Subgroups — C₂₃×#61428 #19209054

Order 5888.

1880 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3394	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3364	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3340	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3337	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3305	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3302	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3300	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3297	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3284	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3282	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3168	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3102	C₂	1	2	yes	maximal, complemented
19	C₂₃×#3102	C₂	1	2	yes	maximal, complemented
20	C₂₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₂₃×#135	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×SD₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×#135	C₂²	1	2	yes	—
25	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
26	C₂₃×#559	—	2	1	no	—
27	C₂₃×#559	C₂²	1	1	yes	characteristic, complemented
28	C₂₃×#557	C₂²	1	1	yes	characteristic, complemented
29	C₂₃×#556	—	2	1	no	—
30	C₂₃×#556	C₂²	1	1	yes	characteristic
31	C₂₃×#556	C₂²	1	1	yes	characteristic, complemented
32	C₂₃×#555	C₂²	1	1	yes	characteristic
33	C₂₃×#554	C₂²	1	1	yes	characteristic
34	C₂₃×#553	—	2	1	no	—
35	C₂₃×#553	—	2	2	no	—
36	C₂₃×#553	C₂²	1	2	yes	—
37	C₂₃×#552	—	2	1	no	—
38	C₂₃×#552	C₂²	1	2	yes	—
39	C₂₃×#551	—	2	2	no	—
40	C₂₃×#550	C₂²	1	1	yes	characteristic, complemented
41	C₂₃×#548	C₂²	1	2	yes	—
42	C₂₃×#547	C₂²	1	1	yes	characteristic
43	C₂₃×#546	C₂²	1	2	yes	—
44	C₂₃×#533	C₂²	1	1	yes	characteristic
45	C₂₃×#532	—	2	1	no	—
46	C₂₃×#532	C₂²	1	1	yes	characteristic
47	C₂₃×#529	—	2	2	no	—
48	C₂₃×#529	—	2	2	no	—
49	C₂₃×#529	C₂²	1	2	yes	—
50	C₂₃×#529	C₂²	1	2	yes	complemented
51	C₂₃×#525	—	2	1	no	—
52	C₄×#41×C₂₃	—	2	1	no	—
53	C₄×#41×C₂₃	C₂²	1	2	yes	—
54	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
55	C₄×#41×C₂₃	C₂²	1	2	yes	complemented
56	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
57	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
58	C₂×C₂₃×#117	—	2	1	no	—
59	C₂₃×#499	C₂²	1	2	yes	complemented
60	C₂₃×#498	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#495	C₂²	1	2	yes	—
62	C₂₃×#492	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#488	C₂²	1	2	yes	—
64	C₂₃×#488	C₂²	1	2	yes	complemented
65	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#485	C₂²	1	2	yes	complemented
68	C₂₃×#485	C₂²	1	2	yes	complemented
69	C₂₃×#484	C₂²	1	2	yes	—
70	C₂₃×#482	C₂²	1	2	yes	—
71	C₂₃×#482	C₂²	1	2	yes	complemented
72	C₂₃×#480	C₂²	1	2	yes	—
73	C₂₃×#479	C₂²	1	2	yes	complemented
74	C₂₃×#479	C₂²	1	2	yes	complemented
75	C₂₃×#478	C₂²	1	2	yes	—
76	C₂₃×#478	C₂²	1	2	yes	complemented
77	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
78	C₂₃×#477	C₂²	1	1	yes	characteristic, complemented
79	C₂₃×#474	C₂²	1	1	yes	characteristic
80	C₂₃×#474	C₂²	1	1	yes	characteristic
81	C₂₃×#467	C₂²	1	2	yes	complemented
82	C₂₃×#466	C₂²	1	2	yes	—
83	C₂₃×#465	C₂²	1	2	yes	—
84	C₂₃×#465	C₂²	1	2	yes	—
85	C₂₃×#465	C₂²	1	2	yes	—
86	C₂₃×#465	C₂²	1	2	yes	complemented
87	C₂₃×#464	C₂²	1	2	yes	—
88	C₂₃×#464	C₂²	1	2	yes	complemented
89	C₂₃×#463	C₂²	1	2	yes	—
90	C₂₃×#463	C₂²	1	2	yes	—
91	C₂₃×#462	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#462	C₂²	1	1	yes	characteristic, complemented
93	C₂₃×#459	C₂²	1	1	yes	characteristic
94	C₂₃×#459	C₂²	1	1	yes	characteristic
95	C₂₃×#452	C₂²	1	2	yes	—
96	C₂₃×#452	C₂²	1	2	yes	complemented
97	C₂₃×#451	C₂²	1	2	yes	—
98	C₂₃×#449	C₂²	1	2	yes	—
99	C₂₃×#449	C₂²	1	2	yes	—
100	C₂₃×#447	C₂²	1	2	yes	—
101	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
103	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
105	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
106	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
107	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
108	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
109	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
110	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
111	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
113	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
114	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
115	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
116	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
118	C₄×D₈×C₂₃	C₂²	1	2	yes	—
119	C₄×D₈×C₂₃	C₂²	1	2	yes	—
120	C₄×D₈×C₂₃	C₂²	1	2	yes	—
121	C₈×D₄×C₂₃	C₂²	1	2	yes	—
122	C₈×D₄×C₂₃	C₂²	1	2	yes	—
123	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
