Subgroups — C₂₃×#61439 #19209065

Order 5888.

2116 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3386	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3368	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3353	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3345	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3332	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3318	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3308	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3265	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3171	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3106	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3105	C₂	1	2	yes	maximal, complemented
19	C₂₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₂₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×SD₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₂₃	—	2	1	no	—
25	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
26	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
27	C₂₃×#559	—	2	1	no	—
28	C₂₃×#559	C₂²	1	1	yes	characteristic, complemented
29	C₂₃×#557	C₂²	1	1	yes	characteristic, complemented
30	C₂₃×#556	—	2	1	no	—
31	C₂₃×#556	C₂²	1	1	yes	characteristic, complemented
32	C₂₃×#553	—	2	2	no	—
33	C₂₃×#553	C₂²	1	2	yes	complemented
34	C₂₃×#550	C₂²	1	1	yes	characteristic
35	C₂₃×#550	C₂²	1	1	yes	characteristic, complemented
36	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
37	C₂₃×#548	—	2	1	no	—
38	C₂₃×#548	C₂²	1	2	yes	complemented
39	C₂₃×#547	C₂²	1	2	yes	—
40	C₂₃×#547	C₂²	1	1	yes	characteristic
41	C₂₃×#546	—	2	2	no	—
42	C₂₃×#546	—	2	1	no	—
43	D₄²×C₂₃	C₂²	1	2	yes	—
44	D₄²×C₂₃	C₂²	1	1	yes	characteristic
45	C₂₃×#532	—	2	1	no	—
46	C₂₃×#532	C₂²	1	1	yes	characteristic
47	C₂₃×#532	C₂²	1	2	yes	—
48	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#529	—	2	2	no	—
50	C₂₃×#529	C₂²	1	2	yes	complemented
51	C₂₃×#525	—	2	1	no	—
52	C₂₃×#525	—	2	2	no	—
53	C₄×#41×C₂₃	—	2	1	no	—
54	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
55	C₄×#41×C₂₃	C₂²	1	2	yes	complemented
56	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
59	C₂₃×#501	C₂²	1	2	yes	complemented
60	C₂₃×#500	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#496	C₂²	1	2	yes	complemented
62	C₂₃×#493	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#490	C₂²	1	2	yes	complemented
64	C₂₃×#489	C₂²	1	2	yes	complemented
65	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#484	C₂²	1	2	yes	complemented
68	C₂₃×#482	C₂²	1	2	yes	complemented
69	C₂₃×#482	C₂²	1	2	yes	complemented
70	C₂₃×#481	C₂²	1	2	yes	complemented
71	C₂₃×#481	C₂²	1	2	yes	complemented
72	C₂₃×#480	C₂²	1	2	yes	complemented
73	C₂₃×#478	C₂²	1	2	yes	—
74	C₂₃×#478	C₂²	1	2	yes	complemented
75	C₂₃×#477	C₂²	1	2	yes	complemented
76	C₂₃×#476	C₂²	1	2	yes	complemented
77	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
78	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
79	C₂₃×#474	C₂²	1	1	yes	characteristic
80	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
81	C₂₃×#469	C₂²	1	2	yes	complemented
82	C₂₃×#469	C₂²	1	2	yes	complemented
83	C₂₃×#468	C₂²	1	2	yes	complemented
84	C₂₃×#468	C₂²	1	2	yes	complemented
85	C₂₃×#466	C₂²	1	2	yes	complemented
86	C₂₃×#466	C₂²	1	2	yes	complemented
87	C₂₃×#463	C₂²	1	2	yes	—
88	C₂₃×#463	C₂²	1	2	yes	complemented
89	C₂₃×#460	C₂²	1	2	yes	complemented
90	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#459	C₂²	1	1	yes	characteristic
93	C₂₃×#459	C₂²	1	2	yes	complemented
94	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
95	C₂₃×#450	C₂²	1	2	yes	—
96	C₂₃×#449	C₂²	1	2	yes	complemented
97	C₂₃×#449	C₂²	1	2	yes	complemented
98	C₂₃×#448	C₂²	1	2	yes	complemented
99	C₂₃×#447	C₂²	1	2	yes	—
100	C₂₃×#447	C₂²	1	2	yes	—
101	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
102	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
103	C₂₃×#442	C₂²	1	2	yes	—
104	C₂₃×#442	C₂²	1	2	yes	complemented
105	C₂₃×#440	C₂²	1	2	yes	—
106	C₂₃×#440	C₂²	1	2	yes	complemented
107	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
108	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
109	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
110	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
111	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
112	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
113	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
117	C₄×D₈×C₂₃	C₂²	1	2	yes	—
118	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
119	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
120	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
121	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
122	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
123	C₂₃×#435	C₂²	1	2	yes	complemented
124	C₂₃×#435	C₂²	1	2	yes	complemented
125	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
126	C₂₃×#431	C₂²	1	2	yes	complemented
127	C₂₃×#428	C₂²	1	2	yes	complemented
128	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic, complemented
129	C₂₃×#418	C₂²	1	2	yes	—
130	C₂₃×#417	C₂²	1	2	yes	complemented
131	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
132	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
133	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₂₃	—	2	1	no	—
136	C₂×#41×C₂₃	—	2	2	no	—
137	C₂×#41×C₂₃	—	2	1	no	—
138	C₂×#41×C₂₃	—	2	2	no	—
139	C₂×#41×C₂₃	—	2	1	no	—
140	C₂×#41×C₂₃	—	2	1	no	—
141	C₂×#41×C₂₃	—	4	8	no	—
142	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
143	C₂×#41×C₂₃	C₂³	1	2	yes	—
144	C₂²×Q₈×C₂₃	—	2	1	no	—
145	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
146	C₂²×D₄×C₂₃	—	2	2	no	—
