Subgroups — C₂×C₂₃×#1881 #19168564

Order 5888.

1682 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#575	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#568	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#421	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1881	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₂₃×#344	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#341	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
10	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
11	C₂₃×#575	—	2	2	no	—
12	C₂₃×#575	—	2	2	no	—
13	C₂₃×#575	C₄	1	4	yes	complemented
14	C₂₃×#575	C₂²	1	4	yes	—
15	C₂×C₂₃×#137	—	2	1	no	—
16	C₂×C₂₃×#137	C₄	1	2	yes	complemented
17	C₂×C₂₃×AGL(1,ℤ/8)	—	2	1	no	—
18	C₂×C₂₃×AGL(1,ℤ/8)	C₄	1	2	yes	complemented
19	C₂×C₂₃×#135	—	2	2	no	—
20	C₂₃×#568	—	2	2	no	—
21	C₂₃×#568	—	2	2	no	—
22	C₂₃×#568	—	2	2	no	—
23	C₂₃×#568	C₂²	1	4	yes	complemented
24	C₂×C₂₃×#131	—	2	2	no	—
25	C₂×C₂₃×#131	—	2	2	no	—
26	C₂²×M₁₆×C₂₃	—	2	2	no	—
27	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
28	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
29	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
30	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
32	C₂₃×#421	—	2	2	no	—
33	C₂₃×#421	C₂²	1	4	yes	complemented
34	C₂×C₂₃×#104	—	2	2	no	—
35	C₂₃×#416	—	2	2	no	—
36	C₂₃×#416	C₂²	1	4	yes	complemented
37	C₂×C₂₃×#103	—	2	1	no	—
38	C₂×C₂₃×#102	—	2	1	no	—
39	C₂₃×#408	—	2	2	no	—
40	C₂₃×#408	C₂²	1	4	yes	complemented
41	C₂×C₂₃×C₂²⋊C₈	—	2	2	no	—
42	C₂₃×#344	C₂²	1	4	yes	complemented
43	C₂₃×#341	C₂²	1	4	yes	complemented
44	C₂×#41×C₂₃	—	2	1	no	—
45	C₂×#41×C₂₃	—	2	1	no	—
46	C₂×#41×C₂₃	—	2	1	no	—
47	C₂×#41×C₂₃	—	2	1	no	—
48	C₂×#41×C₂₃	—	2	1	no	—
49	C₂×#41×C₂₃	—	2	1	no	—
50	C₂×#41×C₂₃	—	2	1	no	—
51	C₂×#41×C₂₃	—	2	1	no	—
52	C₂×#41×C₂₃	—	2	1	no	—
53	C₂×#41×C₂₃	—	2	1	no	—
54	C₂×#41×C₂₃	—	2	1	no	—
55	C₂×#41×C₂₃	—	2	1	no	—
56	C₂×#41×C₂₃	—	2	1	no	—
57	C₂×#41×C₂₃	—	2	1	no	—
58	C₂×#41×C₂₃	—	2	1	no	—
59	C₂×#41×C₂₃	—	2	1	no	—
60	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
61	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
62	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
63	C₂×#41×C₂₃	D₄	1	2	yes	—
64	C₂×#41×C₂₃	D₄	1	2	yes	—
65	C₂×#41×C₂₃	D₄	1	2	yes	—
66	C₂×#41×C₂₃	C₂³	1	2	yes	—
67	C₂×#41×C₂₃	C₂³	1	2	yes	—
68	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
69	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
70	C₂²×D₄×C₂₃	—	2	1	no	—
71	C₂²×D₄×C₂₃	—	2	1	no	—
72	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
73	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
74	C₂³×C₄×C₂₃	—	2	1	no	—
75	C₂³×C₄×C₂₃	—	2	1	no	—
76	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
77	C₂₃×#137	—	2	4	no	—
78	C₂₃×#137	—	2	4	no	—
79	C₂₃×#137	—	2	4	no	—
80	C₂₃×#137	C₂×C₄	1	8	yes	complemented
81	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
82	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
83	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
84	C₂₃×AGL(1,ℤ/8)	C₂×C₄	1	8	yes	complemented
85	C₂₃×#135	—	2	8	no	—
86	C₂₃×#135	—	2	8	no	—
87	C₂×Q₁₆×C₂₃	—	2	2	no	—
88	C₂×SD₁₆×C₂₃	—	2	2	no	—
89	C₂×SD₁₆×C₂₃	—	2	2	no	—
90	C₂×D₈×C₂₃	—	2	2	no	—
91	C₂₃×#131	—	2	8	no	—
92	C₂₃×#131	—	2	8	no	—
93	C₂₃×#131	—	2	8	no	—
94	C₂₃×#131	—	2	8	no	—
95	C₂×M₁₆×C₂₃	—	2	4	no	—
