Subgroups — C₂₃×#60694 #19208320

Order 5888.

1914 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3461	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3179	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3178	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3174	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3173	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3172	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3171	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3168	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3167	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3163	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3154	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3137	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3136	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3062	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3060	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3057	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₂₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₂₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄×SD₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₂₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
27	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
30	C₂₃×#544	C₂²	1	1	yes	characteristic
31	C₂₃×#544	C₂²	1	1	yes	characteristic
32	C₂₃×#542	—	2	1	no	—
33	C₂₃×#542	—	2	1	no	—
34	C₂₃×#542	C₂²	1	2	yes	—
35	C₂₃×#542	C₂²	1	2	yes	complemented
36	C₂₃×#541	—	2	1	no	—
37	C₂₃×#541	C₂²	1	2	yes	complemented
38	C₂₃×#540	—	2	1	no	—
39	C₂₃×#540	C₂²	1	2	yes	—
40	C₂₃×#539	—	2	2	no	—
41	C₂₃×#538	—	2	2	no	—
42	C₂₃×#537	C₂²	1	1	yes	characteristic
43	C₂₃×#537	C₂²	1	1	yes	characteristic
44	C₂₃×#536	C₂²	1	1	yes	characteristic
45	C₂₃×#536	C₂²	1	1	yes	characteristic
46	C₂₃×#535	C₂²	1	1	yes	characteristic
47	C₂₃×#535	C₂²	1	1	yes	characteristic
48	C₂₃×#533	—	2	1	no	—
49	C₂₃×#533	C₂²	1	2	yes	complemented
50	C₂₃×#532	—	2	1	no	—
51	C₂₃×#532	C₂²	1	2	yes	—
52	C₂₃×#529	—	2	1	no	—
53	C₂₃×#529	—	2	2	no	—
54	C₂₃×#529	—	2	1	no	—
55	C₂₃×#529	C₂²	1	2	yes	—
56	C₂₃×#529	C₂²	1	2	yes	complemented
57	C₂₃×#525	—	2	2	no	—
58	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
59	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
60	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
61	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
62	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
63	C₂₃×#501	C₂²	1	2	yes	complemented
64	C₂₃×#501	C₂²	1	2	yes	complemented
65	C₂₃×#499	C₂²	1	2	yes	complemented
66	C₂₃×#498	C₂²	1	2	yes	complemented
67	C₂₃×#497	C₂²	1	2	yes	—
68	C₂₃×#496	C₂²	1	2	yes	—
69	C₂₃×#495	C₂²	1	2	yes	—
70	C₂₃×#492	C₂²	1	2	yes	—
71	C₂₃×#491	C₂²	1	2	yes	complemented
72	C₂₃×#490	C₂²	1	2	yes	—
73	C₂₃×#489	C₂²	1	2	yes	—
74	C₂₃×#489	C₂²	1	2	yes	complemented
75	C₂₃×#488	C₂²	1	2	yes	—
76	C₂₃×#488	C₂²	1	2	yes	complemented
77	C₂₃×#487	C₂²	1	2	yes	complemented
78	C₂₃×#486	C₂²	1	2	yes	—
79	C₂₃×#470	C₂²	1	2	yes	complemented
80	C₂₃×#470	C₂²	1	2	yes	complemented
81	C₂₃×#469	C₂²	1	2	yes	—
82	C₂₃×#469	C₂²	1	2	yes	complemented
83	C₂₃×#468	C₂²	1	2	yes	—
84	C₂₃×#468	C₂²	1	2	yes	—
85	C₂₃×#468	C₂²	1	2	yes	—
86	C₂₃×#468	C₂²	1	2	yes	complemented
87	C₂₃×#467	C₂²	1	2	yes	complemented
88	C₂₃×#466	C₂²	1	2	yes	—
89	C₂₃×#465	C₂²	1	2	yes	—
90	C₂₃×#465	C₂²	1	2	yes	—
91	C₂₃×#465	C₂²	1	2	yes	—
92	C₂₃×#465	C₂²	1	2	yes	complemented
93	C₂₃×#465	C₂²	1	2	yes	complemented
94	C₂₃×#465	C₂²	1	2	yes	complemented
95	C₂₃×#442	C₂²	1	2	yes	—
96	C₂₃×#441	C₂²	1	2	yes	complemented
97	C₂₃×#440	C₂²	1	2	yes	—
98	C₂₃×#440	C₂²	1	2	yes	complemented
99	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
100	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
101	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
102	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
103	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
104	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
105	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
106	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
107	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
108	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
109	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
110	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
111	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
112	C₄×D₈×C₂₃	C₂²	1	2	yes	—
113	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
114	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
115	C₂₃×#428	C₂²	1	1	yes	characteristic
116	C₂₃×#428	C₂²	1	1	yes	characteristic
117	C₂₃×#427	C₂²	1	1	yes	characteristic
118	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
119	C₂₃×#419	C₂²	1	1	yes	characteristic
120	C₂₃×#418	C₂²	1	1	yes	characteristic
121	C₂₃×#417	C₂²	1	1	yes	characteristic
122	C₂₃×#417	C₂²	1	1	yes	characteristic
