Subgroups — C₂₃×#60595 #19208221

Order 5888.

2014 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₂₃×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3125	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3124	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3121	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3121	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3117	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3111	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3108	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3102	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3097	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3096	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3011	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3010	C₂	1	1	yes	maximal, characteristic
19	C₂₃×#2950	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2949	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2947	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2946	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
29	C₂₃×#559	—	2	1	no	—
30	C₂₃×#559	—	2	1	no	—
31	C₂₃×#556	—	2	1	no	—
32	C₂₃×#556	—	2	1	no	—
33	C₂₃×#551	—	2	2	no	—
34	C₂₃×#551	—	2	2	no	—
35	C₂₃×#542	C₂²	1	2	yes	—
36	C₂₃×#542	C₂²	1	2	yes	—
37	C₂₃×#536	C₂²	1	1	yes	characteristic
38	C₂₃×#535	C₂²	1	1	yes	characteristic
39	C₂₃×#533	C₂²	1	1	yes	characteristic
40	C₂₃×#529	C₂²	1	2	yes	—
41	C₂₃×#529	C₂²	1	2	yes	—
42	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
43	C₂₃×#520	—	2	2	no	—
44	C₂₃×#520	—	2	1	no	—
45	C₂₃×#520	C₂²	1	1	yes	characteristic
46	C₂₃×#520	C₂²	1	1	yes	characteristic
47	C₂₃×#520	C₂²	1	2	yes	complemented
48	C₂₃×#519	—	2	1	no	—
49	C₂₃×#519	C₂²	1	1	yes	characteristic
50	C₂₃×#519	C₂²	1	1	yes	characteristic
51	C₂₃×#519	C₂²	1	2	yes	complemented
52	C₂₃×#518	C₂²	1	1	yes	characteristic
53	C₄×#41×C₂₃	—	2	2	no	—
54	C₄×#41×C₂₃	—	2	1	no	—
55	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
56	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
57	C₄×#41×C₂₃	C₂²	1	2	yes	complemented
58	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
59	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
60	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
61	C₂₃×#485	C₂²	1	2	yes	complemented
62	C₂₃×#485	C₂²	1	2	yes	complemented
63	C₂₃×#484	C₂²	1	2	yes	complemented
64	C₂₃×#483	C₂²	1	2	yes	complemented
65	C₂₃×#482	C₂²	1	2	yes	—
66	C₂₃×#482	C₂²	1	2	yes	—
67	C₂₃×#481	C₂²	1	2	yes	—
68	C₂₃×#480	C₂²	1	2	yes	—
69	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
70	C₂₃×#479	C₂²	1	1	yes	characteristic, complemented
71	C₂₃×#479	C₂²	1	2	yes	complemented
72	C₂₃×#479	C₂²	1	2	yes	complemented
73	C₂₃×#478	C₂²	1	1	yes	characteristic, complemented
74	C₂₃×#478	C₂²	1	1	yes	characteristic, complemented
75	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
76	C₂₃×#477	C₂²	1	2	yes	complemented
77	C₂₃×#476	C₂²	1	1	yes	characteristic, complemented
78	C₂₃×#475	C₂²	1	1	yes	characteristic, complemented
79	C₂₃×#475	C₂²	1	2	yes	complemented
80	C₂₃×#474	C₂²	1	1	yes	characteristic, complemented
81	C₂₃×#464	C₂²	1	2	yes	—
82	C₂₃×#464	C₂²	1	2	yes	—
83	C₂₃×#464	C₂²	1	2	yes	—
84	C₂₃×#464	C₂²	1	2	yes	—
85	C₂₃×#464	C₂²	1	2	yes	—
86	C₂₃×#464	C₂²	1	2	yes	—
87	C₂₃×#463	C₂²	1	2	yes	—
88	C₂₃×#463	C₂²	1	2	yes	—
89	C₂₃×#452	C₂²	1	2	yes	complemented
90	C₂₃×#452	C₂²	1	2	yes	complemented
91	C₂₃×#451	C₂²	1	2	yes	complemented
92	C₂₃×#451	C₂²	1	2	yes	complemented
93	C₂₃×#449	C₂²	1	2	yes	—
94	C₂₃×#449	C₂²	1	2	yes	—
95	C₂₃×#448	C₂²	1	2	yes	—
96	C₂₃×#448	C₂²	1	2	yes	—
97	C₂₃×#442	C₂²	1	2	yes	—
98	C₂₃×#441	C₂²	1	2	yes	complemented
99	C₂₃×#441	C₂²	1	2	yes	complemented
100	C₂₃×#441	C₂²	1	2	yes	complemented
101	C₂₃×#440	C₂²	1	2	yes	—
102	C₂₃×#440	C₂²	1	2	yes	—
103	C₂₃×#440	C₂²	1	2	yes	—
104	C₂₃×#440	C₂²	1	2	yes	complemented
105	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
106	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
107	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
108	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
109	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
110	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
111	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
112	C₄×D₈×C₂₃	C₂²	1	2	yes	—
113	C₂₃×#433	C₂²	1	2	yes	complemented
114	C₂₃×#433	C₂²	1	2	yes	complemented
115	C₂₃×#432	C₂²	1	2	yes	complemented
116	C₂₃×#431	C₂²	1	2	yes	complemented
117	C₂₃×#428	C₂²	1	1	yes	characteristic
118	C₂₃×#428	C₂²	1	1	yes	characteristic
119	C₂₃×#427	C₂²	1	1	yes	characteristic
120	C₂₃×#427	C₂²	1	1	yes	characteristic
121	C₂₃×#423	C₂²	1	1	yes	characteristic
122	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
123	C₂₃×#419	C₂²	1	1	yes	characteristic
