Subgroups — C₂×C₂₃×#3380 #19208979

Order 5888.

1918 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#554	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3380	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₂₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#499	C₂	1	2	yes	maximal, complemented
5	C₂×C₂₃×#478	C₂	1	4	yes	maximal, complemented
6	C₂×C₂₃×#476	C₂	1	2	yes	maximal, complemented
7	C₂×C₈×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₈×C₂₃	C₂	1	2	yes	maximal
9	C₂×C₄×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic
10	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
11	C₂₃×#554	—	2	8	no	—
12	C₂₃×#554	C₂²	1	16	yes	complemented
13	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₂₃×#125	C₂²	1	4	yes	—
15	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
16	C₂×C₂₃×C₂²⋊Q₈	—	2	4	no	—
17	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	—
20	C₂²×C₄⋊C₄×C₂₃	—	2	2	no	—
21	C₂₃×#500	C₂²	1	8	yes	complemented
22	C₂₃×#499	C₂²	1	16	yes	complemented
23	C₂₃×#478	C₂²	1	32	yes	complemented
24	C₂₃×#476	C₂²	1	16	yes	complemented
25	C₈×Q₈×C₂₃	C₂²	1	8	yes	complemented
26	C₄×D₈×C₂₃	C₂²	1	16	yes	—
27	C₄×D₈×C₂₃	C₂²	1	8	yes	—
28	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#107	C₂²	1	2	yes	—
30	C₂×C₂₃×#107	C₂²	1	2	yes	—
31	C₂×C₂₃×#106	C₂²	1	4	yes	—
32	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
34	C₂×C₂₃×#102	C₂²	1	4	yes	—
35	C₂×C₂₃×#102	C₂²	1	2	yes	—
36	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
37	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
38	C₂²×Q₈×C₂₃	—	2	2	no	—
39	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
40	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
41	C₂³×C₄×C₂₃	—	2	2	no	—
42	C₂³×C₄×C₂₃	—	2	4	no	—
43	C₂×D₈×C₂₃	Q₈	1	8	yes	complemented
44	C₂×D₈×C₂₃	C₂³	1	4	yes	—
45	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
48	C₂₃×C₄⋊Q₈	—	2	4	no	—
49	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	—
50	C₂₃×#125	—	2	8	no	—
51	C₂₃×#125	C₂³	1	16	yes	—
52	C₂₃×C₂²⋊Q₈	—	2	16	no	—
53	C₂₃×C₂²⋊Q₈	—	2	32	no	—
54	C₄×Q₈×C₂₃	D₄	1	4	yes	—
55	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
56	C₄×D₄×C₂₃	—	2	8	no	—
57	C₄×D₄×C₂₃	—	2	4	no	—
58	C₄×D₄×C₂₃	C₂³	1	8	yes	—
59	C₄×D₄×C₂₃	C₂³	1	16	yes	—
60	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
61	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
62	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
63	C₂×C₄⋊C₄×C₂₃	—	2	16	no	—
64	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
68	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
70	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
71	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
72	C₂₃×#107	C₂³	1	4	yes	—
73	C₂₃×#107	C₂³	1	8	yes	—
74	C₂₃×#107	C₂³	1	8	yes	—
75	C₂₃×#106	C₂³	1	16	yes	—
76	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
77	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
78	C₂₃×#102	C₂³	1	16	yes	—
79	C₂₃×#102	C₂³	1	8	yes	—
80	C₄×C₈×C₂₃	C₂³	1	8	yes	—
81	C₄×C₈×C₂₃	C₂³	1	4	yes	—
82	C₂⁴×C₂₃	—	2	2	no	—
83	C₂×Q₈×C₂₃	—	2	4	no	—
84	C₂×Q₈×C₂₃	—	2	8	no	—
85	C₂×Q₈×C₂₃	—	8	4	no	—
86	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
87	C₂×D₄×C₂₃	—	2	2	no	—
88	C₂×D₄×C₂₃	—	2	4	no	—
89	C₂×D₄×C₂₃	C₂×Q₈	1	8	yes	—
90	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
91	C₂²×C₄×C₂₃	—	2	2	no	—
92	C₂²×C₄×C₂₃	—	2	4	no	—
93	C₂²×C₄×C₂₃	—	2	8	no	—
94	C₂²×C₄×C₂₃	—	2	16	no	—
95	C₂²×C₄×C₂₃	—	4	8	no	—