125	C₂₃×#431	C₂²	1	1	yes	characteristic
126	C₂₃×#431	C₂²	1	2	yes	complemented
127	C₂₃×#427	C₂²	1	2	yes	complemented
128	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
129	C₂₃×#416	C₂²	1	2	yes	—
130	C₂₃×#416	C₂²	1	2	yes	complemented
131	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
132	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
133	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
134	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	complemented
135	C₂×#41×C₂₃	—	2	1	no	—
136	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
137	C₂×#41×C₂₃	C₂³	1	2	yes	—
138	C₂×#41×C₂₃	C₂³	1	2	yes	—
139	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₂₃	—	2	1	no	—
142	C₂₃×#135	—	2	8	no	—
143	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
144	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₂₃	—	2	4	no	—
146	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
152	C₂×D₈×C₂₃	C₂³	1	2	yes	—
153	C₂×D₈×C₂₃	C₂³	1	2	yes	—
154	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
155	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
156	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
157	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
158	C₂₃×C₄⋊Q₈	—	2	1	no	—
159	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₂₃×#127	—	2	1	no	—
163	C₂₃×#127	C₂³	1	1	yes	characteristic
164	C₂₃×#126	—	2	2	no	—
165	C₂₃×#126	—	2	2	no	—
166	C₂₃×#126	—	2	2	no	—
167	C₂₃×#126	—	2	2	no	—
168	C₂₃×#126	—	2	2	no	—
169	C₂₃×#126	—	2	2	no	—
170	C₂₃×#125	—	2	2	no	—
171	C₂₃×#125	—	2	2	no	—
172	C₂₃×#125	—	2	1	no	—
173	C₂₃×#125	C₂³	1	2	yes	—
174	C₂₃×#125	C₂³	1	2	yes	—
175	C₂₃×#124	—	2	1	no	—
176	C₂₃×#124	—	2	1	no	—
177	C₂₃×#124	—	2	2	no	—
178	C₂₃×#124	—	2	2	no	—
179	C₂₃×#124	—	2	1	no	—
180	C₂₃×#124	C₂³	1	2	yes	—
181	C₂₃×#124	C₂³	1	2	yes	—
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×#123	—	2	2	no	—
187	C₂₃×#123	—	2	2	no	—
188	C₂₃×#123	—	2	2	no	—
189	C₂₃×C₂²⋊Q₈	—	2	1	no	—
190	C₂₃×C₂²⋊Q₈	—	2	1	no	—
191	C₂₃×C₂²⋊Q₈	—	2	1	no	—
192	C₂₃×C₂²⋊Q₈	—	2	2	no	—
193	C₂₃×C₂²⋊Q₈	—	2	2	no	—
194	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₂₃×#121	—	2	1	no	—
198	C₂₃×#121	—	2	2	no	—
199	C₂₃×#121	—	2	2	no	—
200	C₂₃×#121	—	2	1	no	—
201	C₂₃×#121	—	2	1	no	—
202	C₂₃×#121	—	2	2	no	—
203	C₂₃×#121	—	2	2	no	—
204	C₂₃×#121	C₂³	1	2	yes	—
205	C₂₃×#121	C₂³	1	2	yes	—
206	C₂₃×#121	C₂³	1	2	yes	—
207	C₂₃×#120	—	2	2	no	—
208	C₄×Q₈×C₂₃	—	2	1	no	—
209	C₄×Q₈×C₂₃	—	2	1	no	—
210	C₄×Q₈×C₂₃	—	2	1	no	—
211	C₄×Q₈×C₂₃	—	2	1	no	—
212	C₄×Q₈×C₂₃	—	2	1	no	—
213	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
214	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
215	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
217	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
221	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
222	C₄×D₄×C₂₃	—	2	2	no	—
223	C₄×D₄×C₂₃	—	2	2	no	—
224	C₄×D₄×C₂₃	—	2	2	no	—
225	C₄×D₄×C₂₃	—	2	2	no	—
226	C₄×D₄×C₂₃	—	2	2	no	—
227	C₄×D₄×C₂₃	—	2	2	no	—
228	C₄×D₄×C₂₃	—	2	1	no	—
229	C₄×D₄×C₂₃	—	2	1	no	—
230	C₄×D₄×C₂₃	—	2	2	no	—
231	C₄×D₄×C₂₃	—	2	2	no	—
232	C₄×D₄×C₂₃	—	2	1	no	—
233	C₄×D₄×C₂₃	—	2	1	no	—
234	C₄×D₄×C₂₃	—	2	1	no	—
235	C₄×D₄×C₂₃	D₄	1	2	yes	—
236	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
237	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₂₃	C₂³	1	2	yes	—
239	C₄×D₄×C₂₃	C₂³	1	2	yes	—
240	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₂₃	C₂³	1	2	yes	—
244	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₂₃	C₂³	1	2	yes	—
246	C₂₃×#117	—	2	1	no	—
247	C₂₃×#117	—	2	1	no	—
248	C₂₃×#117	—	2	1	no	—
249	C₂₃×#117	—	2	2	no	—
250	C₂₃×#117	—	2	2	no	—
251	C₂₃×#117	—	2	2	no	—
252	C₂₃×#117	—	2	2	no	—
253	C₂₃×#117	—	2	2	no	—
254	C₂₃×#117	D₄	1	1	yes	characteristic
255	C₂₃×#117	D₄	1	2	yes	—
256	C₂₃×#117	C₂³	1	2	yes	—
257	C₂₃×#117	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
259	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
260	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
261	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
265	C₂×C₄²×C₂₃	—	2	1	no	—
266	C₂×C₄²×C₂₃	—	2	2	no	—
267	C₂×C₄²×C₂₃	—	2	2	no	—
268	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
269	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
270	C₂₃×#107	C₂³	1	2	yes	—
271	C₂₃×#107	C₂³	1	2	yes	—
272	C₂₃×#107	C₂³	1	2	yes	—
273	C₂₃×#107	C₂³	1	2	yes	—
274	C₂₃×#106	C₂³	1	1	yes	characteristic
275	C₂₃×#106	C₂³	1	1	yes	characteristic
276	C₂₃×#106	C₂³	1	1	yes	characteristic
277	C₂₃×#106	C₂³	1	1	yes	characteristic
278	C₂₃×#106	C₂³	1	2	yes	—
279	C₂₃×#106	C₂³	1	2	yes	—
280	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
283	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
