Subgroups — C₂×C₂₃×#1303 #19155717

Order 5888.

810 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#431	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1303	C₂	1	4	yes	maximal, direct product factor
5	C₂²×M₁₆×C₂₃	—	2	1	no	—
6	C₂²×C₄⋊C₄×C₂₃	—	2	1	no	—
7	C₂²×C₄²×C₂₃	—	2	1	no	—
8	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
9	C₂₃×#431	—	2	1	no	—
10	C₂₃×#431	—	2	1	no	—
11	C₂₃×#431	C₄	1	2	yes	complemented
12	C₂₃×#431	C₂²	1	2	yes	—
13	C₂₃×#423	—	2	1	no	—
14	C₂₃×#423	—	2	1	no	—
15	C₂₃×#423	C₄	1	2	yes	complemented
16	C₂₃×#423	C₂²	1	2	yes	—
17	C₂×C₂₃×C₄⋊C₈	—	2	1	no	—
18	C₂×C₂₃×C₄⋊C₈	C₄	1	2	yes	complemented
19	C₂×C₂₃×C₄⋊C₈	C₄	1	2	yes	complemented
20	C₂×C₂₃×C₂²⋊C₈	—	2	1	no	—
21	C₂×C₄×C₈×C₂₃	—	2	1	no	—
22	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
23	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
24	C₄×C₄⋊C₄×C₂₃	C₄	1	2	yes	—
25	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
26	C₂×C₂₃×#95	C₄	1	2	yes	—
27	C₂³×C₄×C₂₃	—	2	2	no	—
28	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
31	C₂×M₁₆×C₂₃	—	2	2	no	—
32	C₂×M₁₆×C₂₃	—	2	2	no	—
33	C₂×M₁₆×C₂₃	—	4	2	no	—
34	C₂×M₁₆×C₂₃	—	4	2	no	—
35	C₂²×C₈×C₂₃	—	2	2	no	—
36	C₂²×C₈×C₂₃	—	2	2	no	—
37	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
38	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
39	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
40	C₂×C₄²×C₂₃	—	2	2	no	—
41	C₂×C₄²×C₂₃	—	2	2	no	—
42	C₂×C₄²×C₂₃	—	4	2	no	—
43	C₂×C₄²×C₂₃	—	4	2	no	—
44	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₂₃	Q₈	1	1	yes	characteristic
54	C₂×C₄²×C₂₃	Q₈	1	1	yes	characteristic
55	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
56	C₂₃×C₄⋊C₈	—	2	2	no	—
57	C₂₃×C₄⋊C₈	—	2	2	no	—
58	C₂₃×C₄⋊C₈	—	2	2	no	—
59	C₂₃×C₄⋊C₈	—	2	2	no	—
60	C₂₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
61	C₂₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
62	C₂₃×C₂²⋊C₈	—	2	2	no	—
63	C₂₃×C₂²⋊C₈	—	2	2	no	—
64	C₄×C₈×C₂₃	—	2	2	no	—
65	C₄×C₈×C₂₃	—	2	2	no	—
66	C₂₃×#95	—	2	2	no	—
67	C₂₃×#95	C₂×C₄	1	4	yes	—
68	C₂⁴×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₂₃	—	2	4	no	—
70	C₂²×C₄×C₂₃	—	2	8	no	—
71	C₂²×C₄×C₂₃	—	2	4	no	—
72	C₂²×C₄×C₂₃	—	4	2	no	—
73	C₂²×C₄×C₂₃	—	4	4	no	—
74	C₂²×C₄×C₂₃	—	4	4	no	—
75	C₂²×C₄×C₂₃	C₄²	1	1	yes	characteristic
76	C₂²×C₄×C₂₃	C₄²	1	1	yes	characteristic
77	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₂₃	D₈	1	2	yes	—
91	C₂²×C₄×C₂₃	SD₁₆	1	2	yes	—
92	C₂²×C₄×C₂₃	SD₁₆	1	2	yes	—
93	C₂²×C₄×C₂₃	Q₁₆	1	2	yes	—
94	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
97	M₁₆×C₂₃	—	4	4	no	—
98	M₁₆×C₂₃	—	4	2	no	—
99	M₁₆×C₂₃	—	4	2	no	—
100	C₂×C₈×C₂₃	—	2	4	no	—
101	C₂×C₈×C₂₃	—	2	4	no	—
102	C₂×C₈×C₂₃	—	4	4	no	—
103	C₂×C₈×C₂₃	—	4	4	no	—
104	C₄⋊C₄×C₂₃	—	2	8	no	—
105	C₄⋊C₄×C₂₃	—	2	8	no	—
106	C₄²×C₂₃	—	4	4	no	—
107	C₄²×C₂₃	—	4	2	no	—
108	C₄²×C₂₃	—	4	2	no	—
