Subgroups — C₂₃×#61618 #19209244

Order 5888.

2096 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3488	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3323	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3317	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3310	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3300	C₂	1	2	yes	maximal, complemented
7	D₄×SD₁₆×C₂₃	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3278	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3270	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3266	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3222	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3201	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3193	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3187	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3120	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3009	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3007	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2976	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
21	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
25	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
26	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
28	C₂₃×#563	—	2	2	no	—
29	C₂₃×#552	C₂²	1	2	yes	complemented
30	C₂₃×#552	C₂²	1	2	yes	complemented
31	C₂₃×#551	—	2	2	no	—
32	C₂₃×#550	C₂²	1	2	yes	—
33	D₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
34	D₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
35	C₂₃×#548	C₂²	1	2	yes	—
36	C₂₃×#546	—	2	2	no	—
37	C₂₃×#546	C₂²	1	2	yes	—
38	D₄²×C₂₃	—	2	2	no	—
39	D₄²×C₂₃	C₂²	1	2	yes	—
40	C₂₃×#544	—	2	1	no	—
41	C₂₃×#544	—	2	1	no	—
42	C₂₃×#541	C₂²	1	2	yes	complemented
43	C₂₃×#539	—	2	1	no	—
44	C₂₃×#539	—	2	1	no	—
45	C₂₃×#537	—	2	1	no	—
46	C₂₃×#537	C₂²	1	1	yes	characteristic
47	C₂₃×#536	C₂²	1	2	yes	complemented
48	C₂₃×#535	—	2	1	no	—
49	C₂₃×#535	C₂²	1	1	yes	characteristic
50	C₂₃×#525	—	2	1	no	—
51	C₂₃×#525	C₂²	1	1	yes	characteristic
52	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₂₃×#121	—	2	1	no	—
55	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
56	C₂₃×#520	C₂²	1	1	yes	characteristic
57	C₂₃×#497	C₂²	1	2	yes	complemented
58	C₂₃×#492	C₂²	1	2	yes	complemented
59	C₂₃×#490	C₂²	1	2	yes	complemented
60	C₂₃×#488	C₂²	1	2	yes	complemented
61	C₂₃×#485	C₂²	1	2	yes	complemented
62	C₂₃×#484	C₂²	1	2	yes	complemented
63	C₂₃×#483	C₂²	1	2	yes	complemented
64	C₂₃×#482	C₂²	1	2	yes	complemented
65	C₂₃×#481	C₂²	1	2	yes	complemented
66	C₂₃×#480	C₂²	1	2	yes	complemented
67	C₂₃×#479	C₂²	1	2	yes	complemented
68	C₂₃×#478	C₂²	1	2	yes	complemented
69	C₂₃×#470	C₂²	1	2	yes	complemented
70	C₂₃×#468	C₂²	1	2	yes	complemented
71	C₂₃×#468	C₂²	1	2	yes	complemented
72	C₂₃×#468	C₂²	1	2	yes	complemented
73	C₂₃×#467	C₂²	1	2	yes	complemented
74	C₂₃×#465	C₂²	1	2	yes	complemented
75	C₂₃×#465	C₂²	1	2	yes	complemented
76	C₂₃×#465	C₂²	1	2	yes	complemented
77	C₂₃×#464	C₂²	1	2	yes	complemented
78	C₂₃×#464	C₂²	1	2	yes	complemented
79	C₂₃×#462	C₂²	1	2	yes	complemented
80	C₂₃×#461	C₂²	1	2	yes	complemented
81	C₂₃×#460	C₂²	1	2	yes	complemented
82	C₂₃×#460	C₂²	1	2	yes	complemented
83	C₂₃×#452	C₂²	1	2	yes	—
84	C₂₃×#452	C₂²	1	2	yes	—
85	C₂₃×#452	C₂²	1	2	yes	complemented
86	C₂₃×#452	C₂²	1	2	yes	complemented
87	C₂₃×#452	C₂²	1	2	yes	complemented
88	C₂₃×#452	C₂²	1	2	yes	complemented
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×#450	C₂²	1	2	yes	complemented
94	C₂₃×#450	C₂²	1	2	yes	complemented
95	C₂₃×#450	C₂²	1	2	yes	complemented
96	C₂₃×#450	C₂²	1	2	yes	complemented
97	C₂₃×#450	C₂²	1	2	yes	complemented
98	C₂₃×#448	C₂²	1	2	yes	complemented
99	C₂₃×#448	C₂²	1	2	yes	complemented
100	C₂₃×#448	C₂²	1	2	yes	complemented
101	C₂₃×#441	C₂²	1	2	yes	complemented
102	C₂₃×#440	C₂²	1	2	yes	complemented
103	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
105	C₂₃×#436	C₂²	1	2	yes	complemented
106	C₂₃×#435	C₂²	1	2	yes	complemented
107	C₂₃×#435	C₂²	1	2	yes	complemented
108	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
109	C₂₃×#433	C₂²	1	2	yes	complemented
110	C₂₃×#418	C₂²	1	2	yes	complemented
111	C₂₃×#417	C₂²	1	1	yes	characteristic, complemented
112	C₂₃×#417	C₂²	1	1	yes	characteristic, complemented
113	C₂₃×#416	C₂²	1	2	yes	complemented
114	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
116	C₂₃×#408	C₂²	1	2	yes	complemented
117	C₂₃×#407	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
119	C₂₃×H(5,𝔽₂)	—	4	2	no	—
120	C₂₃×H(5,𝔽₂)	—	4	2	no	—
121	C₂×#41×C₂₃	—	2	1	no	—
122	C₂×#41×C₂₃	—	2	1	no	—
123	C₂×#41×C₂₃	—	2	1	no	—
124	C₂×#41×C₂₃	—	4	2	no	—
125	C₂×#41×C₂₃	—	4	2	no	—
126	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
127	C₂×#41×C₂₃	C₂³	1	2	yes	—
128	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
129	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
130	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
131	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
133	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
134	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
135	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₂₃	—	2	1	no	—
137	C₂²×D₄×C₂₃	—	2	1	no	—
138	C₂²×D₄×C₂₃	—	2	1	no	—
139	C₂²×D₄×C₂₃	—	2	2	no	—
140	C₂²×D₄×C₂₃	—	2	2	no	—
141	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
