Subgroups — C₂×C₁₃×#2024 #15709788

Order 3328.

1518 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×#103	C₂	1	2	yes	maximal
3	C₂×C₁₃×#391	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2024	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₃×#340	C₂	1	2	yes	maximal
6	C₂×C₁₃×#336	C₂	1	1	yes	maximal, characteristic
7	C₂³×Q₈×C₁₃	—	2	1	no	—
8	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
10	C₂×C₁₃×C₄⋊Q₈	—	2	8	no	—
11	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	4	yes	—
13	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
14	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#103	—	2	8	no	—
18	C₂×C₁₃×#103	C₂²	1	8	yes	—
19	C₁₃×#391	—	2	2	no	—
20	C₁₃×#391	C₂²	1	4	yes	—
21	C₂×C₁₃×#95	—	2	1	no	—
22	C₂×C₁₃×#95	—	2	1	no	—
23	C₁₃×#340	C₂²	1	8	yes	—
24	C₁₃×#336	C₂²	1	4	yes	—
25	C₂²×Q₈×C₁₃	—	2	8	no	—
26	C₂²×Q₈×C₁₃	—	2	1	no	—
27	C₂²×Q₈×C₁₃	—	2	4	no	—
28	C₂²×Q₈×C₁₃	—	2	2	no	—
29	C₂²×Q₈×C₁₃	—	2	4	no	—
30	C₂²×Q₈×C₁₃	—	2	4	no	—
31	C₂²×Q₈×C₁₃	—	4	4	no	—
32	C₂²×Q₈×C₁₃	—	4	4	no	—
33	C₂²×Q₈×C₁₃	Q₈	1	4	yes	complemented
34	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
35	C₂³×C₄×C₁₃	—	2	2	no	—
36	C₂³×C₄×C₁₃	—	2	1	no	—
37	C₂³×C₄×C₁₃	—	2	1	no	—
38	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₁₃	—	2	4	no	—
42	C₂²×C₈×C₁₃	—	2	4	no	—
43	C₂²×C₈×C₁₃	—	2	4	no	—
44	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
45	C₁₃×C₄⋊Q₈	—	2	16	no	—
46	C₁₃×C₄⋊Q₈	—	2	16	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
53	C₂×C₁₃×C₄⋊C₄	D₄	1	8	yes	—
54	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
56	C₂×C₄²×C₁₃	—	2	4	no	—
57	C₂×C₄²×C₁₃	D₄	1	2	yes	—
58	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
59	C₁₃×#103	—	2	16	no	—
60	C₁₃×#95	—	2	4	no	—
61	C₁₃×#95	—	2	4	no	—
62	C₂×#2024	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
64	C₂×Q₈×C₁₃	—	2	16	no	—
65	C₂×Q₈×C₁₃	—	2	4	no	—
66	C₂×Q₈×C₁₃	—	2	2	no	—
67	C₂×Q₈×C₁₃	—	2	16	no	—
68	C₂×Q₈×C₁₃	—	2	4	no	—
69	C₂×Q₈×C₁₃	—	2	4	no	—
70	C₂×Q₈×C₁₃	—	4	8	no	—
71	C₂×Q₈×C₁₃	—	4	32	no	—
72	C₂×Q₈×C₁₃	—	4	2	no	—
73	C₂×Q₈×C₁₃	—	4	2	no	—
74	C₂×Q₈×C₁₃	—	4	8	no	—
75	C₂×Q₈×C₁₃	—	4	8	no	—
76	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	complemented
77	C₂²×C₄×C₁₃	—	2	2	no	—
78	C₂²×C₄×C₁₃	—	2	2	no	—
79	C₂²×C₄×C₁₃	—	2	2	no	—
80	C₂²×C₄×C₁₃	—	2	2	no	—
81	C₂²×C₄×C₁₃	—	2	8	no	—
82	C₂²×C₄×C₁₃	—	2	4	no	—
83	C₂²×C₄×C₁₃	—	2	2	no	—
84	C₂²×C₄×C₁₃	—	2	4	no	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	4	2	no	—
87	C₂²×C₄×C₁₃	—	4	2	no	—
88	C₂²×C₄×C₁₃	—	4	4	no	—
89	C₂²×C₄×C₁₃	—	4	4	no	—
90	C₂²×C₄×C₁₃	—	4	2	no	—
91	C₂²×C₄×C₁₃	—	4	2	no	—
92	C₂²×C₄×C₁₃	—	4	2	no	—
93	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
94	C₂²×C₄×C₁₃	Q₁₆	1	4	yes	—
95	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
99	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₁₃	#41	1	4	yes	—
101	C₂²×C₄×C₁₃	#41	1	2	yes	—
102	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
103	C₂×C₈×C₁₃	—	2	4	no	—
104	C₂×C₈×C₁₃	—	2	4	no	—