96	C₂²×C₄×C₂₃	—	8	8	no	—
97	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
102	D₈×C₂₃	C₂×Q₈	1	16	yes	complemented
103	C₂×C₈×C₂₃	—	2	4	no	—
104	C₂×C₈×C₂₃	—	2	2	no	—
105	C₂×C₈×C₂₃	C₂×Q₈	1	4	yes	—
106	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
107	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
108	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
109	C₄⋊C₄×C₂₃	—	2	16	no	—
110	C₄⋊C₄×C₂₃	—	2	8	no	—
111	C₄⋊C₄×C₂₃	—	2	16	no	—
112	C₄⋊C₄×C₂₃	—	2	2	no	—
113	C₄⋊C₄×C₂₃	—	2	4	no	—
114	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
115	C₄⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
116	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
117	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
118	C₂²⋊C₄×C₂₃	—	2	8	no	—
119	C₂²⋊C₄×C₂₃	—	2	16	no	—
120	C₄²×C₂₃	C₂×D₄	1	4	yes	—
121	C₄²×C₂₃	C₂×D₄	1	2	yes	—
122	C₄²×C₂₃	C₂⁴	1	4	yes	—
123	C₄²×C₂₃	C₂⁴	1	2	yes	—
124	C₂×#3380	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂³×C₂₃	—	2	8	no	—
126	C₂³×C₂₃	—	2	4	no	—
127	C₂³×C₂₃	—	4	4	no	—
128	C₂³×C₂₃	—	4	4	no	—
129	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
130	Q₈×C₂₃	—	2	8	no	—
131	Q₈×C₂₃	—	8	8	no	—
132	D₄×C₂₃	—	2	8	no	—
133	D₄×C₂₃	—	2	4	no	—
134	D₄×C₂₃	C₂²×Q₈	1	8	yes	—
135	C₂×C₄×C₂₃	—	2	4	no	—
136	C₂×C₄×C₂₃	—	2	4	no	—
137	C₂×C₄×C₂₃	—	2	2	no	—
138	C₂×C₄×C₂₃	—	2	4	no	—
139	C₂×C₄×C₂₃	—	2	8	no	—
140	C₂×C₄×C₂₃	—	4	4	no	—
141	C₂×C₄×C₂₃	—	4	8	no	—
142	C₂×C₄×C₂₃	—	4	16	no	—
143	C₂×C₄×C₂₃	—	8	16	no	—
144	C₂×C₄×C₂₃	#135	1	4	yes	—
145	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
146	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
147	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
148	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
150	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
151	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
152	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
153	C₈×C₂₃	—	2	4	no	—
154	C₈×C₂₃	—	2	2	no	—
155	C₈×C₂₃	C₂²×Q₈	1	4	yes	—
156	C₂×#554	C₂×C₂₃	1	2	yes	complemented
157	#3380	C₂×C₂₃	1	16	yes	direct product factor
158	C₂×#500	C₂×C₂₃	1	1	yes	characteristic, complemented
159	C₂×#499	C₂×C₂₃	1	2	yes	complemented
160	C₂×#478	C₂×C₂₃	1	4	yes	complemented
161	C₂×#476	C₂×C₂₃	1	2	yes	complemented
162	C₂×C₈×Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
163	C₂×C₄×D₈	C₂×C₂₃	1	2	yes	—
164	C₂×C₄×D₈	C₂×C₂₃	1	1	yes	characteristic
165	C₂²×C₂₃	—	2	8	no	—
166	C₂²×C₂₃	—	4	16	no	—
167	C₂²×C₂₃	—	4	4	no	—
168	C₂²×C₂₃	—	4	4	no	—
169	C₂²×C₂₃	D₄×Q₈	1	2	yes	—
170	C₂²×C₂₃	C₂×#135	1	2	yes	—
171	C₂²×C₂₃	#576	1	2	yes	—
172	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
173	C₄×C₂₃	—	2	4	no	—
174	C₄×C₂₃	—	2	4	no	—
175	C₄×C₂₃	—	2	2	no	—
176	C₄×C₂₃	—	4	4	no	—
177	C₄×C₂₃	—	4	8	no	—
178	C₄×C₂₃	D₄×Q₈	1	2	yes	—
179	C₄×C₂₃	C₂×#135	1	4	yes	—
180	C₄×C₂₃	C₂³×Q₈	1	1	yes	characteristic
181	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
182	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
183	#554	—	2	8	no	—
184	#554	C₂²×C₂₃	1	16	yes	complemented
185	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
186	C₂×#125	C₂²×C₂₃	1	4	yes	—
187	C₂×C₂²⋊Q₈	—	2	2	no	—
188	C₂×C₂²⋊Q₈	—	2	4	no	—
189	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
190	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
191	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
192	C₂²×C₄⋊C₄	—	2	2	no	—
193	#500	C₂²×C₂₃	1	8	yes	complemented
194	#499	C₂²×C₂₃	1	16	yes	complemented