143	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₂₃	—	2	1	no	—
145	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
146	C₂₃×#137	—	4	2	no	—
147	C₂₃×#137	—	4	4	no	—
148	C₂₃×#137	—	4	2	no	—
149	C₂×Q₁₆×C₂₃	—	4	2	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×Q₁₆×C₂₃	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₂₃	—	4	2	no	—
155	C₂×SD₁₆×C₂₃	—	4	4	no	—
156	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
164	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
165	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
166	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
167	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
168	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
169	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
170	C₂₃×C₄⋊Q₈	—	2	2	no	—
171	C₂₃×C₄⋊Q₈	—	2	2	no	—
172	C₂₃×C₄⋊Q₈	—	2	2	no	—
173	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
174	C₂₃×#127	—	2	2	no	—
175	C₂₃×#127	C₂³	1	2	yes	—
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	2	no	—
181	C₂₃×#125	—	2	2	no	—
182	C₂₃×#125	—	2	2	no	—
183	C₂₃×#125	—	2	2	no	—
184	C₂₃×#125	C₂³	1	2	yes	—
185	C₂₃×#124	—	2	2	no	—
186	C₂₃×#124	—	2	2	no	—
187	C₂₃×#124	C₂³	1	2	yes	—
188	C₂₃×#123	—	2	2	no	—
189	C₂₃×#123	—	2	2	no	—
190	C₂₃×#123	—	2	2	no	—
191	C₂₃×#123	—	2	2	no	—
192	C₂₃×#123	—	2	2	no	—
193	C₂₃×#123	D₄	1	2	yes	—
194	C₂₃×C₂²⋊Q₈	—	2	1	no	—
195	C₂₃×C₂²⋊Q₈	—	2	1	no	—
196	C₂₃×C₂²⋊Q₈	—	2	1	no	—
197	C₂₃×C₂²⋊Q₈	—	2	1	no	—
198	C₂₃×C₂²⋊Q₈	—	2	1	no	—
199	C₂₃×C₂²⋊Q₈	—	2	2	no	—
200	C₂₃×C₂²⋊Q₈	—	2	2	no	—
201	C₂₃×C₂²⋊Q₈	—	2	2	no	—
202	C₂₃×C₂²⋊Q₈	—	2	2	no	—
203	C₂₃×C₂²⋊Q₈	—	2	2	no	—
204	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
205	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
206	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
207	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₂₃×#121	—	2	2	no	—
214	C₂₃×#121	—	2	1	no	—
215	C₂₃×#121	—	2	2	no	—
216	C₂₃×#121	—	2	1	no	—
217	C₂₃×#121	—	2	1	no	—
218	C₂₃×#121	—	2	1	no	—
219	C₂₃×#121	—	2	1	no	—
220	C₂₃×#121	—	2	2	no	—
221	C₂₃×#121	—	2	2	no	—
222	C₂₃×#121	—	2	2	no	—
223	C₂₃×#121	—	2	2	no	—
224	C₂₃×#121	D₄	1	1	yes	characteristic
225	C₂₃×#121	D₄	1	1	yes	characteristic
226	C₂₃×#121	C₂³	1	2	yes	—
227	C₂₃×#121	C₂³	1	2	yes	—
228	C₂₃×#121	C₂³	1	2	yes	—
229	C₂₃×#120	—	2	2	no	—
230	C₂₃×#120	—	2	2	no	—
231	C₂₃×#120	—	2	2	no	—
232	C₂₃×#120	—	2	2	no	—
233	C₂₃×#120	D₄	1	2	yes	—
234	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
235	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
236	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
237	C₄×D₄×C₂₃	—	2	2	no	—
238	C₄×D₄×C₂₃	—	2	2	no	—
239	C₄×D₄×C₂₃	—	2	2	no	—
240	C₄×D₄×C₂₃	—	2	2	no	—
241	C₄×D₄×C₂₃	—	2	2	no	—
242	C₄×D₄×C₂₃	C₂³	1	2	yes	—
243	C₄×D₄×C₂₃	C₂³	1	2	yes	—
244	C₄×D₄×C₂₃	C₂³	1	2	yes	—
245	C₂₃×#117	—	2	1	no	—
246	C₂₃×#117	—	2	2	no	—
247	C₂₃×#117	—	2	2	no	—
248	C₂₃×#117	C₂³	1	2	yes	—
249	C₂₃×#117	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
251	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
252	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
253	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
257	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
258	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
259	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
260	C₂₃×#107	C₂³	1	2	yes	—
261	C₂₃×#107	C₂³	1	2	yes	—
262	C₂₃×#106	C₂³	1	2	yes	—
263	C₂₃×#106	C₂³	1	2	yes	—
264	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
265	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
266	C₂₃×#103	C₂³	1	2	yes	—
267	C₂₃×#103	C₂³	1	2	yes	—
268	C₂₃×#103	C₂³	1	2	yes	—
269	C₂₃×#103	C₂³	1	2	yes	—
270	C₂₃×#103	C₂³	1	2	yes	—
271	C₂₃×#103	C₂³	1	2	yes	—
272	C₂₃×#103	C₂³	1	2	yes	—
273	C₂₃×#103	C₂³	1	2	yes	—
274	C₂₃×#102	C₂³	1	2	yes	—
275	C₂₃×#102	C₂³	1	2	yes	—
276	C₂₃×#102	C₂³	1	2	yes	—
277	C₂₃×#102	C₂³	1	2	yes	—
278	C₂₃×#102	C₂³	1	2	yes	—
279	C₂₃×#102	C₂³	1	2	yes	—
280	C₂₃×#102	C₂³	1	2	yes	—
281	C₂₃×#102	C₂³	1	2	yes	—
282	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
283	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
284	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
285	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
286	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
287	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
288	C₂₃×#97	C₂³	1	2	yes	—
289	C₄×C₈×C₂₃	C₂³	1	2	yes	—
290	C₂⁴×C₂₃	—	2	1	no	—
291	C₂⁴×C₂₃	—	2	2	no	—
292	C₂⁴×C₂₃	—	2	1	no	—
293	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
294	#41×C₂₃	—	2	2	no	—
295	#41×C₂₃	—	2	2	no	—
296	#41×C₂₃	—	2	2	no	—
297	#41×C₂₃	—	2	4	no	—
298	#41×C₂₃	—	2	2	no	—
299	#41×C₂₃	—	4	1	no	—
300	#41×C₂₃	—	4	1	no	—
301	#41×C₂₃	—	4	1	no	—
302	#41×C₂₃	—	4	1	no	—
303	#41×C₂₃	—	4	1	no	—
304	#41×C₂₃	—	4	1	no	—
305	#41×C₂₃	—	4	2	no	—
306	#41×C₂₃	—	4	4	no	—
307	#41×C₂₃	—	4	4	no	—
308	#41×C₂₃	—	4	4	no	—
309	C₂×Q₈×C₂₃	—	2	1	no	—
310	C₂×Q₈×C₂₃	—	2	1	no	—
311	C₂×Q₈×C₂₃	—	2	1	no	—
312	C₂×Q₈×C₂₃	—	2	2	no	—
313	C₂×Q₈×C₂₃	—	2	2	no	—
314	C₂×Q₈×C₂₃	—	4	1	no	—
315	C₂×Q₈×C₂₃	—	4	1	no	—
316	C₂×Q₈×C₂₃	—	4	2	no	—
317	C₂×Q₈×C₂₃	—	4	1	no	—
318	C₂×Q₈×C₂₃	—	4	1	no	—
319	C₂×Q₈×C₂₃	—	4	1	no	—
320	C₂×Q₈×C₂₃	—	4	2	no	—
321	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