124	C₂₃×#419	C₂²	1	1	yes	characteristic
125	C₂₃×#419	C₂²	1	1	yes	characteristic
126	C₂₃×#418	C₂²	1	1	yes	characteristic
127	C₂₃×#416	C₂²	1	1	yes	characteristic
128	C₂₃×#416	C₂²	1	1	yes	characteristic
129	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
130	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
131	C₂₃×#408	C₂²	1	1	yes	characteristic
132	C₂₃×#408	C₂²	1	1	yes	characteristic
133	C₂₃×#405	C₂²	1	1	yes	characteristic
134	C₂₃×#405	C₂²	1	1	yes	characteristic
135	C₂₃×2₋¹⁺⁴	—	2	4	no	—
136	C₂₃×2₋¹⁺⁴	—	2	4	no	—
137	C₂×#41×C₂₃	—	2	2	no	—
138	C₂×#41×C₂₃	—	2	1	no	—
139	C₂×#41×C₂₃	C₂³	1	2	yes	—
140	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
141	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₂₃	—	2	1	no	—
143	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
144	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
145	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
146	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
147	C₂₃×#137	—	2	4	no	—
148	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
149	C₂×Q₁₆×C₂₃	—	2	4	no	—
150	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
151	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
152	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₂₃	—	2	4	no	—
154	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
158	C₂×D₈×C₂₃	C₂³	1	2	yes	—
159	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
160	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
161	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
162	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
163	C₂₃×C₄⋊Q₈	—	2	1	no	—
164	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₂₃×#127	—	2	1	no	—
167	C₂₃×#126	—	2	2	no	—
168	C₂₃×#126	—	2	2	no	—
169	C₂₃×#126	—	2	2	no	—
170	C₂₃×#126	—	2	2	no	—
171	C₂₃×#125	C₂³	1	1	yes	characteristic
172	C₂₃×#125	C₂³	1	1	yes	characteristic
173	C₂₃×#124	—	2	1	no	—
174	C₂₃×#124	—	2	1	no	—
175	C₂₃×#124	—	2	2	no	—
176	C₂₃×#124	—	2	2	no	—
177	C₂₃×#124	—	2	1	no	—
178	C₂₃×#124	—	2	1	no	—
179	C₂₃×#124	C₂³	1	2	yes	—
180	C₂₃×#124	C₂³	1	2	yes	—
181	C₂₃×#123	—	2	2	no	—
182	C₂₃×#123	—	2	2	no	—
183	C₂₃×#123	—	2	2	no	—
184	C₂₃×#123	—	2	2	no	—
185	C₂₃×#123	—	2	2	no	—
186	C₂₃×C₂²⋊Q₈	—	2	1	no	—
187	C₂₃×C₂²⋊Q₈	—	2	1	no	—
188	C₂₃×C₂²⋊Q₈	—	2	2	no	—
189	C₂₃×C₂²⋊Q₈	—	2	2	no	—
190	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
191	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
192	C₂₃×#121	C₂³	1	2	yes	—
193	C₂₃×#121	C₂³	1	2	yes	—
194	C₂₃×#120	—	2	2	no	—
195	C₄×Q₈×C₂₃	—	2	1	no	—
196	C₄×Q₈×C₂₃	—	2	1	no	—
197	C₄×Q₈×C₂₃	—	2	1	no	—
198	C₄×Q₈×C₂₃	—	2	1	no	—
199	C₄×Q₈×C₂₃	—	2	2	no	—
200	C₄×Q₈×C₂₃	—	2	1	no	—
201	C₄×Q₈×C₂₃	—	2	2	no	—
202	C₄×Q₈×C₂₃	—	2	1	no	—
203	C₄×Q₈×C₂₃	—	2	1	no	—
204	C₄×Q₈×C₂₃	—	2	1	no	—
205	C₄×Q₈×C₂₃	—	2	2	no	—
206	C₄×Q₈×C₂₃	—	2	1	no	—
207	C₄×Q₈×C₂₃	—	2	2	no	—
208	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
209	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
210	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
211	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
212	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
213	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
214	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
215	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
216	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
218	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₂₃	—	2	2	no	—
220	C₄×D₄×C₂₃	—	2	1	no	—
221	C₄×D₄×C₂₃	—	2	2	no	—
222	C₄×D₄×C₂₃	—	2	2	no	—
223	C₄×D₄×C₂₃	—	2	1	no	—
224	C₄×D₄×C₂₃	—	2	2	no	—
225	C₄×D₄×C₂₃	—	2	1	no	—
226	C₄×D₄×C₂₃	—	2	2	no	—
227	C₄×D₄×C₂₃	—	2	1	no	—
228	C₄×D₄×C₂₃	—	2	1	no	—
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	D₄	1	2	yes	—
233	C₄×D₄×C₂₃	D₄	1	2	yes	—
234	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
235	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
236	C₄×D₄×C₂₃	C₂³	1	2	yes	—
237	C₄×D₄×C₂₃	C₂³	1	2	yes	—
238	C₄×D₄×C₂₃	C₂³	1	2	yes	—
239	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
241	C₂₃×#117	—	2	1	no	—
242	C₂₃×#117	—	2	2	no	—
243	C₂₃×#117	—	2	2	no	—
244	C₂₃×#117	—	2	2	no	—
245	C₂₃×#117	—	2	2	no	—
246	C₂₃×#117	—	2	2	no	—
247	C₂₃×#117	—	2	2	no	—
248	C₂₃×#117	—	2	2	no	—
249	C₂₃×#117	—	2	1	no	—
250	C₂₃×#117	—	2	2	no	—
251	C₂₃×#117	C₂³	1	1	yes	characteristic
252	C₂₃×#117	C₂³	1	1	yes	characteristic
253	C₂₃×#117	C₂³	1	1	yes	characteristic
254	C₂₃×#117	C₂³	1	2	yes	—
255	C₂₃×#117	C₂³	1	1	yes	characteristic
256	C₂₃×#117	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
258	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
259	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