109	C₄²×C₂₃	C₄²	1	1	yes	characteristic
110	C₄²×C₂₃	C₄²	1	1	yes	characteristic
111	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
112	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
113	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
114	C₄²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
115	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
116	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
117	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
118	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
119	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
120	C₄²×C₂₃	C₄⋊C₄	1	1	yes	characteristic
121	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₂₃	C₂×Q₈	1	1	yes	characteristic
125	C₂×#1303	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂³×C₂₃	—	2	2	no	—
127	C₂³×C₂₃	—	2	2	no	—
128	C₂³×C₂₃	#95	1	1	yes	characteristic
129	C₂³×C₂₃	#95	1	1	yes	characteristic
130	C₂³×C₂₃	#102	1	2	yes	—
131	C₂³×C₂₃	#103	1	2	yes	—
132	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₂₃	—	2	2	no	—
134	C₂×C₄×C₂₃	—	2	2	no	—
135	C₂×C₄×C₂₃	—	2	2	no	—
136	C₂×C₄×C₂₃	—	2	2	no	—
137	C₂×C₄×C₂₃	—	2	2	no	—
138	C₂×C₄×C₂₃	—	2	2	no	—
139	C₂×C₄×C₂₃	—	2	2	no	—
140	C₂×C₄×C₂₃	—	2	8	no	—
141	C₂×C₄×C₂₃	—	4	1	no	—
142	C₂×C₄×C₂₃	—	4	1	no	—
143	C₂×C₄×C₂₃	—	4	1	no	—
144	C₂×C₄×C₂₃	—	4	1	no	—
145	C₂×C₄×C₂₃	—	4	16	no	—
146	C₂×C₄×C₂₃	—	4	4	no	—
147	C₂×C₄×C₂₃	—	4	4	no	—
148	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
149	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
150	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
151	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
152	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
153	C₂×C₄×C₂₃	#95	1	1	yes	characteristic
154	C₂×C₄×C₂₃	#102	1	2	yes	—
155	C₂×C₄×C₂₃	#102	1	2	yes	—
156	C₂×C₄×C₂₃	#102	1	2	yes	—
157	C₂×C₄×C₂₃	#103	1	2	yes	—
158	C₂×C₄×C₂₃	#103	1	2	yes	—
159	C₂×C₄×C₂₃	#103	1	2	yes	—
160	C₂×C₄×C₂₃	#104	1	4	yes	—
161	C₂×C₄×C₂₃	#106	1	2	yes	—
162	C₂×C₄×C₂₃	#106	1	2	yes	—
163	C₂×C₄×C₂₃	#107	1	2	yes	—
164	C₂×C₄×C₂₃	#107	1	2	yes	—
165	C₂×C₄×C₂₃	C₂×C₄²	1	1	yes	characteristic
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×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
172	C₂×C₄×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
173	C₂×C₄×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
174	C₂×C₄×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
175	C₈×C₂₃	—	4	4	no	—
176	C₈×C₂₃	—	4	4	no	—
177	C₂×#431	C₂×C₂₃	1	1	yes	characteristic
178	C₂×#423	C₂×C₂₃	1	1	yes	characteristic
179	C₂×C₄×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic
180	#1303	C₂×C₂₃	1	4	yes	direct product factor
181	C₂²×C₂₃	—	2	4	no	—
182	C₂²×C₂₃	—	2	4	no	—
183	C₂²×C₂₃	—	2	1	no	—
184	C₂²×C₂₃	—	2	1	no	—
185	C₂²×C₂₃	—	2	1	no	—
186	C₂²×C₂₃	—	2	1	no	—
187	C₂²×C₂₃	#339	1	2	yes	—
188	C₂²×C₂₃	#340	1	2	yes	—