323	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
324	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
325	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
326	C₂×D₄×C₂₃	—	2	1	no	—
327	C₂×D₄×C₂₃	—	2	2	no	—
328	C₂×D₄×C₂₃	—	2	4	no	—
329	C₂×D₄×C₂₃	—	2	2	no	—
330	C₂×D₄×C₂₃	—	2	1	no	—
331	C₂×D₄×C₂₃	—	2	1	no	—
332	C₂×D₄×C₂₃	—	2	2	no	—
333	C₂×D₄×C₂₃	—	2	1	no	—
334	C₂×D₄×C₂₃	—	2	2	no	—
335	C₂×D₄×C₂₃	—	2	2	no	—
336	C₂×D₄×C₂₃	—	2	1	no	—
337	C₂×D₄×C₂₃	—	2	2	no	—
338	C₂×D₄×C₂₃	—	2	1	no	—
339	C₂×D₄×C₂₃	—	2	2	no	—
340	C₂×D₄×C₂₃	—	2	2	no	—
341	C₂×D₄×C₂₃	—	4	1	no	—
342	C₂×D₄×C₂₃	—	4	2	no	—
343	C₂×D₄×C₂₃	—	4	1	no	—
344	C₂×D₄×C₂₃	—	4	1	no	—
345	C₂×D₄×C₂₃	—	4	4	no	—
346	C₂×D₄×C₂₃	—	4	4	no	—
347	C₂×D₄×C₂₃	—	4	8	no	—
348	C₂×D₄×C₂₃	—	8	4	no	—
349	C₂×D₄×C₂₃	—	8	2	no	—
350	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
353	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
354	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
355	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
356	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₂₃	—	2	1	no	—
358	C₂²×C₄×C₂₃	—	2	1	no	—
359	C₂²×C₄×C₂₃	—	2	1	no	—
360	C₂²×C₄×C₂₃	—	2	1	no	—
361	C₂²×C₄×C₂₃	—	2	1	no	—
362	C₂²×C₄×C₂₃	—	2	1	no	—
363	C₂²×C₄×C₂₃	—	2	1	no	—
364	C₂²×C₄×C₂₃	—	2	2	no	—
365	C₂²×C₄×C₂₃	—	2	1	no	—
366	C₂²×C₄×C₂₃	—	2	1	no	—
367	C₂²×C₄×C₂₃	—	2	2	no	—
368	C₂²×C₄×C₂₃	—	2	1	no	—
369	C₂²×C₄×C₂₃	—	2	2	no	—
370	C₂²×C₄×C₂₃	—	4	1	no	—
371	C₂²×C₄×C₂₃	—	4	1	no	—
372	C₂²×C₄×C₂₃	—	4	4	no	—
373	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
374	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
376	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
380	Q₁₆×C₂₃	—	2	4	no	—
381	Q₁₆×C₂₃	—	2	4	no	—
382	Q₁₆×C₂₃	—	4	2	no	—
383	Q₁₆×C₂₃	—	4	2	no	—
384	SD₁₆×C₂₃	—	2	4	no	—
385	SD₁₆×C₂₃	—	2	4	no	—
386	SD₁₆×C₂₃	—	4	2	no	—
387	SD₁₆×C₂₃	—	4	2	no	—
388	SD₁₆×C₂₃	—	4	2	no	—
389	SD₁₆×C₂₃	—	4	2	no	—
390	SD₁₆×C₂₃	—	4	2	no	—
391	SD₁₆×C₂₃	—	4	2	no	—
392	M₁₆×C₂₃	—	4	1	no	—
393	M₁₆×C₂₃	—	4	2	no	—
394	M₁₆×C₂₃	—	4	1	no	—
395	C₂×C₈×C₂₃	—	4	1	no	—
396	C₂×C₈×C₂₃	—	4	2	no	—
397	C₂×C₈×C₂₃	—	4	1	no	—
398	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
399	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
400	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
401	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₂₃	—	2	1	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	1	no	—
409	C₄⋊C₄×C₂₃	—	2	1	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	2	no	—
414	C₄⋊C₄×C₂₃	—	2	2	no	—
415	C₄⋊C₄×C₂₃	—	2	2	no	—
416	C₄⋊C₄×C₂₃	—	2	2	no	—
417	C₄⋊C₄×C₂₃	—	2	2	no	—
418	C₄⋊C₄×C₂₃	—	2	2	no	—
419	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
420	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
421	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
422	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
423	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
424	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
425	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
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	2	no	—
433	C₂²⋊C₄×C₂₃	—	2	2	no	—
434	C₂²⋊C₄×C₂₃	—	2	2	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	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
445	C₄²×C₂₃	—	2	2	no	—
446	C₄²×C₂₃	—	2	2	no	—
447	C₄²×C₂₃	—	2	2	no	—
448	C₄²×C₂₃	—	2	2	no	—
449	C₄²×C₂₃	C₂⁴	1	2	yes	—
450	#61618	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
451	C₂³×C₂₃	—	2	1	no	—
452	C₂³×C₂₃	—	2	2	no	—
453	C₂³×C₂₃	—	2	2	no	—
454	C₂³×C₂₃	—	2	1	no	—
455	C₂³×C₂₃	—	4	1	no	—
456	C₂³×C₂₃	—	4	1	no	—
457	C₂³×C₂₃	—	4	2	no	—
458	C₂³×C₂₃	—	4	4	no	—
459	C₂³×C₂₃	—	4	2	no	—
460	C₂³×C₂₃	—	4	2	no	—
461	C₂³×C₂₃	—	8	1	no	—
462	C₂³×C₂₃	—	8	1	no	—
463	C₂³×C₂₃	—	8	2	no	—
464	C₂³×C₂₃	—	8	2	no	—
465	C₂³×C₂₃	—	8	1	no	—
466	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
467	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
468	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
469	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
470	Q₈×C₂₃	—	2	1	no	—
471	Q₈×C₂₃	—	2	2	no	—
472	Q₈×C₂₃	—	2	2	no	—
473	Q₈×C₂₃	—	2	2	no	—
474	Q₈×C₂₃	—	2	2	no	—
475	Q₈×C₂₃	—	2	1	no	—
476	Q₈×C₂₃	—	2	1	no	—
477	Q₈×C₂₃	—	4	1	no	—
478	Q₈×C₂₃	—	4	2	no	—
479	Q₈×C₂₃	—	8	1	no	—
480	Q₈×C₂₃	—	8	2	no	—
481	Q₈×C₂₃	—	8	1	no	—
482	Q₈×C₂₃	H(5,𝔽₂)	1	2	yes	—
483	D₄×C₂₃	—	2	4	no	—
484	D₄×C₂₃	—	2	4	no	—
485	D₄×C₂₃	—	2	1	no	—
486	D₄×C₂₃	—	2	2	no	—
487	D₄×C₂₃	—	2	1	no	—
488	D₄×C₂₃	—	2	2	no	—
489	D₄×C₂₃	—	2	1	no	—
490	D₄×C₂₃	—	4	1	no	—
491	D₄×C₂₃	—	4	2	no	—
492	D₄×C₂₃	—	4	2	no	—
493	D₄×C₂₃	—	4	4	no	—
494	D₄×C₂₃	—	4	2	no	—
495	D₄×C₂₃	—	4	4	no	—
496	D₄×C₂₃	—	4	2	no	—
497	D₄×C₂₃	—	4	2	no	—
498	D₄×C₂₃	—	4	2	no	—
499	D₄×C₂₃	—	4	2	no	—
500	D₄×C₂₃	—	4	4	no	—
501	D₄×C₂₃	—	8	2	no	—
502	D₄×C₂₃	—	8	2	no	—
503	D₄×C₂₃	—	8	2	no	—
504	D₄×C₂₃	—	8	2	no	—
505	D₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
506	C₂×C₄×C₂₃	—	2	4	no	—
507	C₂×C₄×C₂₃	—	2	1	no	—
508	C₂×C₄×C₂₃	—	2	1	no	—
509	C₂×C₄×C₂₃	—	2	1	no	—
510	C₂×C₄×C₂₃	—	2	2	no	—
511	C₂×C₄×C₂₃	—	2	1	no	—
512	C₂×C₄×C₂₃	—	2	1	no	—
513	C₂×C₄×C₂₃	—	2	2	no	—
514	C₂×C₄×C₂₃	—	2	1	no	—
515	C₂×C₄×C₂₃	—	2	1	no	—
516	C₂×C₄×C₂₃	—	2	2	no	—
517	C₂×C₄×C₂₃	—	2	2	no	—
518	C₂×C₄×C₂₃	—	2	2	no	—
519	C₂×C₄×C₂₃	—	2	2	no	—
520	C₂×C₄×C₂₃	—	2	2	no	—
521	C₂×C₄×C₂₃	—	2	1	no	—