96	C₂×M₁₆×C₂₃	—	2	8	no	—
97	C₂×M₁₆×C₂₃	—	2	1	no	—
98	C₂×M₁₆×C₂₃	—	2	1	no	—
99	C₂×M₁₆×C₂₃	—	2	1	no	—
100	C₂×M₁₆×C₂₃	—	2	1	no	—
101	C₂×M₁₆×C₂₃	—	2	1	no	—
102	C₂×M₁₆×C₂₃	—	2	1	no	—
103	C₂×M₁₆×C₂₃	—	2	1	no	—
104	C₂×M₁₆×C₂₃	—	2	1	no	—
105	C₂×M₁₆×C₂₃	—	2	1	no	—
106	C₂×M₁₆×C₂₃	—	2	1	no	—
107	C₂×M₁₆×C₂₃	—	2	8	no	—
108	C₂×M₁₆×C₂₃	C₂×C₄	1	2	yes	—
109	C₂×M₁₆×C₂₃	C₂×C₄	1	2	yes	—
110	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
111	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
112	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
113	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
114	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
115	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
116	C₂²×C₈×C₂₃	—	2	4	no	—
117	C₂²×C₈×C₂₃	—	2	1	no	—
118	C₂²×C₈×C₂₃	—	2	1	no	—
119	C₂²×C₈×C₂₃	—	2	1	no	—
120	C₂²×C₈×C₂₃	—	2	1	no	—
121	C₂²×C₈×C₂₃	—	2	1	no	—
122	C₂²×C₈×C₂₃	—	2	1	no	—
123	C₂²×C₈×C₂₃	—	2	1	no	—
124	C₂²×C₈×C₂₃	—	2	1	no	—
125	C₂²×C₈×C₂₃	D₄	1	2	yes	—
126	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
127	C₂₃×#117	—	2	1	no	—
128	C₂₃×#117	—	2	1	no	—
129	C₂₃×#117	—	2	1	no	—
130	C₂₃×#117	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
133	C₂×C₄²×C₂₃	—	2	1	no	—
134	C₂₃×#104	—	2	8	no	—
135	C₂₃×#103	—	2	4	no	—
136	C₂₃×#102	—	2	4	no	—
137	C₂₃×C₂²⋊C₈	—	2	8	no	—
138	C₂⁴×C₂₃	—	2	1	no	—
139	C₂⁴×C₂₃	—	2	1	no	—
140	C₂⁴×C₂₃	#41	1	1	yes	characteristic
141	#41×C₂₃	—	2	2	no	—
142	#41×C₂₃	—	2	2	no	—
143	#41×C₂₃	—	2	2	no	—
144	#41×C₂₃	—	2	2	no	—
145	#41×C₂₃	—	2	2	no	—
146	#41×C₂₃	—	2	2	no	—
147	#41×C₂₃	—	2	2	no	—
148	#41×C₂₃	—	2	2	no	—
149	#41×C₂₃	—	2	2	no	—
150	#41×C₂₃	—	2	2	no	—
151	#41×C₂₃	—	2	2	no	—
152	#41×C₂₃	—	2	2	no	—
153	#41×C₂₃	—	2	2	no	—
154	#41×C₂₃	—	2	2	no	—
155	#41×C₂₃	—	2	2	no	—
156	#41×C₂₃	—	2	2	no	—
157	#41×C₂₃	—	2	2	no	—
158	#41×C₂₃	—	2	2	no	—
159	#41×C₂₃	—	2	2	no	—
160	#41×C₂₃	—	2	2	no	—
161	#41×C₂₃	—	4	1	no	—
162	#41×C₂₃	—	4	1	no	—
163	#41×C₂₃	—	4	1	no	—
164	#41×C₂₃	—	4	1	no	—
165	#41×C₂₃	—	4	1	no	—
166	#41×C₂₃	—	4	1	no	—
167	#41×C₂₃	—	4	1	no	—
168	#41×C₂₃	—	4	1	no	—
169	#41×C₂₃	C₂²⋊C₄	1	4	yes	—
170	#41×C₂₃	C₂²⋊C₄	1	4	yes	—
171	#41×C₂₃	C₂²×C₄	1	4	yes	—
172	#41×C₂₃	C₂×D₄	1	4	yes	—
173	C₂×Q₈×C₂₃	—	2	1	no	—
174	C₂×Q₈×C₂₃	—	2	1	no	—
175	C₂×Q₈×C₂₃	—	2	1	no	—
176	C₂×Q₈×C₂₃	—	2	1	no	—
177	C₂×Q₈×C₂₃	—	2	1	no	—
178	C₂×Q₈×C₂₃	—	2	1	no	—
179	C₂×Q₈×C₂₃	—	2	1	no	—
180	C₂×Q₈×C₂₃	—	2	1	no	—
181	C₂×Q₈×C₂₃	C₂²⋊C₄	1	2	yes	—
182	C₂×Q₈×C₂₃	C₂²⋊C₄	1	2	yes	—
183	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
184	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
185	C₂×D₄×C₂₃	—	2	2	no	—
186	C₂×D₄×C₂₃	—	2	2	no	—
187	C₂×D₄×C₂₃	—	2	2	no	—
188	C₂×D₄×C₂₃	—	2	2	no	—
189	C₂×D₄×C₂₃	—	2	2	no	—
190	C₂×D₄×C₂₃	—	2	2	no	—
191	C₂×D₄×C₂₃	—	2	2	no	—
192	C₂×D₄×C₂₃	—	2	2	no	—
193	C₂×D₄×C₂₃	—	2	1	no	—
194	C₂×D₄×C₂₃	—	2	1	no	—
195	C₂×D₄×C₂₃	—	2	1	no	—
196	C₂×D₄×C₂₃	—	2	1	no	—
197	C₂×D₄×C₂₃	—	2	1	no	—
198	C₂×D₄×C₂₃	—	2	1	no	—
199	C₂×D₄×C₂₃	—	2	1	no	—
200	C₂×D₄×C₂₃	—	2	1	no	—
201	C₂×D₄×C₂₃	—	4	1	no	—
202	C₂×D₄×C₂₃	—	4	1	no	—
203	C₂×D₄×C₂₃	—	4	1	no	—
204	C₂×D₄×C₂₃	—	4	1	no	—
205	C₂×D₄×C₂₃	C₂²⋊C₄	1	2	yes	—
206	C₂×D₄×C₂₃	C₂²⋊C₄	1	2	yes	—
207	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
208	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
209	C₂²×C₄×C₂₃	—	2	1	no	—
210	C₂²×C₄×C₂₃	—	2	2	no	—