147	C₂²×D₄×C₂₃	—	2	1	no	—
148	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
149	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
150	C₂³×C₄×C₂₃	—	2	2	no	—
151	C₂³×C₄×C₂₃	—	2	1	no	—
152	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
153	C₂×SD₁₆×C₂₃	—	2	4	no	—
154	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
155	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
156	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
157	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
160	C₂×D₈×C₂₃	C₂³	1	2	yes	—
161	C₂×D₈×C₂₃	C₂³	1	2	yes	—
162	C₂×D₈×C₂₃	C₂³	1	2	yes	—
163	C₂×D₈×C₂₃	C₂³	1	2	yes	—
164	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
165	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
166	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
167	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
168	C₂₃×C₄⋊Q₈	—	2	1	no	—
169	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
171	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₂₃×#127	—	2	1	no	—
173	C₂₃×#127	C₂³	1	2	yes	—
174	C₂₃×#127	C₂³	1	1	yes	characteristic
175	C₂₃×#127	C₂³	1	1	yes	characteristic
176	C₂₃×#126	—	2	2	no	—
177	C₂₃×#126	—	2	2	no	—
178	C₂₃×#126	—	2	2	no	—
179	C₂₃×#125	—	2	2	no	—
180	C₂₃×#125	C₂³	1	2	yes	—
181	C₂₃×#124	—	2	1	no	—
182	C₂₃×#124	—	2	1	no	—
183	C₂₃×#124	—	2	2	no	—
184	C₂₃×#124	—	2	2	no	—
185	C₂₃×#124	—	2	1	no	—
186	C₂₃×#124	—	2	1	no	—
187	C₂₃×#124	C₂³	1	2	yes	—
188	C₂₃×#123	—	2	2	no	—
189	C₂₃×#123	—	2	2	no	—
190	C₂₃×#123	—	2	2	no	—
191	C₂₃×#123	—	2	2	no	—
192	C₂₃×#123	—	2	2	no	—
193	C₂₃×#123	—	2	2	no	—
194	C₂₃×C₂²⋊Q₈	—	2	1	no	—
195	C₂₃×C₂²⋊Q₈	—	2	2	no	—
196	C₂₃×C₂²⋊Q₈	—	2	2	no	—
197	C₂₃×C₂²⋊Q₈	—	2	1	no	—
198	C₂₃×C₂²⋊Q₈	—	2	2	no	—
199	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₂₃×#121	—	2	2	no	—
201	C₂₃×#121	—	2	2	no	—
202	C₂₃×#121	—	2	1	no	—
203	C₂₃×#121	—	2	1	no	—
204	C₂₃×#121	—	2	2	no	—
205	C₂₃×#121	—	2	1	no	—
206	C₂₃×#121	—	2	2	no	—
207	C₂₃×#121	—	2	1	no	—
208	C₂₃×#121	—	2	2	no	—
209	C₂₃×#121	—	2	2	no	—
210	C₂₃×#121	C₂³	1	2	yes	—
211	C₂₃×#121	C₂³	1	2	yes	—
212	C₂₃×#121	C₂³	1	2	yes	—
213	C₂₃×#121	C₂³	1	2	yes	—
214	C₂₃×#121	C₂³	1	2	yes	—
215	C₂₃×#120	—	2	2	no	—
216	C₂₃×#120	—	2	2	no	—
217	C₂₃×#120	—	2	2	no	—
218	C₄×Q₈×C₂₃	—	2	1	no	—
219	C₄×Q₈×C₂₃	—	2	1	no	—
220	C₄×Q₈×C₂₃	—	2	1	no	—
221	C₄×Q₈×C₂₃	—	2	1	no	—
222	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
223	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
224	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
229	C₄×D₄×C₂₃	—	2	2	no	—
230	C₄×D₄×C₂₃	—	2	2	no	—
231	C₄×D₄×C₂₃	—	2	2	no	—
232	C₄×D₄×C₂₃	—	2	1	no	—
233	C₄×D₄×C₂₃	—	2	1	no	—
234	C₄×D₄×C₂₃	—	2	2	no	—
235	C₄×D₄×C₂₃	—	2	2	no	—
236	C₄×D₄×C₂₃	—	2	2	no	—
237	C₄×D₄×C₂₃	—	2	1	no	—
238	C₄×D₄×C₂₃	—	2	2	no	—
239	C₄×D₄×C₂₃	—	2	1	no	—
240	C₄×D₄×C₂₃	—	2	2	no	—
241	C₄×D₄×C₂₃	—	2	1	no	—
242	C₄×D₄×C₂₃	—	2	1	no	—
243	C₄×D₄×C₂₃	D₄	1	2	yes	—
244	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
245	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₂₃	C₂³	1	2	yes	—
247	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₂₃	C₂³	1	2	yes	—
249	C₄×D₄×C₂₃	C₂³	1	2	yes	—
250	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₂₃	C₂³	1	2	yes	—
252	C₄×D₄×C₂₃	C₂³	1	2	yes	—
253	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₂₃	C₂³	1	2	yes	—
255	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
256	C₂₃×#117	—	2	2	no	—
257	C₂₃×#117	—	2	2	no	—
258	C₂₃×#117	D₄	1	1	yes	characteristic
259	C₂₃×#117	D₄	1	2	yes	—
260	C₂₃×#117	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
262	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
264	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
266	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
267	C₂×C₄²×C₂₃	—	2	1	no	—
268	C₂×C₄²×C₂₃	—	2	2	no	—
269	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
270	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
271	C₂₃×#107	C₂³	1	2	yes	—
272	C₂₃×#107	C₂³	1	2	yes	—
273	C₂₃×#107	C₂³	1	2	yes	—
274	C₂₃×#107	C₂³	1	2	yes	—
275	C₂₃×#106	C₂³	1	1	yes	characteristic
276	C₂₃×#106	C₂³	1	1	yes	characteristic
277	C₂₃×#106	C₂³	1	1	yes	characteristic
278	C₂₃×#106	C₂³	1	1	yes	characteristic
279	C₂₃×#106	C₂³	1	2	yes	—
280	C₂₃×#106	C₂³	1	2	yes	—
281	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
282	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
283	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₂₃×#103	C₂³	1	1	yes	characteristic
286	C₂₃×#103	C₂³	1	1	yes	characteristic
287	C₂₃×#103	C₂³	1	1	yes	characteristic
288	C₂₃×#103	C₂³	1	1	yes	characteristic
289	C₂₃×#103	C₂³	1	2	yes	—
290	C₂₃×#103	C₂³	1	2	yes	—
291	C₂₃×#102	C₂³	1	1	yes	characteristic
292	C₂₃×#102	C₂³	1	1	yes	characteristic
293	C₂₃×#102	C₂³	1	1	yes	characteristic
294	C₂₃×#102	C₂³	1	1	yes	characteristic
295	C₂₃×#102	C₂³	1	2	yes	—
296	C₂₃×#102	C₂³	1	2	yes	—
297	C₂₃×#102	C₂³	1	2	yes	—
298	C₂₃×#102	C₂³	1	2	yes	—
299	C₂₃×#102	C₂³	1	2	yes	—
300	C₂₃×#102	C₂³	1	2	yes	—
301	C₂₃×#102	C₂³	1	2	yes	—
302	C₂₃×#102	C₂³	1	2	yes	—
303	C₂₃×#102	C₂³	1	2	yes	—
304	C₂₃×#102	C₂³	1	2	yes	—
305	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₂₃×#97	C₂³	1	2	yes	—
309	C₂₃×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₂₃	C₂³	1	2	yes	—
315	C₂⁴×C₂₃	—	2	2	no	—
316	C₂⁴×C₂₃	—	2	1	no	—
317	#41×C₂₃	—	2	4	no	—
318	#41×C₂₃	—	2	4	no	—
319	#41×C₂₃	—	4	2	no	—
320	#41×C₂₃	—	4	8	no	—
321	#41×C₂₃	—	4	8	no	—
322	#41×C₂₃	—	4	4	no	—
323	#41×C₂₃	—	4	4	no	—
324	#41×C₂₃	—	4	4	no	—
325	#41×C₂₃	—	4	4	no	—
326	C₂×Q₈×C₂₃	—	2	1	no	—
327	C₂×Q₈×C₂₃	—	2	1	no	—
328	C₂×Q₈×C₂₃	—	2	2	no	—
329	C₂×Q₈×C₂₃	—	2	1	no	—
330	C₂×Q₈×C₂₃	—	2	2	no	—
331	C₂×Q₈×C₂₃	—	4	1	no	—