522	C₂×C₄×C₂₃	—	4	1	no	—
523	C₂×C₄×C₂₃	—	4	1	no	—
524	C₂×C₄×C₂₃	—	4	1	no	—
525	C₂×C₄×C₂₃	—	4	2	no	—
526	C₂×C₄×C₂₃	—	4	4	no	—
527	C₂×C₄×C₂₃	—	4	2	no	—
528	C₂×C₄×C₂₃	—	4	2	no	—
529	C₂×C₄×C₂₃	—	4	2	no	—
530	C₂×C₄×C₂₃	—	4	2	no	—
531	C₂×C₄×C₂₃	—	4	2	no	—
532	C₂×C₄×C₂₃	—	8	2	no	—
533	C₂×C₄×C₂₃	—	8	1	no	—
534	C₂×C₄×C₂₃	—	8	1	no	—
535	C₂×C₄×C₂₃	—	8	1	no	—
536	C₂×C₄×C₂₃	—	8	2	no	—
537	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
538	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
539	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
540	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
544	C₈×C₂₃	—	2	2	no	—
545	C₈×C₂₃	—	2	2	no	—
546	C₈×C₂₃	—	2	2	no	—
547	C₈×C₂₃	—	2	2	no	—
548	#3538	C₂×C₂₃	1	1	yes	characteristic, complemented
549	#3488	C₂×C₂₃	1	1	yes	characteristic
550	#3323	C₂×C₂₃	1	2	yes	complemented
551	#3317	C₂×C₂₃	1	2	yes	complemented
552	#3310	C₂×C₂₃	1	2	yes	complemented
553	#3300	C₂×C₂₃	1	2	yes	complemented
554	D₄×SD₁₆	C₂×C₂₃	1	2	yes	complemented
555	#3278	C₂×C₂₃	1	2	yes	complemented
556	#3270	C₂×C₂₃	1	2	yes	complemented
557	#3266	C₂×C₂₃	1	2	yes	complemented
558	#3222	C₂×C₂₃	1	2	yes	complemented
559	#3201	C₂×C₂₃	1	2	yes	complemented
560	#3193	C₂×C₂₃	1	1	yes	characteristic, complemented
561	#3187	C₂×C₂₃	1	1	yes	characteristic, complemented
562	#3120	C₂×C₂₃	1	2	yes	complemented
563	#3009	C₂×C₂₃	1	2	yes	complemented
564	#3007	C₂×C₂₃	1	1	yes	characteristic, complemented
565	C₂×#452	C₂×C₂₃	1	1	yes	characteristic, complemented
566	#2976	C₂×C₂₃	1	1	yes	characteristic, complemented
567	C₂²×C₂₃	—	2	1	no	—
568	C₂²×C₂₃	—	2	1	no	—
569	C₂²×C₂₃	—	2	1	no	—
570	C₂²×C₂₃	—	2	2	no	—
571	C₂²×C₂₃	—	2	1	no	—
572	C₂²×C₂₃	—	2	1	no	—
573	C₂²×C₂₃	—	2	1	no	—
574	C₂²×C₂₃	—	2	2	no	—
575	C₂²×C₂₃	—	2	2	no	—
576	C₂²×C₂₃	—	2	1	no	—
577	C₂²×C₂₃	—	2	2	no	—
578	C₂²×C₂₃	—	2	1	no	—
579	C₂²×C₂₃	—	4	1	no	—
580	C₂²×C₂₃	—	4	1	no	—
581	C₂²×C₂₃	—	4	1	no	—
582	C₂²×C₂₃	—	4	2	no	—
583	C₂²×C₂₃	—	4	1	no	—
584	C₂²×C₂₃	—	4	2	no	—
585	C₂²×C₂₃	—	4	2	no	—
586	C₂²×C₂₃	—	4	1	no	—
587	C₂²×C₂₃	—	8	2	no	—
588	C₂²×C₂₃	—	8	4	no	—
589	C₂²×C₂₃	—	16	4	no	—
590	C₂²×C₂₃	—	16	2	no	—
591	C₂²×C₂₃	#577	1	2	yes	—
592	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
593	C₄×C₂₃	—	2	2	no	—
594	C₄×C₂₃	—	2	1	no	—
595	C₄×C₂₃	—	2	2	no	—
596	C₄×C₂₃	—	2	1	no	—
597	C₄×C₂₃	—	2	2	no	—
598	C₄×C₂₃	—	2	1	no	—
599	C₄×C₂₃	—	2	2	no	—
600	C₄×C₂₃	—	4	2	no	—
601	C₄×C₂₃	—	4	1	no	—
602	C₄×C₂₃	—	4	2	no	—
603	C₄×C₂₃	—	4	2	no	—
604	C₄×C₂₃	—	4	2	no	—
605	C₄×C₂₃	—	4	2	no	—
606	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
607	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
608	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic
609	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
610	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic, complemented
611	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic, complemented
612	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
613	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
614	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
615	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
616	#563	—	2	2	no	—
617	#552	C₂²×C₂₃	1	2	yes	complemented
618	#552	C₂²×C₂₃	1	2	yes	complemented
619	#551	—	2	2	no	—
620	#550	C₂²×C₂₃	1	2	yes	—
621	D₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
622	D₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
623	#548	C₂²×C₂₃	1	2	yes	—
624	#546	—	2	2	no	—
625	#546	C₂²×C₂₃	1	2	yes	—
626	D₄²	—	2	2	no	—
627	D₄²	C₂²×C₂₃	1	2	yes	—
628	#544	—	2	1	no	—
629	#544	—	2	1	no	—
630	#541	C₂²×C₂₃	1	2	yes	complemented
631	#539	—	2	1	no	—
632	#539	—	2	1	no	—
633	#537	—	2	1	no	—
634	#537	C₂²×C₂₃	1	1	yes	characteristic
635	#536	C₂²×C₂₃	1	2	yes	complemented
636	#535	—	2	1	no	—
637	#535	C₂²×C₂₃	1	1	yes	characteristic
638	#525	—	2	1	no	—
639	#525	C₂²×C₂₃	1	1	yes	characteristic
640	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
641	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
642	C₂×#121	—	2	1	no	—
643	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
644	#520	C₂²×C₂₃	1	1	yes	characteristic
645	#497	C₂²×C₂₃	1	2	yes	complemented
646	#492	C₂²×C₂₃	1	2	yes	complemented
647	#490	C₂²×C₂₃	1	2	yes	complemented
648	#488	C₂²×C₂₃	1	2	yes	complemented
649	#485	C₂²×C₂₃	1	2	yes	complemented
650	#484	C₂²×C₂₃	1	2	yes	complemented
651	#483	C₂²×C₂₃	1	2	yes	complemented
652	#482	C₂²×C₂₃	1	2	yes	complemented
653	#481	C₂²×C₂₃	1	2	yes	complemented
654	#480	C₂²×C₂₃	1	2	yes	complemented
655	#479	C₂²×C₂₃	1	2	yes	complemented
656	#478	C₂²×C₂₃	1	2	yes	complemented
657	#470	C₂²×C₂₃	1	2	yes	complemented
658	#468	C₂²×C₂₃	1	2	yes	complemented
659	#468	C₂²×C₂₃	1	2	yes	complemented
660	#468	C₂²×C₂₃	1	2	yes	complemented
661	#467	C₂²×C₂₃	1	2	yes	complemented
662	#465	C₂²×C₂₃	1	2	yes	complemented
663	#465	C₂²×C₂₃	1	2	yes	complemented
664	#465	C₂²×C₂₃	1	2	yes	complemented
665	#464	C₂²×C₂₃	1	2	yes	complemented
666	#464	C₂²×C₂₃	1	2	yes	complemented
667	#462	C₂²×C₂₃	1	2	yes	complemented
668	#461	C₂²×C₂₃	1	2	yes	complemented
669	#460	C₂²×C₂₃	1	2	yes	complemented
670	#460	C₂²×C₂₃	1	2	yes	complemented
671	#452	C₂²×C₂₃	1	2	yes	—
672	#452	C₂²×C₂₃	1	2	yes	—
673	#452	C₂²×C₂₃	1	2	yes	complemented
674	#452	C₂²×C₂₃	1	2	yes	complemented
675	#452	C₂²×C₂₃	1	2	yes	complemented
