Subgroups — #15831993

Order 3328.

668 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	#13123469	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718586	C₂	1	1	yes	maximal, characteristic
3	#13113616	C₂	1	4	yes	maximal, complemented
4	#13113611	C₂	1	2	yes	maximal, complemented
5	#13113607	C₂	1	2	yes	maximal, complemented
6	#13113584	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#431	C₄	1	2	yes	—
10	C₁₃×#431	C₄	1	2	yes	—
11	C₁₃×#431	C₂²	1	1	yes	characteristic
12	C₁₃×#431	C₂²	1	1	yes	characteristic
13	C₁₃×#431	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊C₈	C₄	1	2	yes	—
15	C₂×C₁₃×C₂²⋊C₈	C₄	1	2	yes	—
16	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
17	#11718868	—	2	1	no	—
18	C₂×C₂²⋊#1055	—	2	1	no	—
19	#11718587	—	2	1	no	—
20	#11718587	C₂²	1	2	yes	—
21	#11718586	—	2	1	no	—
22	#11718586	—	2	1	no	—
23	#11718586	—	2	1	no	—
24	#11718586	C₂²	1	2	yes	—
25	#11718586	C₂²	1	2	yes	—
26	#11718586	C₂²	1	2	yes	—
27	#11718585	C₂²	1	2	yes	—
28	C₂×C₄⋊#1055	C₂²	1	2	yes	—
29	C₄×#6099	—	2	1	no	—
30	C₂×C₄×#1055	—	2	1	no	—
31	#11718050	C₂²	1	8	yes	complemented
32	#11718049	C₂²	1	8	yes	complemented
33	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃	Q₈	1	1	yes	characteristic
36	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
37	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₃	Q₈	1	1	yes	characteristic
44	C₂×C₄²×C₁₃	Q₈	1	1	yes	characteristic
45	C₂×C₄²×C₁₃	Q₈	1	1	yes	characteristic
46	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
47	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
48	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
49	C₂×#6099	—	2	2	no	—
50	C₂²×#1055	—	2	2	no	—
51	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
52	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
53	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
54	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
55	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
56	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
57	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
58	C₄×C₈×C₁₃	C₂³	1	2	yes	—
59	C₄×C₈×C₁₃	C₂³	1	2	yes	—
60	C₂²⋊#1055	—	2	2	no	—
61	C₂²⋊#1055	—	2	2	no	—
62	C₂²⋊#1055	—	2	2	no	—
63	C₂²⋊#1055	—	2	2	no	—
64	C₄⋊#1055	—	2	2	no	—
65	C₄⋊#1055	—	2	2	no	—
66	C₄⋊#1055	C₂³	1	4	yes	—
67	C₄⋊#1055	C₂³	1	4	yes	—
68	#88043	—	2	2	no	—
69	C₄×#1055	—	2	2	no	—
70	C₄×#1055	—	2	2	no	—
71	C₄×#1055	—	2	2	no	—
72	#17803	—	13	1	no	maximal, Sylow
73	C₂⁴×C₁₃	C₄⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃	—	2	4	no	—
75	C₂²×C₄×C₁₃	—	2	4	no	—
76	C₂²×C₄×C₁₃	—	4	2	no	—
77	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
95	C₂×C₈×C₁₃	—	2	8	no	—
96	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
97	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
98	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
111	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
112	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
113	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
114	#6099	—	4	4	no	—
115	C₂×#1055	—	2	4	no	—
116	C₂×#1055	—	2	4	no	—
117	C₂×#1055	—	4	4	no	—
118	#2920	—	13	1	no	—