284	C₂₃×#103	C₂³	1	1	yes	characteristic
285	C₂₃×#103	C₂³	1	1	yes	characteristic
286	C₂₃×#103	C₂³	1	1	yes	characteristic
287	C₂₃×#103	C₂³	1	1	yes	characteristic
288	C₂₃×#103	C₂³	1	2	yes	—
289	C₂₃×#103	C₂³	1	2	yes	—
290	C₂₃×#103	C₂³	1	2	yes	—
291	C₂₃×#103	C₂³	1	2	yes	—
292	C₂₃×#103	C₂³	1	2	yes	—
293	C₂₃×#103	C₂³	1	2	yes	—
294	C₂₃×#102	C₂³	1	1	yes	characteristic
295	C₂₃×#102	C₂³	1	1	yes	characteristic
296	C₂₃×#102	C₂³	1	1	yes	characteristic
297	C₂₃×#102	C₂³	1	1	yes	characteristic
298	C₂₃×#102	C₂³	1	2	yes	—
299	C₂₃×#102	C₂³	1	2	yes	—
300	C₂₃×#102	C₂³	1	2	yes	—
301	C₂₃×#102	C₂³	1	2	yes	—
302	C₂₃×#102	C₂³	1	2	yes	—
303	C₂₃×#102	C₂³	1	2	yes	—
304	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₂₃	C₂³	1	2	yes	—
312	C₄×C₈×C₂₃	C₂³	1	2	yes	—
313	C₄×C₈×C₂₃	C₂³	1	2	yes	—
314	C₂⁴×C₂₃	—	2	1	no	—
315	#41×C₂₃	—	2	4	no	—
316	#41×C₂₃	—	2	4	no	—
317	#41×C₂₃	—	2	4	no	—
318	#41×C₂₃	—	4	2	no	—
319	#41×C₂₃	—	4	2	no	—
320	#41×C₂₃	—	4	4	no	—
321	C₂×Q₈×C₂₃	—	2	1	no	—
322	C₂×Q₈×C₂₃	—	2	1	no	—
323	C₂×Q₈×C₂₃	—	2	1	no	—
324	C₂×Q₈×C₂₃	—	2	2	no	—
325	C₂×Q₈×C₂₃	—	4	1	no	—
326	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₂₃	—	2	2	no	—
331	C₂×D₄×C₂₃	—	2	2	no	—
332	C₂×D₄×C₂₃	—	2	2	no	—
333	C₂×D₄×C₂₃	—	2	2	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	1	no	—
338	C₂×D₄×C₂₃	—	2	1	no	—
339	C₂×D₄×C₂₃	—	4	1	no	—
340	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
341	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
342	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
344	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₂₃	—	2	1	no	—
346	C₂²×C₄×C₂₃	—	2	1	no	—
347	C₂²×C₄×C₂₃	—	2	1	no	—
348	C₂²×C₄×C₂₃	—	2	2	no	—
349	C₂²×C₄×C₂₃	—	2	2	no	—
350	C₂²×C₄×C₂₃	—	2	1	no	—
351	C₂²×C₄×C₂₃	—	2	1	no	—
352	C₂²×C₄×C₂₃	—	2	1	no	—
353	C₂²×C₄×C₂₃	—	2	2	no	—
354	C₂²×C₄×C₂₃	—	2	1	no	—
355	C₂²×C₄×C₂₃	—	2	2	no	—
356	C₂²×C₄×C₂₃	—	2	2	no	—
357	C₂²×C₄×C₂₃	—	4	4	no	—
358	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
359	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
361	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
364	Q₁₆×C₂₃	—	2	4	no	—
365	Q₁₆×C₂₃	—	4	2	no	—
366	SD₁₆×C₂₃	—	2	2	no	—
367	SD₁₆×C₂₃	—	2	2	no	—
368	SD₁₆×C₂₃	—	2	2	no	—
369	SD₁₆×C₂₃	—	2	4	no	—
370	SD₁₆×C₂₃	—	4	2	no	—
371	SD₁₆×C₂₃	#41	1	4	yes	complemented
372	D₈×C₂₃	—	2	4	no	—
373	D₈×C₂₃	—	4	2	no	—
374	C₂×C₈×C₂₃	—	2	2	no	—
375	C₂×C₈×C₂₃	—	2	4	no	—
376	C₂×C₈×C₂₃	—	4	2	no	—
377	C₂×C₈×C₂₃	—	4	1	no	—
378	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
382	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
383	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₂₃	—	2	1	no	—
385	C₄⋊C₄×C₂₃	—	2	1	no	—
386	C₄⋊C₄×C₂₃	—	2	1	no	—
387	C₄⋊C₄×C₂₃	—	2	2	no	—
388	C₄⋊C₄×C₂₃	—	2	2	no	—
389	C₄⋊C₄×C₂₃	—	2	1	no	—
390	C₄⋊C₄×C₂₃	—	2	1	no	—
391	C₄⋊C₄×C₂₃	—	2	1	no	—
392	C₄⋊C₄×C₂₃	—	2	1	no	—
393	C₄⋊C₄×C₂₃	—	2	1	no	—
394	C₄⋊C₄×C₂₃	—	2	2	no	—
395	C₄⋊C₄×C₂₃	—	2	2	no	—
396	C₄⋊C₄×C₂₃	—	2	2	no	—
397	C₄⋊C₄×C₂₃	—	2	2	no	—
398	C₄⋊C₄×C₂₃	—	2	2	no	—
399	C₄⋊C₄×C₂₃	—	2	1	no	—
400	C₄⋊C₄×C₂₃	—	2	2	no	—
401	C₄⋊C₄×C₂₃	—	2	2	no	—
402	C₄⋊C₄×C₂₃	—	2	2	no	—
403	C₄⋊C₄×C₂₃	—	2	1	no	—
404	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
414	C₂²⋊C₄×C₂₃	—	2	2	no	—
415	C₂²⋊C₄×C₂₃	—	2	2	no	—
416	C₂²⋊C₄×C₂₃	—	2	2	no	—
417	C₂²⋊C₄×C₂₃	—	2	2	no	—
418	C₂²⋊C₄×C₂₃	—	2	2	no	—
419	C₂²⋊C₄×C₂₃	—	2	1	no	—
420	C₂²⋊C₄×C₂₃	—	2	2	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	1	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	2	no	—
433	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
436	C₄²×C₂₃	—	2	2	no	—
437	C₄²×C₂₃	—	2	2	no	—
438	C₄²×C₂₃	—	2	2	no	—
439	C₄²×C₂₃	—	2	2	no	—
440	C₄²×C₂₃	—	2	1	no	—
441	C₄²×C₂₃	—	2	1	no	—
442	C₄²×C₂₃	—	2	1	no	—
443	C₄²×C₂₃	—	2	1	no	—
444	C₄²×C₂₃	—	2	2	no	—
445	C₄²×C₂₃	C₂×D₄	1	2	yes	—
446	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₂₃	C₂×D₄	1	2	yes	—
448	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₂₃	C₂⁴	1	2	yes	—
450	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
451	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
452	#61428	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
453	C₂³×C₂₃	—	2	1	no	—
454	C₂³×C₂₃	—	2	1	no	—
455	C₂³×C₂₃	—	2	2	no	—
456	C₂³×C₂₃	—	4	2	no	—
457	C₂³×C₂₃	—	4	2	no	—
458	C₂³×C₂₃	—	8	1	no	—
459	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
460	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
461	Q₈×C₂₃	—	2	2	no	—
462	Q₈×C₂₃	—	2	1	no	—
463	Q₈×C₂₃	—	2	1	no	—
464	Q₈×C₂₃	—	2	2	no	—
465	Q₈×C₂₃	—	2	2	no	—
466	Q₈×C₂₃	—	2	1	no	—
467	Q₈×C₂₃	—	4	2	no	—
468	Q₈×C₂₃	—	4	2	no	—
469	Q₈×C₂₃	—	8	1	no	—
470	Q₈×C₂₃	C₂×#41	1	2	yes	—
471	D₄×C₂₃	—	2	4	no	—
472	D₄×C₂₃	—	2	2	no	—
473	D₄×C₂₃	—	2	2	no	—
474	D₄×C₂₃	—	2	1	no	—
475	D₄×C₂₃	—	2	1	no	—