105	C₂×C₈×C₁₃	—	2	4	no	—
106	C₂×C₈×C₁₃	—	4	8	no	—
107	C₁₃×C₄⋊C₄	—	2	16	no	—
108	C₁₃×C₄⋊C₄	—	2	8	no	—
109	C₁₃×C₄⋊C₄	—	2	4	no	—
110	C₁₃×C₄⋊C₄	—	2	4	no	—
111	C₁₃×C₄⋊C₄	—	4	2	no	—
112	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
113	C₄²×C₁₃	—	2	4	no	—
114	C₄²×C₁₃	—	2	4	no	—
115	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
116	C₂²×#103	C₂×C₁₃	1	2	yes	—
117	C₂×#391	C₂×C₁₃	1	1	yes	characteristic
118	#2024	C₂×C₁₃	1	8	yes	direct product factor
119	C₂×#340	C₂×C₁₃	1	2	yes	—
120	C₂×#336	C₂×C₁₃	1	1	yes	characteristic
121	C₂³×C₁₃	#120	1	2	yes	—
122	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
123	C₂³×C₁₃	#124	1	2	yes	—
124	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
125	C₂³×C₁₃	C₂×Q₁₆	1	2	yes	—
126	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
127	C₂³×C₁₃	#137	1	2	yes	—
128	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
129	Q₈×C₁₃	—	2	8	no	—
130	Q₈×C₁₃	—	4	32	no	—
131	Q₈×C₁₃	—	4	4	no	—
132	Q₈×C₁₃	—	4	8	no	—
133	C₂×C₄×C₁₃	—	2	2	no	—
134	C₂×C₄×C₁₃	—	2	2	no	—
135	C₂×C₄×C₁₃	—	2	2	no	—
136	C₂×C₄×C₁₃	—	2	2	no	—
137	C₂×C₄×C₁₃	—	2	8	no	—
138	C₂×C₄×C₁₃	—	2	8	no	—
139	C₂×C₄×C₁₃	—	2	8	no	—
140	C₂×C₄×C₁₃	—	2	4	no	—
141	C₂×C₄×C₁₃	—	4	2	no	—
142	C₂×C₄×C₁₃	—	4	2	no	—
143	C₂×C₄×C₁₃	—	4	4	no	—
144	C₂×C₄×C₁₃	—	4	4	no	—
145	C₂×C₄×C₁₃	—	4	8	no	—
146	C₂×C₄×C₁₃	—	4	16	no	—
147	C₂×C₄×C₁₃	—	4	2	no	—
148	C₂×C₄×C₁₃	—	4	2	no	—
149	C₂×C₄×C₁₃	—	4	2	no	—
150	C₂×C₄×C₁₃	—	8	4	no	—
151	C₂×C₄×C₁₃	#120	1	2	yes	—
152	C₂×C₄×C₁₃	C₂²⋊Q₈	1	8	yes	—
153	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
154	C₂×C₄×C₁₃	#124	1	8	yes	—
155	C₂×C₄×C₁₃	#124	1	2	yes	—
156	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
157	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	—
158	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
159	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
161	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
162	C₈×C₁₃	—	4	4	no	—
163	C₂³×Q₈	—	2	1	no	—
164	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
165	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
166	C₂×C₄⋊Q₈	—	2	8	no	—
167	C₂×C₄⋊Q₈	—	2	2	no	—
168	C₂×C₄⋊Q₈	C₂²×C₁₃	1	4	yes	—
169	C₂²×C₄⋊C₄	—	2	1	no	—
170	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
171	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
172	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
173	C₂×#103	—	2	8	no	—
174	C₂×#103	C₂²×C₁₃	1	8	yes	—
175	#391	—	2	2	no	—
176	#391	C₂²×C₁₃	1	4	yes	—
177	C₂×#95	—	2	1	no	—
178	C₂×#95	—	2	1	no	—
179	#340	C₂²×C₁₃	1	8	yes	—
180	#336	C₂²×C₁₃	1	4	yes	—
181	C₂²×C₁₃	#393	1	4	yes	—
182	C₂²×C₁₃	#450	1	4	yes	—
183	C₂²×C₁₃	#451	1	4	yes	—
184	C₂²×C₁₃	#475	1	4	yes	—
185	C₂²×C₁₃	#477	1	4	yes	—
186	C₂²×C₁₃	#487	1	4	yes	—
187	C₂²×C₁₃	#489	1	4	yes	—
188	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
189	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
190	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
191	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