123	C₂₃×#416	C₂²	1	1	yes	characteristic
124	C₂₃×#416	C₂²	1	1	yes	characteristic
125	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
126	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
127	C₂₃×#405	C₂²	1	1	yes	characteristic
128	C₂₃×#405	C₂²	1	1	yes	characteristic
129	C₂₃×#405	C₂²	1	2	yes	complemented
130	C₂₃×#405	C₂²	1	2	yes	complemented
131	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
132	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
133	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
134	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	complemented
135	C₂×#41×C₂₃	—	2	2	no	—
136	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
137	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
138	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₂₃	—	2	1	no	—
142	C₂₃×#137	—	2	4	no	—
143	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
144	C₂₃×#135	—	2	4	no	—
145	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₂₃	—	2	4	no	—
148	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
154	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
155	C₂×D₈×C₂₃	C₂³	1	2	yes	—
156	C₂₃×#131	—	2	4	no	—
157	C₂₃×#131	—	2	4	no	—
158	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
159	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
160	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
161	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
162	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
163	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
164	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
165	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
166	C₂₃×C₄⋊Q₈	—	2	1	no	—
167	C₂₃×C₄⋊Q₈	—	2	1	no	—
168	C₂₃×C₄⋊Q₈	—	2	1	no	—
169	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
170	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
171	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
172	C₂₃×#127	—	2	1	no	—
173	C₂₃×#127	C₂³	1	2	yes	—
174	C₂₃×#126	—	2	2	no	—
175	C₂₃×#126	—	2	2	no	—
176	C₂₃×#126	—	2	2	no	—
177	C₂₃×#126	—	2	2	no	—
178	C₂₃×#126	—	2	2	no	—
179	C₂₃×#126	—	2	2	no	—
180	C₂₃×#125	—	2	1	no	—
181	C₂₃×#125	—	2	2	no	—
182	C₂₃×#125	—	2	1	no	—
183	C₂₃×#125	—	2	2	no	—
184	C₂₃×#125	—	2	2	no	—
185	C₂₃×#125	C₂³	1	2	yes	—
186	C₂₃×#125	C₂³	1	2	yes	—
187	C₂₃×#124	—	2	1	no	—
188	C₂₃×#124	—	2	1	no	—
189	C₂₃×#124	—	2	2	no	—
190	C₂₃×#124	—	2	2	no	—
191	C₂₃×#124	—	2	2	no	—
192	C₂₃×#124	C₂³	1	2	yes	—
193	C₂₃×#124	C₂³	1	2	yes	—
194	C₂₃×#123	—	2	2	no	—
195	C₂₃×#123	—	2	2	no	—
196	C₂₃×#123	—	2	2	no	—
197	C₂₃×#123	—	2	2	no	—
198	C₂₃×#123	—	2	2	no	—
199	C₂₃×#123	—	2	2	no	—
200	C₂₃×#123	—	2	2	no	—
201	C₂₃×#123	—	2	2	no	—
202	C₂₃×C₂²⋊Q₈	—	2	1	no	—
203	C₂₃×C₂²⋊Q₈	—	2	1	no	—
204	C₂₃×C₂²⋊Q₈	—	2	2	no	—
205	C₂₃×C₂²⋊Q₈	—	2	2	no	—
206	C₂₃×C₂²⋊Q₈	—	2	1	no	—
207	C₂₃×C₂²⋊Q₈	—	2	1	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	1	no	—
218	C₂₃×#121	—	2	1	no	—
219	C₂₃×#121	—	2	2	no	—
220	C₂₃×#121	—	2	1	no	—
221	C₂₃×#121	—	2	1	no	—
222	C₂₃×#121	—	2	2	no	—
223	C₂₃×#121	—	2	2	no	—
224	C₂₃×#121	C₂³	1	2	yes	—
225	C₂₃×#121	C₂³	1	2	yes	—
226	C₂₃×#121	C₂³	1	2	yes	—
227	C₂₃×#121	C₂³	1	2	yes	—
228	C₂₃×#120	—	2	2	no	—
229	C₂₃×#120	—	2	2	no	—
230	C₄×Q₈×C₂₃	—	2	1	no	—
231	C₄×Q₈×C₂₃	—	2	1	no	—
232	C₄×Q₈×C₂₃	—	2	2	no	—
233	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
234	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
235	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
236	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
238	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₂₃	—	2	1	no	—
242	C₄×D₄×C₂₃	—	2	1	no	—
243	C₄×D₄×C₂₃	—	2	1	no	—
244	C₄×D₄×C₂₃	—	2	1	no	—
245	C₄×D₄×C₂₃	—	2	2	no	—
246	C₄×D₄×C₂₃	—	2	2	no	—
247	C₄×D₄×C₂₃	—	2	1	no	—
248	C₄×D₄×C₂₃	—	2	1	no	—
249	C₄×D₄×C₂₃	—	2	2	no	—
250	C₄×D₄×C₂₃	D₄	1	2	yes	—
251	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
252	C₄×D₄×C₂₃	D₄	1	2	yes	—
253	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
254	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₂₃	C₂³	1	2	yes	—
256	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₂₃	C₂³	1	2	yes	—
260	C₂₃×#117	—	2	2	no	—
261	C₂₃×#117	—	2	1	no	—
262	C₂₃×#117	—	2	1	no	—
263	C₂₃×#117	—	2	2	no	—
264	C₂₃×#117	—	2	2	no	—
265	C₂₃×#117	C₂³	1	1	yes	characteristic
266	C₂₃×#117	C₂³	1	1	yes	characteristic
267	C₂₃×#117	C₂³	1	1	yes	characteristic
268	C₂₃×#117	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
270	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
273	C₂×C₄²×C₂₃	—	2	1	no	—
274	C₂×C₄²×C₂₃	—	2	1	no	—
275	C₂×C₄²×C₂₃	—	2	1	no	—
276	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
277	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
278	C₂₃×#107	C₂³	1	1	yes	characteristic
279	C₂₃×#107	C₂³	1	1	yes	characteristic
280	C₂₃×#107	C₂³	1	2	yes	—
281	C₂₃×#107	C₂³	1	2	yes	—
282	C₂₃×#106	C₂³	1	2	yes	—
283	C₂₃×#106	C₂³	1	2	yes	—
284	C₂₃×#106	C₂³	1	1	yes	characteristic