676	#452	C₂²×C₂₃	1	2	yes	complemented
677	#452	C₂²×C₂₃	1	2	yes	complemented
678	#452	C₂²×C₂₃	1	2	yes	complemented
679	#451	C₂²×C₂₃	1	2	yes	complemented
680	#451	C₂²×C₂₃	1	2	yes	complemented
681	#450	C₂²×C₂₃	1	2	yes	complemented
682	#450	C₂²×C₂₃	1	2	yes	complemented
683	#450	C₂²×C₂₃	1	2	yes	complemented
684	#450	C₂²×C₂₃	1	2	yes	complemented
685	#450	C₂²×C₂₃	1	2	yes	complemented
686	#448	C₂²×C₂₃	1	2	yes	complemented
687	#448	C₂²×C₂₃	1	2	yes	complemented
688	#448	C₂²×C₂₃	1	2	yes	complemented
689	#441	C₂²×C₂₃	1	2	yes	complemented
690	#440	C₂²×C₂₃	1	2	yes	complemented
691	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
692	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
693	#436	C₂²×C₂₃	1	2	yes	complemented
694	#435	C₂²×C₂₃	1	2	yes	complemented
695	#435	C₂²×C₂₃	1	2	yes	complemented
696	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
697	#433	C₂²×C₂₃	1	2	yes	complemented
698	#418	C₂²×C₂₃	1	2	yes	complemented
699	#417	C₂²×C₂₃	1	1	yes	characteristic, complemented
700	#417	C₂²×C₂₃	1	1	yes	characteristic, complemented
701	#416	C₂²×C₂₃	1	2	yes	complemented
702	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
703	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
704	#408	C₂²×C₂₃	1	2	yes	complemented
705	#407	C₂²×C₂₃	1	1	yes	characteristic, complemented
706	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
707	C₂×C₂₃	—	2	2	no	—
708	C₂×C₂₃	—	4	1	no	—
709	C₂×C₂₃	—	4	1	no	—
710	C₂×C₂₃	—	4	2	no	—
711	C₂×C₂₃	—	4	2	no	—
712	C₂×C₂₃	—	8	1	no	—
713	C₂×C₂₃	—	8	2	no	—
714	C₂×C₂₃	#3484	1	1	yes	characteristic
715	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
716	C₂×C₂₃	#3586	1	1	yes	characteristic
717	H(5,𝔽₂)	—	4	2	no	—
718	H(5,𝔽₂)	—	4	2	no	—
719	C₂×#41	—	2	1	no	—
720	C₂×#41	—	2	1	no	—
721	C₂×#41	—	2	1	no	—
722	C₂×#41	—	4	2	no	—
723	C₂×#41	—	4	2	no	—
724	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
725	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
726	C₂×#41	C₂³×C₂₃	1	2	yes	—
727	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
728	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
729	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
730	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
731	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
732	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
733	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
734	C₂²×D₄	—	2	1	no	—
735	C₂²×D₄	—	2	1	no	—
736	C₂²×D₄	—	2	1	no	—
737	C₂²×D₄	—	2	2	no	—
738	C₂²×D₄	—	2	2	no	—
739	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
740	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
741	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
742	C₂³×C₄	—	2	1	no	—
743	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
744	#137	—	4	2	no	—
745	#137	—	4	4	no	—
746	#137	—	4	2	no	—
747	C₂×Q₁₆	—	4	2	no	—
748	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
749	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
750	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
751	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
752	C₂×SD₁₆	—	4	2	no	—
753	C₂×SD₁₆	—	4	4	no	—
754	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
755	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
756	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
757	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
758	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
759	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
760	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
761	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
762	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
763	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
764	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
765	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
766	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
767	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
768	C₄⋊Q₈	—	2	2	no	—
769	C₄⋊Q₈	—	2	2	no	—
770	C₄⋊Q₈	—	2	2	no	—
771	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
772	#127	—	2	2	no	—
773	#127	C₂³×C₂₃	1	2	yes	—
774	#126	—	2	2	no	—
775	#126	—	2	2	no	—
776	#126	—	2	2	no	—
777	#126	—	2	2	no	—
778	#125	—	2	2	no	—
779	#125	—	2	2	no	—
780	#125	—	2	2	no	—
781	#125	—	2	2	no	—
782	#125	C₂³×C₂₃	1	2	yes	—
783	#124	—	2	2	no	—
784	#124	—	2	2	no	—
785	#124	C₂³×C₂₃	1	2	yes	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	no	—
791	#123	D₄×C₂₃	1	2	yes	—
792	C₂²⋊Q₈	—	2	1	no	—
793	C₂²⋊Q₈	—	2	1	no	—
794	C₂²⋊Q₈	—	2	1	no	—
795	C₂²⋊Q₈	—	2	1	no	—
796	C₂²⋊Q₈	—	2	1	no	—
797	C₂²⋊Q₈	—	2	2	no	—
798	C₂²⋊Q₈	—	2	2	no	—
799	C₂²⋊Q₈	—	2	2	no	—
800	C₂²⋊Q₈	—	2	2	no	—
801	C₂²⋊Q₈	—	2	2	no	—
802	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
803	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
804	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
805	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
806	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
807	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
808	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
809	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
810	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
811	#121	—	2	1	no	—
812	#121	—	2	2	no	—
813	#121	—	2	2	no	—
814	#121	—	2	1	no	—