192	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
193	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
194	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
195	C₄×C₁₃	—	2	4	no	—
196	C₄×C₁₃	—	2	4	no	—
197	C₄×C₁₃	—	4	4	no	—
198	C₄×C₁₃	—	4	8	no	—
199	C₄×C₁₃	—	8	2	no	—
200	C₄×C₁₃	#393	1	4	yes	—
201	C₄×C₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
202	C₄×C₁₃	C₂×#124	1	2	yes	—
203	C₂²×Q₈	—	2	8	no	—
204	C₂²×Q₈	—	2	4	no	—
205	C₂²×Q₈	—	2	1	no	—
206	C₂²×Q₈	—	2	2	no	—
207	C₂²×Q₈	—	2	4	no	—
208	C₂²×Q₈	—	2	4	no	—
209	C₂²×Q₈	—	4	4	no	—
210	C₂²×Q₈	—	4	4	no	—
211	C₂²×Q₈	Q₈×C₁₃	1	4	yes	complemented
212	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
213	C₂³×C₄	—	2	2	no	—
214	C₂³×C₄	—	2	1	no	—
215	C₂³×C₄	—	2	1	no	—
216	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
217	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
218	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
219	C₂²×C₈	—	2	4	no	—
220	C₂²×C₈	—	2	4	no	—
221	C₂²×C₈	—	2	4	no	—
222	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
223	C₄⋊Q₈	—	2	16	no	—
224	C₄⋊Q₈	—	2	16	no	—
225	C₂×C₄⋊C₄	—	2	8	no	—
226	C₂×C₄⋊C₄	—	2	4	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄⋊C₄	—	2	4	no	—
229	C₂×C₄⋊C₄	—	2	4	no	—
230	C₂×C₄⋊C₄	—	2	1	no	—
231	C₂×C₄⋊C₄	D₄×C₁₃	1	8	yes	—
232	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
233	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
234	C₂×C₄²	—	2	4	no	—
235	C₂×C₄²	D₄×C₁₃	1	2	yes	—
236	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
237	#103	—	2	16	no	—
238	#95	—	2	4	no	—
239	#95	—	2	4	no	—
240	C₂×C₁₃	#2024	1	8	yes	direct product factor
241	C₂×C₁₃	C₂×#393	1	1	yes	characteristic
242	C₂×C₁₃	C₂×#450	1	1	yes	characteristic
243	C₂×C₁₃	C₂×#451	1	1	yes	characteristic
244	C₂×C₁₃	C₂×#475	1	1	yes	characteristic
245	C₂×C₁₃	C₂×#477	1	1	yes	characteristic
246	C₂×C₁₃	C₂×#487	1	1	yes	characteristic
247	C₂×C₁₃	C₂×#489	1	1	yes	characteristic
248	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
249	C₂×Q₈	—	2	16	no	—
250	C₂×Q₈	—	2	4	no	—
251	C₂×Q₈	—	2	2	no	—
252	C₂×Q₈	—	2	16	no	—
253	C₂×Q₈	—	2	4	no	—
254	C₂×Q₈	—	2	4	no	—
255	C₂×Q₈	—	4	32	no	—
256	C₂×Q₈	—	4	8	no	—
257	C₂×Q₈	—	4	2	no	—
258	C₂×Q₈	—	4	8	no	—
259	C₂×Q₈	—	4	2	no	—
260	C₂×Q₈	—	4	8	no	—
261	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	complemented
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	8	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	—	4	4	no	—
274	C₂²×C₄	—	4	4	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	C₁₃×SD₁₆	1	4	yes	—
279	C₂²×C₄	C₁₃×Q₁₆	1	4	yes	—
280	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
284	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
285	C₂²×C₄	C₁₃×#41	1	4	yes	—
286	C₂²×C₄	C₁₃×#41	1	2	yes	—
287	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	—	4	8	no	—
292	C₄⋊C₄	—	2	16	no	—
293	C₄⋊C₄	—	2	8	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	4	2	no	—