285	C₂₃×#106	C₂³	1	1	yes	characteristic
286	C₂₃×#106	C₂³	1	2	yes	—
287	C₂₃×#106	C₂³	1	2	yes	—
288	C₂₃×#103	C₂³	1	2	yes	—
289	C₂₃×#103	C₂³	1	2	yes	—
290	C₂₃×#103	C₂³	1	1	yes	characteristic
291	C₂₃×#103	C₂³	1	1	yes	characteristic
292	C₂₃×#103	C₂³	1	1	yes	characteristic
293	C₂₃×#103	C₂³	1	1	yes	characteristic
294	C₂₃×#103	C₂³	1	2	yes	—
295	C₂₃×#103	C₂³	1	2	yes	—
296	C₂₃×#103	C₂³	1	2	yes	—
297	C₂₃×#103	C₂³	1	2	yes	—
298	C₂₃×#102	C₂³	1	2	yes	—
299	C₂₃×#102	C₂³	1	2	yes	—
300	C₂₃×#102	C₂³	1	1	yes	characteristic
301	C₂₃×#102	C₂³	1	1	yes	characteristic
302	C₂₃×#102	C₂³	1	1	yes	characteristic
303	C₂₃×#102	C₂³	1	1	yes	characteristic
304	C₂₃×#102	C₂³	1	2	yes	—
305	C₂₃×#102	C₂³	1	2	yes	—
306	C₂₃×#102	C₂³	1	2	yes	—
307	C₂₃×#102	C₂³	1	2	yes	—
308	C₂₃×#97	C₂³	1	2	yes	—
309	C₂₃×#97	C₂³	1	2	yes	—
310	C₂₃×#97	C₂³	1	2	yes	—
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	1	yes	characteristic
315	C₄×C₈×C₂₃	C₂³	1	2	yes	—
316	C₄×C₈×C₂₃	C₂³	1	2	yes	—
317	C₄×C₈×C₂₃	C₂³	1	2	yes	—
318	C₂⁴×C₂₃	—	2	1	no	—
319	#41×C₂₃	—	2	2	no	—
320	#41×C₂₃	—	2	2	no	—
321	#41×C₂₃	—	2	2	no	—
322	#41×C₂₃	—	2	2	no	—
323	#41×C₂₃	—	2	2	no	—
324	#41×C₂₃	—	2	2	no	—
325	#41×C₂₃	—	8	4	no	—
326	C₂×Q₈×C₂₃	—	2	1	no	—
327	C₂×Q₈×C₂₃	—	2	2	no	—
328	C₂×Q₈×C₂₃	—	2	2	no	—
329	C₂×Q₈×C₂₃	—	2	2	no	—
330	C₂×Q₈×C₂₃	—	2	2	no	—
331	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
332	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
334	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₂₃	—	2	1	no	—
336	C₂×D₄×C₂₃	—	2	1	no	—
337	C₂×D₄×C₂₃	—	2	2	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	1	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	2	no	—
346	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
347	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
348	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
349	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
350	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₂₃	—	2	1	no	—
352	C₂²×C₄×C₂₃	—	2	1	no	—
353	C₂²×C₄×C₂₃	—	2	1	no	—
354	C₂²×C₄×C₂₃	—	2	1	no	—
355	C₂²×C₄×C₂₃	—	2	1	no	—
356	C₂²×C₄×C₂₃	—	2	1	no	—
357	C₂²×C₄×C₂₃	—	2	1	no	—
358	C₂²×C₄×C₂₃	—	2	2	no	—
359	C₂²×C₄×C₂₃	—	2	1	no	—
360	C₂²×C₄×C₂₃	—	2	1	no	—
361	C₂²×C₄×C₂₃	—	2	2	no	—
362	C₂²×C₄×C₂₃	—	8	2	no	—
363	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
365	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
367	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
368	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
369	Q₁₆×C₂₃	—	2	2	no	—
370	Q₁₆×C₂₃	—	2	4	no	—
371	SD₁₆×C₂₃	—	2	4	no	—
372	SD₁₆×C₂₃	—	2	4	no	—
373	SD₁₆×C₂₃	—	2	2	no	—
374	SD₁₆×C₂₃	—	2	2	no	—
375	SD₁₆×C₂₃	—	2	4	no	—
376	SD₁₆×C₂₃	—	2	4	no	—
377	D₈×C₂₃	—	2	2	no	—
378	D₈×C₂₃	—	2	4	no	—
379	M₁₆×C₂₃	—	2	2	no	—
380	M₁₆×C₂₃	—	2	4	no	—
381	M₁₆×C₂₃	—	2	4	no	—
382	M₁₆×C₂₃	#41	1	4	yes	complemented
383	C₂×C₈×C₂₃	—	2	2	no	—
384	C₂×C₈×C₂₃	—	2	4	no	—
385	C₂×C₈×C₂₃	—	2	4	no	—
386	C₂×C₈×C₂₃	#41	1	4	yes	complemented
387	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
390	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
392	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
393	C₄⋊C₄×C₂₃	—	2	2	no	—
394	C₄⋊C₄×C₂₃	—	2	2	no	—
395	C₄⋊C₄×C₂₃	—	2	1	no	—
396	C₄⋊C₄×C₂₃	—	2	1	no	—
397	C₄⋊C₄×C₂₃	—	2	1	no	—
398	C₄⋊C₄×C₂₃	—	2	1	no	—
399	C₄⋊C₄×C₂₃	—	2	1	no	—
400	C₄⋊C₄×C₂₃	—	2	1	no	—
401	C₄⋊C₄×C₂₃	—	2	2	no	—
402	C₄⋊C₄×C₂₃	—	2	2	no	—
403	C₄⋊C₄×C₂₃	—	2	2	no	—
404	C₄⋊C₄×C₂₃	—	2	2	no	—
405	C₄⋊C₄×C₂₃	—	2	2	no	—
406	C₄⋊C₄×C₂₃	—	2	2	no	—
407	C₄⋊C₄×C₂₃	—	2	2	no	—
408	C₄⋊C₄×C₂₃	—	2	2	no	—
409	C₄⋊C₄×C₂₃	—	2	2	no	—
410	C₄⋊C₄×C₂₃	—	2	2	no	—
411	C₄⋊C₄×C₂₃	—	2	2	no	—
412	C₄⋊C₄×C₂₃	—	2	2	no	—
413	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
415	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
416	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
418	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
421	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
423	C₂²⋊C₄×C₂₃	—	2	2	no	—
424	C₂²⋊C₄×C₂₃	—	2	2	no	—
425	C₂²⋊C₄×C₂₃	—	2	1	no	—
426	C₂²⋊C₄×C₂₃	—	2	1	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	1	no	—
432	C₂²⋊C₄×C₂₃	—	2	1	no	—
433	C₂²⋊C₄×C₂₃	—	2	1	no	—
434	C₂²⋊C₄×C₂₃	—	2	1	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	—	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	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
446	C₄²×C₂₃	—	2	1	no	—
447	C₄²×C₂₃	—	2	1	no	—
448	C₄²×C₂₃	—	2	1	no	—
449	C₄²×C₂₃	—	2	1	no	—
450	C₄²×C₂₃	—	2	2	no	—
451	C₄²×C₂₃	—	2	1	no	—
452	C₄²×C₂₃	—	2	2	no	—
453	C₄²×C₂₃	—	2	1	no	—
454	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
459	C₄²×C₂₃	C₂⁴	1	2	yes	—
460	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
461	#60694	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
462	C₂³×C₂₃	—	2	1	no	—
463	C₂³×C₂₃	—	2	2	no	—
464	C₂³×C₂₃	—	2	1	no	—
465	C₂³×C₂₃	—	4	2	no	—
466	C₂³×C₂₃	—	8	1	no	—
467	C₂³×C₂₃	—	8	1	no	—
468	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