260	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
261	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
263	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
265	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
266	C₂×C₄²×C₂₃	—	2	1	no	—
267	C₂×C₄²×C₂₃	—	2	2	no	—
268	C₂×C₄²×C₂₃	—	2	1	no	—
269	C₂×C₄²×C₂₃	—	2	2	no	—
270	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
271	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
272	C₂₃×#107	C₂³	1	1	yes	characteristic
273	C₂₃×#107	C₂³	1	1	yes	characteristic
274	C₂₃×#107	C₂³	1	1	yes	characteristic
275	C₂₃×#107	C₂³	1	1	yes	characteristic
276	C₂₃×#107	C₂³	1	2	yes	—
277	C₂₃×#107	C₂³	1	2	yes	—
278	C₂₃×#106	C₂³	1	1	yes	characteristic
279	C₂₃×#106	C₂³	1	1	yes	characteristic
280	C₂₃×#106	C₂³	1	1	yes	characteristic
281	C₂₃×#106	C₂³	1	1	yes	characteristic
282	C₂₃×#106	C₂³	1	2	yes	—
283	C₂₃×#106	C₂³	1	2	yes	—
284	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
289	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
290	C₂₃×#103	C₂³	1	2	yes	—
291	C₂₃×#103	C₂³	1	2	yes	—
292	C₂₃×#103	C₂³	1	1	yes	characteristic
293	C₂₃×#103	C₂³	1	1	yes	characteristic
294	C₂₃×#103	C₂³	1	1	yes	characteristic
295	C₂₃×#103	C₂³	1	1	yes	characteristic
296	C₂₃×#103	C₂³	1	2	yes	—
297	C₂₃×#103	C₂³	1	2	yes	—
298	C₂₃×#103	C₂³	1	2	yes	—
299	C₂₃×#103	C₂³	1	2	yes	—
300	C₂₃×#103	C₂³	1	2	yes	—
301	C₂₃×#103	C₂³	1	2	yes	—
302	C₂₃×#102	C₂³	1	2	yes	—
303	C₂₃×#102	C₂³	1	2	yes	—
304	C₂₃×#102	C₂³	1	1	yes	characteristic
305	C₂₃×#102	C₂³	1	1	yes	characteristic
306	C₂₃×#102	C₂³	1	1	yes	characteristic
307	C₂₃×#102	C₂³	1	1	yes	characteristic
308	C₂₃×#102	C₂³	1	2	yes	—
309	C₂₃×#102	C₂³	1	2	yes	—
310	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
314	C₂₃×#97	C₂³	1	2	yes	—
315	C₂₃×#97	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	16	no	—
320	#41×C₂₃	—	2	8	no	—
321	#41×C₂₃	—	2	4	no	—
322	#41×C₂₃	—	2	4	no	—
323	#41×C₂₃	—	2	2	no	—
324	#41×C₂₃	—	2	2	no	—
325	#41×C₂₃	—	2	2	no	—
326	#41×C₂₃	#41	1	4	yes	—
327	C₂×Q₈×C₂₃	—	2	8	no	—
328	C₂×Q₈×C₂₃	—	2	4	no	—
329	C₂×Q₈×C₂₃	—	2	4	no	—
330	C₂×Q₈×C₂₃	—	2	2	no	—
331	C₂×Q₈×C₂₃	—	2	1	no	—
332	C₂×Q₈×C₂₃	—	2	1	no	—
333	C₂×Q₈×C₂₃	—	2	1	no	—
334	C₂×Q₈×C₂₃	—	2	1	no	—
335	C₂×Q₈×C₂₃	—	2	2	no	—
336	C₂×Q₈×C₂₃	—	2	2	no	—
337	C₂×Q₈×C₂₃	—	2	2	no	—
338	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
339	C₂×Q₈×C₂₃	#41	1	4	yes	—
340	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
341	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
342	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
343	C₂×D₄×C₂₃	—	2	2	no	—
344	C₂×D₄×C₂₃	—	2	1	no	—
345	C₂×D₄×C₂₃	—	2	2	no	—
346	C₂×D₄×C₂₃	—	2	2	no	—
347	C₂×D₄×C₂₃	—	2	1	no	—
348	C₂×D₄×C₂₃	—	2	2	no	—
349	C₂×D₄×C₂₃	—	2	2	no	—
350	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
352	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
353	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₂₃	—	2	2	no	—
355	C₂²×C₄×C₂₃	—	2	1	no	—
356	C₂²×C₄×C₂₃	—	2	2	no	—
357	C₂²×C₄×C₂₃	—	2	1	no	—
358	C₂²×C₄×C₂₃	—	2	1	no	—
359	C₂²×C₄×C₂₃	—	2	2	no	—
360	C₂²×C₄×C₂₃	—	2	1	no	—
361	C₂²×C₄×C₂₃	—	2	1	no	—
362	C₂²×C₄×C₂₃	—	2	2	no	—
363	C₂²×C₄×C₂₃	—	2	1	no	—
364	C₂²×C₄×C₂₃	—	2	2	no	—
365	C₂²×C₄×C₂₃	—	2	2	no	—
366	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
368	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
370	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
371	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
372	Q₁₆×C₂₃	—	2	4	no	—
373	Q₁₆×C₂₃	—	2	4	no	—
374	Q₁₆×C₂₃	—	2	4	no	—
375	SD₁₆×C₂₃	—	2	4	no	—
376	SD₁₆×C₂₃	—	2	4	no	—
377	SD₁₆×C₂₃	—	2	4	no	—
378	SD₁₆×C₂₃	—	2	4	no	—
379	D₈×C₂₃	—	2	4	no	—
380	M₁₆×C₂₃	—	2	2	no	—
381	M₁₆×C₂₃	—	2	2	no	—
382	C₂×C₈×C₂₃	—	2	2	no	—
383	C₂×C₈×C₂₃	—	2	2	no	—
384	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
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	C₄⋊C₄×C₂₃	—	2	2	no	—
391	C₄⋊C₄×C₂₃	—	2	2	no	—
392	C₄⋊C₄×C₂₃	—	2	2	no	—
393	C₄⋊C₄×C₂₃	—	2	2	no	—
394	C₄⋊C₄×C₂₃	—	2	1	no	—
395	C₄⋊C₄×C₂₃	—	2	2	no	—
396	C₄⋊C₄×C₂₃	—	2	1	no	—
397	C₄⋊C₄×C₂₃	—	2	2	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	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	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
412	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
414	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
420	C₂²⋊C₄×C₂₃	—	2	1	no	—
421	C₂²⋊C₄×C₂₃	—	2	2	no	—
422	C₂²⋊C₄×C₂₃	—	2	1	no	—
423	C₂²⋊C₄×C₂₃	—	2	1	no	—
424	C₂²⋊C₄×C₂₃	—	2	2	no	—
425	C₂²⋊C₄×C₂₃	—	2	2	no	—
426	C₂²⋊C₄×C₂₃	—	2	2	no	—
427	C₂²⋊C₄×C₂₃	—	2	2	no	—
428	C₂²⋊C₄×C₂₃	—	2	2	no	—
429	C₂²⋊C₄×C₂₃	—	2	2	no	—
430	C₂²⋊C₄×C₂₃	—	2	2	no	—
431	C₂²⋊C₄×C₂₃	—	2	2	no	—
432	C₂²⋊C₄×C₂₃	—	2	1	no	—
433	C₂²⋊C₄×C₂₃	—	2	2	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	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