297	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
298	C₄²	—	2	4	no	—
299	C₄²	—	2	4	no	—
300	C₁₃	C₂×#2024	1	1	yes	characteristic, direct product factor, Sylow
301	C₂³	C₁₃×#120	1	2	yes	—
302	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
303	C₂³	C₁₃×#124	1	2	yes	—
304	C₂³	C₂×C₁₃×SD₁₆	1	2	yes	—
305	C₂³	C₂×C₁₃×Q₁₆	1	2	yes	—
306	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
307	C₂³	C₁₃×#137	1	2	yes	—
308	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
309	Q₈	—	2	8	no	—
310	Q₈	—	4	32	no	—
311	Q₈	—	4	8	no	—
312	Q₈	—	4	4	no	—
313	C₂×C₄	—	2	8	no	—
314	C₂×C₄	—	2	8	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	4	8	no	—
322	C₂×C₄	—	4	16	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	8	4	no	—
331	C₂×C₄	C₁₃×#120	1	2	yes	—
332	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
333	C₂×C₄	C₁₃×C₂²⋊Q₈	1	8	yes	—
334	C₂×C₄	C₁₃×#124	1	2	yes	—
335	C₂×C₄	C₁₃×#124	1	8	yes	—
336	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
337	C₂×C₄	C₂×C₁₃×Q₁₆	1	4	yes	—
338	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
339	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
340	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
341	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
342	C₈	—	4	4	no	—
343	C₂²	C₁₃×#393	1	4	yes	—
344	C₂²	C₁₃×#450	1	4	yes	—
345	C₂²	C₁₃×#451	1	4	yes	—
346	C₂²	C₁₃×#475	1	4	yes	—
347	C₂²	C₁₃×#477	1	4	yes	—
348	C₂²	C₁₃×#487	1	4	yes	—
349	C₂²	C₁₃×#489	1	4	yes	—
350	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
351	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
352	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
353	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
354	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
355	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
356	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
357	C₄	—	2	4	no	—
358	C₄	—	2	4	no	—
359	C₄	—	4	4	no	—
360	C₄	—	4	8	no	—
361	C₄	—	8	2	no	—
362	C₄	C₁₃×#393	1	4	yes	—
363	C₄	C₂×C₁₃×C₂²⋊Q₈	1	2	yes	—
364	C₄	C₂×C₁₃×#124	1	2	yes	—
365	C₂	C₁₃×#2024	1	8	yes	direct product factor
366	C₂	C₂×C₁₃×#393	1	1	yes	characteristic
367	C₂	C₂×C₁₃×#450	1	1	yes	characteristic
368	C₂	C₂×C₁₃×#451	1	1	yes	characteristic
369	C₂	C₂×C₁₃×#475	1	1	yes	characteristic
370	C₂	C₂×C₁₃×#477	1	1	yes	characteristic
371	C₂	C₂×C₁₃×#487	1	1	yes	characteristic
372	C₂	C₂×C₁₃×#489	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₃×#2024	C₂	direct (N × H)
33. C₂²×Q₈×C₁₃	Q₈	semidirect
62. C₂×#2024	C₁₃	direct (N × H)
76. C₂×Q₈×C₁₃	C₂×Q₈	semidirect
118. #2024	C₂×C₁₃	direct (N × H)
211. C₂²×Q₈	Q₈×C₁₃	semidirect
240. C₂×C₁₃	#2024	direct (N × H)
261. C₂×Q₈	C₂×Q₈×C₁₃	semidirect
300. C₁₃	C₂×#2024	direct (N × H)
365. C₂	C₁₃×#2024	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×C₄⋊Q₈	2
C₂²×C₁₃×#103	2
C₂×C₁₃×#391	2
C₁₃×#2024	2
C₂×C₁₃×#340	2
C₂×C₁₃×#336	2
C₂×#2024	13

Subgroups — C2×C13×#2024 #15709788

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2024 #15709788