211	C₂²×C₄×C₂₃	—	2	2	no	—
212	C₂²×C₄×C₂₃	—	2	2	no	—
213	C₂²×C₄×C₂₃	—	2	2	no	—
214	C₂²×C₄×C₂₃	—	2	2	no	—
215	C₂²×C₄×C₂₃	—	2	2	no	—
216	C₂²×C₄×C₂₃	—	2	1	no	—
217	C₂²×C₄×C₂₃	—	2	2	no	—
218	C₂²×C₄×C₂₃	—	2	2	no	—
219	C₂²×C₄×C₂₃	—	4	1	no	—
220	C₂²×C₄×C₂₃	—	4	1	no	—
221	C₂²×C₄×C₂₃	—	4	1	no	—
222	C₂²×C₄×C₂₃	—	4	1	no	—
223	C₂²×C₄×C₂₃	—	4	1	no	—
224	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
225	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
226	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
235	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
236	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
237	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
238	Q₁₆×C₂₃	—	2	8	no	—
239	SD₁₆×C₂₃	—	2	8	no	—
240	SD₁₆×C₂₃	—	2	8	no	—
241	D₈×C₂₃	—	2	8	no	—
242	M₁₆×C₂₃	—	2	16	no	—
243	M₁₆×C₂₃	—	2	2	no	—
244	M₁₆×C₂₃	—	2	2	no	—
245	M₁₆×C₂₃	—	2	2	no	—
246	M₁₆×C₂₃	—	2	2	no	—
247	M₁₆×C₂₃	—	2	2	no	—
248	M₁₆×C₂₃	—	2	2	no	—
249	M₁₆×C₂₃	—	2	2	no	—
250	M₁₆×C₂₃	—	2	2	no	—
251	M₁₆×C₂₃	—	2	2	no	—
252	M₁₆×C₂₃	—	2	2	no	—
253	M₁₆×C₂₃	C₂²×C₄	1	4	yes	—
254	M₁₆×C₂₃	C₂×D₄	1	4	yes	—
255	C₂×C₈×C₂₃	—	2	16	no	—
256	C₂×C₈×C₂₃	—	2	2	no	—
257	C₂×C₈×C₂₃	—	2	2	no	—
258	C₂×C₈×C₂₃	—	2	2	no	—
259	C₂×C₈×C₂₃	—	2	2	no	—
260	C₂×C₈×C₂₃	—	2	2	no	—
261	C₂×C₈×C₂₃	—	2	2	no	—
262	C₂×C₈×C₂₃	—	2	2	no	—
263	C₂×C₈×C₂₃	—	2	2	no	—
264	C₂×C₈×C₂₃	—	2	2	no	—
265	C₂×C₈×C₂₃	—	2	2	no	—
266	C₂×C₈×C₂₃	—	2	2	no	—
267	C₂×C₈×C₂₃	—	4	1	no	—
268	C₂×C₈×C₂₃	—	4	1	no	—
269	C₂×C₈×C₂₃	—	4	1	no	—
270	C₂×C₈×C₂₃	—	4	1	no	—
271	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
272	C₄⋊C₄×C₂₃	—	2	2	no	—
273	C₄⋊C₄×C₂₃	—	4	1	no	—
274	C₂²⋊C₄×C₂₃	—	2	2	no	—
275	C₂²⋊C₄×C₂₃	—	4	1	no	—
276	C₄²×C₂₃	—	2	2	no	—
277	C₄²×C₂₃	—	4	1	no	—
278	C₂×#1881	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
279	C₂³×C₂₃	—	2	2	no	—
280	C₂³×C₂₃	—	2	2	no	—
281	C₂³×C₂₃	—	2	2	no	—
282	C₂³×C₂₃	—	2	2	no	—
283	C₂³×C₂₃	—	4	2	no	—
284	C₂³×C₂₃	—	4	4	no	—
285	C₂³×C₂₃	—	4	1	no	—
286	C₂³×C₂₃	—	4	1	no	—
287	C₂³×C₂₃	—	8	2	no	—
288	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
289	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
290	C₂³×C₂₃	#121	1	1	yes	characteristic
291	C₂³×C₂₃	#121	1	1	yes	characteristic
292	C₂³×C₂₃	#123	1	1	yes	characteristic
293	C₂³×C₂₃	#123	1	1	yes	characteristic
294	C₂³×C₂₃	C₂×#41	1	1	yes	characteristic
295	Q₈×C₂₃	—	2	2	no	—
296	Q₈×C₂₃	—	2	2	no	—
297	Q₈×C₂₃	—	2	2	no	—
298	Q₈×C₂₃	—	2	2	no	—
299	Q₈×C₂₃	—	2	2	no	—
300	Q₈×C₂₃	—	4	1	no	—
301	Q₈×C₂₃	—	4	1	no	—
302	Q₈×C₂₃	C₂×C₂²⋊C₄	1	4	yes	—
303	D₄×C₂₃	—	2	4	no	—
304	D₄×C₂₃	—	2	4	no	—
305	D₄×C₂₃	—	2	4	no	—
306	D₄×C₂₃	—	2	4	no	—
307	D₄×C₂₃	—	2	2	no	—
308	D₄×C₂₃	—	2	2	no	—
309	D₄×C₂₃	—	2	2	no	—
310	D₄×C₂₃	—	2	2	no	—
311	D₄×C₂₃	—	2	2	no	—
312	D₄×C₂₃	—	4	2	no	—
313	D₄×C₂₃	—	4	2	no	—
314	D₄×C₂₃	—	4	2	no	—
315	D₄×C₂₃	—	4	2	no	—
316	D₄×C₂₃	—	4	1	no	—
317	D₄×C₂₃	—	4	1	no	—
318	D₄×C₂₃	C₂×C₂²⋊C₄	1	4	yes	—
319	C₂×C₄×C₂₃	—	2	2	no	—
320	C₂×C₄×C₂₃	—	2	2	no	—
321	C₂×C₄×C₂₃	—	2	2	no	—
322	C₂×C₄×C₂₃	—	2	4	no	—
323	C₂×C₄×C₂₃	—	2	4	no	—
324	C₂×C₄×C₂₃	—	2	4	no	—
325	C₂×C₄×C₂₃	—	2	4	no	—
326	C₂×C₄×C₂₃	—	2	2	no	—
327	C₂×C₄×C₂₃	—	4	1	no	—
328	C₂×C₄×C₂₃	—	4	1	no	—
329	C₂×C₄×C₂₃	—	4	2	no	—
330	C₂×C₄×C₂₃	—	4	2	no	—
331	C₂×C₄×C₂₃	—	4	2	no	—
332	C₂×C₄×C₂₃	—	4	2	no	—
333	C₂×C₄×C₂₃	—	4	2	no	—
334	C₂×C₄×C₂₃	—	8	2	no	—
