Subgroups — C₂₃×#60981 #19208607

Order 5888.

1732 conjugacy classes of subgroups.

The subgroup lattice has 1250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3262	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3258	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3243	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3239	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3225	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3215	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3211	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3196	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3193	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3189	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3188	C₂	1	1	yes	maximal, characteristic
15	C₂₃×#3178	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3175	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3124	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3121	C₂	1	2	yes	maximal, complemented
19	C₂₃×#3117	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#556	—	2	1	no	—
25	C₂₃×#554	—	2	1	no	—
26	C₂₃×#552	—	2	1	no	—
27	C₂₃×#552	—	2	1	no	—
28	C₂₃×#552	—	2	1	no	—
29	C₂₃×#552	—	2	1	no	—
30	C₂₃×#551	—	2	1	no	—
31	C₂₃×#551	—	2	1	no	—
32	C₂₃×#544	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#542	—	2	1	no	—
34	C₂₃×#542	—	2	1	no	—
35	C₂₃×#542	—	2	1	no	—
36	C₂₃×#542	—	2	1	no	—
37	C₂₃×#542	C₂²	1	2	yes	—
38	C₂₃×#542	C₂²	1	2	yes	—
39	C₂₃×#542	C₂²	1	2	yes	—
40	C₂₃×#542	C₂²	1	2	yes	—
41	C₂₃×#542	C₂²	1	1	yes	characteristic, complemented
42	C₂₃×#542	C₂²	1	1	yes	characteristic, complemented
43	C₂₃×#541	C₂²	1	1	yes	characteristic, complemented
44	C₂₃×#541	C₂²	1	1	yes	characteristic, complemented
45	C₂₃×#536	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#533	C₂²	1	1	yes	characteristic
47	C₂₃×#533	C₂²	1	1	yes	characteristic
48	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
49	C₂₃×#529	C₂²	1	1	yes	characteristic
50	C₂₃×#529	C₂²	1	1	yes	characteristic
51	C₂×C₂₃×#126	—	2	1	no	—
52	C₂×C₂₃×#124	—	2	1	no	—
53	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
54	C₂₃×#525	C₂²	1	1	yes	characteristic
55	C₂×C₂₃×#123	—	2	1	no	—
56	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
57	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
59	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
60	C₂₃×#520	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#519	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
63	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
64	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
65	C₂₃×#501	C₂²	1	2	yes	complemented
66	C₂₃×#500	C₂²	1	2	yes	complemented
67	C₂₃×#497	C₂²	1	2	yes	complemented
68	C₂₃×#495	C₂²	1	2	yes	complemented
69	C₂₃×#489	C₂²	1	2	yes	complemented
70	C₂₃×#489	C₂²	1	2	yes	complemented
71	C₂₃×#488	C₂²	1	2	yes	complemented
72	C₂₃×#487	C₂²	1	2	yes	complemented
73	C₂₃×#485	C₂²	1	2	yes	complemented
74	C₂₃×#484	C₂²	1	1	yes	characteristic
75	C₂₃×#484	C₂²	1	1	yes	characteristic
76	C₂₃×#484	C₂²	1	1	yes	characteristic
77	C₂₃×#484	C₂²	1	1	yes	characteristic
78	C₂₃×#484	C₂²	1	1	yes	characteristic
79	C₂₃×#484	C₂²	1	1	yes	characteristic
80	C₂₃×#484	C₂²	1	2	yes	complemented
81	C₂₃×#482	C₂²	1	2	yes	—
82	C₂₃×#481	C₂²	1	1	yes	characteristic
83	C₂₃×#481	C₂²	1	1	yes	characteristic
84	C₂₃×#480	C₂²	1	2	yes	—
85	C₂₃×#479	C₂²	1	2	yes	complemented
86	C₂₃×#478	C₂²	1	2	yes	complemented
87	C₂₃×#477	C₂²	1	2	yes	complemented
88	C₂₃×#477	C₂²	1	2	yes	complemented
89	C₂₃×#477	C₂²	1	2	yes	complemented
90	C₂₃×#475	C₂²	1	2	yes	complemented
91	C₂₃×#474	C₂²	1	2	yes	complemented
92	C₂₃×#474	C₂²	1	2	yes	complemented
93	C₂₃×#470	C₂²	1	2	yes	complemented
94	C₂₃×#468	C₂²	1	2	yes	—
95	C₂₃×#468	C₂²	1	2	yes	—
96	C₂₃×#468	C₂²	1	2	yes	complemented
97	C₂₃×#467	C₂²	1	2	yes	complemented
98	C₂₃×#467	C₂²	1	2	yes	complemented
99	C₂₃×#466	C₂²	1	2	yes	—
100	C₂₃×#465	C₂²	1	2	yes	—
101	C₂₃×#464	C₂²	1	2	yes	complemented
102	C₂₃×#464	C₂²	1	2	yes	complemented
103	C₂₃×#464	C₂²	1	2	yes	complemented
104	C₂₃×#464	C₂²	1	2	yes	complemented
105	C₂₃×#463	C₂²	1	2	yes	complemented
106	C₂₃×#463	C₂²	1	2	yes	complemented
107	C₂₃×#462	C₂²	1	2	yes	complemented
108	C₂₃×#461	C₂²	1	2	yes	complemented
109	C₂₃×#452	C₂²	1	2	yes	complemented
110	C₂₃×#451	C₂²	1	1	yes	characteristic
111	C₂₃×#451	C₂²	1	1	yes	characteristic
112	C₂₃×#451	C₂²	1	1	yes	characteristic
113	C₂₃×#451	C₂²	1	2	yes	complemented
114	C₂₃×#450	C₂²	1	1	yes	characteristic
115	C₂₃×#450	C₂²	1	1	yes	characteristic
116	C₂₃×#450	C₂²	1	1	yes	characteristic
117	C₂₃×#449	C₂²	1	2	yes	—
118	C₂₃×#448	C₂²	1	2	yes	—
119	C₂₃×#448	C₂²	1	1	yes	characteristic
120	C₂₃×#447	C₂²	1	1	yes	characteristic
121	C₂₃×#441	C₂²	1	2	yes	complemented
122	C₂₃×#440	C₂²	1	2	yes	complemented
123	C₂₃×#440	C₂²	1	2	yes	complemented
124	C₂₃×#440	C₂²	1	2	yes	complemented
125	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
126	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
127	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
128	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
129	C₂₃×#433	C₂²	1	2	yes	complemented
130	C₂₃×#433	C₂²	1	2	yes	complemented
131	C₂₃×#432	C₂²	1	1	yes	characteristic
132	C₂₃×#432	C₂²	1	1	yes	characteristic
133	C₂₃×#431	C₂²	1	1	yes	characteristic
134	C₂₃×#431	C₂²	1	1	yes	characteristic
135	C₂₃×#424	C₂²	1	2	yes	complemented
136	C₂₃×#407	C₂²	1	1	yes	characteristic
137	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
138	C₂₃×#405	C₂²	1	2	yes	complemented
139	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
140	C₂²×Q₈×C₂₃	—	2	1	no	—
141	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₂₃	—	2	1	no	—
144	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₂₃	—	2	1	no	—
