Subgroups — C₂×C₂₃×#1559 #19165359

Order 5888.

998 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#432	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×#423	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1559	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₂₃×#333	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₃×#332	C₂	1	2	yes	maximal, complemented
7	C₂²×M₁₆×C₂₃	—	2	1	no	—
8	C₂₃×#533	—	2	2	no	—
9	C₂₃×#533	—	2	2	no	—
10	C₂₃×#533	C₄	1	4	yes	—
11	C₂₃×#533	C₂²	1	4	yes	—
12	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×#125	—	2	1	no	—
15	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
16	C₂×C₂₃×C₂²⋊Q₈	C₄	1	2	yes	—
17	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
18	C₂×C₄×Q₈×C₂₃	C₄	1	2	yes	—
19	C₂×C₂₃×#117	—	2	1	no	—
20	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
21	C₂₃×#432	—	2	2	no	—
22	C₂₃×#432	C₂²	1	4	yes	—
23	C₂₃×#423	—	2	2	no	—
24	C₂₃×#423	C₂²	1	4	yes	—
25	C₂×C₂₃×C₄⋊C₈	—	2	1	no	—
26	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
27	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
28	C₂×C₂₃×C₂²⋊C₈	—	2	1	no	—
29	C₂×C₂₃×#97	—	2	1	no	—
30	C₂₃×#333	C₂²	1	8	yes	complemented
31	C₂₃×#332	C₂²	1	8	yes	complemented
32	C₂²×Q₈×C₂₃	—	2	1	no	—
33	C₂²×Q₈×C₂₃	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
37	C₂×M₁₆×C₂₃	—	2	4	no	—
38	C₂×M₁₆×C₂₃	—	4	4	no	—
39	C₂²×C₈×C₂₃	—	2	2	no	—
40	C₂²×C₈×C₂₃	—	2	2	no	—
41	C₂₃×C₄⋊Q₈	—	2	1	no	—
42	C₂₃×C₄⋊Q₈	—	2	1	no	—
43	C₂₃×C₄⋊Q₈	—	2	1	no	—
44	C₂₃×C₄⋊Q₈	—	2	1	no	—
45	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
46	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
47	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
48	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
49	C₂₃×#125	—	2	4	no	—
50	C₂₃×#125	—	2	4	no	—
51	C₂₃×C₂²⋊Q₈	—	2	4	no	—
52	C₂₃×C₂²⋊Q₈	—	2	4	no	—
53	C₂₃×C₂²⋊Q₈	—	2	4	no	—
54	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
55	C₄×Q₈×C₂₃	—	2	4	no	—
56	C₄×Q₈×C₂₃	—	2	4	no	—
57	C₄×Q₈×C₂₃	—	2	4	no	—
58	C₄×Q₈×C₂₃	C₂×C₄	1	8	yes	—
59	C₂₃×#117	—	2	4	no	—
60	C₂₃×#117	—	2	4	no	—
61	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
62	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
63	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
67	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
68	C₂×C₄²×C₂₃	—	2	2	no	—
69	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
71	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₂₃	D₄	1	2	yes	—
74	C₂×C₄²×C₂₃	D₄	1	2	yes	—
75	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
77	C₂₃×C₄⋊C₈	—	2	4	no	—
78	C₂₃×C₄⋊C₈	—	2	2	no	—
79	C₂₃×C₄⋊C₈	—	2	2	no	—
80	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
81	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
82	C₂₃×C₂²⋊C₈	—	2	4	no	—
83	C₂₃×#97	—	2	4	no	—
84	C₂⁴×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×Q₈×C₂₃	—	2	2	no	—
86	C₂×Q₈×C₂₃	—	2	2	no	—
87	C₂×Q₈×C₂₃	—	2	2	no	—
88	C₂×Q₈×C₂₃	—	4	4	no	—
89	C₂×Q₈×C₂₃	—	4	2	no	—
90	C₂×Q₈×C₂₃	—	4	2	no	—
91	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₂₃	—	2	2	no	—
93	C₂²×C₄×C₂₃	—	2	2	no	—
94	C₂²×C₄×C₂₃	—	2	4	no	—
95	C₂²×C₄×C₂₃	—	2	2	no	—
96	C₂²×C₄×C₂₃	—	2	2	no	—
97	C₂²×C₄×C₂₃	—	4	2	no	—