335	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
336	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
337	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
338	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
339	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
340	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
341	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
342	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
343	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
344	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
345	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
346	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
347	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
348	C₂×C₄×C₂₃	#120	1	1	yes	characteristic
349	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
350	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
351	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
352	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
353	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
354	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
355	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
356	C₂×C₄×C₂₃	#123	1	1	yes	characteristic
357	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
358	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
363	C₈×C₂₃	—	2	4	no	—
364	C₈×C₂₃	—	2	4	no	—
365	C₈×C₂₃	—	2	4	no	—
366	C₈×C₂₃	—	4	2	no	—
367	C₂×#575	C₂×C₂₃	1	1	yes	characteristic
368	C₂×#568	C₂×C₂₃	1	1	yes	characteristic, complemented
369	C₂×#421	C₂×C₂₃	1	1	yes	characteristic, complemented
370	C₂×#416	C₂×C₂₃	1	1	yes	characteristic, complemented
371	C₂×#408	C₂×C₂₃	1	1	yes	characteristic, complemented
372	#1881	C₂×C₂₃	1	8	yes	direct product factor
373	C₂×#344	C₂×C₂₃	1	1	yes	characteristic, complemented
374	C₂×#341	C₂×C₂₃	1	1	yes	characteristic, complemented
375	C₂²×C₂₃	—	2	2	no	—
376	C₂²×C₂₃	—	2	2	no	—
377	C₂²×C₂₃	—	2	2	no	—
378	C₂²×C₂₃	—	2	4	no	—
379	C₂²×C₂₃	—	4	1	no	—
380	C₂²×C₂₃	—	4	1	no	—
381	C₂²×C₂₃	—	4	1	no	—
382	C₂²×C₂₃	—	4	1	no	—
383	C₂²×C₂₃	—	4	4	no	—
384	C₂²×C₂₃	—	4	4	no	—
385	C₂²×C₂₃	—	4	2	no	—
386	C₂²×C₂₃	—	8	2	no	—
387	C₂²×C₂₃	—	8	2	no	—
388	C₂²×C₂₃	—	8	2	no	—
389	C₂²×C₂₃	—	8	2	no	—
390	C₂²×C₂₃	#386	1	1	yes	characteristic
391	C₂²×C₂₃	#386	1	1	yes	characteristic
392	C₂²×C₂₃	#386	1	1	yes	characteristic
393	C₂²×C₂₃	#386	1	1	yes	characteristic
394	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
395	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
396	C₂²×C₂₃	C₂×#123	1	1	yes	characteristic
397	C₄×C₂₃	—	2	4	no	—
398	C₄×C₂₃	—	4	2	no	—
399	C₄×C₂₃	—	8	2	no	—
400	C₄×C₂₃	#386	1	1	yes	characteristic
401	C₄×C₂₃	#386	1	1	yes	characteristic
402	C₄×C₂₃	#386	1	1	yes	characteristic
403	C₄×C₂₃	#386	1	1	yes	characteristic
404	C₄×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
405	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
406	C₄×C₂₃	C₂×#120	1	1	yes	characteristic
407	C₄×C₂₃	C₂×#121	1	1	yes	characteristic
408	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
409	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
410	#575	—	2	2	no	—
411	#575	—	2	2	no	—
412	#575	C₄×C₂₃	1	4	yes	complemented
413	#575	C₂²×C₂₃	1	4	yes	—
414	C₂×#137	—	2	1	no	—
415	C₂×#137	C₄×C₂₃	1	2	yes	complemented