146	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
154	C₂×D₈×C₂₃	C₂³	1	2	yes	—
155	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
156	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
157	C₂₃×C₄⋊Q₈	—	2	1	no	—
158	C₂₃×C₄⋊Q₈	—	2	1	no	—
159	C₂₃×C₄⋊Q₈	—	2	1	no	—
160	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₂₃×#126	—	2	1	no	—
167	C₂₃×#126	—	2	1	no	—
168	C₂₃×#126	—	2	2	no	—
169	C₂₃×#126	—	2	2	no	—
170	C₂₃×#126	—	2	2	no	—
171	C₂₃×#126	—	2	2	no	—
172	C₂₃×#126	—	2	1	no	—
173	C₂₃×#126	—	2	1	no	—
174	C₂₃×#126	—	2	1	no	—
175	C₂₃×#126	—	2	1	no	—
176	C₂₃×#126	—	2	1	no	—
177	C₂₃×#126	—	2	1	no	—
178	C₂₃×#125	—	2	1	no	—
179	C₂₃×#125	—	2	1	no	—
180	C₂₃×#125	—	2	1	no	—
181	C₂₃×#125	—	2	1	no	—
182	C₂₃×#125	—	2	1	no	—
183	C₂₃×#125	—	2	1	no	—
184	C₂₃×#125	—	2	1	no	—
185	C₂₃×#125	C₂³	1	1	yes	characteristic
186	C₂₃×#125	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
193	C₂₃×#124	—	2	1	no	—
194	C₂₃×#124	—	2	1	no	—
195	C₂₃×#124	C₂³	1	1	yes	characteristic
196	C₂₃×#124	C₂³	1	2	yes	—
197	C₂₃×#124	C₂³	1	2	yes	—
198	C₂₃×#124	C₂³	1	1	yes	characteristic
199	C₂₃×#123	—	2	1	no	—
200	C₂₃×#123	—	2	1	no	—
201	C₂₃×#123	—	2	1	no	—
202	C₂₃×#123	—	2	1	no	—
203	C₂₃×#123	—	2	1	no	—
204	C₂₃×#123	—	2	1	no	—
205	C₂₃×#123	—	2	1	no	—
206	C₂₃×#123	—	2	2	no	—
207	C₂₃×#123	—	2	2	no	—
208	C₂₃×#123	—	2	2	no	—
209	C₂₃×#123	—	2	2	no	—
210	C₂₃×C₂²⋊Q₈	—	2	1	no	—
211	C₂₃×C₂²⋊Q₈	—	2	1	no	—
212	C₂₃×C₂²⋊Q₈	—	2	1	no	—
213	C₂₃×C₂²⋊Q₈	—	2	1	no	—
214	C₂₃×C₂²⋊Q₈	—	2	1	no	—
215	C₂₃×C₂²⋊Q₈	—	2	1	no	—
216	C₂₃×C₂²⋊Q₈	—	2	1	no	—
217	C₂₃×C₂²⋊Q₈	—	2	1	no	—
218	C₂₃×C₂²⋊Q₈	—	2	1	no	—
219	C₂₃×C₂²⋊Q₈	—	2	1	no	—
220	C₂₃×C₂²⋊Q₈	—	2	2	no	—
221	C₂₃×C₂²⋊Q₈	—	2	2	no	—
222	C₂₃×C₂²⋊Q₈	—	2	2	no	—
223	C₂₃×C₂²⋊Q₈	—	2	2	no	—
224	C₂₃×C₂²⋊Q₈	—	2	1	no	—
225	C₂₃×C₂²⋊Q₈	—	2	1	no	—
226	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
227	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
228	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
229	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
230	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
231	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
232	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
233	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
234	C₂₃×#121	—	2	1	no	—
235	C₂₃×#121	—	2	1	no	—
236	C₂₃×#121	C₂³	1	1	yes	characteristic
237	C₂₃×#121	C₂³	1	2	yes	—
238	C₂₃×#121	C₂³	1	2	yes	—
239	C₂₃×#121	C₂³	1	1	yes	characteristic
240	C₂₃×#120	—	2	1	no	—
241	C₄×Q₈×C₂₃	—	2	1	no	—
242	C₄×Q₈×C₂₃	—	2	1	no	—
243	C₄×Q₈×C₂₃	—	2	1	no	—
244	C₄×Q₈×C₂₃	—	2	1	no	—
245	C₄×Q₈×C₂₃	—	2	1	no	—
246	C₄×Q₈×C₂₃	—	2	1	no	—
247	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
248	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
249	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
250	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
251	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
252	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
253	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
254	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₂₃	—	2	1	no	—
256	C₄×D₄×C₂₃	—	2	1	no	—
257	C₄×D₄×C₂₃	—	2	1	no	—
258	C₄×D₄×C₂₃	—	2	1	no	—
259	C₄×D₄×C₂₃	—	2	1	no	—
260	C₄×D₄×C₂₃	—	2	1	no	—
261	C₄×D₄×C₂₃	—	2	1	no	—
262	C₄×D₄×C₂₃	—	2	1	no	—
263	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
264	C₄×D₄×C₂₃	C₂³	1	2	yes	—
265	C₄×D₄×C₂₃	C₂³	1	2	yes	—
266	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
267	C₂₃×#117	—	2	1	no	—
268	C₂₃×#117	—	2	1	no	—
269	C₂₃×#117	—	2	1	no	—
270	C₂₃×#117	—	2	1	no	—
271	C₂₃×#117	—	2	1	no	—
272	C₂₃×#117	—	2	1	no	—
273	C₂₃×#117	—	2	1	no	—
274	C₂₃×#117	D₄	1	1	yes	characteristic
275	C₂₃×#117	D₄	1	1	yes	characteristic
276	C₂₃×#117	D₄	1	1	yes	characteristic
277	C₂₃×#117	D₄	1	1	yes	characteristic
278	C₂₃×#117	C₂³	1	1	yes	characteristic
279	C₂₃×#117	C₂³	1	1	yes	characteristic
280	C₂₃×#117	C₂³	1	1	yes	characteristic
281	C₂₃×#117	C₂³	1	1	yes	characteristic
282	C₂₃×#117	C₂³	1	1	yes	characteristic
283	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
284	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
285	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
286	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
287	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
288	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
289	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
290	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
294	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
295	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
296	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
297	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
298	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
299	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
300	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
301	C₂×C₄²×C₂₃	—	2	1	no	—
302	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
303	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
304	C₂₃×#107	C₂³	1	2	yes	—
305	C₂₃×#107	C₂³	1	2	yes	—
306	C₂₃×#107	C₂³	1	2	yes	—
307	C₂₃×#107	C₂³	1	2	yes	—
308	C₂₃×#107	C₂³	1	2	yes	—
309	C₂₃×#107	C₂³	1	2	yes	—
310	C₂₃×#106	C₂³	1	2	yes	—
311	C₂₃×#106	C₂³	1	2	yes	—
312	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
313	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
314	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
315	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
316	C₂₃×#103	C₂³	1	2	yes	—
317	C₂₃×#103	C₂³	1	2	yes	—
318	C₂₃×#103	C₂³	1	2	yes	—
319	C₂₃×#103	C₂³	1	2	yes	—
320	C₂₃×#103	C₂³	1	2	yes	—
321	C₂₃×#103	C₂³	1	2	yes	—
322	C₂₃×#103	C₂³	1	2	yes	—
323	C₂₃×#103	C₂³	1	2	yes	—
324	C₂₃×#103	C₂³	1	2	yes	—
325	C₂₃×#103	C₂³	1	2	yes	—