476	D₄×C₂₃	—	2	1	no	—
477	D₄×C₂₃	—	2	2	no	—
478	D₄×C₂₃	—	4	2	no	—
479	D₄×C₂₃	—	4	4	no	—
480	D₄×C₂₃	—	4	4	no	—
481	D₄×C₂₃	—	4	4	no	—
482	D₄×C₂₃	—	4	2	no	—
483	D₄×C₂₃	—	8	1	no	—
484	D₄×C₂₃	—	8	2	no	—
485	D₄×C₂₃	—	8	2	no	—
486	D₄×C₂₃	C₂×#41	1	2	yes	—
487	C₂×C₄×C₂₃	—	2	1	no	—
488	C₂×C₄×C₂₃	—	2	4	no	—
489	C₂×C₄×C₂₃	—	2	1	no	—
490	C₂×C₄×C₂₃	—	2	2	no	—
491	C₂×C₄×C₂₃	—	2	1	no	—
492	C₂×C₄×C₂₃	—	2	2	no	—
493	C₂×C₄×C₂₃	—	2	1	no	—
494	C₂×C₄×C₂₃	—	2	1	no	—
495	C₂×C₄×C₂₃	—	2	1	no	—
496	C₂×C₄×C₂₃	—	2	2	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	1	no	—
501	C₂×C₄×C₂₃	—	4	2	no	—
502	C₂×C₄×C₂₃	—	4	1	no	—
503	C₂×C₄×C₂₃	—	4	4	no	—
504	C₂×C₄×C₂₃	—	4	2	no	—
505	C₂×C₄×C₂₃	—	4	4	no	—
506	C₂×C₄×C₂₃	—	4	2	no	—
507	C₂×C₄×C₂₃	—	4	2	no	—
508	C₂×C₄×C₂₃	—	4	2	no	—
509	C₂×C₄×C₂₃	—	4	2	no	—
510	C₂×C₄×C₂₃	—	4	2	no	—
511	C₂×C₄×C₂₃	—	4	4	no	—
512	C₂×C₄×C₂₃	—	8	2	no	—
513	C₂×C₄×C₂₃	—	8	2	no	—
514	C₂×C₄×C₂₃	—	8	1	no	—
515	C₂×C₄×C₂₃	#135	1	4	yes	complemented
516	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
523	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
525	C₈×C₂₃	—	2	2	no	—
526	C₈×C₂₃	—	2	1	no	—
527	C₈×C₂₃	—	2	1	no	—
528	C₈×C₂₃	—	2	2	no	—
529	C₈×C₂₃	—	2	1	no	—
530	C₈×C₂₃	C₂×#41	1	2	yes	—
531	#3480	C₂×C₂₃	1	1	yes	characteristic, complemented
532	#3475	C₂×C₂₃	1	1	yes	characteristic, complemented
533	#3394	C₂×C₂₃	1	1	yes	characteristic, complemented
534	#3381	C₂×C₂₃	1	1	yes	characteristic, complemented
535	#3364	C₂×C₂₃	1	1	yes	characteristic, complemented
536	#3361	C₂×C₂₃	1	1	yes	characteristic, complemented
537	#3340	C₂×C₂₃	1	1	yes	characteristic, complemented
538	#3337	C₂×C₂₃	1	2	yes	complemented
539	#3305	C₂×C₂₃	1	1	yes	characteristic, complemented
540	#3302	C₂×C₂₃	1	1	yes	characteristic, complemented
541	#3300	C₂×C₂₃	1	2	yes	complemented
542	#3297	C₂×C₂₃	1	2	yes	complemented
543	#3284	C₂×C₂₃	1	1	yes	characteristic, complemented
544	#3282	C₂×C₂₃	1	2	yes	complemented
545	#3168	C₂×C₂₃	1	2	yes	complemented
546	#3167	C₂×C₂₃	1	1	yes	characteristic, complemented
547	#3104	C₂×C₂₃	1	1	yes	characteristic, complemented
548	#3102	C₂×C₂₃	1	2	yes	complemented
549	#3102	C₂×C₂₃	1	2	yes	complemented
550	#3100	C₂×C₂₃	1	1	yes	characteristic, complemented
551	C₈×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
552	C₄×#135	C₂×C₂₃	1	2	yes	complemented
553	C₂×C₄×SD₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
554	C₂²×C₂₃	—	2	1	no	—
555	C₂²×C₂₃	—	2	1	no	—
556	C₂²×C₂₃	—	2	2	no	—
557	C₂²×C₂₃	—	2	2	no	—
558	C₂²×C₂₃	—	2	2	no	—
559	C₂²×C₂₃	—	2	2	no	—
560	C₂²×C₂₃	—	4	1	no	—
561	C₂²×C₂₃	—	4	1	no	—
562	C₂²×C₂₃	—	4	2	no	—
563	C₂²×C₂₃	—	4	1	no	—
564	C₂²×C₂₃	—	4	2	no	—
565	C₂²×C₂₃	—	4	1	no	—
566	C₂²×C₂₃	—	4	1	no	—
567	C₂²×C₂₃	—	4	2	no	—
568	C₂²×C₂₃	—	8	4	no	—
569	C₂²×C₂₃	C₂×#135	1	2	yes	—
570	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
571	C₄×C₂₃	—	2	1	no	—
572	C₄×C₂₃	—	2	2	no	—
573	C₄×C₂₃	—	2	1	no	—
574	C₄×C₂₃	—	2	2	no	—
575	C₄×C₂₃	—	2	1	no	—
576	C₄×C₂₃	—	2	2	no	—
577	C₄×C₂₃	—	2	2	no	—
578	C₄×C₂₃	—	4	1	no	—
579	C₄×C₂₃	—	4	1	no	—
580	C₄×C₂₃	—	4	2	no	—
581	C₄×C₂₃	—	4	2	no	—
582	C₄×C₂₃	—	4	1	no	—
583	C₄×C₂₃	—	4	1	no	—
584	C₄×C₂₃	—	4	1	no	—
585	C₄×C₂₃	—	4	2	no	—
586	C₄×C₂₃	C₂×#135	1	2	yes	—
587	C₄×C₂₃	C₂×#135	1	2	yes	—
588	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
589	C₄×C₂₃	#585	1	1	yes	characteristic
590	C₂×#135	C₂²×C₂₃	1	2	yes	—
591	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
592	#559	—	2	1	no	—
593	#559	C₂²×C₂₃	1	1	yes	characteristic, complemented
594	#557	C₂²×C₂₃	1	1	yes	characteristic, complemented
595	#556	—	2	1	no	—
596	#556	C₂²×C₂₃	1	1	yes	characteristic
597	#556	C₂²×C₂₃	1	1	yes	characteristic, complemented
598	#555	C₂²×C₂₃	1	1	yes	characteristic
599	#554	C₂²×C₂₃	1	1	yes	characteristic
600	#553	—	2	1	no	—
601	#553	—	2	2	no	—
602	#553	C₂²×C₂₃	1	2	yes	—
603	#552	—	2	1	no	—
604	#552	C₂²×C₂₃	1	2	yes	—
605	#551	—	2	2	no	—
606	#550	C₂²×C₂₃	1	1	yes	characteristic, complemented
607	#548	C₂²×C₂₃	1	2	yes	—
608	#547	C₂²×C₂₃	1	1	yes	characteristic
609	#546	C₂²×C₂₃	1	2	yes	—
610	#533	C₂²×C₂₃	1	1	yes	characteristic
611	#532	—	2	1	no	—
612	#532	C₂²×C₂₃	1	1	yes	characteristic
613	#529	—	2	2	no	—
614	#529	—	2	2	no	—
615	#529	C₂²×C₂₃	1	2	yes	—
616	#529	C₂²×C₂₃	1	2	yes	complemented
617	#525	—	2	1	no	—
618	C₄×#41	—	2	1	no	—
619	C₄×#41	C₂²×C₂₃	1	2	yes	—
620	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
621	C₄×#41	C₂²×C₂₃	1	2	yes	complemented
622	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
623	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
624	C₂×#117	—	2	1	no	—
625	#499	C₂²×C₂₃	1	2	yes	complemented
626	#498	C₂²×C₂₃	1	1	yes	characteristic, complemented
627	#495	C₂²×C₂₃	1	2	yes	—
628	#492	C₂²×C₂₃	1	1	yes	characteristic, complemented