416	C₂×AGL(1,ℤ/8)	—	2	1	no	—
417	C₂×AGL(1,ℤ/8)	C₄×C₂₃	1	2	yes	complemented
418	C₂×#135	—	2	2	no	—
419	#568	—	2	2	no	—
420	#568	—	2	2	no	—
421	#568	—	2	2	no	—
422	#568	C₂²×C₂₃	1	4	yes	complemented
423	C₂×#131	—	2	2	no	—
424	C₂×#131	—	2	2	no	—
425	C₂²×M₁₆	—	2	2	no	—
426	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
427	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
428	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
429	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
430	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
431	#421	—	2	2	no	—
432	#421	C₂²×C₂₃	1	4	yes	complemented
433	C₂×#104	—	2	2	no	—
434	#416	—	2	2	no	—
435	#416	C₂²×C₂₃	1	4	yes	complemented
436	C₂×#103	—	2	1	no	—
437	C₂×#102	—	2	1	no	—
438	#408	—	2	2	no	—
439	#408	C₂²×C₂₃	1	4	yes	complemented
440	C₂×C₂²⋊C₈	—	2	2	no	—
441	#344	C₂²×C₂₃	1	4	yes	complemented
442	#341	C₂²×C₂₃	1	4	yes	complemented
443	C₂×C₂₃	—	2	1	no	—
444	C₂×C₂₃	—	2	1	no	—
445	C₂×C₂₃	—	2	1	no	—
446	C₂×C₂₃	—	2	1	no	—
447	C₂×C₂₃	—	2	1	no	—
448	C₂×C₂₃	—	2	1	no	—
449	C₂×C₂₃	—	4	4	no	—
450	C₂×C₂₃	—	8	2	no	—
451	C₂×C₂₃	#1881	1	2	yes	direct product factor
452	C₂×C₂₃	C₂×#386	1	1	yes	characteristic
453	C₂×#41	—	2	1	no	—
454	C₂×#41	—	2	1	no	—
455	C₂×#41	—	2	1	no	—
456	C₂×#41	—	2	1	no	—
457	C₂×#41	—	2	1	no	—
458	C₂×#41	—	2	1	no	—
459	C₂×#41	—	2	1	no	—
460	C₂×#41	—	2	1	no	—
461	C₂×#41	—	2	1	no	—
462	C₂×#41	—	2	1	no	—
463	C₂×#41	—	2	1	no	—
464	C₂×#41	—	2	1	no	—
465	C₂×#41	—	2	1	no	—
466	C₂×#41	—	2	1	no	—
467	C₂×#41	—	2	1	no	—
468	C₂×#41	—	2	1	no	—
469	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
470	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
471	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
472	C₂×#41	D₄×C₂₃	1	2	yes	—
473	C₂×#41	D₄×C₂₃	1	2	yes	—
474	C₂×#41	D₄×C₂₃	1	2	yes	—
475	C₂×#41	C₂³×C₂₃	1	2	yes	—
476	C₂×#41	C₂³×C₂₃	1	2	yes	—
477	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
478	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
479	C₂²×D₄	—	2	1	no	—
480	C₂²×D₄	—	2	1	no	—
481	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
482	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
483	C₂³×C₄	—	2	1	no	—
484	C₂³×C₄	—	2	1	no	—
485	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
486	#137	—	2	4	no	—
487	#137	—	2	4	no	—
488	#137	—	2	4	no	—
489	#137	C₂×C₄×C₂₃	1	8	yes	complemented
490	AGL(1,ℤ/8)	—	2	4	no	—
491	AGL(1,ℤ/8)	—	2	4	no	—
492	AGL(1,ℤ/8)	—	2	4	no	—
493	AGL(1,ℤ/8)	C₂×C₄×C₂₃	1	8	yes	complemented
494	#135	—	2	8	no	—
495	#135	—	2	8	no	—
496	C₂×Q₁₆	—	2	2	no	—
497	C₂×SD₁₆	—	2	2	no	—
498	C₂×SD₁₆	—	2	2	no	—
499	C₂×D₈	—	2	2	no	—
500	#131	—	2	8	no	—
501	#131	—	2	8	no	—
502	#131	—	2	8	no	—
503	#131	—	2	8	no	—
504	C₂×M₁₆	—	2	4	no	—
505	C₂×M₁₆	—	2	8	no	—
506	C₂×M₁₆	—	2	1	no	—
507	C₂×M₁₆	—	2	1	no	—
508	C₂×M₁₆	—	2	1	no	—
509	C₂×M₁₆	—	2	1	no	—
510	C₂×M₁₆	—	2	1	no	—
511	C₂×M₁₆	—	2	1	no	—
512	C₂×M₁₆	—	2	1	no	—
513	C₂×M₁₆	—	2	1	no	—
514	C₂×M₁₆	—	2	1	no	—
515	C₂×M₁₆	—	2	1	no	—
516	C₂×M₁₆	—	2	8	no	—
517	C₂×M₁₆	C₂×C₄×C₂₃	1	2	yes	—
518	C₂×M₁₆	C₂×C₄×C₂₃	1	2	yes	—
519	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
520	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
521	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
522	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