326	C₂₃×#102	C₂³	1	2	yes	—
327	C₂₃×#102	C₂³	1	2	yes	—
328	C₂₃×#102	C₂³	1	2	yes	—
329	C₂₃×#102	C₂³	1	2	yes	—
330	C₂₃×#102	C₂³	1	2	yes	—
331	C₂₃×#102	C₂³	1	2	yes	—
332	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
333	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
334	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
335	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
336	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
337	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
338	C₂₃×#97	C₂³	1	2	yes	—
339	C₂₃×#97	C₂³	1	2	yes	—
340	C₄×C₈×C₂₃	C₂³	1	2	yes	—
341	C₄×C₈×C₂₃	C₂³	1	2	yes	—
342	C₂⁴×C₂₃	—	2	1	no	—
343	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
344	#41×C₂₃	—	4	2	no	—
345	C₂×Q₈×C₂₃	—	2	1	no	—
346	C₂×Q₈×C₂₃	—	2	1	no	—
347	C₂×Q₈×C₂₃	—	2	1	no	—
348	C₂×Q₈×C₂₃	—	2	1	no	—
349	C₂×Q₈×C₂₃	—	2	2	no	—
350	C₂×Q₈×C₂₃	—	2	2	no	—
351	C₂×Q₈×C₂₃	—	4	2	no	—
352	C₂×Q₈×C₂₃	—	4	2	no	—
353	C₂×Q₈×C₂₃	—	8	2	no	—
354	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
355	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
357	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₂₃	—	2	1	no	—
359	C₂×D₄×C₂₃	—	2	1	no	—
360	C₂×D₄×C₂₃	—	2	1	no	—
361	C₂×D₄×C₂₃	—	2	2	no	—
362	C₂×D₄×C₂₃	—	2	2	no	—
363	C₂×D₄×C₂₃	—	2	1	no	—
364	C₂×D₄×C₂₃	—	4	2	no	—
365	C₂×D₄×C₂₃	—	8	2	no	—
366	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
367	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
368	C₂²×C₄×C₂₃	—	2	1	no	—
369	C₂²×C₄×C₂₃	—	2	1	no	—
370	C₂²×C₄×C₂₃	—	2	1	no	—
371	C₂²×C₄×C₂₃	—	2	1	no	—
372	C₂²×C₄×C₂₃	—	2	1	no	—
373	C₂²×C₄×C₂₃	—	2	1	no	—
374	C₂²×C₄×C₂₃	—	2	1	no	—
375	C₂²×C₄×C₂₃	—	2	1	no	—
376	C₂²×C₄×C₂₃	—	2	2	no	—
377	C₂²×C₄×C₂₃	—	2	2	no	—
378	C₂²×C₄×C₂₃	—	4	2	no	—
379	C₂²×C₄×C₂₃	—	8	2	no	—
380	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
381	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
382	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
383	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
384	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
390	Q₁₆×C₂₃	—	4	2	no	—
391	Q₁₆×C₂₃	—	4	2	no	—
392	Q₁₆×C₂₃	—	4	2	no	—
393	SD₁₆×C₂₃	—	4	2	no	—
394	SD₁₆×C₂₃	—	4	2	no	—
395	SD₁₆×C₂₃	—	4	2	no	—
396	SD₁₆×C₂₃	—	4	2	no	—
397	D₈×C₂₃	—	4	2	no	—
398	M₁₆×C₂₃	—	4	2	no	—
399	C₂×C₈×C₂₃	—	4	2	no	—
400	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
401	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
402	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
403	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
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	1	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	—	2	1	no	—
414	C₄⋊C₄×C₂₃	—	2	1	no	—
415	C₄⋊C₄×C₂₃	—	2	2	no	—
416	C₄⋊C₄×C₂₃	—	2	2	no	—
417	C₄⋊C₄×C₂₃	—	2	1	no	—
418	C₄⋊C₄×C₂₃	—	2	1	no	—
419	C₄⋊C₄×C₂₃	—	2	1	no	—
420	C₄⋊C₄×C₂₃	—	2	1	no	—
421	C₄⋊C₄×C₂₃	—	2	1	no	—
422	C₄⋊C₄×C₂₃	—	2	1	no	—
423	C₄⋊C₄×C₂₃	—	2	1	no	—
424	C₄⋊C₄×C₂₃	—	2	1	no	—
425	C₄⋊C₄×C₂₃	—	2	1	no	—
426	C₄⋊C₄×C₂₃	—	2	1	no	—
427	C₄⋊C₄×C₂₃	—	2	1	no	—
428	C₄⋊C₄×C₂₃	—	2	1	no	—
429	C₄⋊C₄×C₂₃	—	2	1	no	—
430	C₄⋊C₄×C₂₃	—	2	1	no	—
431	C₄⋊C₄×C₂₃	—	2	1	no	—
432	C₄⋊C₄×C₂₃	—	2	1	no	—
433	C₄⋊C₄×C₂₃	—	2	1	no	—
434	C₄⋊C₄×C₂₃	—	2	1	no	—
435	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
436	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
437	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
438	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
439	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
440	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
441	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
444	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
445	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
446	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
447	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
448	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
449	C₂²⋊C₄×C₂₃	—	2	1	no	—
450	C₂²⋊C₄×C₂₃	—	2	1	no	—
451	C₂²⋊C₄×C₂₃	—	2	2	no	—
452	C₂²⋊C₄×C₂₃	—	2	2	no	—
453	C₂²⋊C₄×C₂₃	—	2	1	no	—
454	C₂²⋊C₄×C₂₃	—	2	1	no	—
455	C₂²⋊C₄×C₂₃	—	2	1	no	—
456	C₂²⋊C₄×C₂₃	—	2	1	no	—
457	C₂²⋊C₄×C₂₃	—	2	1	no	—
458	C₂²⋊C₄×C₂₃	—	2	2	no	—
459	C₂²⋊C₄×C₂₃	—	2	2	no	—
460	C₂²⋊C₄×C₂₃	—	2	2	no	—
461	C₂²⋊C₄×C₂₃	—	2	2	no	—
462	C₂²⋊C₄×C₂₃	—	2	2	no	—
463	C₂²⋊C₄×C₂₃	—	2	2	no	—
464	C₂²⋊C₄×C₂₃	—	2	2	no	—
465	C₂²⋊C₄×C₂₃	—	2	2	no	—
466	C₂²⋊C₄×C₂₃	—	2	1	no	—
467	C₂²⋊C₄×C₂₃	—	2	1	no	—
468	C₂²⋊C₄×C₂₃	—	2	1	no	—
469	C₂²⋊C₄×C₂₃	—	2	1	no	—
470	C₂²⋊C₄×C₂₃	—	2	1	no	—
471	C₂²⋊C₄×C₂₃	—	2	1	no	—
472	C₂²⋊C₄×C₂₃	—	2	1	no	—
473	C₂²⋊C₄×C₂₃	—	2	1	no	—
474	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
475	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
476	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
477	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
478	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
479	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
480	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
481	C₂²⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
482	C₄²×C₂₃	—	2	2	no	—
483	C₄²×C₂₃	—	2	2	no	—
484	C₄²×C₂₃	—	2	1	no	—
485	C₄²×C₂₃	—	2	1	no	—
486	C₄²×C₂₃	—	2	1	no	—
487	C₄²×C₂₃	—	2	1	no	—
488	C₄²×C₂₃	—	2	1	no	—
489	C₄²×C₂₃	—	2	1	no	—
490	C₄²×C₂₃	—	2	1	no	—
491	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
492	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
493	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
494	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
495	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
496	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
497	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
498	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