469	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
470	Q₈×C₂₃	—	2	2	no	—
471	Q₈×C₂₃	—	2	2	no	—
472	Q₈×C₂₃	—	2	1	no	—
473	Q₈×C₂₃	—	2	2	no	—
474	Q₈×C₂₃	—	2	1	no	—
475	Q₈×C₂₃	—	2	1	no	—
476	Q₈×C₂₃	—	2	1	no	—
477	Q₈×C₂₃	—	4	2	no	—
478	Q₈×C₂₃	—	8	2	no	—
479	Q₈×C₂₃	—	8	2	no	—
480	D₄×C₂₃	—	2	4	no	—
481	D₄×C₂₃	—	2	2	no	—
482	D₄×C₂₃	—	2	1	no	—
483	D₄×C₂₃	—	2	2	no	—
484	D₄×C₂₃	—	2	1	no	—
485	D₄×C₂₃	—	2	1	no	—
486	D₄×C₂₃	—	2	2	no	—
487	D₄×C₂₃	—	2	1	no	—
488	D₄×C₂₃	—	4	2	no	—
489	D₄×C₂₃	—	4	2	no	—
490	D₄×C₂₃	—	4	2	no	—
491	D₄×C₂₃	—	8	2	no	—
492	D₄×C₂₃	—	8	2	no	—
493	D₄×C₂₃	—	8	2	no	—
494	D₄×C₂₃	—	8	2	no	—
495	D₄×C₂₃	—	8	2	no	—
496	D₄×C₂₃	—	8	2	no	—
497	C₂×C₄×C₂₃	—	2	2	no	—
498	C₂×C₄×C₂₃	—	2	4	no	—
499	C₂×C₄×C₂₃	—	2	2	no	—
500	C₂×C₄×C₂₃	—	2	2	no	—
501	C₂×C₄×C₂₃	—	2	1	no	—
502	C₂×C₄×C₂₃	—	2	1	no	—
503	C₂×C₄×C₂₃	—	2	2	no	—
504	C₂×C₄×C₂₃	—	2	1	no	—
505	C₂×C₄×C₂₃	—	2	1	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	2	no	—
510	C₂×C₄×C₂₃	—	4	1	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	—	4	2	no	—
518	C₂×C₄×C₂₃	—	8	1	no	—
519	C₂×C₄×C₂₃	—	8	1	no	—
520	C₂×C₄×C₂₃	—	8	2	no	—
521	C₂×C₄×C₂₃	—	8	1	no	—
522	C₂×C₄×C₂₃	—	8	1	no	—
523	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
532	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
533	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
534	C₈×C₂₃	—	2	1	no	—
535	C₈×C₂₃	—	2	1	no	—
536	C₈×C₂₃	—	2	2	no	—
537	C₈×C₂₃	C₂×#41	1	2	yes	—
538	C₈×C₂₃	C₂×#41	1	4	yes	—
539	C₈×C₂₃	C₂×#41	1	2	yes	—
540	#3461	C₂×C₂₃	1	1	yes	characteristic, complemented
541	#3460	C₂×C₂₃	1	1	yes	characteristic, complemented
542	#3179	C₂×C₂₃	1	2	yes	complemented
543	#3178	C₂×C₂₃	1	2	yes	complemented
544	#3174	C₂×C₂₃	1	2	yes	complemented
545	#3173	C₂×C₂₃	1	2	yes	complemented
546	#3172	C₂×C₂₃	1	2	yes	complemented
547	#3171	C₂×C₂₃	1	2	yes	complemented
548	#3168	C₂×C₂₃	1	2	yes	complemented
549	#3167	C₂×C₂₃	1	2	yes	complemented
550	#3163	C₂×C₂₃	1	1	yes	characteristic, complemented
551	#3154	C₂×C₂₃	1	1	yes	characteristic, complemented
552	#3137	C₂×C₂₃	1	1	yes	characteristic, complemented
553	#3136	C₂×C₂₃	1	1	yes	characteristic, complemented
554	#3063	C₂×C₂₃	1	1	yes	characteristic, complemented
555	#3062	C₂×C₂₃	1	1	yes	characteristic, complemented
556	#3060	C₂×C₂₃	1	1	yes	characteristic, complemented
557	#3057	C₂×C₂₃	1	1	yes	characteristic, complemented
558	C₄×#137	C₂×C₂₃	1	1	yes	characteristic, complemented
559	C₄×AGL(1,ℤ/8)	C₂×C₂₃	1	1	yes	characteristic, complemented
560	C₄×#135	C₂×C₂₃	1	1	yes	characteristic, complemented
561	C₂×C₄×SD₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
562	C₄×#131	C₂×C₂₃	1	1	yes	characteristic, complemented
563	C₂²×C₂₃	—	2	1	no	—
564	C₂²×C₂₃	—	2	1	no	—
565	C₂²×C₂₃	—	2	2	no	—
566	C₂²×C₂₃	—	2	2	no	—
567	C₂²×C₂₃	—	2	2	no	—
568	C₂²×C₂₃	—	4	1	no	—
569	C₂²×C₂₃	—	4	1	no	—
570	C₂²×C₂₃	—	4	2	no	—
571	C₂²×C₂₃	—	4	1	no	—
572	C₂²×C₂₃	—	4	1	no	—
573	C₂²×C₂₃	—	4	2	no	—
574	C₂²×C₂₃	—	4	2	no	—
575	C₂²×C₂₃	—	4	1	no	—
576	C₂²×C₂₃	—	4	1	no	—
577	C₂²×C₂₃	—	8	4	no	—
578	C₂²×C₂₃	#532	1	2	yes	—
579	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
580	C₄×C₂₃	—	2	1	no	—
581	C₄×C₂₃	—	2	1	no	—
582	C₄×C₂₃	—	2	2	no	—
583	C₄×C₂₃	—	2	2	no	—
584	C₄×C₂₃	—	2	1	no	—
585	C₄×C₂₃	—	2	2	no	—
586	C₄×C₂₃	—	4	1	no	—
587	C₄×C₂₃	—	4	2	no	—
588	C₄×C₂₃	—	4	1	no	—
589	C₄×C₂₃	—	4	1	no	—
590	C₄×C₂₃	—	4	1	no	—
591	C₄×C₂₃	—	4	2	no	—
592	C₄×C₂₃	—	4	1	no	—
593	C₄×C₂₃	—	4	2	no	—
594	C₄×C₂₃	—	4	1	no	—
595	C₄×C₂₃	#532	1	2	yes	—
596	C₄×C₂₃	#577	1	2	yes	—
597	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
598	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
599	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
600	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
601	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
602	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
603	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
604	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
605	#544	C₂²×C₂₃	1	1	yes	characteristic
606	#544	C₂²×C₂₃	1	1	yes	characteristic
607	#542	—	2	1	no	—
608	#542	—	2	1	no	—
609	#542	C₂²×C₂₃	1	2	yes	—
610	#542	C₂²×C₂₃	1	2	yes	complemented
611	#541	—	2	1	no	—
612	#541	C₂²×C₂₃	1	2	yes	complemented
613	#540	—	2	1	no	—
614	#540	C₂²×C₂₃	1	2	yes	—
615	#539	—	2	2	no	—
616	#538	—	2	2	no	—
617	#537	C₂²×C₂₃	1	1	yes	characteristic
618	#537	C₂²×C₂₃	1	1	yes	characteristic
619	#536	C₂²×C₂₃	1	1	yes	characteristic
620	#536	C₂²×C₂₃	1	1	yes	characteristic
621	#535	C₂²×C₂₃	1	1	yes	characteristic
622	#535	C₂²×C₂₃	1	1	yes	characteristic
623	#533	—	2	1	no	—
624	#533	C₂²×C₂₃	1	2	yes	complemented
625	#532	—	2	1	no	—
626	#532	C₂²×C₂₃	1	2	yes	—
627	#529	—	2	1	no	—
628	#529	—	2	2	no	—
629	#529	—	2	1	no	—
630	#529	C₂²×C₂₃	1	2	yes	—
631	#529	C₂²×C₂₃	1	2	yes	complemented
632	#525	—	2	2	no	—
633	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
634	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