523	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
524	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
525	C₂²×C₈	—	2	4	no	—
526	C₂²×C₈	—	2	1	no	—
527	C₂²×C₈	—	2	1	no	—
528	C₂²×C₈	—	2	1	no	—
529	C₂²×C₈	—	2	1	no	—
530	C₂²×C₈	—	2	1	no	—
531	C₂²×C₈	—	2	1	no	—
532	C₂²×C₈	—	2	1	no	—
533	C₂²×C₈	—	2	1	no	—
534	C₂²×C₈	D₄×C₂₃	1	2	yes	—
535	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
536	#117	—	2	1	no	—
537	#117	—	2	1	no	—
538	#117	—	2	1	no	—
539	#117	C₂³×C₂₃	1	2	yes	—
540	C₂×C₄⋊C₄	—	2	1	no	—
541	C₂×C₂²⋊C₄	—	2	1	no	—
542	C₂×C₄²	—	2	1	no	—
543	#104	—	2	8	no	—
544	#103	—	2	4	no	—
545	#102	—	2	4	no	—
546	C₂²⋊C₈	—	2	8	no	—
547	C₂₃	C₂×#1881	1	1	yes	characteristic, direct product factor, Sylow
548	C₂⁴	—	2	1	no	—
549	C₂⁴	—	2	1	no	—
550	C₂⁴	#41×C₂₃	1	1	yes	characteristic
551	#41	—	2	2	no	—
552	#41	—	2	2	no	—
553	#41	—	2	2	no	—
554	#41	—	2	2	no	—
555	#41	—	2	2	no	—
556	#41	—	2	2	no	—
557	#41	—	2	2	no	—
558	#41	—	2	2	no	—
559	#41	—	2	2	no	—
560	#41	—	2	2	no	—
561	#41	—	2	2	no	—
562	#41	—	2	2	no	—
563	#41	—	2	2	no	—
564	#41	—	2	2	no	—
565	#41	—	2	2	no	—
566	#41	—	2	2	no	—
567	#41	—	2	2	no	—
568	#41	—	2	2	no	—
569	#41	—	2	2	no	—
570	#41	—	2	2	no	—
571	#41	—	4	1	no	—
572	#41	—	4	1	no	—
573	#41	—	4	1	no	—
574	#41	—	4	1	no	—
575	#41	—	4	1	no	—
576	#41	—	4	1	no	—
577	#41	—	4	1	no	—
578	#41	—	4	1	no	—
579	#41	C₂²⋊C₄×C₂₃	1	4	yes	—
580	#41	C₂²⋊C₄×C₂₃	1	4	yes	—
581	#41	C₂²×C₄×C₂₃	1	4	yes	—
582	#41	C₂×D₄×C₂₃	1	4	yes	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	—	2	1	no	—
585	C₂×Q₈	—	2	1	no	—
586	C₂×Q₈	—	2	1	no	—
587	C₂×Q₈	—	2	1	no	—
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	—	2	1	no	—
590	C₂×Q₈	—	2	1	no	—
591	C₂×Q₈	C₂²⋊C₄×C₂₃	1	2	yes	—
592	C₂×Q₈	C₂²⋊C₄×C₂₃	1	2	yes	—
593	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
594	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	1	no	—
604	C₂×D₄	—	2	1	no	—
605	C₂×D₄	—	2	1	no	—
606	C₂×D₄	—	2	1	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	2	1	no	—
609	C₂×D₄	—	2	1	no	—
610	C₂×D₄	—	2	1	no	—
611	C₂×D₄	—	4	1	no	—
612	C₂×D₄	—	4	1	no	—
613	C₂×D₄	—	4	1	no	—
614	C₂×D₄	—	4	1	no	—
615	C₂×D₄	C₂²⋊C₄×C₂₃	1	2	yes	—
616	C₂×D₄	C₂²⋊C₄×C₂₃	1	2	yes	—
617	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
618	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	4	1	no	—
630	C₂²×C₄	—	4	1	no	—
631	C₂²×C₄	—	4	1	no	—
632	C₂²×C₄	—	4	1	no	—
633	C₂²×C₄	—	4	1	no	—
634	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
635	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
636	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
637	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
638	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
639	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
640	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
641	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
642	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
643	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
644	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
645	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
646	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
647	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
648	Q₁₆	—	2	8	no	—
649	SD₁₆	—	2	8	no	—
650	SD₁₆	—	2	8	no	—
651	D₈	—	2	8	no	—
652	M₁₆	—	2	16	no	—