499	#60981	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
500	C₂³×C₂₃	—	2	2	no	—
501	C₂³×C₂₃	—	2	1	no	—
502	C₂³×C₂₃	—	2	2	no	—
503	C₂³×C₂₃	—	4	1	no	—
504	C₂³×C₂₃	—	4	1	no	—
505	C₂³×C₂₃	—	4	2	no	—
506	C₂³×C₂₃	—	4	2	no	—
507	C₂³×C₂₃	—	4	2	no	—
508	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
509	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
510	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
511	Q₈×C₂₃	—	2	2	no	—
512	Q₈×C₂₃	—	2	2	no	—
513	Q₈×C₂₃	—	2	2	no	—
514	Q₈×C₂₃	—	2	2	no	—
515	Q₈×C₂₃	—	2	2	no	—
516	Q₈×C₂₃	—	4	2	no	—
517	Q₈×C₂₃	—	4	2	no	—
518	Q₈×C₂₃	—	8	1	no	—
519	Q₈×C₂₃	—	8	1	no	—
520	Q₈×C₂₃	—	8	2	no	—
521	Q₈×C₂₃	—	8	2	no	—
522	D₄×C₂₃	—	2	2	no	—
523	D₄×C₂₃	—	2	2	no	—
524	D₄×C₂₃	—	2	2	no	—
525	D₄×C₂₃	—	4	2	no	—
526	D₄×C₂₃	—	4	2	no	—
527	D₄×C₂₃	—	4	2	no	—
528	D₄×C₂₃	—	8	1	no	—
529	D₄×C₂₃	—	8	2	no	—
530	D₄×C₂₃	—	8	2	no	—
531	C₂×C₄×C₂₃	—	2	2	no	—
532	C₂×C₄×C₂₃	—	2	2	no	—
533	C₂×C₄×C₂₃	—	2	2	no	—
534	C₂×C₄×C₂₃	—	2	2	no	—
535	C₂×C₄×C₂₃	—	2	2	no	—
536	C₂×C₄×C₂₃	—	2	1	no	—
537	C₂×C₄×C₂₃	—	2	1	no	—
538	C₂×C₄×C₂₃	—	2	2	no	—
539	C₂×C₄×C₂₃	—	2	1	no	—
540	C₂×C₄×C₂₃	—	2	1	no	—
541	C₂×C₄×C₂₃	—	2	1	no	—
542	C₂×C₄×C₂₃	—	2	2	no	—
543	C₂×C₄×C₂₃	—	2	1	no	—
544	C₂×C₄×C₂₃	—	2	1	no	—
545	C₂×C₄×C₂₃	—	2	2	no	—
546	C₂×C₄×C₂₃	—	4	1	no	—
547	C₂×C₄×C₂₃	—	4	1	no	—
548	C₂×C₄×C₂₃	—	4	1	no	—
549	C₂×C₄×C₂₃	—	4	1	no	—
550	C₂×C₄×C₂₃	—	4	1	no	—
551	C₂×C₄×C₂₃	—	4	2	no	—
552	C₂×C₄×C₂₃	—	4	2	no	—
553	C₂×C₄×C₂₃	—	4	2	no	—
554	C₂×C₄×C₂₃	—	4	2	no	—
555	C₂×C₄×C₂₃	—	4	2	no	—
556	C₂×C₄×C₂₃	—	8	1	no	—
557	C₂×C₄×C₂₃	—	8	1	no	—
558	C₂×C₄×C₂₃	—	8	2	no	—
559	C₂×C₄×C₂₃	—	8	2	no	—
560	C₂×C₄×C₂₃	—	8	1	no	—
561	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
562	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
563	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
564	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
565	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
568	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
570	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
571	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
573	C₈×C₂₃	—	2	2	no	—
574	C₈×C₂₃	—	2	2	no	—
575	C₈×C₂₃	—	2	2	no	—
576	C₈×C₂₃	—	2	2	no	—
577	#3495	C₂×C₂₃	1	1	yes	characteristic, complemented
578	C₂×#542	C₂×C₂₃	1	1	yes	characteristic, complemented
579	#3262	C₂×C₂₃	1	2	yes	complemented
580	#3258	C₂×C₂₃	1	2	yes	complemented
581	#3243	C₂×C₂₃	1	2	yes	complemented
582	#3239	C₂×C₂₃	1	1	yes	characteristic, complemented
583	#3230	C₂×C₂₃	1	1	yes	characteristic, complemented
584	#3225	C₂×C₂₃	1	2	yes	complemented
585	#3215	C₂×C₂₃	1	1	yes	characteristic, complemented
586	#3211	C₂×C₂₃	1	1	yes	characteristic, complemented
587	#3196	C₂×C₂₃	1	1	yes	characteristic, complemented
588	#3193	C₂×C₂₃	1	1	yes	characteristic, complemented
589	#3189	C₂×C₂₃	1	1	yes	characteristic, complemented
590	#3188	C₂×C₂₃	1	1	yes	characteristic
591	#3178	C₂×C₂₃	1	2	yes	complemented
592	#3175	C₂×C₂₃	1	2	yes	complemented
593	#3124	C₂×C₂₃	1	2	yes	complemented
594	#3121	C₂×C₂₃	1	2	yes	complemented
595	#3117	C₂×C₂₃	1	1	yes	characteristic, complemented
596	#3110	C₂×C₂₃	1	1	yes	characteristic, complemented
597	#3105	C₂×C₂₃	1	1	yes	characteristic, complemented
598	#3104	C₂×C₂₃	1	1	yes	characteristic, complemented
599	#2924	C₂×C₂₃	1	1	yes	characteristic, complemented
600	C₂²×C₂₃	—	2	1	no	—
601	C₂²×C₂₃	—	2	1	no	—
602	C₂²×C₂₃	—	2	1	no	—
603	C₂²×C₂₃	—	2	1	no	—
604	C₂²×C₂₃	—	2	1	no	—
605	C₂²×C₂₃	—	2	1	no	—
606	C₂²×C₂₃	—	2	1	no	—
607	C₂²×C₂₃	—	2	1	no	—
608	C₂²×C₂₃	—	4	2	no	—
609	C₂²×C₂₃	—	4	1	no	—
610	C₂²×C₂₃	—	4	1	no	—
611	C₂²×C₂₃	—	4	2	no	—
612	C₂²×C₂₃	—	4	1	no	—
613	C₂²×C₂₃	—	4	2	no	—
614	C₂²×C₂₃	—	8	2	no	—
615	C₂²×C₂₃	—	8	4	no	—
616	C₂²×C₂₃	#578	1	2	yes	—
617	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
618	C₄×C₂₃	—	2	1	no	—
619	C₄×C₂₃	—	2	1	no	—
620	C₄×C₂₃	—	2	1	no	—
621	C₄×C₂₃	—	2	1	no	—
622	C₄×C₂₃	—	2	1	no	—
623	C₄×C₂₃	—	2	1	no	—
624	C₄×C₂₃	—	2	1	no	—
625	C₄×C₂₃	—	2	1	no	—
626	C₄×C₂₃	—	2	1	no	—
627	C₄×C₂₃	—	2	1	no	—
628	C₄×C₂₃	—	2	1	no	—
629	C₄×C₂₃	—	4	2	no	—
630	C₄×C₂₃	—	4	2	no	—
631	C₄×C₂₃	—	4	1	no	—
632	C₄×C₂₃	—	4	1	no	—
633	C₄×C₂₃	—	4	1	no	—
634	C₄×C₂₃	—	4	1	no	—
635	C₄×C₂₃	—	4	2	no	—
636	C₄×C₂₃	—	4	1	no	—
637	C₄×C₂₃	—	4	1	no	—
638	C₄×C₂₃	—	4	1	no	—
639	C₄×C₂₃	#585	1	2	yes	—
640	#556	—	2	1	no	—
641	#554	—	2	1	no	—
642	#552	—	2	1	no	—
643	#552	—	2	1	no	—
644	#552	—	2	1	no	—
645	#552	—	2	1	no	—
646	#551	—	2	1	no	—
647	#551	—	2	1	no	—
648	#544	C₂²×C₂₃	1	1	yes	characteristic, complemented
649	#542	—	2	1	no	—
650	#542	—	2	1	no	—
651	#542	—	2	1	no	—
652	#542	—	2	1	no	—
653	#542	C₂²×C₂₃	1	2	yes	—
654	#542	C₂²×C₂₃	1	2	yes	—
655	#542	C₂²×C₂₃	1	2	yes	—
656	#542	C₂²×C₂₃	1	2	yes	—
657	#542	C₂²×C₂₃	1	1	yes	characteristic, complemented
658	#542	C₂²×C₂₃	1	1	yes	characteristic, complemented
659	#541	C₂²×C₂₃	1	1	yes	characteristic, complemented
660	#541	C₂²×C₂₃	1	1	yes	characteristic, complemented
661	#536	C₂²×C₂₃	1	1	yes	characteristic, complemented
662	#533	C₂²×C₂₃	1	1	yes	characteristic
663	#533	C₂²×C₂₃	1	1	yes	characteristic
664	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
665	#529	C₂²×C₂₃	1	1	yes	characteristic
666	#529	C₂²×C₂₃	1	1	yes	characteristic
667	C₂×#126	—	2	1	no	—
668	C₂×#124	—	2	1	no	—
669	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
670	#525	C₂²×C₂₃	1	1	yes	characteristic
671	C₂×#123	—	2	1	no	—
672	C₂×C₂²⋊Q₈	—	2	1	no	—
673	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
674	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
675	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
676	#520	C₂²×C₂₃	1	1	yes	characteristic, complemented
677	#519	C₂²×C₂₃	1	1	yes	characteristic, complemented
678	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