815	#121	—	2	1	no	—
816	#121	—	2	1	no	—
817	#121	—	2	1	no	—
818	#121	—	2	2	no	—
819	#121	—	2	2	no	—
820	#121	—	2	2	no	—
821	#121	—	2	2	no	—
822	#121	D₄×C₂₃	1	1	yes	characteristic
823	#121	D₄×C₂₃	1	1	yes	characteristic
824	#121	C₂³×C₂₃	1	2	yes	—
825	#121	C₂³×C₂₃	1	2	yes	—
826	#121	C₂³×C₂₃	1	2	yes	—
827	#120	—	2	2	no	—
828	#120	—	2	2	no	—
829	#120	—	2	2	no	—
830	#120	—	2	2	no	—
831	#120	D₄×C₂₃	1	2	yes	—
832	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
833	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
834	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
835	C₄×D₄	—	2	2	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	—	2	2	no	—
838	C₄×D₄	—	2	2	no	—
839	C₄×D₄	—	2	2	no	—
840	C₄×D₄	C₂³×C₂₃	1	2	yes	—
841	C₄×D₄	C₂³×C₂₃	1	2	yes	—
842	C₄×D₄	C₂³×C₂₃	1	2	yes	—
843	#117	—	2	1	no	—
844	#117	—	2	2	no	—
845	#117	—	2	2	no	—
846	#117	C₂³×C₂₃	1	2	yes	—
847	#117	C₂³×C₂₃	1	1	yes	characteristic
848	C₂×C₄⋊C₄	—	2	1	no	—
849	C₂×C₄⋊C₄	—	2	1	no	—
850	C₂×C₄⋊C₄	—	2	1	no	—
851	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
852	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
853	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
854	C₂×C₂²⋊C₄	—	2	1	no	—
855	C₂×C₂²⋊C₄	—	2	1	no	—
856	C₂×C₂²⋊C₄	—	2	1	no	—
857	C₂×C₂²⋊C₄	—	2	2	no	—
858	#107	C₂³×C₂₃	1	2	yes	—
859	#107	C₂³×C₂₃	1	2	yes	—
860	#106	C₂³×C₂₃	1	2	yes	—
861	#106	C₂³×C₂₃	1	2	yes	—
862	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
863	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
864	#103	C₂³×C₂₃	1	2	yes	—
865	#103	C₂³×C₂₃	1	2	yes	—
866	#103	C₂³×C₂₃	1	2	yes	—
867	#103	C₂³×C₂₃	1	2	yes	—
868	#103	C₂³×C₂₃	1	2	yes	—
869	#103	C₂³×C₂₃	1	2	yes	—
870	#103	C₂³×C₂₃	1	2	yes	—
871	#103	C₂³×C₂₃	1	2	yes	—
872	#102	C₂³×C₂₃	1	2	yes	—
873	#102	C₂³×C₂₃	1	2	yes	—
874	#102	C₂³×C₂₃	1	2	yes	—
875	#102	C₂³×C₂₃	1	2	yes	—
876	#102	C₂³×C₂₃	1	2	yes	—
877	#102	C₂³×C₂₃	1	2	yes	—
878	#102	C₂³×C₂₃	1	2	yes	—
879	#102	C₂³×C₂₃	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
884	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
885	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
886	#97	C₂³×C₂₃	1	2	yes	—
887	C₄×C₈	C₂³×C₂₃	1	2	yes	—
888	C₂₃	#61618	1	1	yes	characteristic, direct product factor, Sylow
889	C₂⁴	—	2	1	no	—
890	C₂⁴	—	2	2	no	—
891	C₂⁴	—	2	1	no	—
892	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
893	#41	—	2	2	no	—
894	#41	—	2	2	no	—
895	#41	—	2	2	no	—
896	#41	—	2	4	no	—
897	#41	—	2	2	no	—
898	#41	—	4	1	no	—
899	#41	—	4	1	no	—
900	#41	—	4	1	no	—
901	#41	—	4	1	no	—
902	#41	—	4	1	no	—
903	#41	—	4	1	no	—
904	#41	—	4	2	no	—
905	#41	—	4	4	no	—
906	#41	—	4	4	no	—
907	#41	—	4	4	no	—
908	C₂×Q₈	—	2	1	no	—
909	C₂×Q₈	—	2	1	no	—
910	C₂×Q₈	—	2	1	no	—
911	C₂×Q₈	—	2	2	no	—
912	C₂×Q₈	—	2	2	no	—
913	C₂×Q₈	—	4	1	no	—
914	C₂×Q₈	—	4	1	no	—
915	C₂×Q₈	—	4	2	no	—
916	C₂×Q₈	—	4	1	no	—
917	C₂×Q₈	—	4	1	no	—
918	C₂×Q₈	—	4	1	no	—
919	C₂×Q₈	—	4	2	no	—
920	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
921	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
922	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
923	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
924	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	4	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	1	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	4	1	no	—
941	C₂×D₄	—	4	2	no	—
942	C₂×D₄	—	4	1	no	—
943	C₂×D₄	—	4	1	no	—
944	C₂×D₄	—	4	4	no	—
945	C₂×D₄	—	4	4	no	—
946	C₂×D₄	—	4	8	no	—
947	C₂×D₄	—	8	4	no	—
948	C₂×D₄	—	8	2	no	—
949	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
950	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
951	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
952	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
953	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
954	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
955	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	1	no	—
958	C₂²×C₄	—	2	1	no	—
959	C₂²×C₄	—	2	1	no	—
960	C₂²×C₄	—	2	1	no	—
961	C₂²×C₄	—	2	1	no	—
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	2	no	—
964	C₂²×C₄	—	2	1	no	—
965	C₂²×C₄	—	2	1	no	—
966	C₂²×C₄	—	2	2	no	—
967	C₂²×C₄	—	2	1	no	—
968	C₂²×C₄	—	2	2	no	—
969	C₂²×C₄	—	4	1	no	—
970	C₂²×C₄	—	4	1	no	—
971	C₂²×C₄	—	4	4	no	—
972	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
973	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
974	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
975	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
976	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
977	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
978	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
979	Q₁₆	—	2	4	no	—
980	Q₁₆	—	2	4	no	—
981	Q₁₆	—	4	2	no	—
982	Q₁₆	—	4	2	no	—
983	SD₁₆	—	2	4	no	—
984	SD₁₆	—	2	4	no	—
985	SD₁₆	—	4	2	no	—
986	SD₁₆	—	4	2	no	—
987	SD₁₆	—	4	2	no	—
988	SD₁₆	—	4	2	no	—
989	SD₁₆	—	4	2	no	—
990	SD₁₆	—	4	2	no	—
991	M₁₆	—	4	1	no	—
992	M₁₆	—	4	2	no	—
993	M₁₆	—	4	1	no	—
994	C₂×C₈	—	4	1	no	—
995	C₂×C₈	—	4	2	no	—
996	C₂×C₈	—	4	1	no	—
997	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
998	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
999	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1000	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	—	2	1	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	2	no	—