332	C₂×Q₈×C₂₃	—	4	4	no	—
333	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
334	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
335	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₂₃	—	2	2	no	—
337	C₂×D₄×C₂₃	—	2	4	no	—
338	C₂×D₄×C₂₃	—	2	2	no	—
339	C₂×D₄×C₂₃	—	2	2	no	—
340	C₂×D₄×C₂₃	—	2	2	no	—
341	C₂×D₄×C₂₃	—	2	2	no	—
342	C₂×D₄×C₂₃	—	2	2	no	—
343	C₂×D₄×C₂₃	—	2	2	no	—
344	C₂×D₄×C₂₃	—	2	2	no	—
345	C₂×D₄×C₂₃	—	2	1	no	—
346	C₂×D₄×C₂₃	—	2	1	no	—
347	C₂×D₄×C₂₃	—	2	2	no	—
348	C₂×D₄×C₂₃	—	2	1	no	—
349	C₂×D₄×C₂₃	—	2	2	no	—
350	C₂×D₄×C₂₃	—	2	1	no	—
351	C₂×D₄×C₂₃	—	2	1	no	—
352	C₂×D₄×C₂₃	—	4	1	no	—
353	C₂×D₄×C₂₃	—	4	2	no	—
354	C₂×D₄×C₂₃	—	4	8	no	—
355	C₂×D₄×C₂₃	—	4	4	no	—
356	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
357	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
358	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
359	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
360	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
361	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₂₃	—	2	1	no	—
363	C₂²×C₄×C₂₃	—	2	2	no	—
364	C₂²×C₄×C₂₃	—	2	1	no	—
365	C₂²×C₄×C₂₃	—	2	1	no	—
366	C₂²×C₄×C₂₃	—	2	2	no	—
367	C₂²×C₄×C₂₃	—	2	2	no	—
368	C₂²×C₄×C₂₃	—	2	1	no	—
369	C₂²×C₄×C₂₃	—	2	2	no	—
370	C₂²×C₄×C₂₃	—	2	1	no	—
371	C₂²×C₄×C₂₃	—	2	2	no	—
372	C₂²×C₄×C₂₃	—	2	1	no	—
373	C₂²×C₄×C₂₃	—	2	2	no	—
374	C₂²×C₄×C₂₃	—	2	1	no	—
375	C₂²×C₄×C₂₃	—	2	2	no	—
376	C₂²×C₄×C₂₃	—	4	8	no	—
377	C₂²×C₄×C₂₃	—	4	4	no	—
378	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
379	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
380	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
381	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
382	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
384	SD₁₆×C₂₃	—	2	2	no	—
385	SD₁₆×C₂₃	—	2	4	no	—
386	SD₁₆×C₂₃	—	2	2	no	—
387	SD₁₆×C₂₃	—	2	2	no	—
388	SD₁₆×C₂₃	—	4	2	no	—
389	SD₁₆×C₂₃	#41	1	4	yes	complemented
390	D₈×C₂₃	—	2	4	no	—
391	D₈×C₂₃	—	2	4	no	—
392	D₈×C₂₃	—	4	2	no	—
393	D₈×C₂₃	—	4	2	no	—
394	M₁₆×C₂₃	—	2	4	no	—
395	M₁₆×C₂₃	—	4	2	no	—
396	C₂×C₈×C₂₃	—	2	2	no	—
397	C₂×C₈×C₂₃	—	4	1	no	—
398	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
399	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
400	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
401	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
402	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
403	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₂₃	—	2	1	no	—
405	C₄⋊C₄×C₂₃	—	2	1	no	—
406	C₄⋊C₄×C₂₃	—	2	1	no	—
407	C₄⋊C₄×C₂₃	—	2	1	no	—
408	C₄⋊C₄×C₂₃	—	2	2	no	—
409	C₄⋊C₄×C₂₃	—	2	1	no	—
410	C₄⋊C₄×C₂₃	—	2	1	no	—
411	C₄⋊C₄×C₂₃	—	2	2	no	—
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	1	no	—
416	C₄⋊C₄×C₂₃	—	2	1	no	—
417	C₄⋊C₄×C₂₃	—	2	2	no	—
418	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
420	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
422	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
425	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
427	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
428	C₂²⋊C₄×C₂₃	—	2	2	no	—
429	C₂²⋊C₄×C₂₃	—	2	2	no	—
430	C₂²⋊C₄×C₂₃	—	2	1	no	—
431	C₂²⋊C₄×C₂₃	—	2	2	no	—
432	C₂²⋊C₄×C₂₃	—	2	1	no	—
433	C₂²⋊C₄×C₂₃	—	2	2	no	—
434	C₂²⋊C₄×C₂₃	—	2	1	no	—
435	C₂²⋊C₄×C₂₃	—	2	1	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	—	2	2	no	—
440	C₂²⋊C₄×C₂₃	—	2	2	no	—
441	C₂²⋊C₄×C₂₃	—	2	2	no	—
442	C₂²⋊C₄×C₂₃	—	2	2	no	—
443	C₂²⋊C₄×C₂₃	—	2	2	no	—
444	C₂²⋊C₄×C₂₃	—	2	2	no	—
445	C₂²⋊C₄×C₂₃	—	2	2	no	—
446	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
447	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
448	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
449	C₄²×C₂₃	—	2	2	no	—
450	C₄²×C₂₃	—	2	2	no	—
451	C₄²×C₂₃	—	2	1	no	—
452	C₄²×C₂₃	—	2	1	no	—
453	C₄²×C₂₃	—	2	1	no	—
454	C₄²×C₂₃	—	2	1	no	—
455	C₄²×C₂₃	C₂×D₄	1	2	yes	—
456	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₂₃	C₂×D₄	1	2	yes	—
458	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₂₃	C₂⁴	1	2	yes	—
460	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
461	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
462	#61439	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
463	C₂³×C₂₃	—	2	1	no	—
464	C₂³×C₂₃	—	2	2	no	—
465	C₂³×C₂₃	—	2	2	no	—
466	C₂³×C₂₃	—	2	1	no	—
467	C₂³×C₂₃	—	4	2	no	—
468	C₂³×C₂₃	—	4	4	no	—
469	C₂³×C₂₃	—	4	4	no	—
470	C₂³×C₂₃	—	4	2	no	—
471	C₂³×C₂₃	—	8	1	no	—
472	C₂³×C₂₃	—	8	2	no	—
473	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
474	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
475	Q₈×C₂₃	—	2	2	no	—
476	Q₈×C₂₃	—	2	1	no	—
477	Q₈×C₂₃	—	2	1	no	—
478	Q₈×C₂₃	—	2	1	no	—
479	Q₈×C₂₃	—	4	2	no	—
480	Q₈×C₂₃	—	4	4	no	—
481	Q₈×C₂₃	—	4	2	no	—
482	Q₈×C₂₃	—	4	2	no	—
483	Q₈×C₂₃	C₂×#41	1	2	yes	complemented
484	D₄×C₂₃	—	2	4	no	—
485	D₄×C₂₃	—	2	2	no	—
486	D₄×C₂₃	—	2	2	no	—
487	D₄×C₂₃	—	2	2	no	—
488	D₄×C₂₃	—	2	1	no	—
489	D₄×C₂₃	—	2	1	no	—
490	D₄×C₂₃	—	2	1	no	—
491	D₄×C₂₃	—	2	2	no	—
492	D₄×C₂₃	—	2	2	no	—
493	D₄×C₂₃	—	4	4	no	—
494	D₄×C₂₃	—	4	2	no	—
495	D₄×C₂₃	—	4	4	no	—
496	D₄×C₂₃	—	4	4	no	—
497	D₄×C₂₃	—	4	4	no	—
498	D₄×C₂₃	—	4	4	no	—
499	D₄×C₂₃	—	4	4	no	—
500	D₄×C₂₃	—	4	4	no	—
501	D₄×C₂₃	—	4	2	no	—
502	D₄×C₂₃	—	4	2	no	—
503	D₄×C₂₃	—	8	2	no	—
504	D₄×C₂₃	—	8	1	no	—
505	D₄×C₂₃	—	8	1	no	—
506	D₄×C₂₃	—	8	2	no	—
507	D₄×C₂₃	C₂×#41	1	2	yes	—
508	C₂×C₄×C₂₃	—	2	1	no	—
509	C₂×C₄×C₂₃	—	2	4	no	—
510	C₂×C₄×C₂₃	—	2	1	no	—
511	C₂×C₄×C₂₃	—	2	2	no	—
512	C₂×C₄×C₂₃	—	2	1	no	—
513	C₂×C₄×C₂₃	—	2	2	no	—
514	C₂×C₄×C₂₃	—	2	1	no	—
515	C₂×C₄×C₂₃	—	2	1	no	—
516	C₂×C₄×C₂₃	—	2	2	no	—
517	C₂×C₄×C₂₃	—	2	1	no	—
518	C₂×C₄×C₂₃	—	2	1	no	—
519	C₂×C₄×C₂₃	—	2	2	no	—
520	C₂×C₄×C₂₃	—	2	1	no	—
521	C₂×C₄×C₂₃	—	4	2	no	—
