semidirect
831. #107	C₂³×C₂₃	semidirect
832. #106	C₂³×C₂₃	semidirect
833. #106	C₂³×C₂₃	semidirect
834. #103	C₂³×C₂₃	semidirect
835. #103	C₂³×C₂₃	semidirect
836. #103	C₂³×C₂₃	semidirect
837. #103	C₂³×C₂₃	semidirect
838. #102	C₂³×C₂₃	semidirect
839. #102	C₂³×C₂₃	semidirect
840. #102	C₂³×C₂₃	semidirect
841. #102	C₂³×C₂₃	semidirect
848. C₂₃	#60752	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#525	2
C₂₃×#3197	2
C₂₃×#3196	2
C₂₃×#3194	2
C₂₃×#3191	2
C₂₃×#3190	2
C₂₃×#3188	2
C₂₃×#3095	2
C₂₃×#3094	2
C₂₃×#3093	2
C₂₃×#3056	2
C₂₃×#3055	2
C₂₃×#3007	2
C₂₃×#3006	2
C₂₃×#3005	2
C₂×C₂₃×#407	2
#60752	23

Subgroups — C23×#60752 #19208378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60752 #19208378