679	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
680	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
681	#501	C₂²×C₂₃	1	2	yes	complemented
682	#500	C₂²×C₂₃	1	2	yes	complemented
683	#497	C₂²×C₂₃	1	2	yes	complemented
684	#495	C₂²×C₂₃	1	2	yes	complemented
685	#489	C₂²×C₂₃	1	2	yes	complemented
686	#489	C₂²×C₂₃	1	2	yes	complemented
687	#488	C₂²×C₂₃	1	2	yes	complemented
688	#487	C₂²×C₂₃	1	2	yes	complemented
689	#485	C₂²×C₂₃	1	2	yes	complemented
690	#484	C₂²×C₂₃	1	1	yes	characteristic
691	#484	C₂²×C₂₃	1	1	yes	characteristic
692	#484	C₂²×C₂₃	1	1	yes	characteristic
693	#484	C₂²×C₂₃	1	1	yes	characteristic
694	#484	C₂²×C₂₃	1	1	yes	characteristic
695	#484	C₂²×C₂₃	1	1	yes	characteristic
696	#484	C₂²×C₂₃	1	2	yes	complemented
697	#482	C₂²×C₂₃	1	2	yes	—
698	#481	C₂²×C₂₃	1	1	yes	characteristic
699	#481	C₂²×C₂₃	1	1	yes	characteristic
700	#480	C₂²×C₂₃	1	2	yes	—
701	#479	C₂²×C₂₃	1	2	yes	complemented
702	#478	C₂²×C₂₃	1	2	yes	complemented
703	#477	C₂²×C₂₃	1	2	yes	complemented
704	#477	C₂²×C₂₃	1	2	yes	complemented
705	#477	C₂²×C₂₃	1	2	yes	complemented
706	#475	C₂²×C₂₃	1	2	yes	complemented
707	#474	C₂²×C₂₃	1	2	yes	complemented
708	#474	C₂²×C₂₃	1	2	yes	complemented
709	#470	C₂²×C₂₃	1	2	yes	complemented
710	#468	C₂²×C₂₃	1	2	yes	—
711	#468	C₂²×C₂₃	1	2	yes	—
712	#468	C₂²×C₂₃	1	2	yes	complemented
713	#467	C₂²×C₂₃	1	2	yes	complemented
714	#467	C₂²×C₂₃	1	2	yes	complemented
715	#466	C₂²×C₂₃	1	2	yes	—
716	#465	C₂²×C₂₃	1	2	yes	—
717	#464	C₂²×C₂₃	1	2	yes	complemented
718	#464	C₂²×C₂₃	1	2	yes	complemented
719	#464	C₂²×C₂₃	1	2	yes	complemented
720	#464	C₂²×C₂₃	1	2	yes	complemented
721	#463	C₂²×C₂₃	1	2	yes	complemented
722	#463	C₂²×C₂₃	1	2	yes	complemented
723	#462	C₂²×C₂₃	1	2	yes	complemented
724	#461	C₂²×C₂₃	1	2	yes	complemented
725	#452	C₂²×C₂₃	1	2	yes	complemented
726	#451	C₂²×C₂₃	1	1	yes	characteristic
727	#451	C₂²×C₂₃	1	1	yes	characteristic
728	#451	C₂²×C₂₃	1	1	yes	characteristic
729	#451	C₂²×C₂₃	1	2	yes	complemented
730	#450	C₂²×C₂₃	1	1	yes	characteristic
731	#450	C₂²×C₂₃	1	1	yes	characteristic
732	#450	C₂²×C₂₃	1	1	yes	characteristic
733	#449	C₂²×C₂₃	1	2	yes	—
734	#448	C₂²×C₂₃	1	1	yes	characteristic
735	#448	C₂²×C₂₃	1	2	yes	—
736	#447	C₂²×C₂₃	1	1	yes	characteristic
737	#441	C₂²×C₂₃	1	2	yes	complemented
738	#440	C₂²×C₂₃	1	2	yes	complemented
739	#440	C₂²×C₂₃	1	2	yes	complemented
740	#440	C₂²×C₂₃	1	2	yes	complemented
741	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
742	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
743	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
744	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
745	#433	C₂²×C₂₃	1	2	yes	complemented
746	#433	C₂²×C₂₃	1	2	yes	complemented
747	#432	C₂²×C₂₃	1	1	yes	characteristic
748	#432	C₂²×C₂₃	1	1	yes	characteristic
749	#431	C₂²×C₂₃	1	1	yes	characteristic
750	#431	C₂²×C₂₃	1	1	yes	characteristic
751	#424	C₂²×C₂₃	1	2	yes	complemented
752	#407	C₂²×C₂₃	1	1	yes	characteristic
753	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
754	#405	C₂²×C₂₃	1	2	yes	complemented
755	C₂×C₂₃	—	2	2	no	—
756	C₂×C₂₃	—	4	1	no	—
757	C₂×C₂₃	—	4	1	no	—
758	C₂×C₂₃	—	8	1	no	—
759	C₂×C₂₃	—	8	2	no	—
760	C₂×C₂₃	#3449	1	1	yes	characteristic
761	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
762	C₂×C₂₃	#3585	1	1	yes	characteristic
763	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
764	C₂²×Q₈	—	2	1	no	—
765	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
766	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
767	C₂²×D₄	—	2	1	no	—
768	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
769	C₂³×C₄	—	2	1	no	—
770	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
771	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
772	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
773	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
774	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
775	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
776	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
777	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
778	C₂×D₈	C₂³×C₂₃	1	2	yes	—
779	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
780	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
781	C₄⋊Q₈	—	2	1	no	—
782	C₄⋊Q₈	—	2	1	no	—
783	C₄⋊Q₈	—	2	1	no	—
784	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
785	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
786	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
787	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
788	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
789	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
790	#126	—	2	2	no	—
791	#126	—	2	2	no	—
792	#126	—	2	2	no	—
793	#126	—	2	2	no	—
794	#126	—	2	1	no	—
795	#126	—	2	1	no	—
796	#126	—	2	1	no	—
797	#126	—	2	1	no	—
798	#126	—	2	1	no	—
799	#126	—	2	1	no	—
800	#126	—	2	1	no	—
801	#126	—	2	1	no	—
802	#125	—	2	1	no	—
803	#125	—	2	1	no	—
804	#125	—	2	1	no	—
805	#125	—	2	1	no	—
806	#125	—	2	1	no	—
807	#125	—	2	1	no	—
808	#125	—	2	1	no	—
809	#125	C₂³×C₂₃	1	1	yes	characteristic
810	#125	C₂³×C₂₃	1	1	yes	characteristic
811	#124	—	2	2	no	—
812	#124	—	2	2	no	—
813	#124	—	2	2	no	—
814	#124	—	2	2	no	—
815	#124	—	2	1	no	—
816	#124	—	2	1	no	—
817	#124	—	2	1	no	—
818	#124	—	2	1	no	—
819	#124	C₂³×C₂₃	1	2	yes	—
820	#124	C₂³×C₂₃	1	2	yes	—
821	#124	C₂³×C₂₃	1	1	yes	characteristic
822	#124	C₂³×C₂₃	1	1	yes	characteristic
823	#123	—	2	1	no	—
824	#123	—	2	1	no	—
825	#123	—	2	1	no	—
826	#123	—	2	2	no	—
827	#123	—	2	2	no	—
828	#123	—	2	2	no	—
829	#123	—	2	2	no	—
830	#123	—	2	1	no	—
831	#123	—	2	1	no	—
832	#123	—	2	1	no	—
833	#123	—	2	1	no	—
834	C₂²⋊Q₈	—	2	1	no	—
835	C₂²⋊Q₈	—	2	1	no	—
836	C₂²⋊Q₈	—	2	1	no	—
837	C₂²⋊Q₈	—	2	1	no	—
838	C₂²⋊Q₈	—	2	1	no	—
839	C₂²⋊Q₈	—	2	1	no	—