522	C₂×C₄×C₂₃	—	4	1	no	—
523	C₂×C₄×C₂₃	—	4	4	no	—
524	C₂×C₄×C₂₃	—	4	2	no	—
525	C₂×C₄×C₂₃	—	4	4	no	—
526	C₂×C₄×C₂₃	—	4	4	no	—
527	C₂×C₄×C₂₃	—	4	4	no	—
528	C₂×C₄×C₂₃	—	4	2	no	—
529	C₂×C₄×C₂₃	—	4	2	no	—
530	C₂×C₄×C₂₃	—	4	2	no	—
531	C₂×C₄×C₂₃	—	4	2	no	—
532	C₂×C₄×C₂₃	—	4	4	no	—
533	C₂×C₄×C₂₃	—	4	2	no	—
534	C₂×C₄×C₂₃	—	4	4	no	—
535	C₂×C₄×C₂₃	—	8	2	no	—
536	C₂×C₄×C₂₃	—	8	1	no	—
537	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	4	yes	complemented
538	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
539	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
540	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
544	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
547	C₈×C₂₃	—	2	1	no	—
548	C₈×C₂₃	—	2	2	no	—
549	C₈×C₂₃	—	2	1	no	—
550	C₈×C₂₃	—	2	1	no	—
551	C₈×C₂₃	—	2	2	no	—
552	C₈×C₂₃	C₂×#41	1	2	yes	complemented
553	#3480	C₂×C₂₃	1	1	yes	characteristic, complemented
554	D₄×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
555	#3399	C₂×C₂₃	1	1	yes	characteristic, complemented
556	#3386	C₂×C₂₃	1	1	yes	characteristic, complemented
557	#3373	C₂×C₂₃	1	1	yes	characteristic, complemented
558	#3368	C₂×C₂₃	1	1	yes	characteristic, complemented
559	#3353	C₂×C₂₃	1	1	yes	characteristic, complemented
560	#3345	C₂×C₂₃	1	2	yes	complemented
561	#3332	C₂×C₂₃	1	1	yes	characteristic, complemented
562	#3324	C₂×C₂₃	1	1	yes	characteristic, complemented
563	#3318	C₂×C₂₃	1	2	yes	complemented
564	#3308	C₂×C₂₃	1	2	yes	complemented
565	#3274	C₂×C₂₃	1	1	yes	characteristic, complemented
566	#3265	C₂×C₂₃	1	2	yes	complemented
567	#3171	C₂×C₂₃	1	2	yes	complemented
568	#3169	C₂×C₂₃	1	1	yes	characteristic, complemented
569	#3106	C₂×C₂₃	1	2	yes	complemented
570	#3105	C₂×C₂₃	1	2	yes	complemented
571	#3103	C₂×C₂₃	1	1	yes	characteristic, complemented
572	#3100	C₂×C₂₃	1	1	yes	characteristic, complemented
573	#2965	C₂×C₂₃	1	1	yes	characteristic, complemented
574	C₄×AGL(1,ℤ/8)	C₂×C₂₃	1	2	yes	complemented
575	C₂×C₄×SD₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
576	C₂²×C₂₃	—	2	1	no	—
577	C₂²×C₂₃	—	2	1	no	—
578	C₂²×C₂₃	—	2	2	no	—
579	C₂²×C₂₃	—	2	2	no	—
580	C₂²×C₂₃	—	2	2	no	—
581	C₂²×C₂₃	—	2	2	no	—
582	C₂²×C₂₃	—	4	1	no	—
583	C₂²×C₂₃	—	4	1	no	—
584	C₂²×C₂₃	—	4	2	no	—
585	C₂²×C₂₃	—	4	1	no	—
586	C₂²×C₂₃	—	4	2	no	—
587	C₂²×C₂₃	—	4	2	no	—
588	C₂²×C₂₃	—	4	2	no	—
589	C₂²×C₂₃	—	4	1	no	—
590	C₂²×C₂₃	—	4	2	no	—
591	C₂²×C₂₃	—	4	1	no	—
592	C₂²×C₂₃	—	4	2	no	—
593	C₂²×C₂₃	—	8	4	no	—
594	C₂²×C₂₃	—	8	8	no	—
595	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
596	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
597	C₄×C₂₃	—	2	1	no	—
598	C₄×C₂₃	—	2	2	no	—
599	C₄×C₂₃	—	2	1	no	—
600	C₄×C₂₃	—	2	2	no	—
601	C₄×C₂₃	—	2	1	no	—
602	C₄×C₂₃	—	2	2	no	—
603	C₄×C₂₃	—	2	2	no	—
604	C₄×C₂₃	—	4	1	no	—
605	C₄×C₂₃	—	4	1	no	—
606	C₄×C₂₃	—	4	1	no	—
607	C₄×C₂₃	—	4	1	no	—
608	C₄×C₂₃	—	4	2	no	—
609	C₄×C₂₃	—	4	1	no	—
610	C₄×C₂₃	—	4	2	no	—
611	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
612	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
613	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
614	C₄×C₂₃	#585	1	1	yes	characteristic
615	C₂²×#41	—	2	1	no	—
616	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
617	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
618	#559	—	2	1	no	—
619	#559	C₂²×C₂₃	1	1	yes	characteristic, complemented
620	#557	C₂²×C₂₃	1	1	yes	characteristic, complemented
621	#556	—	2	1	no	—
622	#556	C₂²×C₂₃	1	1	yes	characteristic, complemented
623	#553	—	2	2	no	—
624	#553	C₂²×C₂₃	1	2	yes	complemented
625	#550	C₂²×C₂₃	1	1	yes	characteristic
626	#550	C₂²×C₂₃	1	1	yes	characteristic, complemented
627	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
628	#548	—	2	1	no	—
629	#548	C₂²×C₂₃	1	2	yes	complemented
630	#547	C₂²×C₂₃	1	1	yes	characteristic
631	#547	C₂²×C₂₃	1	2	yes	—
632	#546	—	2	2	no	—
633	#546	—	2	1	no	—
634	D₄²	C₂²×C₂₃	1	2	yes	—
635	D₄²	C₂²×C₂₃	1	1	yes	characteristic
636	#532	—	2	1	no	—
637	#532	C₂²×C₂₃	1	1	yes	characteristic
638	#532	C₂²×C₂₃	1	2	yes	—
639	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
640	#529	—	2	2	no	—
641	#529	C₂²×C₂₃	1	2	yes	complemented
642	#525	—	2	1	no	—
643	#525	—	2	2	no	—
644	C₄×#41	—	2	1	no	—
645	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
646	C₄×#41	C₂²×C₂₃	1	2	yes	complemented
647	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
648	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
649	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
650	#501	C₂²×C₂₃	1	2	yes	complemented
651	#500	C₂²×C₂₃	1	1	yes	characteristic, complemented
652	#496	C₂²×C₂₃	1	2	yes	complemented
653	#493	C₂²×C₂₃	1	1	yes	characteristic, complemented
654	#490	C₂²×C₂₃	1	2	yes	complemented
655	#489	C₂²×C₂₃	1	2	yes	complemented
656	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
657	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
658	#484	C₂²×C₂₃	1	2	yes	complemented
659	#482	C₂²×C₂₃	1	2	yes	complemented
660	#482	C₂²×C₂₃	1	2	yes	complemented
661	#481	C₂²×C₂₃	1	2	yes	complemented
662	#481	C₂²×C₂₃	1	2	yes	complemented
663	#480	C₂²×C₂₃	1	2	yes	complemented
664	#478	C₂²×C₂₃	1	2	yes	—
665	#478	C₂²×C₂₃	1	2	yes	complemented
666	#477	C₂²×C₂₃	1	2	yes	complemented
667	#476	C₂²×C₂₃	1	2	yes	complemented
668	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
669	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
670	#474	C₂²×C₂₃	1	1	yes	characteristic
671	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
672	#469	C₂²×C₂₃	1	2	yes	complemented
673	#469	C₂²×C₂₃	1	2	yes	complemented
674	#468	C₂²×C₂₃	1	2	yes	complemented
675	#468	C₂²×C₂₃	1	2	yes	complemented
676	#466	C₂²×C₂₃	1	2	yes	complemented