635	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
636	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
637	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
638	#501	C₂²×C₂₃	1	2	yes	complemented
639	#501	C₂²×C₂₃	1	2	yes	complemented
640	#499	C₂²×C₂₃	1	2	yes	complemented
641	#498	C₂²×C₂₃	1	2	yes	complemented
642	#497	C₂²×C₂₃	1	2	yes	—
643	#496	C₂²×C₂₃	1	2	yes	—
644	#495	C₂²×C₂₃	1	2	yes	—
645	#492	C₂²×C₂₃	1	2	yes	—
646	#491	C₂²×C₂₃	1	2	yes	complemented
647	#490	C₂²×C₂₃	1	2	yes	—
648	#489	C₂²×C₂₃	1	2	yes	—
649	#489	C₂²×C₂₃	1	2	yes	complemented
650	#488	C₂²×C₂₃	1	2	yes	—
651	#488	C₂²×C₂₃	1	2	yes	complemented
652	#487	C₂²×C₂₃	1	2	yes	complemented
653	#486	C₂²×C₂₃	1	2	yes	—
654	#470	C₂²×C₂₃	1	2	yes	complemented
655	#470	C₂²×C₂₃	1	2	yes	complemented
656	#469	C₂²×C₂₃	1	2	yes	—
657	#469	C₂²×C₂₃	1	2	yes	complemented
658	#468	C₂²×C₂₃	1	2	yes	—
659	#468	C₂²×C₂₃	1	2	yes	—
660	#468	C₂²×C₂₃	1	2	yes	—
661	#468	C₂²×C₂₃	1	2	yes	complemented
662	#467	C₂²×C₂₃	1	2	yes	complemented
663	#466	C₂²×C₂₃	1	2	yes	—
664	#465	C₂²×C₂₃	1	2	yes	—
665	#465	C₂²×C₂₃	1	2	yes	—
666	#465	C₂²×C₂₃	1	2	yes	—
667	#465	C₂²×C₂₃	1	2	yes	complemented
668	#465	C₂²×C₂₃	1	2	yes	complemented
669	#465	C₂²×C₂₃	1	2	yes	complemented
670	#442	C₂²×C₂₃	1	2	yes	—
671	#441	C₂²×C₂₃	1	2	yes	complemented
672	#440	C₂²×C₂₃	1	2	yes	—
673	#440	C₂²×C₂₃	1	2	yes	complemented
674	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
675	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
676	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
677	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
678	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
679	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
680	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
681	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
682	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
683	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
684	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
685	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
686	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
687	C₄×D₈	C₂²×C₂₃	1	2	yes	—
688	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
689	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
690	#428	C₂²×C₂₃	1	1	yes	characteristic
691	#428	C₂²×C₂₃	1	1	yes	characteristic
692	#427	C₂²×C₂₃	1	1	yes	characteristic
693	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
694	#419	C₂²×C₂₃	1	1	yes	characteristic
695	#418	C₂²×C₂₃	1	1	yes	characteristic
696	#417	C₂²×C₂₃	1	1	yes	characteristic
697	#417	C₂²×C₂₃	1	1	yes	characteristic
698	#416	C₂²×C₂₃	1	1	yes	characteristic
699	#416	C₂²×C₂₃	1	1	yes	characteristic
700	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
701	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
702	#405	C₂²×C₂₃	1	1	yes	characteristic
703	#405	C₂²×C₂₃	1	1	yes	characteristic
704	#405	C₂²×C₂₃	1	2	yes	complemented
705	#405	C₂²×C₂₃	1	2	yes	complemented
706	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
707	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
708	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
709	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	complemented
710	C₂×C₂₃	—	2	2	no	—
711	C₂×C₂₃	—	4	2	no	—
712	C₂×C₂₃	—	8	1	no	—
713	C₂×C₂₃	—	8	1	no	—
714	C₂×C₂₃	—	8	2	no	—
715	C₂×C₂₃	C₂×#532	1	1	yes	characteristic
716	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
717	C₂×C₂₃	#3584	1	1	yes	characteristic
718	C₂×#41	—	2	2	no	—
719	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
720	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
721	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
722	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
723	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
724	C₂³×C₄	—	2	1	no	—
725	#137	—	2	4	no	—
726	AGL(1,ℤ/8)	—	2	4	no	—
727	#135	—	2	4	no	—
728	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
729	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
730	C₂×SD₁₆	—	2	4	no	—
731	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
734	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
735	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
737	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
738	C₂×D₈	C₂³×C₂₃	1	2	yes	—
739	#131	—	2	4	no	—
740	#131	—	2	4	no	—
741	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
742	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
743	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
744	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
745	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
746	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
747	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
748	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
749	C₄⋊Q₈	—	2	1	no	—
750	C₄⋊Q₈	—	2	1	no	—
751	C₄⋊Q₈	—	2	1	no	—