98	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
99	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
100	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
101	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
102	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
103	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
104	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
110	M₁₆×C₂₃	—	4	8	no	—
111	C₂×C₈×C₂₃	—	2	4	no	—
112	C₂×C₈×C₂₃	—	2	4	no	—
113	C₂×C₈×C₂₃	—	4	4	no	—
114	C₂×C₈×C₂₃	—	4	4	no	—
115	C₄⋊C₄×C₂₃	—	2	2	no	—
116	C₄⋊C₄×C₂₃	—	2	2	no	—
117	C₄⋊C₄×C₂₃	—	2	2	no	—
118	C₄⋊C₄×C₂₃	—	2	8	no	—
119	C₄⋊C₄×C₂₃	—	2	8	no	—
120	C₄⋊C₄×C₂₃	—	2	2	no	—
121	C₄⋊C₄×C₂₃	—	2	2	no	—
122	C₄⋊C₄×C₂₃	—	2	2	no	—
123	C₄⋊C₄×C₂₃	—	2	2	no	—
124	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
125	C₂²⋊C₄×C₂₃	—	2	8	no	—
126	C₄²×C₂₃	—	2	8	no	—
127	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
128	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
129	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
130	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
131	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₂₃	C₂×D₄	1	2	yes	—
133	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₂₃	C₂×D₄	1	2	yes	—
136	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
137	C₂×#1559	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂³×C₂₃	—	2	2	no	—
139	C₂³×C₂₃	—	2	2	no	—
140	C₂³×C₂₃	—	2	2	no	—
141	C₂³×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
142	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	Q₈×C₂₃	—	4	4	no	—
144	Q₈×C₂₃	—	4	4	no	—
145	Q₈×C₂₃	—	4	2	no	—
146	Q₈×C₂₃	—	4	2	no	—
147	Q₈×C₂₃	—	4	4	no	—
148	C₂×C₄×C₂₃	—	2	2	no	—
149	C₂×C₄×C₂₃	—	2	2	no	—
150	C₂×C₄×C₂₃	—	2	2	no	—
151	C₂×C₄×C₂₃	—	2	2	no	—
152	C₂×C₄×C₂₃	—	2	2	no	—
153	C₂×C₄×C₂₃	—	2	4	no	—
154	C₂×C₄×C₂₃	—	2	2	no	—
155	C₂×C₄×C₂₃	—	2	4	no	—
156	C₂×C₄×C₂₃	—	2	4	no	—
157	C₂×C₄×C₂₃	—	2	4	no	—
158	C₂×C₄×C₂₃	—	2	4	no	—
159	C₂×C₄×C₂₃	—	4	2	no	—
160	C₂×C₄×C₂₃	—	4	2	no	—
161	C₂×C₄×C₂₃	—	4	4	no	—
162	C₂×C₄×C₂₃	—	4	4	no	—
163	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
170	C₂×C₄×C₂₃	#137	1	2	yes	—
171	C₂×C₄×C₂₃	#137	1	4	yes	—
172	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
175	C₈×C₂₃	—	4	4	no	—
176	C₈×C₂₃	—	4	4	no	—
177	C₂×#533	C₂×C₂₃	1	1	yes	characteristic
178	C₂×#432	C₂×C₂₃	1	1	yes	characteristic
179	C₂×#423	C₂×C₂₃	1	1	yes	characteristic
180	#1559	C₂×C₂₃	1	8	yes	direct product factor
181	C₂×#333	C₂×C₂₃	1	2	yes	complemented
182	C₂×#332	C₂×C₂₃	1	2	yes	complemented
183	C₂²×C₂₃	—	2	2	no	—
184	C₂²×C₂₃	—	2	2	no	—
185	C₂²×C₂₃	—	2	2	no	—
186	C₂²×C₂₃	—	4	4	no	—
187	C₂²×C₂₃	#413	1	2	yes	—
188	C₂²×C₂₃	#417	1	2	yes	—
189	C₂²×C₂₃	#419	1	2	yes	—
190	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
191	C₄×C₂₃	—	2	2	no	—
192	C₄×C₂₃	—	2	1	no	—
193	C₄×C₂₃	—	2	1	no	—
194	C₄×C₂₃	—	2	2	no	—
195	C₄×C₂₃	—	2	2	no	—
196	C₄×C₂₃	—	4	4	no	—
197	C₄×C₂₃	—	4	4	no	—
198	C₄×C₂₃	#417	1	2	yes	—
199	C₄×C₂₃	#419	1	2	yes	—
200	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
201	C₄×C₂₃	C₂×#137	1	2	yes	—
202	C₄×C₂₃	C₂×#137	1	1	yes	characteristic
203	C₂²×M₁₆	—	2	1	no	—
204	#533	—	2	2	no	—
205	#533	—	2	2	no	—
206	#533	C₄×C₂₃	1	4	yes	—
