Subgroups — C₂×C₂₃×#1554 #19165338

Order 5888.

974 conjugacy classes of subgroups.

The subgroup lattice has 388 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×#431	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1554	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	C₂₃×#533	—	2	2	no	—
8	C₂₃×#533	—	2	2	no	—
9	C₂₃×#533	C₄	1	4	yes	—
10	C₂₃×#533	C₂²	1	4	yes	—
11	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₂₃×#125	—	2	1	no	—
14	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
15	C₂×C₂₃×C₂²⋊Q₈	C₄	1	2	yes	—
16	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
17	C₂×C₄×Q₈×C₂₃	C₄	1	2	yes	—
18	C₂×C₂₃×#117	—	2	1	no	—
19	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×#432	—	2	2	no	—
21	C₂₃×#432	C₂²	1	4	yes	—
22	C₂₃×#431	—	2	2	no	—
23	C₂₃×#431	C₂²	1	4	yes	—
24	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
26	C₂×C₂₃×C₂²⋊C₈	—	2	1	no	—
27	C₂×C₂₃×C₂²⋊C₈	—	2	1	no	—
28	C₂×C₂₃×#97	—	2	1	no	—
29	C₂×C₄×C₈×C₂₃	—	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	C₂²×C₈×C₂₃	—	2	2	no	—
38	C₂²×C₈×C₂₃	—	2	2	no	—
39	C₂₃×C₄⋊Q₈	—	2	1	no	—
40	C₂₃×C₄⋊Q₈	—	2	1	no	—
41	C₂₃×C₄⋊Q₈	—	2	1	no	—
42	C₂₃×C₄⋊Q₈	—	2	1	no	—
43	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
44	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
45	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
46	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
47	C₂₃×#125	—	2	4	no	—
48	C₂₃×#125	—	2	4	no	—
49	C₂₃×C₂²⋊Q₈	—	2	4	no	—
50	C₂₃×C₂²⋊Q₈	—	2	4	no	—
51	C₂₃×C₂²⋊Q₈	—	2	4	no	—
52	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
53	C₄×Q₈×C₂₃	—	2	4	no	—
54	C₄×Q₈×C₂₃	—	2	4	no	—
55	C₄×Q₈×C₂₃	—	2	4	no	—
56	C₄×Q₈×C₂₃	C₂×C₄	1	8	yes	—
57	C₂₃×#117	—	2	4	no	—
58	C₂₃×#117	—	2	4	no	—
59	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
60	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
65	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
66	C₂×C₄²×C₂₃	—	2	2	no	—
67	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₂₃	C₂×C₄	1	2	yes	—
69	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₂₃	D₄	1	2	yes	—
72	C₂×C₄²×C₂₃	D₄	1	2	yes	—
73	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
75	C₂₃×C₄⋊C₈	—	2	2	no	—
76	C₂₃×C₄⋊C₈	—	2	2	no	—
77	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
78	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
79	C₂₃×C₂²⋊C₈	—	2	4	no	—
80	C₂₃×C₂²⋊C₈	—	2	4	no	—
81	C₂₃×#97	—	2	4	no	—
82	C₄×C₈×C₂₃	—	2	4	no	—
83	C₂⁴×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
84	C₂×Q₈×C₂₃	—	2	2	no	—
85	C₂×Q₈×C₂₃	—	2	2	no	—
86	C₂×Q₈×C₂₃	—	2	2	no	—
87	C₂×Q₈×C₂₃	—	4	4	no	—
88	C₂×Q₈×C₂₃	—	4	4	no	—
89	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₂₃	—	2	4	no	—
91	C₂²×C₄×C₂₃	—	2	4	no	—
92	C₂²×C₄×C₂₃	—	2	2	no	—
93	C₂²×C₄×C₂₃	—	2	2	no	—
94	C₂²×C₄×C₂₃	—	4	2	no	—
95	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
96	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
97	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
101	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
107	C₂×C₈×C₂₃	—	2	4	no	—
108	C₂×C₈×C₂₃	—	2	4	no	—
109	C₂×C₈×C₂₃	—	4	4	no	—
110	C₂×C₈×C₂₃	—	4	4	no	—
111	C₄⋊C₄×C₂₃	—	2	2	no	—
112	C₄⋊C₄×C₂₃	—	2	2	no	—
113	C₄⋊C₄×C₂₃	—	2	2	no	—
114	C₄⋊C₄×C₂₃	—	2	8	no	—
115	C₄⋊C₄×C₂₃	—	2	8	no	—
116	C₄⋊C₄×C₂₃	—	2	2	no	—
117	C₄⋊C₄×C₂₃	—	2	2	no	—
118	C₄⋊C₄×C₂₃	—	2	2	no	—
119	C₄⋊C₄×C₂₃	—	2	2	no	—
120	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
121	C₂²⋊C₄×C₂₃	—	2	8	no	—
122	C₄²×C₂₃	—	2	8	no	—
123	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
124	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
125	C₄²×C₂₃	C₂²⋊C₄	1	2	yes	—
126	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
127	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₂₃	C₂×D₄	1	2	yes	—
131	C₄²×C₂₃	C₂×D₄	1	2	yes	—
132	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
133	C₂×#1554	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂³×C₂₃	—	2	2	no	—