189	C₂²×C₂₃	#340	1	2	yes	—
190	C₂²×C₂₃	#344	1	2	yes	—
191	C₂²×C₂₃	C₂×#95	1	1	yes	characteristic
192	C₂²×C₂₃	C₂×#102	1	1	yes	characteristic
193	C₂²×C₂₃	C₂×#103	1	1	yes	characteristic
194	C₄×C₂₃	—	2	1	no	—
195	C₄×C₂₃	—	2	1	no	—
196	C₄×C₂₃	—	2	1	no	—
197	C₄×C₂₃	—	2	1	no	—
198	C₄×C₂₃	—	2	1	no	—
199	C₄×C₂₃	—	2	1	no	—
200	C₄×C₂₃	—	4	8	no	—
201	C₄×C₂₃	#339	1	2	yes	—
202	C₄×C₂₃	#340	1	2	yes	—
203	C₄×C₂₃	#340	1	2	yes	—
204	C₄×C₂₃	C₂×#102	1	1	yes	characteristic
205	C₄×C₂₃	C₂×#103	1	1	yes	characteristic
206	C₄×C₂₃	C₂×#104	1	2	yes	—
207	C₄×C₂₃	C₂×#106	1	1	yes	characteristic
208	C₄×C₂₃	C₂×#107	1	1	yes	characteristic
209	C₂²×M₁₆	—	2	1	no	—
210	C₂²×C₄⋊C₄	—	2	1	no	—
211	C₂²×C₄²	—	2	1	no	—
212	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
213	#431	—	2	1	no	—
214	#431	—	2	1	no	—
215	#431	C₄×C₂₃	1	2	yes	complemented
216	#431	C₂²×C₂₃	1	2	yes	—
217	#423	—	2	1	no	—
218	#423	—	2	1	no	—
219	#423	C₄×C₂₃	1	2	yes	complemented
220	#423	C₂²×C₂₃	1	2	yes	—
221	C₂×C₄⋊C₈	—	2	1	no	—
222	C₂×C₄⋊C₈	C₄×C₂₃	1	2	yes	complemented
223	C₂×C₄⋊C₈	C₄×C₂₃	1	2	yes	complemented
224	C₂×C₂²⋊C₈	—	2	1	no	—
225	C₂×C₄×C₈	—	2	1	no	—
226	C₄×C₄⋊C₄	—	2	1	no	—
227	C₄×C₄⋊C₄	—	2	1	no	—
228	C₄×C₄⋊C₄	C₄×C₂₃	1	2	yes	—
229	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
230	C₂×#95	C₄×C₂₃	1	2	yes	—
231	C₂×C₂₃	—	2	1	no	—
232	C₂×C₂₃	—	2	2	no	—
233	C₂×C₂₃	—	2	1	no	—
234	C₂×C₂₃	#1303	1	4	yes	direct product factor
235	C₂×C₂₃	C₂×#339	1	1	yes	characteristic
236	C₂×C₂₃	C₂×#340	1	1	yes	characteristic
237	C₂×C₂₃	C₂×#344	1	1	yes	characteristic
238	C₂³×C₄	—	2	2	no	—
239	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
240	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
241	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
242	C₂×M₁₆	—	2	2	no	—
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	—	4	2	no	—
245	C₂×M₁₆	—	4	2	no	—
246	C₂²×C₈	—	2	2	no	—
247	C₂²×C₈	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	8	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	—	4	2	no	—
254	C₂×C₄²	—	4	2	no	—
255	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
256	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
257	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
258	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
259	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
260	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
261	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
262	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
263	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
264	C₂×C₄²	Q₈×C₂₃	1	1	yes	characteristic
265	C₂×C₄²	Q₈×C₂₃	1	1	yes	characteristic
266	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	2	2	no	—
269	C₄⋊C₈	—	2	2	no	—
270	C₄⋊C₈	—	2	2	no	—
271	C₄⋊C₈	C₂×C₄×C₂₃	1	4	yes	complemented
272	C₄⋊C₈	C₂×C₄×C₂₃	1	4	yes	complemented