195	#478	C₂²×C₂₃	1	32	yes	complemented
196	#476	C₂²×C₂₃	1	16	yes	complemented
197	C₈×Q₈	C₂²×C₂₃	1	8	yes	complemented
198	C₄×D₈	C₂²×C₂₃	1	16	yes	—
199	C₄×D₈	C₂²×C₂₃	1	8	yes	—
200	C₂×#107	C₂²×C₂₃	1	2	yes	—
201	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
202	C₂×#107	C₂²×C₂₃	1	2	yes	—
203	C₂×#106	C₂²×C₂₃	1	4	yes	—
204	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
205	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
206	C₂×#102	C₂²×C₂₃	1	2	yes	—
207	C₂×#102	C₂²×C₂₃	1	4	yes	—
208	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
209	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
210	C₂×C₂₃	—	4	8	no	—
211	C₂×C₂₃	#3380	1	4	yes	direct product factor
212	C₂×C₂₃	C₂×D₄×Q₈	1	1	yes	characteristic
213	C₂×C₂₃	C₂²×#135	1	1	yes	characteristic
214	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
215	C₂²×Q₈	—	2	2	no	—
216	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
217	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
218	C₂³×C₄	—	2	2	no	—
219	C₂³×C₄	—	2	4	no	—
220	C₂×D₈	Q₈×C₂₃	1	8	yes	complemented
221	C₂×D₈	C₂³×C₂₃	1	4	yes	—
222	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
223	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
224	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
225	C₄⋊Q₈	—	2	4	no	—
226	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	—
227	#125	—	2	8	no	—
228	#125	C₂³×C₂₃	1	16	yes	—
229	C₂²⋊Q₈	—	2	16	no	—
230	C₂²⋊Q₈	—	2	32	no	—
231	C₄×Q₈	D₄×C₂₃	1	4	yes	—
232	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
233	C₄×D₄	—	2	8	no	—
234	C₄×D₄	—	2	4	no	—
235	C₄×D₄	C₂³×C₂₃	1	8	yes	—
236	C₄×D₄	C₂³×C₂₃	1	16	yes	—
237	C₂×C₄⋊C₄	—	2	4	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	4	no	—
240	C₂×C₄⋊C₄	—	2	16	no	—
241	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
242	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
243	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
244	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
245	C₂×C₂²⋊C₄	—	2	2	no	—
246	C₂×C₂²⋊C₄	—	2	4	no	—
247	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
248	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
249	#107	C₂³×C₂₃	1	4	yes	—
250	#107	C₂³×C₂₃	1	8	yes	—
251	#107	C₂³×C₂₃	1	8	yes	—
252	#106	C₂³×C₂₃	1	16	yes	—
253	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
254	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
255	#102	C₂³×C₂₃	1	16	yes	—
256	#102	C₂³×C₂₃	1	8	yes	—
257	C₄×C₈	C₂³×C₂₃	1	8	yes	—
258	C₄×C₈	C₂³×C₂₃	1	4	yes	—
259	C₂₃	C₂×#3380	1	1	yes	characteristic, direct product factor, Sylow
260	C₂⁴	—	2	2	no	—
261	C₂×Q₈	—	2	4	no	—
262	C₂×Q₈	—	2	8	no	—
263	C₂×Q₈	—	8	4	no	—
264	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
265	C₂×D₄	—	2	2	no	—
266	C₂×D₄	—	2	4	no	—
267	C₂×D₄	C₂×Q₈×C₂₃	1	8	yes	—
268	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	8	no	—
272	C₂²×C₄	—	2	16	no	—
273	C₂²×C₄	—	4	8	no	—
274	C₂²×C₄	—	8	8	no	—
275	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
276	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
278	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
279	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
280	D₈	C₂×Q₈×C₂₃	1	16	yes	complemented
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	C₂×Q₈×C₂₃	1	4	yes	—
284	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
285	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
286	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
287	C₄⋊C₄	—	2	16	no	—