440	C₄²×C₂₃	—	2	2	no	—
441	C₄²×C₂₃	—	2	1	no	—
442	C₄²×C₂₃	—	2	2	no	—
443	C₄²×C₂₃	—	2	1	no	—
444	C₄²×C₂₃	—	2	2	no	—
445	C₄²×C₂₃	—	2	2	no	—
446	C₄²×C₂₃	—	2	2	no	—
447	C₄²×C₂₃	—	2	2	no	—
448	C₄²×C₂₃	—	2	1	no	—
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	C₂×D₄	1	2	yes	—
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	C₂⁴	1	1	yes	characteristic
458	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
459	C₄²×C₂₃	C₂⁴	1	2	yes	—
460	#60595	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
461	C₂³×C₂₃	—	2	1	no	—
462	C₂³×C₂₃	—	2	2	no	—
463	C₂³×C₂₃	—	4	2	no	—
464	C₂³×C₂₃	—	8	1	no	—
465	C₂³×C₂₃	—	8	1	no	—
466	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
467	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
468	Q₈×C₂₃	—	2	8	no	—
469	Q₈×C₂₃	—	2	2	no	—
470	Q₈×C₂₃	—	2	4	no	—
471	Q₈×C₂₃	—	2	1	no	—
472	Q₈×C₂₃	—	2	2	no	—
473	Q₈×C₂₃	—	2	2	no	—
474	Q₈×C₂₃	—	2	2	no	—
475	Q₈×C₂₃	—	4	2	no	—
476	Q₈×C₂₃	—	8	1	no	—
477	Q₈×C₂₃	—	8	1	no	—
478	Q₈×C₂₃	C₂×#41	1	2	yes	—
479	Q₈×C₂₃	C₂×#41	1	4	yes	—
480	D₄×C₂₃	—	2	8	no	—
481	D₄×C₂₃	—	2	4	no	—
482	D₄×C₂₃	—	2	4	no	—
483	D₄×C₂₃	—	2	2	no	—
484	D₄×C₂₃	—	2	1	no	—
485	D₄×C₂₃	—	2	2	no	—
486	D₄×C₂₃	—	2	2	no	—
487	D₄×C₂₃	—	4	2	no	—
488	D₄×C₂₃	—	8	2	no	—
489	D₄×C₂₃	—	8	2	no	—
490	D₄×C₂₃	C₂×#41	1	2	yes	—
491	C₂×C₄×C₂₃	—	2	8	no	—
492	C₂×C₄×C₂₃	—	2	8	no	—
493	C₂×C₄×C₂₃	—	2	4	no	—
494	C₂×C₄×C₂₃	—	2	2	no	—
495	C₂×C₄×C₂₃	—	2	1	no	—
496	C₂×C₄×C₂₃	—	2	4	no	—
497	C₂×C₄×C₂₃	—	2	2	no	—
498	C₂×C₄×C₂₃	—	2	2	no	—
499	C₂×C₄×C₂₃	—	2	1	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	1	no	—
504	C₂×C₄×C₂₃	—	2	2	no	—
505	C₂×C₄×C₂₃	—	2	1	no	—
506	C₂×C₄×C₂₃	—	2	1	no	—
507	C₂×C₄×C₂₃	—	4	2	no	—
508	C₂×C₄×C₂₃	—	4	1	no	—
509	C₂×C₄×C₂₃	—	4	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	—	8	2	no	—
514	C₂×C₄×C₂₃	—	8	2	no	—
515	C₂×C₄×C₂₃	—	8	1	no	—
516	C₂×C₄×C₂₃	—	8	2	no	—
517	C₂×C₄×C₂₃	—	8	1	no	—
518	C₂×C₄×C₂₃	—	8	2	no	—
519	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
527	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
528	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
529	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
530	C₈×C₂₃	—	2	1	no	—
531	C₈×C₂₃	—	2	1	no	—
532	C₈×C₂₃	—	2	1	no	—
533	C₈×C₂₃	—	2	1	no	—
534	C₈×C₂₃	—	2	2	no	—
535	C₈×C₂₃	—	2	2	no	—
536	#3510	C₂×C₂₃	1	1	yes	characteristic, complemented
537	C₄×2₋¹⁺⁴	C₂×C₂₃	1	1	yes	characteristic, complemented
538	#3125	C₂×C₂₃	1	2	yes	complemented
539	#3124	C₂×C₂₃	1	2	yes	complemented
540	#3121	C₂×C₂₃	1	2	yes	complemented
541	#3121	C₂×C₂₃	1	2	yes	complemented
542	#3117	C₂×C₂₃	1	2	yes	complemented
543	#3111	C₂×C₂₃	1	2	yes	complemented
544	#3108	C₂×C₂₃	1	2	yes	complemented
545	#3102	C₂×C₂₃	1	2	yes	complemented
546	#3097	C₂×C₂₃	1	1	yes	characteristic, complemented
547	#3096	C₂×C₂₃	1	1	yes	characteristic, complemented
548	#3078	C₂×C₂₃	1	1	yes	characteristic, complemented
549	#3076	C₂×C₂₃	1	1	yes	characteristic, complemented
550	#3040	C₂×C₂₃	1	1	yes	characteristic, complemented
551	C₂×#464	C₂×C₂₃	1	1	yes	characteristic, complemented
552	#3011	C₂×C₂₃	1	1	yes	characteristic, complemented
553	#3010	C₂×C₂₃	1	1	yes	characteristic
554	#2950	C₂×C₂₃	1	1	yes	characteristic, complemented
555	#2949	C₂×C₂₃	1	1	yes	characteristic, complemented
556	#2947	C₂×C₂₃	1	1	yes	characteristic, complemented
557	#2946	C₂×C₂₃	1	1	yes	characteristic, complemented
558	#2925	C₂×C₂₃	1	1	yes	characteristic, complemented
559	C₂²×C₂₃	—	2	1	no	—
560	C₂²×C₂₃	—	2	1	no	—
561	C₂²×C₂₃	—	2	2	no	—
562	C₂²×C₂₃	—	2	2	no	—
563	C₂²×C₂₃	—	2	2	no	—
564	C₂²×C₂₃	—	2	2	no	—
565	C₂²×C₂₃	—	4	1	no	—
566	C₂²×C₂₃	—	4	1	no	—
567	C₂²×C₂₃	—	4	2	no	—
568	C₂²×C₂₃	—	4	2	no	—
569	C₂²×C₂₃	—	4	2	no	—
570	C₂²×C₂₃	—	16	2	no	—
571	C₂²×C₂₃	#525	1	2	yes	—
572	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
573	C₄×C₂₃	—	2	1	no	—
574	C₄×C₂₃	—	2	2	no	—
575	C₄×C₂₃	—	2	1	no	—
576	C₄×C₂₃	—	2	1	no	—
577	C₄×C₂₃	—	2	2	no	—
578	C₄×C₂₃	—	2	1	no	—
579	C₄×C₂₃	—	2	4	no	—
580	C₄×C₂₃	—	2	2	no	—
581	C₄×C₂₃	—	2	2	no	—
582	C₄×C₂₃	—	4	2	no	—
583	C₄×C₂₃	—	4	1	no	—
584	C₄×C₂₃	—	4	1	no	—
585	C₄×C₂₃	—	4	1	no	—
586	C₄×C₂₃	—	4	1	no	—
587	C₄×C₂₃	—	4	1	no	—
588	C₄×C₂₃	—	4	1	no	—
589	C₄×C₂₃	—	4	2	no	—
590	C₄×C₂₃	#525	1	2	yes	—
591	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
592	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
593	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic
594	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
595	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
596	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
597	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
598	#559	—	2	1	no	—
599	#559	—	2	1	no	—