207	#533	C₂²×C₂₃	1	4	yes	—
208	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
209	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
210	C₂×#125	—	2	1	no	—
211	C₂×C₂²⋊Q₈	—	2	1	no	—
212	C₂×C₂²⋊Q₈	C₄×C₂₃	1	2	yes	—
213	C₂×C₄×Q₈	—	2	1	no	—
214	C₂×C₄×Q₈	C₄×C₂₃	1	2	yes	—
215	C₂×#117	—	2	1	no	—
216	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
217	#432	—	2	2	no	—
218	#432	C₂²×C₂₃	1	4	yes	—
219	#423	—	2	2	no	—
220	#423	C₂²×C₂₃	1	4	yes	—
221	C₂×C₄⋊C₈	—	2	1	no	—
222	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
223	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
224	C₂×C₂²⋊C₈	—	2	1	no	—
225	C₂×#97	—	2	1	no	—
226	#333	C₂²×C₂₃	1	8	yes	complemented
227	#332	C₂²×C₂₃	1	8	yes	complemented
228	C₂×C₂₃	—	4	2	no	—
229	C₂×C₂₃	#1559	1	4	yes	direct product factor
230	C₂×C₂₃	C₂×#413	1	1	yes	characteristic
231	C₂×C₂₃	C₂×#419	1	1	yes	characteristic
232	C₂×C₂₃	C₂×#417	1	1	yes	characteristic
233	C₂²×Q₈	—	2	1	no	—
234	C₂²×Q₈	C₂×C₄×C₂₃	1	2	yes	—
235	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
236	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
237	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
238	C₂×M₁₆	—	2	4	no	—
239	C₂×M₁₆	—	4	4	no	—
240	C₂²×C₈	—	2	2	no	—
241	C₂²×C₈	—	2	2	no	—
242	C₄⋊Q₈	—	2	1	no	—
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	—	2	1	no	—
246	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
247	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
248	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
249	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
250	#125	—	2	4	no	—
251	#125	—	2	4	no	—
252	C₂²⋊Q₈	—	2	4	no	—
253	C₂²⋊Q₈	—	2	4	no	—
254	C₂²⋊Q₈	—	2	4	no	—
255	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	—
256	C₄×Q₈	—	2	4	no	—
257	C₄×Q₈	—	2	4	no	—
258	C₄×Q₈	—	2	4	no	—
259	C₄×Q₈	C₂×C₄×C₂₃	1	8	yes	—
260	#117	—	2	4	no	—
261	#117	—	2	4	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
271	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
272	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
273	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
274	C₂×C₄²	D₄×C₂₃	1	2	yes	—
275	C₂×C₄²	D₄×C₂₃	1	2	yes	—
276	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
278	C₄⋊C₈	—	2	4	no	—
279	C₄⋊C₈	—	2	2	no	—
280	C₄⋊C₈	—	2	2	no	—
281	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
282	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
283	C₂²⋊C₈	—	2	4	no	—
284	#97	—	2	4	no	—
285	C₂₃	C₂×#1559	1	1	yes	characteristic, direct product factor, Sylow
286	C₂⁴	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	4	4	no	—
291	C₂×Q₈	—	4	2	no	—
292	C₂×Q₈	—	4	2	no	—
293	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	4	2	no	—
300	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
301	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
302	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
303	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
304	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
305	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
306	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
307	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
312	M₁₆	—	4	8	no	—