1011	C₄⋊C₄	—	2	2	no	—
1012	C₄⋊C₄	—	2	2	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	2	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1019	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
1020	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1021	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1022	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1023	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1024	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1040	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1041	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1042	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1043	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1044	C₄²	—	2	2	no	—
1045	C₄²	—	2	2	no	—
1046	C₄²	—	2	2	no	—
1047	C₄²	—	2	2	no	—
1048	C₄²	C₂⁴×C₂₃	1	2	yes	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	2	2	no	—
1051	C₂³	—	2	2	no	—
1052	C₂³	—	2	1	no	—
1053	C₂³	—	4	1	no	—
1054	C₂³	—	4	1	no	—
1055	C₂³	—	4	2	no	—
1056	C₂³	—	4	4	no	—
1057	C₂³	—	4	2	no	—
1058	C₂³	—	4	2	no	—
1059	C₂³	—	8	1	no	—
1060	C₂³	—	8	1	no	—
1061	C₂³	—	8	2	no	—
1062	C₂³	—	8	2	no	—
1063	C₂³	—	8	1	no	—
1064	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1065	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1066	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1067	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1068	Q₈	—	2	1	no	—
1069	Q₈	—	2	2	no	—
1070	Q₈	—	2	2	no	—
1071	Q₈	—	2	2	no	—
1072	Q₈	—	2	2	no	—
1073	Q₈	—	2	1	no	—
1074	Q₈	—	2	1	no	—
1075	Q₈	—	4	1	no	—
1076	Q₈	—	4	2	no	—
1077	Q₈	—	8	1	no	—
1078	Q₈	—	8	2	no	—
1079	Q₈	—	8	1	no	—
1080	Q₈	C₂₃×H(5,𝔽₂)	1	2	yes	—
1081	D₄	—	2	4	no	—
1082	D₄	—	2	4	no	—
1083	D₄	—	2	1	no	—
1084	D₄	—	2	2	no	—
1085	D₄	—	2	1	no	—
1086	D₄	—	2	2	no	—
1087	D₄	—	2	1	no	—
1088	D₄	—	4	1	no	—
1089	D₄	—	4	2	no	—
1090	D₄	—	4	2	no	—
1091	D₄	—	4	4	no	—
1092	D₄	—	4	2	no	—
1093	D₄	—	4	4	no	—
1094	D₄	—	4	2	no	—
1095	D₄	—	4	2	no	—
1096	D₄	—	4	2	no	—
1097	D₄	—	4	2	no	—
1098	D₄	—	4	4	no	—
1099	D₄	—	8	2	no	—
1100	D₄	—	8	2	no	—
1101	D₄	—	8	2	no	—
1102	D₄	—	8	2	no	—
1103	D₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1104	C₂×C₄	—	2	4	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	2	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	2	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	4	1	no	—
1121	C₂×C₄	—	4	1	no	—
1122	C₂×C₄	—	4	1	no	—
1123	C₂×C₄	—	4	2	no	—
1124	C₂×C₄	—	4	4	no	—
1125	C₂×C₄	—	4	2	no	—
1126	C₂×C₄	—	4	2	no	—
1127	C₂×C₄	—	4	2	no	—
1128	C₂×C₄	—	4	2	no	—
1129	C₂×C₄	—	4	2	no	—
1130	C₂×C₄	—	8	2	no	—
1131	C₂×C₄	—	8	1	no	—
1132	C₂×C₄	—	8	1	no	—
1133	C₂×C₄	—	8	1	no	—
1134	C₂×C₄	—	8	2	no	—
1135	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1136	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1137	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1138	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1139	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1140	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1141	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1142	C₈	—	2	2	no	—
1143	C₈	—	2	2	no	—
1144	C₈	—	2	2	no	—
1145	C₈	—	2	2	no	—
1146	C₂²	—	2	1	no	—
1147	C₂²	—	2	1	no	—
1148	C₂²	—	2	1	no	—
1149	C₂²	—	2	1	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	2	no	—
1152	C₂²	—	2	1	no	—
1153	C₂²	—	2	2	no	—
1154	C₂²	—	2	1	no	—
1155	C₂²	—	2	1	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	2	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	2	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	1	no	—
1165	C₂²	—	4	2	no	—
1166	C₂²	—	8	2	no	—
1167	C₂²	—	8	4	no	—
1168	C₂²	—	16	4	no	—
1169	C₂²	—	16	2	no	—
1170	C₂²	C₂₃×#577	1	2	yes	—
1171	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1172	C₄	—	2	1	no	—
1173	C₄	—	2	2	no	—
1174	C₄	—	2	1	no	—
1175	C₄	—	2	2	no	—
1176	C₄	—	2	1	no	—
1177	C₄	—	2	2	no	—
1178	C₄	—	2	2	no	—
1179	C₄	—	4	1	no	—
1180	C₄	—	4	2	no	—
1181	C₄	—	4	2	no	—
1182	C₄	—	4	2	no	—
1183	C₄	—	4	2	no	—
1184	C₄	—	4	2	no	—
1185	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1186	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1187	C₂	—	2	2	no	—
1188	C₂	—	4	1	no	—
1189	C₂	—	4	1	no	—
1190	C₂	—	4	2	no	—
1191	C₂	—	4	2	no	—
1192	C₂	—	8	1	no	—
1193	C₂	—	8	2	no	—
1194	C₂	C₂₃×#3484	1	1	yes	characteristic
1195	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
1196	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×#3488	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3538	C₂	semidirect
3. C₂₃×#3323	C₂	semidirect
4. C₂₃×#3317	C₂	semidirect
5. C₂₃×#3310	C₂	semidirect
6. C₂₃×#3300	C₂	semidirect
7. D₄×SD₁₆×C₂₃	C₂	semidirect
8. C₂₃×#3278	C₂	semidirect
9. C₂₃×#3270	C₂	semidirect
10. C₂₃×#3266	C₂	semidirect
11. C₂₃×#3222	C₂	semidirect
12. C₂₃×#3201	C₂	semidirect
13. C₂₃×#3193	C₂	semidirect
14. C₂₃×#3187	C₂	semidirect
15. C₂₃×#3120	C₂	semidirect
16. C₂₃×#3009	C₂	semidirect
17. C₂₃×#3007	C₂	semidirect
18. C₂×C₂₃×#452	C₂	semidirect
19. C₂₃×#2976	C₂	semidirect
22. C₂×C₂₃×#137	C₂²	semidirect
23. C₂×C₂₃×#137	C₂²	semidirect
24. C₂×C₂₃×#137	C₂²	semidirect
25. C₂²×Q₁₆×C₂₃	C₂²	semidirect
26. C₂²×SD₁₆×C₂₃	C₂²	semidirect
27. C₂²×SD₁₆×C₂₃	C₂²	semidirect
29. C₂₃×#552	C₂²	semidirect
30. C₂₃×#552	C₂²	semidirect
33. D₄×Q₈×C₂₃	C₂²	semidirect