135	C₂³×C₂₃	—	2	2	no	—
136	C₂³×C₂₃	—	2	2	no	—
137	C₂³×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
138	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	Q₈×C₂₃	—	4	4	no	—
140	Q₈×C₂₃	—	4	4	no	—
141	Q₈×C₂₃	—	4	4	no	—
142	Q₈×C₂₃	—	4	4	no	—
143	C₂×C₄×C₂₃	—	2	2	no	—
144	C₂×C₄×C₂₃	—	2	2	no	—
145	C₂×C₄×C₂₃	—	2	2	no	—
146	C₂×C₄×C₂₃	—	2	2	no	—
147	C₂×C₄×C₂₃	—	2	4	no	—
148	C₂×C₄×C₂₃	—	2	4	no	—
149	C₂×C₄×C₂₃	—	2	4	no	—
150	C₂×C₄×C₂₃	—	2	4	no	—
151	C₂×C₄×C₂₃	—	2	4	no	—
152	C₂×C₄×C₂₃	—	2	4	no	—
153	C₂×C₄×C₂₃	—	4	2	no	—
154	C₂×C₄×C₂₃	—	4	2	no	—
155	C₂×C₄×C₂₃	—	4	4	no	—
156	C₂×C₄×C₂₃	—	4	4	no	—
157	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
160	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₂₃	#135	1	4	yes	—
164	C₂×C₄×C₂₃	#137	1	4	yes	—
165	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
168	C₈×C₂₃	—	4	4	no	—
169	C₈×C₂₃	—	4	4	no	—
170	C₂×#533	C₂×C₂₃	1	1	yes	characteristic
171	C₂×#432	C₂×C₂₃	1	1	yes	characteristic
172	C₂×#431	C₂×C₂₃	1	1	yes	characteristic
173	#1554	C₂×C₂₃	1	8	yes	direct product factor
174	C₂×#333	C₂×C₂₃	1	2	yes	complemented
175	C₂×#332	C₂×C₂₃	1	2	yes	complemented
176	C₂²×C₂₃	—	2	2	no	—
177	C₂²×C₂₃	—	2	2	no	—
178	C₂²×C₂₃	—	2	2	no	—
179	C₂²×C₂₃	—	4	4	no	—
180	C₂²×C₂₃	#413	1	2	yes	—
181	C₂²×C₂₃	#416	1	2	yes	—
182	C₂²×C₂₃	#419	1	2	yes	—
183	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
184	C₄×C₂₃	—	2	2	no	—
185	C₄×C₂₃	—	2	1	no	—
186	C₄×C₂₃	—	2	1	no	—
187	C₄×C₂₃	—	2	2	no	—
188	C₄×C₂₃	—	2	2	no	—
189	C₄×C₂₃	—	4	4	no	—
190	C₄×C₂₃	—	4	4	no	—
191	C₄×C₂₃	#416	1	2	yes	—
192	C₄×C₂₃	#419	1	2	yes	—
193	C₄×C₂₃	C₂×#135	1	2	yes	—
194	C₄×C₂₃	C₂×#137	1	2	yes	—
195	#533	—	2	2	no	—
196	#533	—	2	2	no	—
197	#533	C₄×C₂₃	1	4	yes	—
198	#533	C₂²×C₂₃	1	4	yes	—
199	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
200	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
201	C₂×#125	—	2	1	no	—
202	C₂×C₂²⋊Q₈	—	2	1	no	—
203	C₂×C₂²⋊Q₈	C₄×C₂₃	1	2	yes	—
204	C₂×C₄×Q₈	—	2	1	no	—
205	C₂×C₄×Q₈	C₄×C₂₃	1	2	yes	—
206	C₂×#117	—	2	1	no	—
207	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
208	#432	—	2	2	no	—
209	#432	C₂²×C₂₃	1	4	yes	—
210	#431	—	2	2	no	—
211	#431	C₂²×C₂₃	1	4	yes	—
212	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
213	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
214	C₂×C₂²⋊C₈	—	2	1	no	—
215	C₂×C₂²⋊C₈	—	2	1	no	—
216	C₂×#97	—	2	1	no	—
217	C₂×C₄×C₈	—	2	1	no	—
218	#333	C₂²×C₂₃	1	8	yes	complemented
219	#332	C₂²×C₂₃	1	8	yes	complemented
220	C₂×C₂₃	—	4	2	no	—
221	C₂×C₂₃	#1554	1	4	yes	direct product factor
222	C₂×C₂₃	C₂×#413	1	1	yes	characteristic
223	C₂×C₂₃	C₂×#416	1	1	yes	characteristic
224	C₂×C₂₃	C₂×#419	1	1	yes	characteristic
225	C₂²×Q₈	—	2	1	no	—
226	C₂²×Q₈	C₂×C₄×C₂₃	1	2	yes	—
227	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
228	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
229	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
230	C₂²×C₈	—	2	2	no	—
231	C₂²×C₈	—	2	2	no	—
232	C₄⋊Q₈	—	2	1	no	—
233	C₄⋊Q₈	—	2	1	no	—
234	C₄⋊Q₈	—	2	1	no	—
235	C₄⋊Q₈	—	2	1	no	—
236	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
237	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
238	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
239	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
240	#125	—	2	4	no	—
241	#125	—	2	4	no	—
242	C₂²⋊Q₈	—	2	4	no	—
243	C₂²⋊Q₈	—	2	4	no	—
244	C₂²⋊Q₈	—	2	4	no	—
245	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	—
246	C₄×Q₈	—	2	4	no	—
247	C₄×Q₈	—	2	4	no	—
248	C₄×Q₈	—	2	4	no	—
249	C₄×Q₈	C₂×C₄×C₂₃	1	8	yes	—
250	#117	—	2	4	no	—
251	#117	—	2	4	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₄²	—	2	2	no	—
260	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
261	C₂×C₄²	C₂×C₄×C₂₃	1	2	yes	—
262	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
263	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
264	C₂×C₄²	D₄×C₂₃	1	2	yes	—
265	C₂×C₄²	D₄×C₂₃	1	2	yes	—