629	#488	C₂²×C₂₃	1	2	yes	—
630	#488	C₂²×C₂₃	1	2	yes	complemented
631	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
632	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
633	#485	C₂²×C₂₃	1	2	yes	complemented
634	#485	C₂²×C₂₃	1	2	yes	complemented
635	#484	C₂²×C₂₃	1	2	yes	—
636	#482	C₂²×C₂₃	1	2	yes	—
637	#482	C₂²×C₂₃	1	2	yes	complemented
638	#480	C₂²×C₂₃	1	2	yes	—
639	#479	C₂²×C₂₃	1	2	yes	complemented
640	#479	C₂²×C₂₃	1	2	yes	complemented
641	#478	C₂²×C₂₃	1	2	yes	—
642	#478	C₂²×C₂₃	1	2	yes	complemented
643	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
644	#477	C₂²×C₂₃	1	1	yes	characteristic, complemented
645	#474	C₂²×C₂₃	1	1	yes	characteristic
646	#474	C₂²×C₂₃	1	1	yes	characteristic
647	#467	C₂²×C₂₃	1	2	yes	complemented
648	#466	C₂²×C₂₃	1	2	yes	—
649	#465	C₂²×C₂₃	1	2	yes	—
650	#465	C₂²×C₂₃	1	2	yes	—
651	#465	C₂²×C₂₃	1	2	yes	—
652	#465	C₂²×C₂₃	1	2	yes	complemented
653	#464	C₂²×C₂₃	1	2	yes	—
654	#464	C₂²×C₂₃	1	2	yes	complemented
655	#463	C₂²×C₂₃	1	2	yes	—
656	#463	C₂²×C₂₃	1	2	yes	—
657	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
658	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
659	#459	C₂²×C₂₃	1	1	yes	characteristic
660	#459	C₂²×C₂₃	1	1	yes	characteristic
661	#452	C₂²×C₂₃	1	2	yes	—
662	#452	C₂²×C₂₃	1	2	yes	complemented
663	#451	C₂²×C₂₃	1	2	yes	—
664	#449	C₂²×C₂₃	1	2	yes	—
665	#449	C₂²×C₂₃	1	2	yes	—
666	#447	C₂²×C₂₃	1	2	yes	—
667	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
668	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
669	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
670	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
671	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
672	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
673	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
674	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
675	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
676	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
677	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
678	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
679	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
680	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
681	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
682	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
683	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
684	C₄×D₈	C₂²×C₂₃	1	2	yes	—
685	C₄×D₈	C₂²×C₂₃	1	2	yes	—
686	C₄×D₈	C₂²×C₂₃	1	2	yes	—
687	C₈×D₄	C₂²×C₂₃	1	2	yes	—
688	C₈×D₄	C₂²×C₂₃	1	2	yes	—
689	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
690	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
691	#431	C₂²×C₂₃	1	1	yes	characteristic
692	#431	C₂²×C₂₃	1	2	yes	complemented
693	#427	C₂²×C₂₃	1	2	yes	complemented
694	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
695	#416	C₂²×C₂₃	1	2	yes	—
696	#416	C₂²×C₂₃	1	2	yes	complemented
697	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
698	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
699	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
700	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	complemented
701	C₂×C₂₃	—	2	2	no	—
702	C₂×C₂₃	—	4	2	no	—
703	C₂×C₂₃	—	4	2	no	—
704	C₂×C₂₃	—	8	2	no	—
705	C₂×C₂₃	—	8	1	no	—
706	C₂×C₂₃	D₄×#41	1	1	yes	characteristic
707	C₂×C₂₃	C₂²×#135	1	1	yes	characteristic
708	C₂×C₂₃	#3584	1	1	yes	characteristic
709	C₂×#41	—	2	1	no	—
710	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
711	C₂×#41	C₂³×C₂₃	1	2	yes	—
712	C₂×#41	C₂³×C₂₃	1	2	yes	—
713	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
714	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
715	C₂³×C₄	—	2	1	no	—
716	#135	—	2	8	no	—
717	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
718	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
719	C₂×SD₁₆	—	2	4	no	—
720	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
721	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
722	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
723	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
724	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
725	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
726	C₂×D₈	C₂³×C₂₃	1	2	yes	—
727	C₂×D₈	C₂³×C₂₃	1	2	yes	—
728	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
729	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
730	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
731	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
732	C₄⋊Q₈	—	2	1	no	—
733	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
734	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
735	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