840	C₂²⋊Q₈	—	2	2	no	—
841	C₂²⋊Q₈	—	2	2	no	—
842	C₂²⋊Q₈	—	2	2	no	—
843	C₂²⋊Q₈	—	2	2	no	—
844	C₂²⋊Q₈	—	2	1	no	—
845	C₂²⋊Q₈	—	2	1	no	—
846	C₂²⋊Q₈	—	2	1	no	—
847	C₂²⋊Q₈	—	2	1	no	—
848	C₂²⋊Q₈	—	2	1	no	—
849	C₂²⋊Q₈	—	2	1	no	—
850	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
851	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
852	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
853	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
854	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
855	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
856	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
857	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
858	#121	—	2	1	no	—
859	#121	—	2	1	no	—
860	#121	C₂³×C₂₃	1	2	yes	—
861	#121	C₂³×C₂₃	1	2	yes	—
862	#121	C₂³×C₂₃	1	1	yes	characteristic
863	#121	C₂³×C₂₃	1	1	yes	characteristic
864	#120	—	2	1	no	—
865	C₄×Q₈	—	2	1	no	—
866	C₄×Q₈	—	2	1	no	—
867	C₄×Q₈	—	2	1	no	—
868	C₄×Q₈	—	2	1	no	—
869	C₄×Q₈	—	2	1	no	—
870	C₄×Q₈	—	2	1	no	—
871	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
872	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
873	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
874	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
875	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
876	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
877	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
878	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
879	C₄×D₄	—	2	1	no	—
880	C₄×D₄	—	2	1	no	—
881	C₄×D₄	—	2	1	no	—
882	C₄×D₄	—	2	1	no	—
883	C₄×D₄	—	2	1	no	—
884	C₄×D₄	—	2	1	no	—
885	C₄×D₄	—	2	1	no	—
886	C₄×D₄	—	2	1	no	—
887	C₄×D₄	C₂³×C₂₃	1	2	yes	—
888	C₄×D₄	C₂³×C₂₃	1	2	yes	—
889	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
890	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
891	#117	—	2	1	no	—
892	#117	—	2	1	no	—
893	#117	—	2	1	no	—
894	#117	—	2	1	no	—
895	#117	—	2	1	no	—
896	#117	—	2	1	no	—
897	#117	—	2	1	no	—
898	#117	D₄×C₂₃	1	1	yes	characteristic
899	#117	D₄×C₂₃	1	1	yes	characteristic
900	#117	D₄×C₂₃	1	1	yes	characteristic
901	#117	D₄×C₂₃	1	1	yes	characteristic
902	#117	C₂³×C₂₃	1	1	yes	characteristic
903	#117	C₂³×C₂₃	1	1	yes	characteristic
904	#117	C₂³×C₂₃	1	1	yes	characteristic
905	#117	C₂³×C₂₃	1	1	yes	characteristic
906	#117	C₂³×C₂₃	1	1	yes	characteristic
907	C₂×C₄⋊C₄	—	2	1	no	—
908	C₂×C₄⋊C₄	—	2	1	no	—
909	C₂×C₄⋊C₄	—	2	1	no	—
910	C₂×C₄⋊C₄	—	2	1	no	—
911	C₂×C₄⋊C₄	—	2	1	no	—
912	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
913	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
914	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
915	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
916	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
917	C₂×C₂²⋊C₄	—	2	1	no	—
918	C₂×C₂²⋊C₄	—	2	1	no	—
919	C₂×C₂²⋊C₄	—	2	1	no	—
920	C₂×C₂²⋊C₄	—	2	1	no	—
921	C₂×C₂²⋊C₄	—	2	1	no	—
922	C₂×C₂²⋊C₄	—	2	1	no	—
923	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
924	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
925	C₂×C₄²	—	2	1	no	—
926	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
927	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
928	#107	C₂³×C₂₃	1	2	yes	—
929	#107	C₂³×C₂₃	1	2	yes	—
930	#107	C₂³×C₂₃	1	2	yes	—
931	#107	C₂³×C₂₃	1	2	yes	—
932	#107	C₂³×C₂₃	1	2	yes	—
933	#107	C₂³×C₂₃	1	2	yes	—
934	#106	C₂³×C₂₃	1	2	yes	—
935	#106	C₂³×C₂₃	1	2	yes	—
936	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
937	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
938	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
939	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
940	#103	C₂³×C₂₃	1	2	yes	—
941	#103	C₂³×C₂₃	1	2	yes	—
942	#103	C₂³×C₂₃	1	2	yes	—
943	#103	C₂³×C₂₃	1	2	yes	—
944	#103	C₂³×C₂₃	1	2	yes	—
945	#103	C₂³×C₂₃	1	2	yes	—
946	#103	C₂³×C₂₃	1	2	yes	—
947	#103	C₂³×C₂₃	1	2	yes	—
948	#103	C₂³×C₂₃	1	2	yes	—
949	#103	C₂³×C₂₃	1	2	yes	—
950	#102	C₂³×C₂₃	1	2	yes	—
951	#102	C₂³×C₂₃	1	2	yes	—
952	#102	C₂³×C₂₃	1	2	yes	—
953	#102	C₂³×C₂₃	1	2	yes	—
954	#102	C₂³×C₂₃	1	2	yes	—
955	#102	C₂³×C₂₃	1	2	yes	—
956	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
957	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
958	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
959	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
960	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
961	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
962	#97	C₂³×C₂₃	1	2	yes	—
963	#97	C₂³×C₂₃	1	2	yes	—
964	C₄×C₈	C₂³×C₂₃	1	2	yes	—
965	C₄×C₈	C₂³×C₂₃	1	2	yes	—
966	C₂₃	#60981	1	1	yes	characteristic, direct product factor, Sylow
967	C₂⁴	—	2	1	no	—
968	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
969	#41	—	4	2	no	—
970	C₂×Q₈	—	2	1	no	—
971	C₂×Q₈	—	2	1	no	—
972	C₂×Q₈	—	2	1	no	—
973	C₂×Q₈	—	2	1	no	—
974	C₂×Q₈	—	2	2	no	—
975	C₂×Q₈	—	2	2	no	—
976	C₂×Q₈	—	4	2	no	—
977	C₂×Q₈	—	4	2	no	—
978	C₂×Q₈	—	8	2	no	—
979	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
980	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
981	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
982	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
983	C₂×D₄	—	2	1	no	—
984	C₂×D₄	—	2	1	no	—
985	C₂×D₄	—	2	1	no	—
986	C₂×D₄	—	2	2	no	—
987	C₂×D₄	—	2	2	no	—
988	C₂×D₄	—	2	1	no	—
989	C₂×D₄	—	4	2	no	—
990	C₂×D₄	—	8	2	no	—
991	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
992	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
993	C₂²×C₄	—	2	1	no	—
994	C₂²×C₄	—	2	1	no	—
995	C₂²×C₄	—	2	1	no	—
996	C₂²×C₄	—	2	1	no	—
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	1	no	—
999	C₂²×C₄	—	2	1	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	2	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	4	2	no	—
1004	C₂²×C₄	—	8	2	no	—