600	#556	—	2	1	no	—
601	#556	—	2	1	no	—
602	#551	—	2	2	no	—
603	#551	—	2	2	no	—
604	#542	C₂²×C₂₃	1	2	yes	—
605	#542	C₂²×C₂₃	1	2	yes	—
606	#536	C₂²×C₂₃	1	1	yes	characteristic
607	#535	C₂²×C₂₃	1	1	yes	characteristic
608	#533	C₂²×C₂₃	1	1	yes	characteristic
609	#529	C₂²×C₂₃	1	2	yes	—
610	#529	C₂²×C₂₃	1	2	yes	—
611	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
612	#520	—	2	2	no	—
613	#520	—	2	1	no	—
614	#520	C₂²×C₂₃	1	1	yes	characteristic
615	#520	C₂²×C₂₃	1	1	yes	characteristic
616	#520	C₂²×C₂₃	1	2	yes	complemented
617	#519	—	2	1	no	—
618	#519	C₂²×C₂₃	1	1	yes	characteristic
619	#519	C₂²×C₂₃	1	1	yes	characteristic
620	#519	C₂²×C₂₃	1	2	yes	complemented
621	#518	C₂²×C₂₃	1	1	yes	characteristic
622	C₄×#41	—	2	2	no	—
623	C₄×#41	—	2	1	no	—
624	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
625	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
626	C₄×#41	C₂²×C₂₃	1	2	yes	complemented
627	C₂×C₄×Q₈	—	2	1	no	—
628	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
629	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
630	#485	C₂²×C₂₃	1	2	yes	complemented
631	#485	C₂²×C₂₃	1	2	yes	complemented
632	#484	C₂²×C₂₃	1	2	yes	complemented
633	#483	C₂²×C₂₃	1	2	yes	complemented
634	#482	C₂²×C₂₃	1	2	yes	—
635	#482	C₂²×C₂₃	1	2	yes	—
636	#481	C₂²×C₂₃	1	2	yes	—
637	#480	C₂²×C₂₃	1	2	yes	—
638	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
639	#479	C₂²×C₂₃	1	1	yes	characteristic, complemented
640	#479	C₂²×C₂₃	1	2	yes	complemented
641	#479	C₂²×C₂₃	1	2	yes	complemented
642	#478	C₂²×C₂₃	1	1	yes	characteristic, complemented
643	#478	C₂²×C₂₃	1	1	yes	characteristic, complemented
644	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
645	#477	C₂²×C₂₃	1	2	yes	complemented
646	#476	C₂²×C₂₃	1	1	yes	characteristic, complemented
647	#475	C₂²×C₂₃	1	1	yes	characteristic, complemented
648	#475	C₂²×C₂₃	1	2	yes	complemented
649	#474	C₂²×C₂₃	1	1	yes	characteristic, complemented
650	#464	C₂²×C₂₃	1	2	yes	—
651	#464	C₂²×C₂₃	1	2	yes	—
652	#464	C₂²×C₂₃	1	2	yes	—
653	#464	C₂²×C₂₃	1	2	yes	—
654	#464	C₂²×C₂₃	1	2	yes	—
655	#464	C₂²×C₂₃	1	2	yes	—
656	#463	C₂²×C₂₃	1	2	yes	—
657	#463	C₂²×C₂₃	1	2	yes	—
658	#452	C₂²×C₂₃	1	2	yes	complemented
659	#452	C₂²×C₂₃	1	2	yes	complemented
660	#451	C₂²×C₂₃	1	2	yes	complemented
661	#451	C₂²×C₂₃	1	2	yes	complemented
662	#449	C₂²×C₂₃	1	2	yes	—
663	#449	C₂²×C₂₃	1	2	yes	—
664	#448	C₂²×C₂₃	1	2	yes	—
665	#448	C₂²×C₂₃	1	2	yes	—
666	#442	C₂²×C₂₃	1	2	yes	—
667	#441	C₂²×C₂₃	1	2	yes	complemented
668	#441	C₂²×C₂₃	1	2	yes	complemented
669	#441	C₂²×C₂₃	1	2	yes	complemented
670	#440	C₂²×C₂₃	1	2	yes	—
671	#440	C₂²×C₂₃	1	2	yes	—
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	2	yes	complemented
676	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	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	complemented
681	C₄×D₈	C₂²×C₂₃	1	2	yes	—
682	#433	C₂²×C₂₃	1	2	yes	complemented
683	#433	C₂²×C₂₃	1	2	yes	complemented
684	#432	C₂²×C₂₃	1	2	yes	complemented
685	#431	C₂²×C₂₃	1	2	yes	complemented
686	#428	C₂²×C₂₃	1	1	yes	characteristic
687	#428	C₂²×C₂₃	1	1	yes	characteristic
688	#427	C₂²×C₂₃	1	1	yes	characteristic
689	#427	C₂²×C₂₃	1	1	yes	characteristic
690	#423	C₂²×C₂₃	1	1	yes	characteristic
691	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
692	#419	C₂²×C₂₃	1	1	yes	characteristic
693	#419	C₂²×C₂₃	1	1	yes	characteristic
694	#419	C₂²×C₂₃	1	1	yes	characteristic
695	#418	C₂²×C₂₃	1	1	yes	characteristic
696	#416	C₂²×C₂₃	1	1	yes	characteristic
697	#416	C₂²×C₂₃	1	1	yes	characteristic
698	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
699	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
700	#408	C₂²×C₂₃	1	1	yes	characteristic
701	#408	C₂²×C₂₃	1	1	yes	characteristic
702	#405	C₂²×C₂₃	1	1	yes	characteristic
703	#405	C₂²×C₂₃	1	1	yes	characteristic
704	C₂×C₂₃	—	2	2	no	—
705	C₂×C₂₃	—	4	2	no	—
706	C₂×C₂₃	—	4	2	no	—
707	C₂×C₂₃	—	8	2	no	—
708	C₂×C₂₃	C₂×#525	1	1	yes	characteristic
709	C₂×C₂₃	#3584	1	1	yes	characteristic
710	C₂×C₂₃	#3586	1	1	yes	characteristic
711	2₋¹⁺⁴	—	2	4	no	—
712	2₋¹⁺⁴	—	2	4	no	—
713	C₂×#41	—	2	2	no	—
714	C₂×#41	—	2	1	no	—
715	C₂×#41	C₂³×C₂₃	1	2	yes	—
716	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
717	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
718	C₂²×Q₈	—	2	1	no	—
719	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
720	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
721	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
722	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
723	#137	—	2	4	no	—
724	AGL(1,ℤ/8)	—	2	4	no	—
725	C₂×Q₁₆	—	2	4	no	—
726	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
727	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
728	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