653	M₁₆	—	2	2	no	—
654	M₁₆	—	2	2	no	—
655	M₁₆	—	2	2	no	—
656	M₁₆	—	2	2	no	—
657	M₁₆	—	2	2	no	—
658	M₁₆	—	2	2	no	—
659	M₁₆	—	2	2	no	—
660	M₁₆	—	2	2	no	—
661	M₁₆	—	2	2	no	—
662	M₁₆	—	2	2	no	—
663	M₁₆	C₂²×C₄×C₂₃	1	4	yes	—
664	M₁₆	C₂×D₄×C₂₃	1	4	yes	—
665	C₂×C₈	—	2	16	no	—
666	C₂×C₈	—	2	2	no	—
667	C₂×C₈	—	2	2	no	—
668	C₂×C₈	—	2	2	no	—
669	C₂×C₈	—	2	2	no	—
670	C₂×C₈	—	2	2	no	—
671	C₂×C₈	—	2	2	no	—
672	C₂×C₈	—	2	2	no	—
673	C₂×C₈	—	2	2	no	—
674	C₂×C₈	—	2	2	no	—
675	C₂×C₈	—	2	2	no	—
676	C₂×C₈	—	2	2	no	—
677	C₂×C₈	—	4	1	no	—
678	C₂×C₈	—	4	1	no	—
679	C₂×C₈	—	4	1	no	—
680	C₂×C₈	—	4	1	no	—
681	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	4	1	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	4	1	no	—
686	C₄²	—	2	2	no	—
687	C₄²	—	4	1	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	4	2	no	—
693	C₂³	—	4	4	no	—
694	C₂³	—	4	1	no	—
695	C₂³	—	4	1	no	—
696	C₂³	—	8	2	no	—
697	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
698	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
699	C₂³	C₂₃×#121	1	1	yes	characteristic
700	C₂³	C₂₃×#121	1	1	yes	characteristic
701	C₂³	C₂₃×#123	1	1	yes	characteristic
702	C₂³	C₂₃×#123	1	1	yes	characteristic
703	C₂³	C₂×#41×C₂₃	1	1	yes	characteristic
704	Q₈	—	2	2	no	—
705	Q₈	—	2	2	no	—
706	Q₈	—	2	2	no	—
707	Q₈	—	2	2	no	—
708	Q₈	—	2	2	no	—
709	Q₈	—	4	1	no	—
710	Q₈	—	4	1	no	—
711	Q₈	C₂×C₂²⋊C₄×C₂₃	1	4	yes	—
712	D₄	—	2	4	no	—
713	D₄	—	2	4	no	—
714	D₄	—	2	4	no	—
715	D₄	—	2	4	no	—
716	D₄	—	2	2	no	—
717	D₄	—	2	2	no	—
718	D₄	—	2	2	no	—
719	D₄	—	2	2	no	—
720	D₄	—	2	2	no	—
721	D₄	—	4	2	no	—
722	D₄	—	4	2	no	—
723	D₄	—	4	2	no	—
724	D₄	—	4	2	no	—
725	D₄	—	4	1	no	—
726	D₄	—	4	1	no	—
727	D₄	C₂×C₂²⋊C₄×C₂₃	1	4	yes	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	4	no	—
732	C₂×C₄	—	2	4	no	—
733	C₂×C₄	—	2	4	no	—
734	C₂×C₄	—	2	4	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	2	no	—
739	C₂×C₄	—	4	2	no	—
740	C₂×C₄	—	4	2	no	—
741	C₂×C₄	—	4	2	no	—
742	C₂×C₄	—	4	2	no	—
743	C₂×C₄	—	8	2	no	—
744	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
745	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
746	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
747	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
748	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
749	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
750	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
751	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
752	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
753	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
754	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
755	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
756	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
757	C₂×C₄	C₂₃×#120	1	1	yes	characteristic
758	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
759	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
760	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
761	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
762	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
763	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
764	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
765	C₂×C₄	C₂₃×#123	1	1	yes	characteristic
766	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