273	C₂²⋊C₈	—	2	2	no	—
274	C₂²⋊C₈	—	2	2	no	—
275	C₄×C₈	—	2	2	no	—
276	C₄×C₈	—	2	2	no	—
277	#95	—	2	2	no	—
278	#95	C₂×C₄×C₂₃	1	4	yes	—
279	C₂₃	C₂×#1303	1	1	yes	characteristic, direct product factor, Sylow
280	C₂⁴	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	8	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	4	no	—
286	C₂²×C₄	—	4	4	no	—
287	C₂²×C₄	C₄²×C₂₃	1	1	yes	characteristic
288	C₂²×C₄	C₄²×C₂₃	1	1	yes	characteristic
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	1	yes	characteristic
292	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
293	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
294	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
295	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
296	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
297	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
298	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
299	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
300	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
301	C₂²×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
302	C₂²×C₄	D₈×C₂₃	1	2	yes	—
303	C₂²×C₄	SD₁₆×C₂₃	1	2	yes	—
304	C₂²×C₄	SD₁₆×C₂₃	1	2	yes	—
305	C₂²×C₄	Q₁₆×C₂₃	1	2	yes	—
306	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
309	M₁₆	—	4	4	no	—
310	M₁₆	—	4	2	no	—
311	M₁₆	—	4	2	no	—
312	C₂×C₈	—	2	4	no	—
313	C₂×C₈	—	2	4	no	—
314	C₂×C₈	—	4	4	no	—
315	C₂×C₈	—	4	4	no	—
316	C₄⋊C₄	—	2	8	no	—
317	C₄⋊C₄	—	2	8	no	—
318	C₄²	—	4	4	no	—
319	C₄²	—	4	2	no	—
320	C₄²	—	4	2	no	—
321	C₄²	C₄²×C₂₃	1	1	yes	characteristic
322	C₄²	C₄²×C₂₃	1	1	yes	characteristic
323	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
324	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
325	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
326	C₄²	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
327	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
328	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
329	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
330	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
331	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
332	C₄²	C₄⋊C₄×C₂₃	1	1	yes	characteristic
333	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
334	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
335	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
336	C₄²	C₂×Q₈×C₂₃	1	1	yes	characteristic
337	C₂³	—	2	2	no	—
338	C₂³	—	2	2	no	—
339	C₂³	C₂₃×#95	1	1	yes	characteristic
340	C₂³	C₂₃×#95	1	1	yes	characteristic
341	C₂³	C₂₃×#102	1	2	yes	—
342	C₂³	C₂₃×#103	1	2	yes	—
343	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	16	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
360	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
361	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
362	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