752	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
753	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
754	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
755	#127	—	2	1	no	—
756	#127	C₂³×C₂₃	1	2	yes	—
757	#126	—	2	2	no	—
758	#126	—	2	2	no	—
759	#126	—	2	2	no	—
760	#126	—	2	2	no	—
761	#126	—	2	2	no	—
762	#126	—	2	2	no	—
763	#125	—	2	1	no	—
764	#125	—	2	2	no	—
765	#125	—	2	1	no	—
766	#125	—	2	2	no	—
767	#125	—	2	2	no	—
768	#125	C₂³×C₂₃	1	2	yes	—
769	#125	C₂³×C₂₃	1	2	yes	—
770	#124	—	2	1	no	—
771	#124	—	2	1	no	—
772	#124	—	2	2	no	—
773	#124	—	2	2	no	—
774	#124	—	2	2	no	—
775	#124	C₂³×C₂₃	1	2	yes	—
776	#124	C₂³×C₂₃	1	2	yes	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	C₂²⋊Q₈	—	2	1	no	—
786	C₂²⋊Q₈	—	2	1	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	2	1	no	—
790	C₂²⋊Q₈	—	2	1	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
795	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
796	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
797	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
798	#121	—	2	2	no	—
799	#121	—	2	2	no	—
800	#121	—	2	1	no	—
801	#121	—	2	1	no	—
802	#121	—	2	2	no	—
803	#121	—	2	1	no	—
804	#121	—	2	1	no	—
805	#121	—	2	2	no	—
806	#121	—	2	2	no	—
807	#121	C₂³×C₂₃	1	2	yes	—
808	#121	C₂³×C₂₃	1	2	yes	—
809	#121	C₂³×C₂₃	1	2	yes	—
810	#121	C₂³×C₂₃	1	2	yes	—
811	#120	—	2	2	no	—
812	#120	—	2	2	no	—
813	C₄×Q₈	—	2	1	no	—
814	C₄×Q₈	—	2	1	no	—
815	C₄×Q₈	—	2	2	no	—
816	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
817	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
818	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
819	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
820	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
821	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
822	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
823	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	—	2	2	no	—
833	C₄×D₄	D₄×C₂₃	1	2	yes	—
834	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
835	C₄×D₄	D₄×C₂₃	1	2	yes	—
836	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
837	C₄×D₄	C₂³×C₂₃	1	2	yes	—
838	C₄×D₄	C₂³×C₂₃	1	2	yes	—
839	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
840	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
841	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
842	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
843	#117	—	2	2	no	—
844	#117	—	2	1	no	—
845	#117	—	2	1	no	—
846	#117	—	2	2	no	—
847	#117	—	2	2	no	—
848	#117	C₂³×C₂₃	1	1	yes	characteristic
849	#117	C₂³×C₂₃	1	1	yes	characteristic
850	#117	C₂³×C₂₃	1	1	yes	characteristic
851	#117	C₂³×C₂₃	1	2	yes	—
852	C₂×C₄⋊C₄	—	2	1	no	—
853	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
854	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
855	C₂×C₂²⋊C₄	—	2	1	no	—
856	C₂×C₄²	—	2	1	no	—
857	C₂×C₄²	—	2	1	no	—
858	C₂×C₄²	—	2	1	no	—
859	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
860	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
861	#107	C₂³×C₂₃	1	1	yes	characteristic
862	#107	C₂³×C₂₃	1	1	yes	characteristic
863	#107	C₂³×C₂₃	1	2	yes	—
864	#107	C₂³×C₂₃	1	2	yes	—
865	#106	C₂³×C₂₃	1	2	yes	—
866	#106	C₂³×C₂₃	1	2	yes	—
867	#106	C₂³×C₂₃	1	1	yes	characteristic
868	#106	C₂³×C₂₃	1	1	yes	characteristic
869	#106	C₂³×C₂₃	1	2	yes	—
870	#106	C₂³×C₂₃	1	2	yes	—
871	#103	C₂³×C₂₃	1	2	yes	—
872	#103	C₂³×C₂₃	1	2	yes	—
873	#103	C₂³×C₂₃	1	1	yes	characteristic
874	#103	C₂³×C₂₃	1	1	yes	characteristic
875	#103	C₂³×C₂₃	1	1	yes	characteristic
876	#103	C₂³×C₂₃	1	1	yes	characteristic
877	#103	C₂³×C₂₃	1	2	yes	—
878	#103	C₂³×C₂₃	1	2	yes	—
879	#103	C₂³×C₂₃	1	2	yes	—
880	#103	C₂³×C₂₃	1	2	yes	—
881	#102	C₂³×C₂₃	1	2	yes	—
882	#102	C₂³×C₂₃	1	2	yes	—
883	#102	C₂³×C₂₃	1	1	yes	characteristic
884	#102	C₂³×C₂₃	1	1	yes	characteristic
885	#102	C₂³×C₂₃	1	1	yes	characteristic
886	#102	C₂³×C₂₃	1	1	yes	characteristic
887	#102	C₂³×C₂₃	1	2	yes	—
888	#102	C₂³×C₂₃	1	2	yes	—
889	#102	C₂³×C₂₃	1	2	yes	—
890	#102	C₂³×C₂₃	1	2	yes	—
891	#97	C₂³×C₂₃	1	2	yes	—
892	#97	C₂³×C₂₃	1	2	yes	—
893	#97	C₂³×C₂₃	1	2	yes	—
894	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
895	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
896	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
897	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
898	C₄×C₈	C₂³×C₂₃	1	2	yes	—
899	C₄×C₈	C₂³×C₂₃	1	2	yes	—
900	C₄×C₈	C₂³×C₂₃	1	2	yes	—
901	C₂₃	#60694	1	1	yes	characteristic, direct product factor, Sylow
902	C₂⁴	—	2	1	no	—
903	#41	—	2	2	no	—
904	#41	—	2	2	no	—
905	#41	—	2	2	no	—
906	#41	—	2	2	no	—
907	#41	—	2	2	no	—
908	#41	—	2	2	no	—
909	#41	—	8	4	no	—
910	C₂×Q₈	—	2	1	no	—
911	C₂×Q₈	—	2	2	no	—
912	C₂×Q₈	—	2	2	no	—
913	C₂×Q₈	—	2	2	no	—
914	C₂×Q₈	—	2	2	no	—
915	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
916	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
917	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