729	C₂×SD₁₆	—	2	4	no	—
730	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
734	C₂×D₈	C₂³×C₂₃	1	2	yes	—
735	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
736	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
737	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
738	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
739	C₄⋊Q₈	—	2	1	no	—
740	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
741	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
742	#127	—	2	1	no	—
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#126	—	2	2	no	—
747	#125	C₂³×C₂₃	1	1	yes	characteristic
748	#125	C₂³×C₂₃	1	1	yes	characteristic
749	#124	—	2	1	no	—
750	#124	—	2	1	no	—
751	#124	—	2	2	no	—
752	#124	—	2	2	no	—
753	#124	—	2	1	no	—
754	#124	—	2	1	no	—
755	#124	C₂³×C₂₃	1	2	yes	—
756	#124	C₂³×C₂₃	1	2	yes	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	C₂²⋊Q₈	—	2	1	no	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
767	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
768	#121	C₂³×C₂₃	1	2	yes	—
769	#121	C₂³×C₂₃	1	2	yes	—
770	#120	—	2	2	no	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	2	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	2	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	2	2	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	—	2	2	no	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
785	C₄×Q₈	D₄×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	2	yes	—
790	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
791	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
792	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
793	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
794	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	D₄×C₂₃	1	2	yes	—
809	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
810	C₄×D₄	D₄×C₂₃	1	2	yes	—
811	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
812	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
813	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₂₃	1	2	yes	—
815	C₄×D₄	C₂³×C₂₃	1	2	yes	—
816	C₄×D₄	C₂³×C₂₃	1	2	yes	—
817	#117	—	2	1	no	—
818	#117	—	2	2	no	—
819	#117	—	2	2	no	—
820	#117	—	2	2	no	—
821	#117	—	2	2	no	—
822	#117	—	2	2	no	—
823	#117	—	2	1	no	—
824	#117	—	2	2	no	—
825	#117	—	2	2	no	—
826	#117	—	2	2	no	—
827	#117	C₂³×C₂₃	1	1	yes	characteristic
828	#117	C₂³×C₂₃	1	2	yes	—
829	#117	C₂³×C₂₃	1	1	yes	characteristic
830	#117	C₂³×C₂₃	1	1	yes	characteristic
831	#117	C₂³×C₂₃	1	1	yes	characteristic
832	#117	C₂³×C₂₃	1	2	yes	—
833	C₂×C₄⋊C₄	—	2	1	no	—
834	C₂×C₄⋊C₄	—	2	2	no	—
835	C₂×C₄⋊C₄	—	2	1	no	—
836	C₂×C₄⋊C₄	—	2	2	no	—
837	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
838	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
839	C₂×C₂²⋊C₄	—	2	1	no	—
840	C₂×C₂²⋊C₄	—	2	1	no	—
841	C₂×C₂²⋊C₄	—	2	2	no	—
842	C₂×C₄²	—	2	1	no	—
843	C₂×C₄²	—	2	2	no	—
844	C₂×C₄²	—	2	1	no	—
845	C₂×C₄²	—	2	2	no	—
846	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
847	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
848	#107	C₂³×C₂₃	1	1	yes	characteristic
849	#107	C₂³×C₂₃	1	1	yes	characteristic
850	#107	C₂³×C₂₃	1	1	yes	characteristic
851	#107	C₂³×C₂₃	1	1	yes	characteristic
852	#107	C₂³×C₂₃	1	2	yes	—
853	#107	C₂³×C₂₃	1	2	yes	—
854	#106	C₂³×C₂₃	1	1	yes	characteristic
855	#106	C₂³×C₂₃	1	1	yes	characteristic
856	#106	C₂³×C₂₃	1	1	yes	characteristic
857	#106	C₂³×C₂₃	1	1	yes	characteristic
858	#106	C₂³×C₂₃	1	2	yes	—
859	#106	C₂³×C₂₃	1	2	yes	—
860	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
863	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
864	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
865	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
866	#103	C₂³×C₂₃	1	2	yes	—
867	#103	C₂³×C₂₃	1	2	yes	—
868	#103	C₂³×C₂₃	1	1	yes	characteristic
869	#103	C₂³×C₂₃	1	1	yes	characteristic
870	#103	C₂³×C₂₃	1	1	yes	characteristic
871	#103	C₂³×C₂₃	1	1	yes	characteristic
872	#103	C₂³×C₂₃	1	2	yes	—
873	#103	C₂³×C₂₃	1	2	yes	—
874	#103	C₂³×C₂₃	1	2	yes	—
875	#103	C₂³×C₂₃	1	2	yes	—
876	#103	C₂³×C₂₃	1	2	yes	—
877	#103	C₂³×C₂₃	1	2	yes	—
878	#102	C₂³×C₂₃	1	2	yes	—
879	#102	C₂³×C₂₃	1	2	yes	—
880	#102	C₂³×C₂₃	1	1	yes	characteristic
881	#102	C₂³×C₂₃	1	1	yes	characteristic
882	#102	C₂³×C₂₃	1	1	yes	characteristic
883	#102	C₂³×C₂₃	1	1	yes	characteristic
884	#102	C₂³×C₂₃	1	2	yes	—
885	#102	C₂³×C₂₃	1	2	yes	—
886	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
887	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
890	#97	C₂³×C₂₃	1	2	yes	—
891	#97	C₂³×C₂₃	1	2	yes	—
892	C₄×C₈	C₂³×C₂₃	1	2	yes	—
893	C₄×C₈	C₂³×C₂₃	1	2	yes	—
894	C₂₃	#60595	1	1	yes	characteristic, direct product factor, Sylow
895	C₂⁴	—	2	1	no	—