736	#127	—	2	1	no	—
737	#127	C₂³×C₂₃	1	1	yes	characteristic
738	#126	—	2	2	no	—
739	#126	—	2	2	no	—
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#125	—	2	2	no	—
745	#125	—	2	2	no	—
746	#125	—	2	1	no	—
747	#125	C₂³×C₂₃	1	2	yes	—
748	#125	C₂³×C₂₃	1	2	yes	—
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	C₂³×C₂₃	1	2	yes	—
755	#124	C₂³×C₂₃	1	2	yes	—
756	#123	—	2	2	no	—
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	#123	—	2	2	no	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
769	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
770	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
771	#121	—	2	1	no	—
772	#121	—	2	1	no	—
773	#121	—	2	2	no	—
774	#121	—	2	2	no	—
775	#121	—	2	1	no	—
776	#121	—	2	2	no	—
777	#121	—	2	2	no	—
778	#121	C₂³×C₂₃	1	2	yes	—
779	#121	C₂³×C₂₃	1	2	yes	—
780	#121	C₂³×C₂₃	1	2	yes	—
781	#120	—	2	2	no	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	—	2	1	no	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
788	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
789	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
790	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
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×Q₈	C₂³×C₂₃	1	1	yes	characteristic
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	D₄×C₂₃	1	2	yes	—
810	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
811	C₄×D₄	C₂³×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	1	yes	characteristic
815	C₄×D₄	C₂³×C₂₃	1	2	yes	—
816	C₄×D₄	C₂³×C₂₃	1	2	yes	—
817	C₄×D₄	C₂³×C₂₃	1	2	yes	—
818	C₄×D₄	C₂³×C₂₃	1	2	yes	—
819	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
820	#117	—	2	1	no	—
821	#117	—	2	1	no	—
822	#117	—	2	1	no	—
823	#117	—	2	2	no	—
824	#117	—	2	2	no	—
825	#117	—	2	2	no	—
826	#117	—	2	2	no	—
827	#117	—	2	2	no	—
828	#117	D₄×C₂₃	1	1	yes	characteristic
829	#117	D₄×C₂₃	1	2	yes	—
830	#117	C₂³×C₂₃	1	2	yes	—
831	#117	C₂³×C₂₃	1	2	yes	—
832	C₂×C₄⋊C₄	—	2	1	no	—
833	C₂×C₄⋊C₄	—	2	1	no	—
834	C₂×C₄⋊C₄	—	2	1	no	—
835	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
836	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
837	C₂×C₂²⋊C₄	—	2	1	no	—
838	C₂×C₂²⋊C₄	—	2	2	no	—
839	C₂×C₄²	—	2	1	no	—
840	C₂×C₄²	—	2	2	no	—
841	C₂×C₄²	—	2	2	no	—
842	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
843	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
844	#107	C₂³×C₂₃	1	2	yes	—
845	#107	C₂³×C₂₃	1	2	yes	—
846	#107	C₂³×C₂₃	1	2	yes	—
847	#107	C₂³×C₂₃	1	2	yes	—
848	#106	C₂³×C₂₃	1	1	yes	characteristic
849	#106	C₂³×C₂₃	1	1	yes	characteristic
850	#106	C₂³×C₂₃	1	1	yes	characteristic
851	#106	C₂³×C₂₃	1	1	yes	characteristic
852	#106	C₂³×C₂₃	1	2	yes	—
853	#106	C₂³×C₂₃	1	2	yes	—
854	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
855	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
856	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
857	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
858	#103	C₂³×C₂₃	1	1	yes	characteristic
859	#103	C₂³×C₂₃	1	1	yes	characteristic
860	#103	C₂³×C₂₃	1	1	yes	characteristic
861	#103	C₂³×C₂₃	1	1	yes	characteristic
862	#103	C₂³×C₂₃	1	2	yes	—
863	#103	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	#102	C₂³×C₂₃	1	1	yes	characteristic
869	#102	C₂³×C₂₃	1	1	yes	characteristic
870	#102	C₂³×C₂₃	1	1	yes	characteristic
871	#102	C₂³×C₂₃	1	1	yes	characteristic
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	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
881	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
882	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
883	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
884	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
885	C₄×C₈	C₂³×C₂₃	1	2	yes	—
886	C₄×C₈	C₂³×C₂₃	1	2	yes	—
887	C₄×C₈	C₂³×C₂₃	1	2	yes	—
888	C₂₃	#61428	1	1	yes	characteristic, direct product factor, Sylow
889	C₂⁴	—	2	1	no	—
890	#41	—	2	4	no	—
891	#41	—	2	4	no	—
892	#41	—	2	4	no	—
893	#41	—	4	2	no	—
894	#41	—	4	2	no	—
895	#41	—	4	4	no	—
896	C₂×Q₈	—	2	1	no	—
897	C₂×Q₈	—	2	1	no	—
898	C₂×Q₈	—	2	1	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	4	1	no	—
901	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
902	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
903	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
904	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	1	no	—
914	C₂×D₄	—	4	1	no	—
915	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
916	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
917	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
918	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
919	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	4	4	no	—