918	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	1	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	1	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
931	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
932	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
933	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
934	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	8	2	no	—
947	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
948	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
949	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
950	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
951	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
952	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
953	Q₁₆	—	2	2	no	—
954	Q₁₆	—	2	4	no	—
955	SD₁₆	—	2	4	no	—
956	SD₁₆	—	2	4	no	—
957	SD₁₆	—	2	2	no	—
958	SD₁₆	—	2	2	no	—
959	SD₁₆	—	2	4	no	—
960	SD₁₆	—	2	4	no	—
961	D₈	—	2	2	no	—
962	D₈	—	2	4	no	—
963	M₁₆	—	2	2	no	—
964	M₁₆	—	2	4	no	—
965	M₁₆	—	2	4	no	—
966	M₁₆	#41×C₂₃	1	4	yes	complemented
967	C₂×C₈	—	2	2	no	—
968	C₂×C₈	—	2	4	no	—
969	C₂×C₈	—	2	4	no	—
970	C₂×C₈	#41×C₂₃	1	4	yes	complemented
971	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
972	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
973	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
974	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
975	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
976	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
998	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
999	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1000	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1001	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1002	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1003	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1004	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1005	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1006	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	1	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	C₂×D₄×C₂₃	1	2	yes	—
1028	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1029	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	2	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	1	no	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	1	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	2	2	no	—
1038	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1039	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1040	C₄²	C₂×D₄×C₂₃	1	2	yes	—
1041	C₄²	C₂×D₄×C₂₃	1	2	yes	—
1042	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1043	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1044	C₄²	C₂⁴×C₂₃	1	2	yes	—
1045	C₂³	—	2	1	no	—
1046	C₂³	—	2	2	no	—
1047	C₂³	—	2	1	no	—
1048	C₂³	—	4	2	no	—
1049	C₂³	—	8	1	no	—
1050	C₂³	—	8	1	no	—
1051	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1052	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1053	Q₈	—	2	2	no	—
1054	Q₈	—	2	2	no	—
1055	Q₈	—	2	1	no	—
1056	Q₈	—	2	2	no	—
1057	Q₈	—	2	1	no	—
1058	Q₈	—	2	1	no	—
1059	Q₈	—	2	1	no	—
1060	Q₈	—	4	2	no	—
1061	Q₈	—	8	2	no	—
1062	Q₈	—	8	2	no	—
1063	D₄	—	2	4	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	2	1	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	2	2	no	—
1069	D₄	—	2	1	no	—
1070	D₄	—	2	2	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	2	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	8	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	2	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	4	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	4	1	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	4	4	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	1	no	—
1103	C₂×C₄	—	8	1	no	—
1104	C₂×C₄	—	8	1	no	—
1105	C₂×C₄	—	8	1	no	—
1106	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
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	2	yes	—
1110	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1111	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1112	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1113	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1114	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1115	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1116	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1117	C₈	—	2	1	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	2	no	—
1120	C₈	C₂×#41×C₂₃	1	2	yes	—
1121	C₈	C₂×#41×C₂₃	1	4	yes	—
1122	C₈	C₂×#41×C₂₃	1	2	yes	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	1	no	—
1125	C₂²	—	2	2	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	2	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	4	2	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	2	no	—
1137	C₂²	—	8	4	no	—
1138	C₂²	C₂₃×#532	1	2	yes	—
1139	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1140	C₄	—	2	2	no	—