34. D₄×Q₈×C₂₃	C₂²	semidirect
42. C₂₃×#541	C₂²	semidirect
47. C₂₃×#536	C₂²	semidirect
52. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
53. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
57. C₂₃×#497	C₂²	semidirect
58. C₂₃×#492	C₂²	semidirect
59. C₂₃×#490	C₂²	semidirect
60. C₂₃×#488	C₂²	semidirect
61. C₂₃×#485	C₂²	semidirect
62. C₂₃×#484	C₂²	semidirect
63. C₂₃×#483	C₂²	semidirect
64. C₂₃×#482	C₂²	semidirect
65. C₂₃×#481	C₂²	semidirect
66. C₂₃×#480	C₂²	semidirect
67. C₂₃×#479	C₂²	semidirect
68. C₂₃×#478	C₂²	semidirect
69. C₂₃×#470	C₂²	semidirect
70. C₂₃×#468	C₂²	semidirect
71. C₂₃×#468	C₂²	semidirect
72. C₂₃×#468	C₂²	semidirect
73. C₂₃×#467	C₂²	semidirect
74. C₂₃×#465	C₂²	semidirect
75. C₂₃×#465	C₂²	semidirect
76. C₂₃×#465	C₂²	semidirect
77. C₂₃×#464	C₂²	semidirect
78. C₂₃×#464	C₂²	semidirect
79. C₂₃×#462	C₂²	semidirect
80. C₂₃×#461	C₂²	semidirect
81. C₂₃×#460	C₂²	semidirect
82. C₂₃×#460	C₂²	semidirect
85. C₂₃×#452	C₂²	semidirect
86. C₂₃×#452	C₂²	semidirect
87. C₂₃×#452	C₂²	semidirect
88. C₂₃×#452	C₂²	semidirect
89. C₂₃×#452	C₂²	semidirect
90. C₂₃×#452	C₂²	semidirect
91. C₂₃×#451	C₂²	semidirect
92. C₂₃×#451	C₂²	semidirect
93. C₂₃×#450	C₂²	semidirect
94. C₂₃×#450	C₂²	semidirect
95. C₂₃×#450	C₂²	semidirect
96. C₂₃×#450	C₂²	semidirect
97. C₂₃×#450	C₂²	semidirect
98. C₂₃×#448	C₂²	semidirect
99. C₂₃×#448	C₂²	semidirect
100. C₂₃×#448	C₂²	semidirect
101. C₂₃×#441	C₂²	semidirect
102. C₂₃×#440	C₂²	semidirect
103. C₄×Q₁₆×C₂₃	C₂²	semidirect
104. C₄×SD₁₆×C₂₃	C₂²	semidirect
105. C₂₃×#436	C₂²	semidirect
106. C₂₃×#435	C₂²	semidirect
107. C₂₃×#435	C₂²	semidirect
108. C₈×D₄×C₂₃	C₂²	semidirect
109. C₂₃×#433	C₂²	semidirect
110. C₂₃×#418	C₂²	semidirect
111. C₂₃×#417	C₂²	semidirect
112. C₂₃×#417	C₂²	semidirect
113. C₂₃×#416	C₂²	semidirect
114. C₂×C₂₃×#103	C₂²	semidirect
115. C₂×C₂₃×#102	C₂²	semidirect
116. C₂₃×#408	C₂²	semidirect
117. C₂₃×#407	C₂²	semidirect
118. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
450. #61618	C₂₃	direct (N × H)
548. #3538	C₂×C₂₃	semidirect
550. #3323	C₂×C₂₃	semidirect
551. #3317	C₂×C₂₃	semidirect
552. #3310	C₂×C₂₃	semidirect
553. #3300	C₂×C₂₃	semidirect
554. D₄×SD₁₆	C₂×C₂₃	semidirect
555. #3278	C₂×C₂₃	semidirect
556. #3270	C₂×C₂₃	semidirect
557. #3266	C₂×C₂₃	semidirect
558. #3222	C₂×C₂₃	semidirect
559. #3201	C₂×C₂₃	semidirect
560. #3193	C₂×C₂₃	semidirect
561. #3187	C₂×C₂₃	semidirect
562. #3120	C₂×C₂₃	semidirect
563. #3009	C₂×C₂₃	semidirect
564. #3007	C₂×C₂₃	semidirect
565. C₂×#452	C₂×C₂₃	semidirect
566. #2976	C₂×C₂₃	semidirect
610. C₂×#137	C₂²×C₂₃	semidirect
611. C₂×#137	C₂²×C₂₃	semidirect
612. C₂×#137	C₂²×C₂₃	semidirect
613. C₂²×Q₁₆	C₂²×C₂₃	semidirect
614. C₂²×SD₁₆	C₂²×C₂₃	semidirect
615. C₂²×SD₁₆	C₂²×C₂₃	semidirect
617. #552	C₂²×C₂₃	semidirect
618. #552	C₂²×C₂₃	semidirect
621. D₄×Q₈	C₂²×C₂₃	semidirect
622. D₄×Q₈	C₂²×C₂₃	semidirect
630. #541	C₂²×C₂₃	semidirect
635. #536	C₂²×C₂₃	semidirect
640. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
641. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
645. #497	C₂²×C₂₃	semidirect
646. #492	C₂²×C₂₃	semidirect
647. #490	C₂²×C₂₃	semidirect
648. #488	C₂²×C₂₃	semidirect
649. #485	C₂²×C₂₃	semidirect
650. #484	C₂²×C₂₃	semidirect
651. #483	C₂²×C₂₃	semidirect
652. #482	C₂²×C₂₃	semidirect
653. #481	C₂²×C₂₃	semidirect
654. #480	C₂²×C₂₃	semidirect
655. #479	C₂²×C₂₃	semidirect
656. #478	C₂²×C₂₃	semidirect
657. #470	C₂²×C₂₃	semidirect
658. #468	C₂²×C₂₃	semidirect
659. #468	C₂²×C₂₃	semidirect
660. #468	C₂²×C₂₃	semidirect
661. #467	C₂²×C₂₃	semidirect
662. #465	C₂²×C₂₃	semidirect
663. #465	C₂²×C₂₃	semidirect
664. #465	C₂²×C₂₃	semidirect
665. #464	C₂²×C₂₃	semidirect
666. #464	C₂²×C₂₃	semidirect
667. #462	C₂²×C₂₃	semidirect
668. #461	C₂²×C₂₃	semidirect
669. #460	C₂²×C₂₃	semidirect
670. #460	C₂²×C₂₃	semidirect
673. #452	C₂²×C₂₃	semidirect
674. #452	C₂²×C₂₃	semidirect
675. #452	C₂²×C₂₃	semidirect
676. #452	C₂²×C₂₃	semidirect
677. #452	C₂²×C₂₃	semidirect
678. #452	C₂²×C₂₃	semidirect
679. #451	C₂²×C₂₃	semidirect
680. #451	C₂²×C₂₃	semidirect
681. #450	C₂²×C₂₃	semidirect
682. #450	C₂²×C₂₃	semidirect
683. #450	C₂²×C₂₃	semidirect
684. #450	C₂²×C₂₃	semidirect
685. #450	C₂²×C₂₃	semidirect
686. #448	C₂²×C₂₃	semidirect
687. #448	C₂²×C₂₃	semidirect
688. #448	C₂²×C₂₃	semidirect
689. #441	C₂²×C₂₃	semidirect
690. #440	C₂²×C₂₃	semidirect
691. C₄×Q₁₆	C₂²×C₂₃	semidirect
692. C₄×SD₁₆	C₂²×C₂₃	semidirect
693. #436	C₂²×C₂₃	semidirect
694. #435	C₂²×C₂₃	semidirect
695. #435	C₂²×C₂₃	semidirect
696. C₈×D₄	C₂²×C₂₃	semidirect
697. #433	C₂²×C₂₃	semidirect
698. #418	C₂²×C₂₃	semidirect
699. #417	C₂²×C₂₃	semidirect
700. #417	C₂²×C₂₃	semidirect
701. #416	C₂²×C₂₃	semidirect
702. C₂×#103	C₂²×C₂₃	semidirect
703. C₂×#102	C₂²×C₂₃	semidirect
704. #408	C₂²×C₂₃	semidirect
705. #407	C₂²×C₂₃	semidirect
706. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
888. C₂₃	#61618	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×#3538	2
C₂₃×#3488	2
C₂₃×#3323	2
C₂₃×#3317	2
C₂₃×#3310	2
C₂₃×#3300	2
D₄×SD₁₆×C₂₃	2
C₂₃×#3278	2
C₂₃×#3270	2
C₂₃×#3266	2
C₂₃×#3222	2
C₂₃×#3201	2
C₂₃×#3193	2
C₂₃×#3187	2
C₂₃×#3120	2
C₂₃×#3009	2
C₂₃×#3007	2
C₂×C₂₃×#452	2
C₂₃×#2976	2
#61618	23

Subgroups — C23×#61618 #19209244

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61618 #19209244