677	#466	C₂²×C₂₃	1	2	yes	complemented
678	#463	C₂²×C₂₃	1	2	yes	—
679	#463	C₂²×C₂₃	1	2	yes	complemented
680	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
681	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
682	#460	C₂²×C₂₃	1	2	yes	complemented
683	#459	C₂²×C₂₃	1	1	yes	characteristic
684	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
685	#459	C₂²×C₂₃	1	2	yes	complemented
686	#450	C₂²×C₂₃	1	2	yes	—
687	#449	C₂²×C₂₃	1	2	yes	complemented
688	#449	C₂²×C₂₃	1	2	yes	complemented
689	#448	C₂²×C₂₃	1	2	yes	complemented
690	#447	C₂²×C₂₃	1	2	yes	—
691	#447	C₂²×C₂₃	1	2	yes	—
692	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
693	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
694	#442	C₂²×C₂₃	1	2	yes	—
695	#442	C₂²×C₂₃	1	2	yes	complemented
696	#440	C₂²×C₂₃	1	2	yes	—
697	#440	C₂²×C₂₃	1	2	yes	complemented
698	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
699	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
700	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
701	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
702	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
703	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
704	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
705	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
706	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
707	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
708	C₄×D₈	C₂²×C₂₃	1	2	yes	—
709	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
710	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
711	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
712	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
713	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
714	#435	C₂²×C₂₃	1	2	yes	complemented
715	#435	C₂²×C₂₃	1	2	yes	complemented
716	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
717	#431	C₂²×C₂₃	1	2	yes	complemented
718	#428	C₂²×C₂₃	1	2	yes	complemented
719	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
720	#418	C₂²×C₂₃	1	2	yes	—
721	#417	C₂²×C₂₃	1	2	yes	complemented
722	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
723	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
724	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
725	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
726	C₂×C₂₃	—	2	2	no	—
727	C₂×C₂₃	—	4	2	no	—
728	C₂×C₂₃	—	4	2	no	—
729	C₂×C₂₃	—	8	2	no	—
730	C₂×C₂₃	—	8	1	no	—
731	C₂×C₂₃	—	8	2	no	—
732	C₂×C₂₃	D₄×#41	1	1	yes	characteristic
733	C₂×C₂₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
734	C₂×C₂₃	#3584	1	1	yes	characteristic
735	C₂×#41	—	2	1	no	—
736	C₂×#41	—	2	2	no	—
737	C₂×#41	—	2	1	no	—
738	C₂×#41	—	2	1	no	—
739	C₂×#41	—	2	2	no	—
740	C₂×#41	—	2	1	no	—
741	C₂×#41	—	4	8	no	—
742	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
743	C₂×#41	C₂³×C₂₃	1	2	yes	—
744	C₂²×Q₈	—	2	1	no	—
745	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
746	C₂²×D₄	—	2	2	no	—
747	C₂²×D₄	—	2	1	no	—
748	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
749	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
750	C₂³×C₄	—	2	2	no	—
751	C₂³×C₄	—	2	1	no	—
752	AGL(1,ℤ/8)	—	2	8	no	—
753	C₂×SD₁₆	—	2	4	no	—
754	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
755	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
756	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
757	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
758	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
759	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
760	C₂×D₈	C₂³×C₂₃	1	2	yes	—
761	C₂×D₈	C₂³×C₂₃	1	2	yes	—
762	C₂×D₈	C₂³×C₂₃	1	2	yes	—
763	C₂×D₈	C₂³×C₂₃	1	2	yes	—
764	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
765	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
766	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
767	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
768	C₄⋊Q₈	—	2	1	no	—
769	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
770	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
771	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
772	#127	—	2	1	no	—
773	#127	C₂³×C₂₃	1	2	yes	—
774	#127	C₂³×C₂₃	1	1	yes	characteristic
775	#127	C₂³×C₂₃	1	1	yes	characteristic
776	#126	—	2	2	no	—
777	#126	—	2	2	no	—
778	#126	—	2	2	no	—
779	#125	—	2	2	no	—
780	#125	C₂³×C₂₃	1	2	yes	—
781	#124	—	2	1	no	—
782	#124	—	2	1	no	—
783	#124	—	2	2	no	—
784	#124	—	2	2	no	—
785	#124	—	2	1	no	—
786	#124	—	2	1	no	—
787	#124	C₂³×C₂₃	1	2	yes	—
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	no	—
791	#123	—	2	2	no	—
792	#123	—	2	2	no	—
793	#123	—	2	2	no	—
794	C₂²⋊Q₈	—	2	1	no	—
795	C₂²⋊Q₈	—	2	2	no	—
796	C₂²⋊Q₈	—	2	1	no	—
797	C₂²⋊Q₈	—	2	2	no	—
798	C₂²⋊Q₈	—	2	2	no	—
799	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	1	no	—
803	#121	—	2	2	no	—
804	#121	—	2	1	no	—
805	#121	—	2	1	no	—
806	#121	—	2	2	no	—
807	#121	—	2	1	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	C₂³×C₂₃	1	2	yes	—
811	#121	C₂³×C₂₃	1	2	yes	—
812	#121	C₂³×C₂₃	1	2	yes	—
813	#121	C₂³×C₂₃	1	2	yes	—
814	#121	C₂³×C₂₃	1	2	yes	—
815	#120	—	2	2	no	—
816	#120	—	2	2	no	—
817	#120	—	2	2	no	—
818	C₄×Q₈	—	2	1	no	—
819	C₄×Q₈	—	2	1	no	—
820	C₄×Q₈	—	2	1	no	—
821	C₄×Q₈	—	2	1	no	—
822	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
823	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
824	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
825	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
826	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
827	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