896	#41	—	2	16	no	—
897	#41	—	2	8	no	—
898	#41	—	2	4	no	—
899	#41	—	2	4	no	—
900	#41	—	2	2	no	—
901	#41	—	2	2	no	—
902	#41	—	2	2	no	—
903	#41	#41×C₂₃	1	4	yes	—
904	C₂×Q₈	—	2	8	no	—
905	C₂×Q₈	—	2	4	no	—
906	C₂×Q₈	—	2	4	no	—
907	C₂×Q₈	—	2	2	no	—
908	C₂×Q₈	—	2	1	no	—
909	C₂×Q₈	—	2	1	no	—
910	C₂×Q₈	—	2	1	no	—
911	C₂×Q₈	—	2	1	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	#41×C₂₃	1	4	yes	—
917	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
918	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
919	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
928	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
929	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
930	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
944	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
945	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
946	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
947	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
948	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
949	Q₁₆	—	2	4	no	—
950	Q₁₆	—	2	4	no	—
951	Q₁₆	—	2	4	no	—
952	SD₁₆	—	2	4	no	—
953	SD₁₆	—	2	4	no	—
954	SD₁₆	—	2	4	no	—
955	SD₁₆	—	2	4	no	—
956	D₈	—	2	4	no	—
957	M₁₆	—	2	2	no	—
958	M₁₆	—	2	2	no	—
959	C₂×C₈	—	2	2	no	—
960	C₂×C₈	—	2	2	no	—
961	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
962	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
964	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
965	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
966	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
987	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
988	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
989	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
990	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
991	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
992	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
993	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
995	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	2	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	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1015	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1016	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	2	no	—
1023	C₄²	—	2	2	no	—
1024	C₄²	—	2	2	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	C₂×D₄×C₂₃	1	2	yes	—
1031	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1032	C₄²	C₂×D₄×C₂₃	1	2	yes	—
1033	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1034	C₄²	C₂⁴×C₂₃	1	2	yes	—
1035	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1036	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	4	2	no	—
1040	C₂³	—	8	1	no	—
1041	C₂³	—	8	1	no	—
1042	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1043	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1044	Q₈	—	2	8	no	—
1045	Q₈	—	2	1	no	—
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	2	no	—
1048	Q₈	—	2	4	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	2	no	—
1051	Q₈	—	4	2	no	—
1052	Q₈	—	8	1	no	—
1053	Q₈	—	8	1	no	—
1054	Q₈	C₂×#41×C₂₃	1	2	yes	—
1055	Q₈	C₂×#41×C₂₃	1	4	yes	—
1056	D₄	—	2	8	no	—
1057	D₄	—	2	4	no	—
1058	D₄	—	2	4	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	2	no	—
1063	D₄	—	4	2	no	—
1064	D₄	—	8	2	no	—
1065	D₄	—	8	2	no	—
1066	D₄	C₂×#41×C₂₃	1	2	yes	—
1067	C₂×C₄	—	2	8	no	—
1068	C₂×C₄	—	2	8	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	4	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	4	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	4	1	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	1	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	8	2	no	—
1090	C₂×C₄	—	8	2	no	—
1091	C₂×C₄	—	8	1	no	—
1092	C₂×C₄	—	8	2	no	—
1093	C₂×C₄	—	8	1	no	—
1094	C₂×C₄	—	8	2	no	—
1095	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1096	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1097	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1098	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1099	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1100	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1102	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1103	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1104	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1105	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1106	C₈	—	2	1	no	—
1107	C₈	—	2	1	no	—
1108	C₈	—	2	1	no	—
1109	C₈	—	2	1	no	—
1110	C₈	—	2	2	no	—
1111	C₈	—	2	2	no	—
1112	C₂²	—	2	1	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	2	2	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	4	1	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	2	no	—