266	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
268	C₄⋊C₈	—	2	2	no	—
269	C₄⋊C₈	—	2	2	no	—
270	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
271	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
272	C₂²⋊C₈	—	2	4	no	—
273	C₂²⋊C₈	—	2	4	no	—
274	#97	—	2	4	no	—
275	C₄×C₈	—	2	4	no	—
276	C₂₃	C₂×#1554	1	1	yes	characteristic, direct product factor, Sylow
277	C₂⁴	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	4	4	no	—
282	C₂×Q₈	—	4	4	no	—
283	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
290	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
291	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
292	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
293	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
294	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
295	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
296	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
297	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
298	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
299	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
301	C₂×C₈	—	2	4	no	—
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	4	4	no	—
304	C₂×C₈	—	4	4	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	8	no	—
309	C₄⋊C₄	—	2	8	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
315	C₂²⋊C₄	—	2	8	no	—
316	C₄²	—	2	8	no	—
317	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
318	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
319	C₄²	C₂²⋊C₄×C₂₃	1	2	yes	—
320	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
321	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
322	C₄²	C₂×D₄×C₂₃	1	2	yes	—
323	C₄²	C₂×D₄×C₂₃	1	2	yes	—
324	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
325	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
326	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
327	C₂³	—	2	2	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
331	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
332	Q₈	—	4	4	no	—
333	Q₈	—	4	4	no	—
334	Q₈	—	4	4	no	—
335	Q₈	—	4	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
351	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
352	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
353	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
354	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
355	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
356	C₂×C₄	C₂₃×#135	1	4	yes	—
357	C₂×C₄	C₂₃×#137	1	4	yes	—
358	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
359	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
360	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
361	C₈	—	4	4	no	—
362	C₈	—	4	4	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	4	no	—
367	C₂²	C₂₃×#413	1	2	yes	—
368	C₂²	C₂₃×#416	1	2	yes	—
369	C₂²	C₂₃×#419	1	2	yes	—
370	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
371	C₄	—	2	1	no	—
372	C₄	—	2	2	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	4	4	no	—
377	C₄	—	4	4	no	—
378	C₄	C₂₃×#416	1	2	yes	—
379	C₄	C₂₃×#419	1	2	yes	—
380	C₄	C₂×C₂₃×#135	1	2	yes	—
381	C₄	C₂×C₂₃×#137	1	2	yes	—
382	C₂	—	4	2	no	—
383	C₂	C₂₃×#1554	1	4	yes	direct product factor
384	C₂	C₂×C₂₃×#413	1	1	yes	characteristic
385	C₂	C₂×C₂₃×#416	1	1	yes	characteristic
386	C₂	C₂×C₂₃×#419	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×#1554	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
133. C₂×#1554	C₂₃	direct (N × H)
173. #1554	C₂×C₂₃	direct (N × H)
174. C₂×#333	C₂×C₂₃	semidirect
175. C₂×#332	C₂×C₂₃	semidirect
218. #333	C₂²×C₂₃	semidirect
219. #332	C₂²×C₂₃	semidirect
221. C₂×C₂₃	#1554	direct (N × H)
276. C₂₃	C₂×#1554	direct (N × H)
383. C₂	C₂₃×#1554	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×#431	2
C₂₃×#1554	2
C₂×C₂₃×#333	2
C₂×C₂₃×#332	2
C₂×#1554	23

Subgroups — C2×C23×#1554 #19165338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#1554 #19165338