363	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
364	C₂×C₄	C₂₃×#95	1	1	yes	characteristic
365	C₂×C₄	C₂₃×#102	1	2	yes	—
366	C₂×C₄	C₂₃×#102	1	2	yes	—
367	C₂×C₄	C₂₃×#102	1	2	yes	—
368	C₂×C₄	C₂₃×#103	1	2	yes	—
369	C₂×C₄	C₂₃×#103	1	2	yes	—
370	C₂×C₄	C₂₃×#103	1	2	yes	—
371	C₂×C₄	C₂₃×#104	1	4	yes	—
372	C₂×C₄	C₂₃×#106	1	2	yes	—
373	C₂×C₄	C₂₃×#106	1	2	yes	—
374	C₂×C₄	C₂₃×#107	1	2	yes	—
375	C₂×C₄	C₂₃×#107	1	2	yes	—
376	C₂×C₄	C₂×C₄²×C₂₃	1	1	yes	characteristic
377	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
378	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
379	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
380	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
381	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
382	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
383	C₂×C₄	C₂×SD₁₆×C₂₃	1	1	yes	characteristic
384	C₂×C₄	C₂×SD₁₆×C₂₃	1	1	yes	characteristic
385	C₂×C₄	C₂×Q₁₆×C₂₃	1	1	yes	characteristic
386	C₈	—	4	4	no	—
387	C₈	—	4	4	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	4	no	—
393	C₂²	—	2	4	no	—
394	C₂²	C₂₃×#339	1	2	yes	—
395	C₂²	C₂₃×#340	1	2	yes	—
396	C₂²	C₂₃×#340	1	2	yes	—
397	C₂²	C₂₃×#344	1	2	yes	—
398	C₂²	C₂×C₂₃×#95	1	1	yes	characteristic
399	C₂²	C₂×C₂₃×#102	1	1	yes	characteristic
400	C₂²	C₂×C₂₃×#103	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	4	8	no	—
408	C₄	C₂₃×#339	1	2	yes	—
409	C₄	C₂₃×#340	1	2	yes	—
410	C₄	C₂₃×#340	1	2	yes	—
411	C₄	C₂×C₂₃×#102	1	1	yes	characteristic
412	C₄	C₂×C₂₃×#103	1	1	yes	characteristic
413	C₄	C₂×C₂₃×#104	1	2	yes	—
414	C₄	C₂×C₂₃×#106	1	1	yes	characteristic
415	C₄	C₂×C₂₃×#107	1	1	yes	characteristic
416	C₂	—	2	1	no	—
417	C₂	—	2	2	no	—
418	C₂	—	2	1	no	—
419	C₂	C₂₃×#1303	1	4	yes	direct product factor
420	C₂	C₂×C₂₃×#339	1	1	yes	characteristic
421	C₂	C₂×C₂₃×#340	1	1	yes	characteristic
422	C₂	C₂×C₂₃×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₂₃
Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
socle	C₂³×C₂₃	#95
prime radical	C₂⁴×C₂₃	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₃×#1303	C₂	direct (N × H)
11. C₂₃×#431	C₄	semidirect
15. C₂₃×#423	C₄	semidirect
18. C₂×C₂₃×C₄⋊C₈	C₄	semidirect
19. C₂×C₂₃×C₄⋊C₈	C₄	semidirect
60. C₂₃×C₄⋊C₈	C₂×C₄	semidirect
61. C₂₃×C₄⋊C₈	C₂×C₄	semidirect
125. C₂×#1303	C₂₃	direct (N × H)
180. #1303	C₂×C₂₃	direct (N × H)
215. #431	C₄×C₂₃	semidirect
219. #423	C₄×C₂₃	semidirect
222. C₂×C₄⋊C₈	C₄×C₂₃	semidirect
223. C₂×C₄⋊C₈	C₄×C₂₃	semidirect
234. C₂×C₂₃	#1303	direct (N × H)
271. C₄⋊C₈	C₂×C₄×C₂₃	semidirect
272. C₄⋊C₈	C₂×C₄×C₂₃	semidirect
279. C₂₃	C₂×#1303	direct (N × H)
419. C₂	C₂₃×#1303	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×#431	2
C₂×C₂₃×#423	2
C₂×C₄×C₄⋊C₄×C₂₃	2
C₂₃×#1303	2
C₂×#1303	23

Subgroups — C2×C23×#1303 #19155717

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#1303 #19155717