1121	C₂²	—	4	2	no	—
1122	C₂²	—	4	2	no	—
1123	C₂²	—	16	2	no	—
1124	C₂²	C₂₃×#525	1	2	yes	—
1125	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1126	C₄	—	2	4	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	2	no	—
1129	C₄	—	2	1	no	—
1130	C₄	—	2	2	no	—
1131	C₄	—	2	1	no	—
1132	C₄	—	2	1	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	4	2	no	—
1136	C₄	—	4	2	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	1	no	—
1143	C₄	C₂₃×#525	1	2	yes	—
1144	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1145	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1146	C₂	—	2	2	no	—
1147	C₂	—	4	2	no	—
1148	C₂	—	4	2	no	—
1149	C₂	—	8	2	no	—
1150	C₂	C₂×C₂₃×#525	1	1	yes	characteristic
1151	C₂	C₂₃×#3584	1	1	yes	characteristic
1152	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3010	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3510	C₂	semidirect
2. C₄×C₂₃×2₋¹⁺⁴	C₂	semidirect
3. C₂₃×#3125	C₂	semidirect
4. C₂₃×#3124	C₂	semidirect
5. C₂₃×#3121	C₂	semidirect
6. C₂₃×#3121	C₂	semidirect
7. C₂₃×#3117	C₂	semidirect
8. C₂₃×#3111	C₂	semidirect
9. C₂₃×#3108	C₂	semidirect
10. C₂₃×#3102	C₂	semidirect
11. C₂₃×#3097	C₂	semidirect
12. C₂₃×#3096	C₂	semidirect
13. C₂₃×#3078	C₂	semidirect
14. C₂₃×#3076	C₂	semidirect
15. C₂₃×#3040	C₂	semidirect
16. C₂×C₂₃×#464	C₂	semidirect
17. C₂₃×#3011	C₂	semidirect
19. C₂₃×#2950	C₂	semidirect
20. C₂₃×#2949	C₂	semidirect
21. C₂₃×#2947	C₂	semidirect
22. C₂₃×#2946	C₂	semidirect
23. C₂₃×#2925	C₂	semidirect
47. C₂₃×#520	C₂²	semidirect
51. C₂₃×#519	C₂²	semidirect
57. C₄×#41×C₂₃	C₂²	semidirect
60. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
61. C₂₃×#485	C₂²	semidirect
62. C₂₃×#485	C₂²	semidirect
63. C₂₃×#484	C₂²	semidirect
64. C₂₃×#483	C₂²	semidirect
69. C₂₃×#479	C₂²	semidirect
70. C₂₃×#479	C₂²	semidirect
71. C₂₃×#479	C₂²	semidirect
72. C₂₃×#479	C₂²	semidirect
73. C₂₃×#478	C₂²	semidirect
74. C₂₃×#478	C₂²	semidirect
75. C₂₃×#477	C₂²	semidirect
76. C₂₃×#477	C₂²	semidirect
77. C₂₃×#476	C₂²	semidirect
78. C₂₃×#475	C₂²	semidirect
79. C₂₃×#475	C₂²	semidirect
80. C₂₃×#474	C₂²	semidirect
89. C₂₃×#452	C₂²	semidirect
90. C₂₃×#452	C₂²	semidirect
91. C₂₃×#451	C₂²	semidirect
92. C₂₃×#451	C₂²	semidirect
98. C₂₃×#441	C₂²	semidirect
99. C₂₃×#441	C₂²	semidirect
100. C₂₃×#441	C₂²	semidirect
104. C₂₃×#440	C₂²	semidirect
105. C₄×Q₁₆×C₂₃	C₂²	semidirect
106. C₄×Q₁₆×C₂₃	C₂²	semidirect
107. C₄×Q₁₆×C₂₃	C₂²	semidirect
111. C₄×SD₁₆×C₂₃	C₂²	semidirect
113. C₂₃×#433	C₂²	semidirect
114. C₂₃×#433	C₂²	semidirect
115. C₂₃×#432	C₂²	semidirect
116. C₂₃×#431	C₂²	semidirect
460. #60595	C₂₃	direct (N × H)
536. #3510	C₂×C₂₃	semidirect
537. C₄×2₋¹⁺⁴	C₂×C₂₃	semidirect
538. #3125	C₂×C₂₃	semidirect
539. #3124	C₂×C₂₃	semidirect
540. #3121	C₂×C₂₃	semidirect
541. #3121	C₂×C₂₃	semidirect
542. #3117	C₂×C₂₃	semidirect
543. #3111	C₂×C₂₃	semidirect
544. #3108	C₂×C₂₃	semidirect
545. #3102	C₂×C₂₃	semidirect
546. #3097	C₂×C₂₃	semidirect
547. #3096	C₂×C₂₃	semidirect
548. #3078	C₂×C₂₃	semidirect
549. #3076	C₂×C₂₃	semidirect
550. #3040	C₂×C₂₃	semidirect
551. C₂×#464	C₂×C₂₃	semidirect
552. #3011	C₂×C₂₃	semidirect
554. #2950	C₂×C₂₃	semidirect
555. #2949	C₂×C₂₃	semidirect
556. #2947	C₂×C₂₃	semidirect
557. #2946	C₂×C₂₃	semidirect
558. #2925	C₂×C₂₃	semidirect
616. #520	C₂²×C₂₃	semidirect
620. #519	C₂²×C₂₃	semidirect
626. C₄×#41	C₂²×C₂₃	semidirect
629. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
630. #485	C₂²×C₂₃	semidirect
631. #485	C₂²×C₂₃	semidirect
632. #484	C₂²×C₂₃	semidirect
633. #483	C₂²×C₂₃	semidirect
638. #479	C₂²×C₂₃	semidirect
639. #479	C₂²×C₂₃	semidirect
640. #479	C₂²×C₂₃	semidirect
641. #479	C₂²×C₂₃	semidirect
642. #478	C₂²×C₂₃	semidirect
643. #478	C₂²×C₂₃	semidirect
644. #477	C₂²×C₂₃	semidirect
645. #477	C₂²×C₂₃	semidirect
646. #476	C₂²×C₂₃	semidirect
647. #475	C₂²×C₂₃	semidirect
648. #475	C₂²×C₂₃	semidirect
649. #474	C₂²×C₂₃	semidirect
658. #452	C₂²×C₂₃	semidirect
659. #452	C₂²×C₂₃	semidirect
660. #451	C₂²×C₂₃	semidirect
661. #451	C₂²×C₂₃	semidirect
667. #441	C₂²×C₂₃	semidirect
668. #441	C₂²×C₂₃	semidirect
669. #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
680. C₄×SD₁₆	C₂²×C₂₃	semidirect
682. #433	C₂²×C₂₃	semidirect
683. #433	C₂²×C₂₃	semidirect
684. #432	C₂²×C₂₃	semidirect
685. #431	C₂²×C₂₃	semidirect
894. C₂₃	#60595	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×#3510	2
C₄×C₂₃×2₋¹⁺⁴	2
C₂₃×#3125	2
C₂₃×#3124	2
C₂₃×#3121	2
C₂₃×#3117	2
C₂₃×#3111	2
C₂₃×#3108	2
C₂₃×#3102	2
C₂₃×#3097	2
C₂₃×#3096	2
C₂₃×#3078	2
C₂₃×#3076	2
C₂₃×#3040	2
C₂×C₂₃×#464	2
C₂₃×#3011	2
C₂₃×#3010	2
C₂₃×#2950	2
C₂₃×#2949	2
C₂₃×#2947	2
C₂₃×#2946	2
C₂₃×#2925	2
#60595	23

Subgroups — C23×#60595 #19208221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60595 #19208221