933	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
934	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
935	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
936	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
937	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
938	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
939	Q₁₆	—	2	4	no	—
940	Q₁₆	—	4	2	no	—
941	SD₁₆	—	2	2	no	—
942	SD₁₆	—	2	2	no	—
943	SD₁₆	—	2	2	no	—
944	SD₁₆	—	2	4	no	—
945	SD₁₆	—	4	2	no	—
946	SD₁₆	#41×C₂₃	1	4	yes	complemented
947	D₈	—	2	4	no	—
948	D₈	—	4	2	no	—
949	C₂×C₈	—	2	2	no	—
950	C₂×C₈	—	2	4	no	—
951	C₂×C₈	—	4	2	no	—
952	C₂×C₈	—	4	1	no	—
953	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
954	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
955	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
956	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
957	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
958	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
980	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
981	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
982	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
983	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
984	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
985	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
986	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
987	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
988	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	2	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	C₂×D₄×C₂₃	1	2	yes	—
1009	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1010	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	2	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	C₂×D₄×C₂₃	1	2	yes	—
1021	C₄²	C₂×D₄×C₂₃	1	2	yes	—
1022	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1023	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
1024	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1025	C₄²	C₂⁴×C₂₃	1	2	yes	—
1026	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	2	no	—
1030	C₂³	—	4	2	no	—
1031	C₂³	—	4	2	no	—
1032	C₂³	—	8	1	no	—
1033	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
1034	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
1035	Q₈	—	2	2	no	—
1036	Q₈	—	2	1	no	—
1037	Q₈	—	2	1	no	—
1038	Q₈	—	2	2	no	—
1039	Q₈	—	2	2	no	—
1040	Q₈	—	2	1	no	—
1041	Q₈	—	4	2	no	—
1042	Q₈	—	4	2	no	—
1043	Q₈	—	8	1	no	—
1044	Q₈	C₂×#41×C₂₃	1	2	yes	—
1045	D₄	—	2	4	no	—
1046	D₄	—	2	2	no	—
1047	D₄	—	2	2	no	—
1048	D₄	—	2	1	no	—
1049	D₄	—	2	1	no	—
1050	D₄	—	2	1	no	—
1051	D₄	—	2	2	no	—
1052	D₄	—	4	2	no	—
1053	D₄	—	4	4	no	—
1054	D₄	—	4	4	no	—
1055	D₄	—	4	4	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	8	1	no	—
1058	D₄	—	8	2	no	—
1059	D₄	—	8	2	no	—
1060	D₄	C₂×#41×C₂₃	1	2	yes	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	4	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	4	1	no	—
1077	C₂×C₄	—	4	4	no	—
1078	C₂×C₄	—	4	2	no	—
1079	C₂×C₄	—	4	4	no	—
1080	C₂×C₄	—	4	2	no	—
1081	C₂×C₄	—	4	2	no	—
1082	C₂×C₄	—	4	2	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	4	4	no	—
1086	C₂×C₄	—	8	2	no	—
1087	C₂×C₄	—	8	2	no	—
1088	C₂×C₄	—	8	1	no	—
1089	C₂×C₄	C₂₃×#135	1	4	yes	complemented
1090	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1091	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1092	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1093	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1094	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1095	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1096	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1097	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1098	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1099	C₈	—	2	2	no	—
1100	C₈	—	2	1	no	—
1101	C₈	—	2	1	no	—
1102	C₈	—	2	2	no	—
1103	C₈	—	2	1	no	—
1104	C₈	C₂×#41×C₂₃	1	2	yes	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	2	no	—
1109	C₂²	—	2	2	no	—
1110	C₂²	—	2	2	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	2	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	4	2	no	—
1117	C₂²	—	4	2	no	—
1118	C₂²	—	4	1	no	—
1119	C₂²	—	8	4	no	—
1120	C₂²	C₂×C₂₃×#135	1	2	yes	—
1121	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1122	C₄	—	2	2	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	2	no	—
1125	C₄	—	2	2	no	—
1126	C₄	—	2	1	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	1	no	—
1129	C₄	—	4	2	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	1	no	—
1132	C₄	—	4	1	no	—
1133	C₄	—	4	2	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	2	no	—
1137	C₄	C₂×C₂₃×#135	1	2	yes	—
1138	C₄	C₂×C₂₃×#135	1	2	yes	—