828	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	2	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	—	2	2	no	—
839	C₄×D₄	—	2	1	no	—
840	C₄×D₄	—	2	2	no	—
841	C₄×D₄	—	2	1	no	—
842	C₄×D₄	—	2	1	no	—
843	C₄×D₄	D₄×C₂₃	1	2	yes	—
844	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
845	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
846	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
847	C₄×D₄	C₂³×C₂₃	1	2	yes	—
848	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
849	C₄×D₄	C₂³×C₂₃	1	2	yes	—
850	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
851	C₄×D₄	C₂³×C₂₃	1	2	yes	—
852	C₄×D₄	C₂³×C₂₃	1	2	yes	—
853	C₄×D₄	C₂³×C₂₃	1	2	yes	—
854	C₄×D₄	C₂³×C₂₃	1	2	yes	—
855	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
856	#117	—	2	2	no	—
857	#117	—	2	2	no	—
858	#117	D₄×C₂₃	1	1	yes	characteristic
859	#117	D₄×C₂₃	1	2	yes	—
860	#117	C₂³×C₂₃	1	2	yes	—
861	C₂×C₄⋊C₄	—	2	1	no	—
862	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
863	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
864	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
865	C₂×C₂²⋊C₄	—	2	1	no	—
866	C₂×C₂²⋊C₄	—	2	2	no	—
867	C₂×C₄²	—	2	1	no	—
868	C₂×C₄²	—	2	2	no	—
869	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
870	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
871	#107	C₂³×C₂₃	1	2	yes	—
872	#107	C₂³×C₂₃	1	2	yes	—
873	#107	C₂³×C₂₃	1	2	yes	—
874	#107	C₂³×C₂₃	1	2	yes	—
875	#106	C₂³×C₂₃	1	1	yes	characteristic
876	#106	C₂³×C₂₃	1	1	yes	characteristic
877	#106	C₂³×C₂₃	1	1	yes	characteristic
878	#106	C₂³×C₂₃	1	1	yes	characteristic
879	#106	C₂³×C₂₃	1	2	yes	—
880	#106	C₂³×C₂₃	1	2	yes	—
881	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
882	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
883	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
884	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
885	#103	C₂³×C₂₃	1	1	yes	characteristic
886	#103	C₂³×C₂₃	1	1	yes	characteristic
887	#103	C₂³×C₂₃	1	1	yes	characteristic
888	#103	C₂³×C₂₃	1	1	yes	characteristic
889	#103	C₂³×C₂₃	1	2	yes	—
890	#103	C₂³×C₂₃	1	2	yes	—
891	#102	C₂³×C₂₃	1	1	yes	characteristic
892	#102	C₂³×C₂₃	1	1	yes	characteristic
893	#102	C₂³×C₂₃	1	1	yes	characteristic
894	#102	C₂³×C₂₃	1	1	yes	characteristic
895	#102	C₂³×C₂₃	1	2	yes	—
896	#102	C₂³×C₂₃	1	2	yes	—
897	#102	C₂³×C₂₃	1	2	yes	—
898	#102	C₂³×C₂₃	1	2	yes	—
899	#102	C₂³×C₂₃	1	2	yes	—
900	#102	C₂³×C₂₃	1	2	yes	—
901	#102	C₂³×C₂₃	1	2	yes	—
902	#102	C₂³×C₂₃	1	2	yes	—
903	#102	C₂³×C₂₃	1	2	yes	—
904	#102	C₂³×C₂₃	1	2	yes	—
905	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
906	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
907	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
908	#97	C₂³×C₂₃	1	2	yes	—
909	#97	C₂³×C₂₃	1	2	yes	—
910	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
911	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
912	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
913	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
914	C₄×C₈	C₂³×C₂₃	1	2	yes	—
915	C₂₃	#61439	1	1	yes	characteristic, direct product factor, Sylow
916	C₂⁴	—	2	2	no	—
917	C₂⁴	—	2	1	no	—
918	#41	—	2	4	no	—
919	#41	—	2	4	no	—
920	#41	—	4	2	no	—
921	#41	—	4	8	no	—
922	#41	—	4	8	no	—
923	#41	—	4	4	no	—
924	#41	—	4	4	no	—
925	#41	—	4	4	no	—
926	#41	—	4	4	no	—
927	C₂×Q₈	—	2	1	no	—
928	C₂×Q₈	—	2	1	no	—
929	C₂×Q₈	—	2	2	no	—
930	C₂×Q₈	—	2	1	no	—
931	C₂×Q₈	—	2	2	no	—
932	C₂×Q₈	—	4	1	no	—
933	C₂×Q₈	—	4	4	no	—
934	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
935	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
936	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	4	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	2	2	no	—
944	C₂×D₄	—	2	2	no	—
945	C₂×D₄	—	2	2	no	—
946	C₂×D₄	—	2	1	no	—
947	C₂×D₄	—	2	1	no	—
948	C₂×D₄	—	2	2	no	—
949	C₂×D₄	—	2	1	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	1	no	—
952	C₂×D₄	—	2	1	no	—
953	C₂×D₄	—	4	1	no	—
954	C₂×D₄	—	4	2	no	—
955	C₂×D₄	—	4	8	no	—
956	C₂×D₄	—	4	4	no	—
957	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
958	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
959	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
960	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
961	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
962	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
963	C₂²×C₄	—	2	1	no	—
964	C₂²×C₄	—	2	2	no	—
965	C₂²×C₄	—	2	1	no	—
966	C₂²×C₄	—	2	1	no	—
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	2	no	—
969	C₂²×C₄	—	2	1	no	—
970	C₂²×C₄	—	2	2	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	2	no	—
973	C₂²×C₄	—	2	1	no	—
974	C₂²×C₄	—	2	2	no	—
975	C₂²×C₄	—	2	1	no	—
976	C₂²×C₄	—	2	2	no	—
977	C₂²×C₄	—	4	8	no	—
978	C₂²×C₄	—	4	4	no	—
979	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
980	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
981	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
982	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
983	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
984	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
985	SD₁₆	—	2	2	no	—
986	SD₁₆	—	2	4	no	—
987	SD₁₆	—	2	2	no	—
988	SD₁₆	—	2	2	no	—
989	SD₁₆	—	4	2	no	—
990	SD₁₆	#41×C₂₃	1	4	yes	complemented
991	D₈	—	2	4	no	—
992	D₈	—	2	4	no	—
993	D₈	—	4	2	no	—
994	D₈	—	4	2	no	—
995	M₁₆	—	2	4	no	—
996	M₁₆	—	4	2	no	—
997	C₂×C₈	—	2	2	no	—
998	C₂×C₈	—	4	1	no	—
999	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1000	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1001	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1002	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1003	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1004	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	—	2	1	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	2	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	1	no	—