313	C₂×C₈	—	2	4	no	—
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	—	4	4	no	—
316	C₂×C₈	—	4	4	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	8	no	—
321	C₄⋊C₄	—	2	8	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
327	C₂²⋊C₄	—	2	8	no	—
328	C₄²	—	2	8	no	—
329	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
330	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
331	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
332	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
333	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
334	C₄²	C₂×D₄×C₂₃	1	2	yes	—
335	C₄²	C₂×D₄×C₂₃	1	2	yes	—
336	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
337	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
338	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
339	C₂³	—	2	2	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	2	2	no	—
342	C₂³	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
343	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
344	Q₈	—	4	4	no	—
345	Q₈	—	4	4	no	—
346	Q₈	—	4	2	no	—
347	Q₈	—	4	2	no	—
348	Q₈	—	4	4	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
365	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
366	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
367	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
368	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
369	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
370	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
371	C₂×C₄	C₂₃×#137	1	2	yes	—
372	C₂×C₄	C₂₃×#137	1	4	yes	—
373	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
375	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
376	C₈	—	4	4	no	—
377	C₈	—	4	4	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	4	4	no	—
382	C₂²	C₂₃×#413	1	2	yes	—
383	C₂²	C₂₃×#417	1	2	yes	—
384	C₂²	C₂₃×#419	1	2	yes	—
385	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
386	C₄	—	2	1	no	—
387	C₄	—	2	2	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	4	4	no	—
392	C₄	—	4	4	no	—
393	C₄	C₂₃×#417	1	2	yes	—
394	C₄	C₂₃×#419	1	2	yes	—
395	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
396	C₄	C₂×C₂₃×#137	1	2	yes	—
397	C₄	C₂×C₂₃×#137	1	1	yes	characteristic
398	C₂	—	4	2	no	—
399	C₂	C₂₃×#1559	1	4	yes	direct product factor
400	C₂	C₂×C₂₃×#413	1	1	yes	characteristic
401	C₂	C₂×C₂₃×#419	1	1	yes	characteristic
402	C₂	C₂×C₂₃×#417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₄²	C₂⁴×C₂₃
prime radical	C₂⁴×C₂₃	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₃×#1559	C₂	direct (N × H)
5. C₂×C₂₃×#333	C₂	semidirect
6. C₂×C₂₃×#332	C₂	semidirect
30. C₂₃×#333	C₂²	semidirect
31. C₂₃×#332	C₂²	semidirect
137. C₂×#1559	C₂₃	direct (N × H)
180. #1559	C₂×C₂₃	direct (N × H)
181. C₂×#333	C₂×C₂₃	semidirect
182. C₂×#332	C₂×C₂₃	semidirect
226. #333	C₂²×C₂₃	semidirect
227. #332	C₂²×C₂₃	semidirect
229. C₂×C₂₃	#1559	direct (N × H)
285. C₂₃	C₂×#1559	direct (N × H)
399. C₂	C₂₃×#1559	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×#533	2
C₂×C₂₃×#432	2
C₂×C₂₃×#423	2
C₂₃×#1559	2
C₂×C₂₃×#333	2
C₂×C₂₃×#332	2
C₂×#1559	23

Subgroups — C2×C23×#1559 #19165359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#1559 #19165359