1139	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
1140	C₄	C₂₃×#585	1	1	yes	characteristic
1141	C₂	—	2	2	no	—
1142	C₂	—	4	2	no	—
1143	C₂	—	4	2	no	—
1144	C₂	—	8	1	no	—
1145	C₂	—	8	2	no	—
1146	C₂	D₄×#41×C₂₃	1	1	yes	characteristic
1147	C₂	C₂²×C₂₃×#135	1	1	yes	characteristic
1148	C₂	C₂₃×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3480	C₂	semidirect
2. C₂₃×#3475	C₂	semidirect
3. C₂₃×#3394	C₂	semidirect
4. C₂₃×#3381	C₂	semidirect
5. C₂₃×#3364	C₂	semidirect
6. C₂₃×#3361	C₂	semidirect
7. C₂₃×#3340	C₂	semidirect
8. C₂₃×#3337	C₂	semidirect
9. C₂₃×#3305	C₂	semidirect
10. C₂₃×#3302	C₂	semidirect
11. C₂₃×#3300	C₂	semidirect
12. C₂₃×#3297	C₂	semidirect
13. C₂₃×#3284	C₂	semidirect
14. C₂₃×#3282	C₂	semidirect
15. C₂₃×#3168	C₂	semidirect
16. C₂₃×#3167	C₂	semidirect
17. C₂₃×#3104	C₂	semidirect
18. C₂₃×#3102	C₂	semidirect
19. C₂₃×#3102	C₂	semidirect
20. C₂₃×#3100	C₂	semidirect
21. C₈×#41×C₂₃	C₂	semidirect
22. C₄×C₂₃×#135	C₂	semidirect
23. C₂×C₄×SD₁₆×C₂₃	C₂	semidirect
27. C₂₃×#559	C₂²	semidirect
28. C₂₃×#557	C₂²	semidirect
31. C₂₃×#556	C₂²	semidirect
40. C₂₃×#550	C₂²	semidirect
50. C₂₃×#529	C₂²	semidirect
55. C₄×#41×C₂₃	C₂²	semidirect
59. C₂₃×#499	C₂²	semidirect
60. C₂₃×#498	C₂²	semidirect
62. C₂₃×#492	C₂²	semidirect
64. C₂₃×#488	C₂²	semidirect
65. C₂₃×#487	C₂²	semidirect
66. C₂₃×#486	C₂²	semidirect
67. C₂₃×#485	C₂²	semidirect
68. C₂₃×#485	C₂²	semidirect
71. C₂₃×#482	C₂²	semidirect
73. C₂₃×#479	C₂²	semidirect
74. C₂₃×#479	C₂²	semidirect
76. C₂₃×#478	C₂²	semidirect
77. C₂₃×#477	C₂²	semidirect
78. C₂₃×#477	C₂²	semidirect
81. C₂₃×#467	C₂²	semidirect
86. C₂₃×#465	C₂²	semidirect
88. C₂₃×#464	C₂²	semidirect
91. C₂₃×#462	C₂²	semidirect
92. C₂₃×#462	C₂²	semidirect
96. C₂₃×#452	C₂²	semidirect
101. C₈×Q₈×C₂₃	C₂²	semidirect
102. C₈×Q₈×C₂₃	C₂²	semidirect
103. C₄×Q₁₆×C₂₃	C₂²	semidirect
104. C₄×Q₁₆×C₂₃	C₂²	semidirect
105. C₄×Q₁₆×C₂₃	C₂²	semidirect
115. C₄×SD₁₆×C₂₃	C₂²	semidirect
116. C₄×SD₁₆×C₂₃	C₂²	semidirect
117. C₄×SD₁₆×C₂₃	C₂²	semidirect
123. C₈×D₄×C₂₃	C₂²	semidirect
124. C₈×D₄×C₂₃	C₂²	semidirect
126. C₂₃×#431	C₂²	semidirect
127. C₂₃×#427	C₂²	semidirect
130. C₂₃×#416	C₂²	semidirect
134. C₂×C₄×C₈×C₂₃	C₂²	semidirect
371. SD₁₆×C₂₃	#41	semidirect
452. #61428	C₂₃	direct (N × H)
515. C₂×C₄×C₂₃	#135	semidirect
531. #3480	C₂×C₂₃	semidirect
532. #3475	C₂×C₂₃	semidirect
533. #3394	C₂×C₂₃	semidirect
534. #3381	C₂×C₂₃	semidirect
535. #3364	C₂×C₂₃	semidirect
536. #3361	C₂×C₂₃	semidirect
537. #3340	C₂×C₂₃	semidirect
538. #3337	C₂×C₂₃	semidirect
539. #3305	C₂×C₂₃	semidirect
540. #3302	C₂×C₂₃	semidirect
541. #3300	C₂×C₂₃	semidirect
542. #3297	C₂×C₂₃	semidirect
543. #3284	C₂×C₂₃	semidirect
544. #3282	C₂×C₂₃	semidirect
545. #3168	C₂×C₂₃	semidirect
546. #3167	C₂×C₂₃	semidirect
547. #3104	C₂×C₂₃	semidirect
548. #3102	C₂×C₂₃	semidirect
549. #3102	C₂×C₂₃	semidirect
550. #3100	C₂×C₂₃	semidirect
551. C₈×#41	C₂×C₂₃	semidirect
552. C₄×#135	C₂×C₂₃	semidirect
553. C₂×C₄×SD₁₆	C₂×C₂₃	semidirect
593. #559	C₂²×C₂₃	semidirect
594. #557	C₂²×C₂₃	semidirect
597. #556	C₂²×C₂₃	semidirect
606. #550	C₂²×C₂₃	semidirect
616. #529	C₂²×C₂₃	semidirect
621. C₄×#41	C₂²×C₂₃	semidirect
625. #499	C₂²×C₂₃	semidirect
626. #498	C₂²×C₂₃	semidirect
628. #492	C₂²×C₂₃	semidirect
630. #488	C₂²×C₂₃	semidirect
631. #487	C₂²×C₂₃	semidirect
632. #486	C₂²×C₂₃	semidirect
633. #485	C₂²×C₂₃	semidirect
634. #485	C₂²×C₂₃	semidirect
637. #482	C₂²×C₂₃	semidirect
639. #479	C₂²×C₂₃	semidirect
640. #479	C₂²×C₂₃	semidirect
642. #478	C₂²×C₂₃	semidirect
643. #477	C₂²×C₂₃	semidirect
644. #477	C₂²×C₂₃	semidirect
647. #467	C₂²×C₂₃	semidirect
652. #465	C₂²×C₂₃	semidirect
654. #464	C₂²×C₂₃	semidirect
657. #462	C₂²×C₂₃	semidirect
658. #462	C₂²×C₂₃	semidirect
662. #452	C₂²×C₂₃	semidirect
667. C₈×Q₈	C₂²×C₂₃	semidirect
668. C₈×Q₈	C₂²×C₂₃	semidirect
669. C₄×Q₁₆	C₂²×C₂₃	semidirect
670. C₄×Q₁₆	C₂²×C₂₃	semidirect
671. C₄×Q₁₆	C₂²×C₂₃	semidirect
681. C₄×SD₁₆	C₂²×C₂₃	semidirect
682. C₄×SD₁₆	C₂²×C₂₃	semidirect
683. C₄×SD₁₆	C₂²×C₂₃	semidirect
689. C₈×D₄	C₂²×C₂₃	semidirect
690. C₈×D₄	C₂²×C₂₃	semidirect
692. #431	C₂²×C₂₃	semidirect
693. #427	C₂²×C₂₃	semidirect
696. #416	C₂²×C₂₃	semidirect
700. C₂×C₄×C₈	C₂²×C₂₃	semidirect
888. C₂₃	#61428	direct (N × H)
946. SD₁₆	#41×C₂₃	semidirect
1089. C₂×C₄	C₂₃×#135	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3480	2
C₂₃×#3475	2
C₂₃×#3394	2
C₂₃×#3381	2
C₂₃×#3364	2
C₂₃×#3361	2
C₂₃×#3340	2
C₂₃×#3337	2
C₂₃×#3305	2
C₂₃×#3302	2
C₂₃×#3300	2
C₂₃×#3297	2
C₂₃×#3284	2
C₂₃×#3282	2
C₂₃×#3168	2
C₂₃×#3167	2
C₂₃×#3104	2
C₂₃×#3102	2
C₂₃×#3100	2
C₈×#41×C₂₃	2
C₄×C₂₃×#135	2
C₂×C₄×SD₁₆×C₂₃	2
#61428	23

Subgroups — C23×#61428 #19209054

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61428 #19209054