1018	C₄⋊C₄	—	2	2	no	—
1019	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1020	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1021	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1022	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1023	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1024	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1025	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1026	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1027	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1028	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	1	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1048	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1049	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1050	C₄²	—	2	1	no	—
1051	C₄²	—	2	1	no	—
1052	C₄²	—	2	2	no	—
1053	C₄²	—	2	2	no	—
1054	C₄²	—	2	1	no	—
1055	C₄²	—	2	1	no	—
1056	C₄²	C₂×D₄×C₂₃	1	2	yes	—
1057	C₄²	C₂×D₄×C₂₃	1	2	yes	—
1058	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1059	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1060	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1061	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1062	C₄²	C₂⁴×C₂₃	1	2	yes	—
1063	C₂³	—	2	1	no	—
1064	C₂³	—	2	2	no	—
1065	C₂³	—	2	2	no	—
1066	C₂³	—	2	1	no	—
1067	C₂³	—	4	2	no	—
1068	C₂³	—	4	4	no	—
1069	C₂³	—	4	4	no	—
1070	C₂³	—	4	2	no	—
1071	C₂³	—	8	1	no	—
1072	C₂³	—	8	2	no	—
1073	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1074	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1075	Q₈	—	2	2	no	—
1076	Q₈	—	2	1	no	—
1077	Q₈	—	2	1	no	—
1078	Q₈	—	2	1	no	—
1079	Q₈	—	4	2	no	—
1080	Q₈	—	4	4	no	—
1081	Q₈	—	4	2	no	—
1082	Q₈	—	4	2	no	—
1083	Q₈	C₂×#41×C₂₃	1	2	yes	complemented
1084	D₄	—	2	4	no	—
1085	D₄	—	2	2	no	—
1086	D₄	—	2	2	no	—
1087	D₄	—	2	2	no	—
1088	D₄	—	2	1	no	—
1089	D₄	—	2	1	no	—
1090	D₄	—	2	1	no	—
1091	D₄	—	2	2	no	—
1092	D₄	—	2	2	no	—
1093	D₄	—	4	4	no	—
1094	D₄	—	4	2	no	—
1095	D₄	—	4	4	no	—
1096	D₄	—	4	4	no	—
1097	D₄	—	4	4	no	—
1098	D₄	—	4	4	no	—
1099	D₄	—	4	4	no	—
1100	D₄	—	4	4	no	—
1101	D₄	—	4	2	no	—
1102	D₄	—	4	2	no	—
1103	D₄	—	8	2	no	—
1104	D₄	—	8	1	no	—
1105	D₄	—	8	1	no	—
1106	D₄	—	8	2	no	—
1107	D₄	C₂×#41×C₂₃	1	2	yes	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	4	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	4	2	no	—
1122	C₂×C₄	—	4	1	no	—
1123	C₂×C₄	—	4	4	no	—
1124	C₂×C₄	—	4	2	no	—
1125	C₂×C₄	—	4	4	no	—
1126	C₂×C₄	—	4	4	no	—
1127	C₂×C₄	—	4	4	no	—
1128	C₂×C₄	—	4	2	no	—
1129	C₂×C₄	—	4	2	no	—
1130	C₂×C₄	—	4	2	no	—
1131	C₂×C₄	—	4	2	no	—
1132	C₂×C₄	—	4	4	no	—
1133	C₂×C₄	—	4	2	no	—
1134	C₂×C₄	—	4	4	no	—
1135	C₂×C₄	—	8	2	no	—
1136	C₂×C₄	—	8	1	no	—
1137	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	4	yes	complemented
1138	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1139	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1140	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1141	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1142	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1143	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1144	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1145	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1146	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1147	C₈	—	2	1	no	—
1148	C₈	—	2	2	no	—
1149	C₈	—	2	1	no	—
1150	C₈	—	2	1	no	—
1151	C₈	—	2	2	no	—
1152	C₈	C₂×#41×C₂₃	1	2	yes	complemented
1153	C₂²	—	2	1	no	—
1154	C₂²	—	2	1	no	—
1155	C₂²	—	2	2	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	2	2	no	—
1158	C₂²	—	2	2	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	2	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	4	2	no	—
1170	C₂²	—	8	4	no	—
1171	C₂²	—	8	8	no	—
1172	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
1173	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1174	C₄	—	2	2	no	—
1175	C₄	—	2	1	no	—
1176	C₄	—	2	2	no	—
1177	C₄	—	2	2	no	—
1178	C₄	—	2	1	no	—
1179	C₄	—	2	2	no	—
1180	C₄	—	2	1	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	2	no	—
1184	C₄	—	4	1	no	—
1185	C₄	—	4	2	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	1	no	—
1188	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
1189	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
1190	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1191	C₄	C₂₃×#585	1	1	yes	characteristic
1192	C₂	—	2	2	no	—
1193	C₂	—	4	2	no	—
1194	C₂	—	4	2	no	—
1195	C₂	—	8	1	no	—
1196	C₂	—	8	2	no	—
1197	C₂	—	8	2	no	—
1198	C₂	D₄×#41×C₂₃	1	1	yes	characteristic
1199	C₂	C₂²×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
1200	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 ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3480	C₂	semidirect
2. D₄×#41×C₂₃	C₂	semidirect
3. C₂₃×#3399	C₂	semidirect
4. C₂₃×#3386	C₂	semidirect
5. C₂₃×#3373	C₂	semidirect
6. C₂₃×#3368	C₂	semidirect
7. C₂₃×#3353	C₂	semidirect
8. C₂₃×#3345	C₂	semidirect
9. C₂₃×#3332	C₂	semidirect
10. C₂₃×#3324	C₂	semidirect
11. C₂₃×#3318	C₂	semidirect
12. C₂₃×#3308	C₂	semidirect
13. C₂₃×#3274	C₂	semidirect
14. C₂₃×#3265	C₂	semidirect
15. C₂₃×#3171	C₂	semidirect
16. C₂₃×#3169	C₂	semidirect
17. C₂₃×#3106	C₂	semidirect
18. C₂₃×#3105	C₂	semidirect
19. C₂₃×#3103	C₂	semidirect
20. C₂₃×#3100	C₂	semidirect
21. C₂₃×#2965	C₂	semidirect
22. C₄×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
23. C₂×C₄×SD₁₆×C₂₃	C₂	semidirect
28. C₂₃×#559	C₂²	semidirect
29. C₂₃×#557	C₂²	semidirect
31. C₂₃×#556	C₂²	semidirect