767	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
768	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
769	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
770	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
771	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
772	C₈	—	2	4	no	—
773	C₈	—	2	4	no	—
774	C₈	—	2	4	no	—
775	C₈	—	4	2	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	2	4	no	—
780	C₂²	—	4	1	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	4	no	—
785	C₂²	—	4	4	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	8	2	no	—
788	C₂²	—	8	2	no	—
789	C₂²	—	8	2	no	—
790	C₂²	—	8	2	no	—
791	C₂²	C₂₃×#386	1	1	yes	characteristic
792	C₂²	C₂₃×#386	1	1	yes	characteristic
793	C₂²	C₂₃×#386	1	1	yes	characteristic
794	C₂²	C₂₃×#386	1	1	yes	characteristic
795	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
796	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
797	C₂²	C₂×C₂₃×#123	1	1	yes	characteristic
798	C₄	—	2	4	no	—
799	C₄	—	4	2	no	—
800	C₄	—	8	2	no	—
801	C₄	C₂₃×#386	1	1	yes	characteristic
802	C₄	C₂₃×#386	1	1	yes	characteristic
803	C₄	C₂₃×#386	1	1	yes	characteristic
804	C₄	C₂₃×#386	1	1	yes	characteristic
805	C₄	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
806	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
807	C₄	C₂×C₂₃×#120	1	1	yes	characteristic
808	C₄	C₂×C₂₃×#121	1	1	yes	characteristic
809	C₂	—	2	1	no	—
810	C₂	—	2	1	no	—
811	C₂	—	2	1	no	—
812	C₂	—	2	1	no	—
813	C₂	—	2	1	no	—
814	C₂	—	2	1	no	—
815	C₂	—	4	4	no	—
816	C₂	—	8	2	no	—
817	C₂	C₂₃×#1881	1	2	yes	direct product factor
818	C₂	C₂×C₂₃×#386	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	#120
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂²×C₂₃	#386
prime radical	C₂×C₂₃×#575	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#568	C₂	semidirect
3. C₂×C₂₃×#421	C₂	semidirect
4. C₂×C₂₃×#416	C₂	semidirect
5. C₂×C₂₃×#408	C₂	semidirect
6. C₂₃×#1881	C₂	direct (N × H)
7. C₂×C₂₃×#344	C₂	semidirect
8. C₂×C₂₃×#341	C₂	semidirect
13. C₂₃×#575	C₄	semidirect
16. C₂×C₂₃×#137	C₄	semidirect
18. C₂×C₂₃×AGL(1,ℤ/8)	C₄	semidirect
23. C₂₃×#568	C₂²	semidirect
33. C₂₃×#421	C₂²	semidirect
36. C₂₃×#416	C₂²	semidirect
40. C₂₃×#408	C₂²	semidirect
42. C₂₃×#344	C₂²	semidirect
43. C₂₃×#341	C₂²	semidirect
80. C₂₃×#137	C₂×C₄	semidirect
84. C₂₃×AGL(1,ℤ/8)	C₂×C₄	semidirect
278. C₂×#1881	C₂₃	direct (N × H)
368. C₂×#568	C₂×C₂₃	semidirect
369. C₂×#421	C₂×C₂₃	semidirect
370. C₂×#416	C₂×C₂₃	semidirect
371. C₂×#408	C₂×C₂₃	semidirect
372. #1881	C₂×C₂₃	direct (N × H)
373. C₂×#344	C₂×C₂₃	semidirect
374. C₂×#341	C₂×C₂₃	semidirect
412. #575	C₄×C₂₃	semidirect
415. C₂×#137	C₄×C₂₃	semidirect
417. C₂×AGL(1,ℤ/8)	C₄×C₂₃	semidirect
422. #568	C₂²×C₂₃	semidirect
432. #421	C₂²×C₂₃	semidirect
435. #416	C₂²×C₂₃	semidirect
439. #408	C₂²×C₂₃	semidirect
441. #344	C₂²×C₂₃	semidirect
442. #341	C₂²×C₂₃	semidirect
451. C₂×C₂₃	#1881	direct (N × H)
489. #137	C₂×C₄×C₂₃	semidirect
493. AGL(1,ℤ/8)	C₂×C₄×C₂₃	semidirect
547. C₂₃	C₂×#1881	direct (N × H)
817. C₂	C₂₃×#1881	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#575	2
C₂×C₂₃×#568	2
C₂×C₂₃×#421	2
C₂×C₂₃×#416	2
C₂×C₂₃×#408	2
C₂₃×#1881	2
C₂×C₂₃×#344	2
C₂×C₂₃×#341	2
C₂×#1881	23

Subgroups — C2×C23×#1881 #19168564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#1881 #19168564