288	C₄⋊C₄	—	2	8	no	—
289	C₄⋊C₄	—	2	16	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
293	C₄⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
294	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
295	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
296	C₂²⋊C₄	—	2	8	no	—
297	C₂²⋊C₄	—	2	16	no	—
298	C₄²	C₂×D₄×C₂₃	1	4	yes	—
299	C₄²	C₂×D₄×C₂₃	1	2	yes	—
300	C₄²	C₂⁴×C₂₃	1	4	yes	—
301	C₄²	C₂⁴×C₂₃	1	2	yes	—
302	C₂³	—	2	8	no	—
303	C₂³	—	2	4	no	—
304	C₂³	—	4	4	no	—
305	C₂³	—	4	4	no	—
306	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
307	Q₈	—	2	8	no	—
308	Q₈	—	8	8	no	—
309	D₄	—	2	8	no	—
310	D₄	—	2	4	no	—
311	D₄	C₂²×Q₈×C₂₃	1	8	yes	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	4	8	no	—
319	C₂×C₄	—	4	16	no	—
320	C₂×C₄	—	8	16	no	—
321	C₂×C₄	C₂₃×#135	1	4	yes	—
322	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
323	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
324	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
325	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
326	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
327	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
328	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
329	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
330	C₈	—	2	4	no	—
331	C₈	—	2	2	no	—
332	C₈	C₂²×Q₈×C₂₃	1	4	yes	—
333	C₂²	—	2	8	no	—
334	C₂²	—	4	4	no	—
335	C₂²	—	4	4	no	—
336	C₂²	—	4	16	no	—
337	C₂²	D₄×Q₈×C₂₃	1	2	yes	—
338	C₂²	C₂×C₂₃×#135	1	2	yes	—
339	C₂²	C₂₃×#576	1	2	yes	—
340	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
341	C₄	—	2	4	no	—
342	C₄	—	2	4	no	—
343	C₄	—	2	2	no	—
344	C₄	—	4	4	no	—
345	C₄	—	4	8	no	—
346	C₄	D₄×Q₈×C₂₃	1	2	yes	—
347	C₄	C₂×C₂₃×#135	1	4	yes	—
348	C₄	C₂³×Q₈×C₂₃	1	1	yes	characteristic
349	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
350	C₂	—	4	8	no	—
351	C₂	C₂₃×#3380	1	4	yes	direct product factor
352	C₂	C₂×D₄×Q₈×C₂₃	1	1	yes	characteristic
353	C₂	C₂²×C₂₃×#135	1	1	yes	characteristic
354	C₂	C₂×C₂₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂²×D₈×C₂₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄×Q₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#554	C₂	semidirect
2. C₂₃×#3380	C₂	direct (N × H)
3. C₂×C₂₃×#500	C₂	semidirect
4. C₂×C₂₃×#499	C₂	semidirect
5. C₂×C₂₃×#478	C₂	semidirect
6. C₂×C₂₃×#476	C₂	semidirect
7. C₂×C₈×Q₈×C₂₃	C₂	semidirect
12. C₂₃×#554	C₂²	semidirect
21. C₂₃×#500	C₂²	semidirect
22. C₂₃×#499	C₂²	semidirect
23. C₂₃×#478	C₂²	semidirect
24. C₂₃×#476	C₂²	semidirect
25. C₈×Q₈×C₂₃	C₂²	semidirect
43. C₂×D₈×C₂₃	Q₈	semidirect
102. D₈×C₂₃	C₂×Q₈	semidirect
124. C₂×#3380	C₂₃	direct (N × H)
156. C₂×#554	C₂×C₂₃	semidirect
157. #3380	C₂×C₂₃	direct (N × H)
158. C₂×#500	C₂×C₂₃	semidirect
159. C₂×#499	C₂×C₂₃	semidirect
160. C₂×#478	C₂×C₂₃	semidirect
161. C₂×#476	C₂×C₂₃	semidirect
162. C₂×C₈×Q₈	C₂×C₂₃	semidirect
184. #554	C₂²×C₂₃	semidirect
193. #500	C₂²×C₂₃	semidirect
194. #499	C₂²×C₂₃	semidirect
195. #478	C₂²×C₂₃	semidirect
196. #476	C₂²×C₂₃	semidirect
197. C₈×Q₈	C₂²×C₂₃	semidirect
211. C₂×C₂₃	#3380	direct (N × H)
220. C₂×D₈	Q₈×C₂₃	semidirect
259. C₂₃	C₂×#3380	direct (N × H)
280. D₈	C₂×Q₈×C₂₃	semidirect
351. C₂	C₂₃×#3380	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×#554	2
C₂₃×#3380	2
C₂×C₂₃×#500	2
C₂×C₂₃×#499	2
C₂×C₂₃×#478	2
C₂×C₂₃×#476	2
C₂×C₈×Q₈×C₂₃	2
C₂×C₄×D₈×C₂₃	2
C₂×#3380	23

Subgroups — C2×C23×#3380 #19208979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3380 #19208979