1005	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1006	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1007	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1008	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1009	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1010	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1011	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1012	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1013	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1014	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1015	Q₁₆	—	4	2	no	—
1016	Q₁₆	—	4	2	no	—
1017	Q₁₆	—	4	2	no	—
1018	SD₁₆	—	4	2	no	—
1019	SD₁₆	—	4	2	no	—
1020	SD₁₆	—	4	2	no	—
1021	SD₁₆	—	4	2	no	—
1022	D₈	—	4	2	no	—
1023	M₁₆	—	4	2	no	—
1024	C₂×C₈	—	4	2	no	—
1025	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1026	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1027	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1028	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	2	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	1	no	—
1058	C₄⋊C₄	—	2	1	no	—
1059	C₄⋊C₄	—	2	1	no	—
1060	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1061	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1062	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1063	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1064	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1065	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1066	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1067	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1068	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1069	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1070	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1071	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1072	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1073	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	1	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	1	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	2	no	—
1088	C₂²⋊C₄	—	2	2	no	—
1089	C₂²⋊C₄	—	2	2	no	—
1090	C₂²⋊C₄	—	2	2	no	—
1091	C₂²⋊C₄	—	2	1	no	—
1092	C₂²⋊C₄	—	2	1	no	—
1093	C₂²⋊C₄	—	2	1	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	—	2	1	no	—
1099	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1100	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1101	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1102	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1103	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1104	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1105	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1106	C₂²⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1107	C₄²	—	2	2	no	—
1108	C₄²	—	2	2	no	—
1109	C₄²	—	2	1	no	—
1110	C₄²	—	2	1	no	—
1111	C₄²	—	2	1	no	—
1112	C₄²	—	2	1	no	—
1113	C₄²	—	2	1	no	—
1114	C₄²	—	2	1	no	—
1115	C₄²	—	2	1	no	—
1116	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1117	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1118	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1119	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1120	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1121	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1122	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1123	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1124	C₂³	—	2	2	no	—
1125	C₂³	—	2	1	no	—
1126	C₂³	—	2	2	no	—
1127	C₂³	—	4	1	no	—
1128	C₂³	—	4	1	no	—
1129	C₂³	—	4	2	no	—
1130	C₂³	—	4	2	no	—
1131	C₂³	—	4	2	no	—
1132	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1133	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1134	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1135	Q₈	—	2	2	no	—
1136	Q₈	—	2	2	no	—
1137	Q₈	—	2	2	no	—
1138	Q₈	—	2	2	no	—
1139	Q₈	—	2	2	no	—
1140	Q₈	—	4	2	no	—
1141	Q₈	—	4	2	no	—
1142	Q₈	—	8	2	no	—
1143	Q₈	—	8	2	no	—
1144	Q₈	—	8	1	no	—
1145	Q₈	—	8	1	no	—
1146	D₄	—	2	2	no	—
1147	D₄	—	2	2	no	—
1148	D₄	—	2	2	no	—
1149	D₄	—	4	2	no	—
1150	D₄	—	4	2	no	—
1151	D₄	—	4	2	no	—
1152	D₄	—	8	2	no	—
1153	D₄	—	8	2	no	—
1154	D₄	—	8	1	no	—
1155	C₂×C₄	—	2	2	no	—
1156	C₂×C₄	—	2	2	no	—
1157	C₂×C₄	—	2	2	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	2	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	4	1	no	—
1171	C₂×C₄	—	4	1	no	—
1172	C₂×C₄	—	4	1	no	—
1173	C₂×C₄	—	4	1	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	4	2	no	—
1176	C₂×C₄	—	4	2	no	—
1177	C₂×C₄	—	4	2	no	—
1178	C₂×C₄	—	4	2	no	—
1179	C₂×C₄	—	4	2	no	—
1180	C₂×C₄	—	8	2	no	—
1181	C₂×C₄	—	8	2	no	—
1182	C₂×C₄	—	8	1	no	—
1183	C₂×C₄	—	8	1	no	—
1184	C₂×C₄	—	8	1	no	—
1185	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1186	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1187	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1188	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1189	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1190	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1191	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1192	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1193	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1194	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1195	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1196	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1197	C₈	—	2	2	no	—
1198	C₈	—	2	2	no	—
1199	C₈	—	2	2	no	—
1200	C₈	—	2	2	no	—
1201	C₂²	—	2	1	no	—
1202	C₂²	—	2	1	no	—
1203	C₂²	—	2	1	no	—
1204	C₂²	—	2	1	no	—
1205	C₂²	—	2	1	no	—
1206	C₂²	—	2	1	no	—
1207	C₂²	—	2	1	no	—
1208	C₂²	—	2	1	no	—
1209	C₂²	—	4	1	no	—
1210	C₂²	—	4	2	no	—
1211	C₂²	—	4	1	no	—
1212	C₂²	—	4	2	no	—
1213	C₂²	—	4	2	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	8	2	no	—