1141	C₄	—	2	1	no	—
1142	C₄	—	2	2	no	—
1143	C₄	—	2	1	no	—
1144	C₄	—	2	1	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	2	no	—
1149	C₄	—	4	2	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	4	1	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	2	no	—
1154	C₄	—	4	1	no	—
1155	C₄	C₂₃×#532	1	2	yes	—
1156	C₄	C₂₃×#577	1	2	yes	—
1157	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1158	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1159	C₂	—	2	2	no	—
1160	C₂	—	4	2	no	—
1161	C₂	—	8	2	no	—
1162	C₂	—	8	1	no	—
1163	C₂	—	8	1	no	—
1164	C₂	C₂×C₂₃×#532	1	1	yes	characteristic
1165	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
1166	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×#3461	C₂	semidirect
2. C₂₃×#3460	C₂	semidirect
3. C₂₃×#3179	C₂	semidirect
4. C₂₃×#3178	C₂	semidirect
5. C₂₃×#3174	C₂	semidirect
6. C₂₃×#3173	C₂	semidirect
7. C₂₃×#3172	C₂	semidirect
8. C₂₃×#3171	C₂	semidirect
9. C₂₃×#3168	C₂	semidirect
10. C₂₃×#3167	C₂	semidirect
11. C₂₃×#3163	C₂	semidirect
12. C₂₃×#3154	C₂	semidirect
13. C₂₃×#3137	C₂	semidirect
14. C₂₃×#3136	C₂	semidirect
15. C₂₃×#3063	C₂	semidirect
16. C₂₃×#3062	C₂	semidirect
17. C₂₃×#3060	C₂	semidirect
18. C₂₃×#3057	C₂	semidirect
19. C₄×C₂₃×#137	C₂	semidirect
20. C₄×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
21. C₄×C₂₃×#135	C₂	semidirect
22. C₂×C₄×SD₁₆×C₂₃	C₂	semidirect
23. C₄×C₂₃×#131	C₂	semidirect
35. C₂₃×#542	C₂²	semidirect
37. C₂₃×#541	C₂²	semidirect
49. C₂₃×#533	C₂²	semidirect
56. C₂₃×#529	C₂²	semidirect
63. C₂₃×#501	C₂²	semidirect
64. C₂₃×#501	C₂²	semidirect
65. C₂₃×#499	C₂²	semidirect
66. C₂₃×#498	C₂²	semidirect
71. C₂₃×#491	C₂²	semidirect
74. C₂₃×#489	C₂²	semidirect
76. C₂₃×#488	C₂²	semidirect
77. C₂₃×#487	C₂²	semidirect
79. C₂₃×#470	C₂²	semidirect
80. C₂₃×#470	C₂²	semidirect
82. C₂₃×#469	C₂²	semidirect
86. C₂₃×#468	C₂²	semidirect
87. C₂₃×#467	C₂²	semidirect
92. C₂₃×#465	C₂²	semidirect
93. C₂₃×#465	C₂²	semidirect
94. C₂₃×#465	C₂²	semidirect
96. C₂₃×#441	C₂²	semidirect
98. C₂₃×#440	C₂²	semidirect
99. C₄×Q₁₆×C₂₃	C₂²	semidirect
100. C₄×Q₁₆×C₂₃	C₂²	semidirect
101. C₄×Q₁₆×C₂₃	C₂²	semidirect
107. C₄×SD₁₆×C₂₃	C₂²	semidirect
108. C₄×SD₁₆×C₂₃	C₂²	semidirect
109. C₄×SD₁₆×C₂₃	C₂²	semidirect
110. C₄×SD₁₆×C₂₃	C₂²	semidirect
111. C₄×SD₁₆×C₂₃	C₂²	semidirect
113. C₄×D₈×C₂₃	C₂²	semidirect
114. C₄×D₈×C₂₃	C₂²	semidirect
129. C₂₃×#405	C₂²	semidirect
130. C₂₃×#405	C₂²	semidirect
132. C₄×M₁₆×C₂₃	C₂²	semidirect
134. C₂×C₄×C₈×C₂₃	C₂²	semidirect
382. M₁₆×C₂₃	#41	semidirect
386. C₂×C₈×C₂₃	#41	semidirect
461. #60694	C₂₃	direct (N × H)
540. #3461	C₂×C₂₃	semidirect
541. #3460	C₂×C₂₃	semidirect
542. #3179	C₂×C₂₃	semidirect
543. #3178	C₂×C₂₃	semidirect
544. #3174	C₂×C₂₃	semidirect
545. #3173	C₂×C₂₃	semidirect
546. #3172	C₂×C₂₃	semidirect
547. #3171	C₂×C₂₃	semidirect
548. #3168	C₂×C₂₃	semidirect
549. #3167	C₂×C₂₃	semidirect
550. #3163	C₂×C₂₃	semidirect
551. #3154	C₂×C₂₃	semidirect
552. #3137	C₂×C₂₃	semidirect
553. #3136	C₂×C₂₃	semidirect
554. #3063	C₂×C₂₃	semidirect
555. #3062	C₂×C₂₃	semidirect
556. #3060	C₂×C₂₃	semidirect
557. #3057	C₂×C₂₃	semidirect
558. C₄×#137	C₂×C₂₃	semidirect
559. C₄×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
560. C₄×#135	C₂×C₂₃	semidirect
561. C₂×C₄×SD₁₆	C₂×C₂₃	semidirect
562. C₄×#131	C₂×C₂₃	semidirect
610. #542	C₂²×C₂₃	semidirect
612. #541	C₂²×C₂₃	semidirect
624. #533	C₂²×C₂₃	semidirect
631. #529	C₂²×C₂₃	semidirect
638. #501	C₂²×C₂₃	semidirect
639. #501	C₂²×C₂₃	semidirect
640. #499	C₂²×C₂₃	semidirect
641. #498	C₂²×C₂₃	semidirect
646. #491	C₂²×C₂₃	semidirect
649. #489	C₂²×C₂₃	semidirect
651. #488	C₂²×C₂₃	semidirect
652. #487	C₂²×C₂₃	semidirect
654. #470	C₂²×C₂₃	semidirect
655. #470	C₂²×C₂₃	semidirect
657. #469	C₂²×C₂₃	semidirect
661. #468	C₂²×C₂₃	semidirect
662. #467	C₂²×C₂₃	semidirect
667. #465	C₂²×C₂₃	semidirect
668. #465	C₂²×C₂₃	semidirect
669. #465	C₂²×C₂₃	semidirect
671. #441	C₂²×C₂₃	semidirect
673. #440	C₂²×C₂₃	semidirect
674. C₄×Q₁₆	C₂²×C₂₃	semidirect
675. C₄×Q₁₆	C₂²×C₂₃	semidirect
676. C₄×Q₁₆	C₂²×C₂₃	semidirect
682. C₄×SD₁₆	C₂²×C₂₃	semidirect
683. C₄×SD₁₆	C₂²×C₂₃	semidirect
684. C₄×SD₁₆	C₂²×C₂₃	semidirect
685. C₄×SD₁₆	C₂²×C₂₃	semidirect
686. C₄×SD₁₆	C₂²×C₂₃	semidirect
688. C₄×D₈	C₂²×C₂₃	semidirect
689. C₄×D₈	C₂²×C₂₃	semidirect
704. #405	C₂²×C₂₃	semidirect
705. #405	C₂²×C₂₃	semidirect
707. C₄×M₁₆	C₂²×C₂₃	semidirect
709. C₂×C₄×C₈	C₂²×C₂₃	semidirect
901. C₂₃	#60694	direct (N × H)
966. M₁₆	#41×C₂₃	semidirect
970. C₂×C₈	#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×#3461	2
C₂₃×#3460	2
C₂₃×#3179	2
C₂₃×#3178	2
C₂₃×#3174	2
C₂₃×#3173	2
C₂₃×#3172	2
C₂₃×#3171	2
C₂₃×#3168	2
C₂₃×#3167	2
C₂₃×#3163	2
C₂₃×#3154	2
C₂₃×#3137	2
C₂₃×#3136	2
C₂₃×#3063	2
C₂₃×#3062	2
C₂₃×#3060	2
C₂₃×#3057	2
C₄×C₂₃×#137	2
C₄×C₂₃×AGL(1,ℤ/8)	2
C₄×C₂₃×#135	2
C₂×C₄×SD₁₆×C₂₃	2
C₄×C₂₃×#131	2
#60694	23

Subgroups — C23×#60694 #19208320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60694 #19208320