33. C₂₃×#553	C₂²	semidirect
35. C₂₃×#550	C₂²	semidirect
38. C₂₃×#548	C₂²	semidirect
48. C₂₃×#532	C₂²	semidirect
50. C₂₃×#529	C₂²	semidirect
55. C₄×#41×C₂₃	C₂²	semidirect
56. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
59. C₂₃×#501	C₂²	semidirect
60. C₂₃×#500	C₂²	semidirect
61. C₂₃×#496	C₂²	semidirect
62. C₂₃×#493	C₂²	semidirect
63. C₂₃×#490	C₂²	semidirect
64. C₂₃×#489	C₂²	semidirect
65. C₂₃×#486	C₂²	semidirect
66. C₂₃×#486	C₂²	semidirect
67. C₂₃×#484	C₂²	semidirect
68. C₂₃×#482	C₂²	semidirect
69. C₂₃×#482	C₂²	semidirect
70. C₂₃×#481	C₂²	semidirect
71. C₂₃×#481	C₂²	semidirect
72. C₂₃×#480	C₂²	semidirect
74. C₂₃×#478	C₂²	semidirect
75. C₂₃×#477	C₂²	semidirect
76. C₂₃×#476	C₂²	semidirect
77. C₂₃×#475	C₂²	semidirect
78. C₂₃×#475	C₂²	semidirect
80. C₂₃×#474	C₂²	semidirect
81. C₂₃×#469	C₂²	semidirect
82. C₂₃×#469	C₂²	semidirect
83. C₂₃×#468	C₂²	semidirect
84. C₂₃×#468	C₂²	semidirect
85. C₂₃×#466	C₂²	semidirect
86. C₂₃×#466	C₂²	semidirect
88. C₂₃×#463	C₂²	semidirect
89. C₂₃×#460	C₂²	semidirect
90. C₂₃×#460	C₂²	semidirect
91. C₂₃×#460	C₂²	semidirect
93. C₂₃×#459	C₂²	semidirect
94. C₂₃×#459	C₂²	semidirect
96. C₂₃×#449	C₂²	semidirect
97. C₂₃×#449	C₂²	semidirect
98. C₂₃×#448	C₂²	semidirect
101. C₂₃×#446	C₂²	semidirect
102. C₂₃×#446	C₂²	semidirect
104. C₂₃×#442	C₂²	semidirect
106. C₂₃×#440	C₂²	semidirect
111. C₄×SD₁₆×C₂₃	C₂²	semidirect
112. C₄×SD₁₆×C₂₃	C₂²	semidirect
113. C₄×SD₁₆×C₂₃	C₂²	semidirect
114. C₄×SD₁₆×C₂₃	C₂²	semidirect
115. C₄×SD₁₆×C₂₃	C₂²	semidirect
116. C₄×SD₁₆×C₂₃	C₂²	semidirect
118. C₄×D₈×C₂₃	C₂²	semidirect
119. C₄×D₈×C₂₃	C₂²	semidirect
120. C₄×D₈×C₂₃	C₂²	semidirect
121. C₂₃×#436	C₂²	semidirect
122. C₂₃×#436	C₂²	semidirect
123. C₂₃×#435	C₂²	semidirect
124. C₂₃×#435	C₂²	semidirect
125. C₂₃×#431	C₂²	semidirect
126. C₂₃×#431	C₂²	semidirect
127. C₂₃×#428	C₂²	semidirect
128. C₂×C₂₃×#106	C₂²	semidirect
130. C₂₃×#417	C₂²	semidirect
131. C₂×C₂₃×#103	C₂²	semidirect
133. C₄×M₁₆×C₂₃	C₂²	semidirect
134. C₂×C₄×C₈×C₂₃	C₂²	semidirect
389. SD₁₆×C₂₃	#41	semidirect
462. #61439	C₂₃	direct (N × H)
483. Q₈×C₂₃	C₂×#41	semidirect
537. C₂×C₄×C₂₃	AGL(1,ℤ/8)	semidirect
552. C₈×C₂₃	C₂×#41	semidirect
553. #3480	C₂×C₂₃	semidirect
554. D₄×#41	C₂×C₂₃	semidirect
555. #3399	C₂×C₂₃	semidirect
556. #3386	C₂×C₂₃	semidirect
557. #3373	C₂×C₂₃	semidirect
558. #3368	C₂×C₂₃	semidirect
559. #3353	C₂×C₂₃	semidirect
560. #3345	C₂×C₂₃	semidirect
561. #3332	C₂×C₂₃	semidirect
562. #3324	C₂×C₂₃	semidirect
563. #3318	C₂×C₂₃	semidirect
564. #3308	C₂×C₂₃	semidirect
565. #3274	C₂×C₂₃	semidirect
566. #3265	C₂×C₂₃	semidirect
567. #3171	C₂×C₂₃	semidirect
568. #3169	C₂×C₂₃	semidirect
569. #3106	C₂×C₂₃	semidirect
570. #3105	C₂×C₂₃	semidirect
571. #3103	C₂×C₂₃	semidirect
572. #3100	C₂×C₂₃	semidirect
573. #2965	C₂×C₂₃	semidirect
574. C₄×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
575. C₂×C₄×SD₁₆	C₂×C₂₃	semidirect
619. #559	C₂²×C₂₃	semidirect
620. #557	C₂²×C₂₃	semidirect
622. #556	C₂²×C₂₃	semidirect
624. #553	C₂²×C₂₃	semidirect
626. #550	C₂²×C₂₃	semidirect
629. #548	C₂²×C₂₃	semidirect
639. #532	C₂²×C₂₃	semidirect
641. #529	C₂²×C₂₃	semidirect
646. C₄×#41	C₂²×C₂₃	semidirect
647. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
650. #501	C₂²×C₂₃	semidirect
651. #500	C₂²×C₂₃	semidirect
652. #496	C₂²×C₂₃	semidirect
653. #493	C₂²×C₂₃	semidirect
654. #490	C₂²×C₂₃	semidirect
655. #489	C₂²×C₂₃	semidirect
656. #486	C₂²×C₂₃	semidirect
657. #486	C₂²×C₂₃	semidirect
658. #484	C₂²×C₂₃	semidirect
659. #482	C₂²×C₂₃	semidirect
660. #482	C₂²×C₂₃	semidirect
661. #481	C₂²×C₂₃	semidirect
662. #481	C₂²×C₂₃	semidirect
663. #480	C₂²×C₂₃	semidirect
665. #478	C₂²×C₂₃	semidirect
666. #477	C₂²×C₂₃	semidirect
667. #476	C₂²×C₂₃	semidirect
668. #475	C₂²×C₂₃	semidirect
669. #475	C₂²×C₂₃	semidirect
671. #474	C₂²×C₂₃	semidirect
672. #469	C₂²×C₂₃	semidirect
673. #469	C₂²×C₂₃	semidirect
674. #468	C₂²×C₂₃	semidirect
675. #468	C₂²×C₂₃	semidirect
676. #466	C₂²×C₂₃	semidirect
677. #466	C₂²×C₂₃	semidirect
679. #463	C₂²×C₂₃	semidirect
680. #460	C₂²×C₂₃	semidirect
681. #460	C₂²×C₂₃	semidirect
682. #460	C₂²×C₂₃	semidirect
684. #459	C₂²×C₂₃	semidirect
685. #459	C₂²×C₂₃	semidirect
687. #449	C₂²×C₂₃	semidirect
688. #449	C₂²×C₂₃	semidirect
689. #448	C₂²×C₂₃	semidirect
692. #446	C₂²×C₂₃	semidirect
693. #446	C₂²×C₂₃	semidirect
695. #442	C₂²×C₂₃	semidirect
697. #440	C₂²×C₂₃	semidirect
702. C₄×SD₁₆	C₂²×C₂₃	semidirect
703. C₄×SD₁₆	C₂²×C₂₃	semidirect
704. C₄×SD₁₆	C₂²×C₂₃	semidirect
705. C₄×SD₁₆	C₂²×C₂₃	semidirect
706. C₄×SD₁₆	C₂²×C₂₃	semidirect
707. C₄×SD₁₆	C₂²×C₂₃	semidirect
709. C₄×D₈	C₂²×C₂₃	semidirect
710. C₄×D₈	C₂²×C₂₃	semidirect
711. C₄×D₈	C₂²×C₂₃	semidirect
712. #436	C₂²×C₂₃	semidirect
713. #436	C₂²×C₂₃	semidirect
714. #435	C₂²×C₂₃	semidirect
715. #435	C₂²×C₂₃	semidirect
716. #431	C₂²×C₂₃	semidirect
717. #431	C₂²×C₂₃	semidirect
718. #428	C₂²×C₂₃	semidirect
719. C₂×#106	C₂²×C₂₃	semidirect
721. #417	C₂²×C₂₃	semidirect
722. C₂×#103	C₂²×C₂₃	semidirect
724. C₄×M₁₆	C₂²×C₂₃	semidirect
725. C₂×C₄×C₈	C₂²×C₂₃	semidirect
915. C₂₃	#61439	direct (N × H)
990. SD₁₆	#41×C₂₃	semidirect
1083. Q₈	C₂×#41×C₂₃	semidirect
1137. C₂×C₄	C₂₃×AGL(1,ℤ/8)	semidirect
1152. C₈	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
C₂₃×#3480	2
D₄×#41×C₂₃	2
C₂₃×#3399	2
C₂₃×#3386	2
C₂₃×#3373	2
C₂₃×#3368	2
C₂₃×#3353	2
C₂₃×#3345	2
C₂₃×#3332	2
C₂₃×#3324	2
C₂₃×#3318	2
C₂₃×#3308	2
C₂₃×#3274	2
C₂₃×#3265	2
C₂₃×#3171	2
C₂₃×#3169	2
C₂₃×#3106	2
C₂₃×#3105	2
C₂₃×#3103	2
C₂₃×#3100	2
C₂₃×#2965	2
C₄×C₂₃×AGL(1,ℤ/8)	2
C₂×C₄×SD₁₆×C₂₃	2
#61439	23

Subgroups — C23×#61439 #19209065

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61439 #19209065