1216	C₂²	—	8	4	no	—
1217	C₂²	C₂₃×#578	1	2	yes	—
1218	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1219	C₄	—	2	1	no	—
1220	C₄	—	2	1	no	—
1221	C₄	—	2	1	no	—
1222	C₄	—	2	1	no	—
1223	C₄	—	2	1	no	—
1224	C₄	—	2	1	no	—
1225	C₄	—	2	1	no	—
1226	C₄	—	2	1	no	—
1227	C₄	—	2	1	no	—
1228	C₄	—	2	1	no	—
1229	C₄	—	2	1	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	2	no	—
1232	C₄	—	4	1	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	1	no	—
1235	C₄	—	4	2	no	—
1236	C₄	—	4	2	no	—
1237	C₄	—	4	1	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	4	1	no	—
1240	C₄	C₂₃×#585	1	2	yes	—
1241	C₂	—	2	2	no	—
1242	C₂	—	4	1	no	—
1243	C₂	—	4	1	no	—
1244	C₂	—	8	2	no	—
1245	C₂	—	8	1	no	—
1246	C₂	C₂₃×#3449	1	1	yes	characteristic
1247	C₂	C₂×C₂₃×#578	1	1	yes	characteristic
1248	C₂	C₂₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3188	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3495	C₂	semidirect
2. C₂×C₂₃×#542	C₂	semidirect
3. C₂₃×#3262	C₂	semidirect
4. C₂₃×#3258	C₂	semidirect
5. C₂₃×#3243	C₂	semidirect
6. C₂₃×#3239	C₂	semidirect
7. C₂₃×#3230	C₂	semidirect
8. C₂₃×#3225	C₂	semidirect
9. C₂₃×#3215	C₂	semidirect
10. C₂₃×#3211	C₂	semidirect
11. C₂₃×#3196	C₂	semidirect
12. C₂₃×#3193	C₂	semidirect
13. C₂₃×#3189	C₂	semidirect
15. C₂₃×#3178	C₂	semidirect
16. C₂₃×#3175	C₂	semidirect
17. C₂₃×#3124	C₂	semidirect
18. C₂₃×#3121	C₂	semidirect
19. C₂₃×#3117	C₂	semidirect
20. C₂₃×#3110	C₂	semidirect
21. C₂₃×#3105	C₂	semidirect
22. C₂₃×#3104	C₂	semidirect
23. C₂₃×#2924	C₂	semidirect
32. C₂₃×#544	C₂²	semidirect
41. C₂₃×#542	C₂²	semidirect
42. C₂₃×#542	C₂²	semidirect
43. C₂₃×#541	C₂²	semidirect
44. C₂₃×#541	C₂²	semidirect
45. C₂₃×#536	C₂²	semidirect
60. C₂₃×#520	C₂²	semidirect
61. C₂₃×#519	C₂²	semidirect
65. C₂₃×#501	C₂²	semidirect
66. C₂₃×#500	C₂²	semidirect
67. C₂₃×#497	C₂²	semidirect
68. C₂₃×#495	C₂²	semidirect
69. C₂₃×#489	C₂²	semidirect
70. C₂₃×#489	C₂²	semidirect
71. C₂₃×#488	C₂²	semidirect
72. C₂₃×#487	C₂²	semidirect
73. C₂₃×#485	C₂²	semidirect
80. C₂₃×#484	C₂²	semidirect
85. C₂₃×#479	C₂²	semidirect
86. C₂₃×#478	C₂²	semidirect
87. C₂₃×#477	C₂²	semidirect
88. C₂₃×#477	C₂²	semidirect
89. C₂₃×#477	C₂²	semidirect
90. C₂₃×#475	C₂²	semidirect
91. C₂₃×#474	C₂²	semidirect
92. C₂₃×#474	C₂²	semidirect
93. C₂₃×#470	C₂²	semidirect
96. C₂₃×#468	C₂²	semidirect
97. C₂₃×#467	C₂²	semidirect
98. C₂₃×#467	C₂²	semidirect
101. C₂₃×#464	C₂²	semidirect
102. C₂₃×#464	C₂²	semidirect
103. C₂₃×#464	C₂²	semidirect
104. C₂₃×#464	C₂²	semidirect
105. C₂₃×#463	C₂²	semidirect
106. C₂₃×#463	C₂²	semidirect
107. C₂₃×#462	C₂²	semidirect
108. C₂₃×#461	C₂²	semidirect
109. C₂₃×#452	C₂²	semidirect
113. C₂₃×#451	C₂²	semidirect
121. C₂₃×#441	C₂²	semidirect
122. C₂₃×#440	C₂²	semidirect
123. C₂₃×#440	C₂²	semidirect
124. C₂₃×#440	C₂²	semidirect
125. C₄×Q₁₆×C₂₃	C₂²	semidirect
126. C₄×Q₁₆×C₂₃	C₂²	semidirect
127. C₄×SD₁₆×C₂₃	C₂²	semidirect
128. C₄×D₈×C₂₃	C₂²	semidirect
129. C₂₃×#433	C₂²	semidirect
130. C₂₃×#433	C₂²	semidirect
135. C₂₃×#424	C₂²	semidirect
138. C₂₃×#405	C₂²	semidirect
499. #60981	C₂₃	direct (N × H)
577. #3495	C₂×C₂₃	semidirect
578. C₂×#542	C₂×C₂₃	semidirect
579. #3262	C₂×C₂₃	semidirect
580. #3258	C₂×C₂₃	semidirect
581. #3243	C₂×C₂₃	semidirect
582. #3239	C₂×C₂₃	semidirect
583. #3230	C₂×C₂₃	semidirect
584. #3225	C₂×C₂₃	semidirect
585. #3215	C₂×C₂₃	semidirect
586. #3211	C₂×C₂₃	semidirect
587. #3196	C₂×C₂₃	semidirect
588. #3193	C₂×C₂₃	semidirect
589. #3189	C₂×C₂₃	semidirect
591. #3178	C₂×C₂₃	semidirect
592. #3175	C₂×C₂₃	semidirect
593. #3124	C₂×C₂₃	semidirect
594. #3121	C₂×C₂₃	semidirect
595. #3117	C₂×C₂₃	semidirect
596. #3110	C₂×C₂₃	semidirect
597. #3105	C₂×C₂₃	semidirect
598. #3104	C₂×C₂₃	semidirect
599. #2924	C₂×C₂₃	semidirect
648. #544	C₂²×C₂₃	semidirect
657. #542	C₂²×C₂₃	semidirect
658. #542	C₂²×C₂₃	semidirect
659. #541	C₂²×C₂₃	semidirect
660. #541	C₂²×C₂₃	semidirect
661. #536	C₂²×C₂₃	semidirect
676. #520	C₂²×C₂₃	semidirect
677. #519	C₂²×C₂₃	semidirect
681. #501	C₂²×C₂₃	semidirect
682. #500	C₂²×C₂₃	semidirect
683. #497	C₂²×C₂₃	semidirect
684. #495	C₂²×C₂₃	semidirect
685. #489	C₂²×C₂₃	semidirect
686. #489	C₂²×C₂₃	semidirect
687. #488	C₂²×C₂₃	semidirect
688. #487	C₂²×C₂₃	semidirect
689. #485	C₂²×C₂₃	semidirect
696. #484	C₂²×C₂₃	semidirect
701. #479	C₂²×C₂₃	semidirect
702. #478	C₂²×C₂₃	semidirect
703. #477	C₂²×C₂₃	semidirect
704. #477	C₂²×C₂₃	semidirect
705. #477	C₂²×C₂₃	semidirect
706. #475	C₂²×C₂₃	semidirect
707. #474	C₂²×C₂₃	semidirect
708. #474	C₂²×C₂₃	semidirect
709. #470	C₂²×C₂₃	semidirect
712. #468	C₂²×C₂₃	semidirect
713. #467	C₂²×C₂₃	semidirect
714. #467	C₂²×C₂₃	semidirect
717. #464	C₂²×C₂₃	semidirect
718. #464	C₂²×C₂₃	semidirect
719. #464	C₂²×C₂₃	semidirect
720. #464	C₂²×C₂₃	semidirect
721. #463	C₂²×C₂₃	semidirect
722. #463	C₂²×C₂₃	semidirect
723. #462	C₂²×C₂₃	semidirect
724. #461	C₂²×C₂₃	semidirect
725. #452	C₂²×C₂₃	semidirect
729. #451	C₂²×C₂₃	semidirect
737. #441	C₂²×C₂₃	semidirect
738. #440	C₂²×C₂₃	semidirect
739. #440	C₂²×C₂₃	semidirect
740. #440	C₂²×C₂₃	semidirect
741. C₄×Q₁₆	C₂²×C₂₃	semidirect
742. C₄×Q₁₆	C₂²×C₂₃	semidirect
743. C₄×SD₁₆	C₂²×C₂₃	semidirect
744. C₄×D₈	C₂²×C₂₃	semidirect
745. #433	C₂²×C₂₃	semidirect
746. #433	C₂²×C₂₃	semidirect
751. #424	C₂²×C₂₃	semidirect
754. #405	C₂²×C₂₃	semidirect
966. C₂₃	#60981	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3495	2
C₂×C₂₃×#542	2
C₂₃×#3262	2
C₂₃×#3258	2
C₂₃×#3243	2
C₂₃×#3239	2
C₂₃×#3230	2
C₂₃×#3225	2
C₂₃×#3215	2
C₂₃×#3211	2
C₂₃×#3196	2
C₂₃×#3193	2
C₂₃×#3189	2
C₂₃×#3188	2
C₂₃×#3178	2
C₂₃×#3175	2
C₂₃×#3124	2
C₂₃×#3121	2
C₂₃×#3117	2
C₂₃×#3110	2
C₂₃×#3105	2
C₂₃×#3104	2
C₂₃×#2924	2
#60981	23

Subgroups — C23×#60981 #19208607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60981 #19208607