119	C₂×#431	—	13	1	no	—
120	C₂×#431	D₁₃	1	1	yes	characteristic
121	#1572	—	13	4	no	—
122	#1571	—	13	2	no	—
123	#1570	—	13	2	no	—
124	#1564	—	13	4	no	—
125	C₂³×C₁₃	—	2	2	no	—
126	C₂³×C₁₃	—	2	2	no	—
127	C₂³×C₁₃	—	4	1	no	—
128	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₁₃	—	2	2	no	—
132	C₂×C₄×C₁₃	—	2	2	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	2	no	—
138	C₂×C₄×C₁₃	—	2	2	no	—
139	C₂×C₄×C₁₃	—	2	2	no	—
140	C₂×C₄×C₁₃	—	2	2	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	2	no	—
143	C₂×C₄×C₁₃	—	2	2	no	—
144	C₂×C₄×C₁₃	—	4	1	no	—
145	C₂×C₄×C₁₃	—	4	1	no	—
146	C₂×C₄×C₁₃	—	4	1	no	—
147	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃	#131	1	4	yes	—
157	C₂×C₄×C₁₃	#135	1	4	yes	—
158	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
161	C₈×C₁₃	—	2	4	no	—
162	C₈×C₁₃	—	2	4	no	—
163	#1055	—	4	4	no	—
164	#1055	—	4	4	no	—
165	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
166	#432	—	13	2	no	—
167	#432	—	26	1	no	—
168	#431	—	13	2	no	—
169	#431	—	13	2	no	—
170	#431	—	13	2	no	—
171	#431	—	26	1	no	—
172	#431	—	26	1	no	—
173	#431	—	26	1	no	—
174	#431	Dic₁₃	1	2	yes	—
175	#431	Dic₁₃	1	2	yes	—
176	#431	C₂×D₁₃	1	1	yes	characteristic
177	#431	C₂×D₁₃	1	1	yes	characteristic
178	#431	C₂×D₁₃	1	2	yes	—
179	#423	—	13	2	no	—
180	C₂×C₄⋊C₈	—	13	2	no	—
181	C₂×C₄⋊C₈	Dic₁₃	1	2	yes	—
182	#407	—	26	1	no	—
183	C₂×C₂²⋊C₈	—	26	1	no	—
184	C₂×C₂²⋊C₈	Dic₁₃	1	2	yes	—
185	C₄×M₁₆	—	26	1	no	—
186	C₂×C₄×C₈	—	26	1	no	—
187	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
188	#335	—	13	8	no	—
189	#334	—	13	8	no	—
190	C₂²×C₁₃	—	2	1	no	—
191	C₂²×C₁₃	—	2	1	no	—
192	C₂²×C₁₃	—	2	1	no	—
193	C₂²×C₁₃	—	2	1	no	—
194	C₂²×C₁₃	—	2	1	no	—
195	C₂²×C₁₃	—	2	1	no	—
196	C₂²×C₁₃	—	2	1	no	—
197	C₂²×C₁₃	—	4	4	no	—
198	C₂²×C₁₃	#424	1	2	yes	—
199	C₂²×C₁₃	#427	1	2	yes	—
200	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
201	C₄×C₁₃	—	2	1	no	—
202	C₄×C₁₃	—	2	1	no	—
203	C₄×C₁₃	—	2	1	no	—
204	C₄×C₁₃	—	2	1	no	—
205	C₄×C₁₃	—	2	1	no	—
206	C₄×C₁₃	—	2	1	no	—
207	C₄×C₁₃	—	2	1	no	—
208	C₄×C₁₃	#424	1	2	yes	—
209	C₄×C₁₃	#427	1	2	yes	—
210	C₄×C₁₃	#430	1	2	yes	—
211	C₄×C₁₃	C₂×#131	1	2	yes	—
212	C₄×C₁₃	C₂×#135	1	2	yes	—
213	C₂³×C₄	Dic₂₆	1	1	yes	characteristic
214	C₂³×C₄	D₅₂	1	1	yes	characteristic
215	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
216	C₂×M₁₆	—	26	2	no	—
217	C₂²×C₈	—	26	2	no	—
218	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
219	C₂×C₄²	Dic₂₆	1	1	yes	characteristic
220	C₂×C₄²	Dic₂₆	1	1	yes	characteristic
221	C₂×C₄²	Dic₂₆	1	1	yes	characteristic
222	C₂×C₄²	D₅₂	1	1	yes	characteristic
223	C₂×C₄²	D₅₂	1	1	yes	characteristic
224	C₂×C₄²	D₅₂	1	1	yes	characteristic
225	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
226	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
227	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
228	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
229	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
230	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
231	C₄⋊C₈	—	13	4	no	—
232	C₄⋊C₈	—	13	4	no	—
233	C₄⋊C₈	—	26	2	no	—
234	C₄⋊C₈	—	26	2	no	—
235	C₄⋊C₈	C₂×Dic₁₃	1	2	yes	—
236	C₄⋊C₈	C₂×Dic₁₃	1	2	yes	—
237	C₄⋊C₈	C₂×Dic₁₃	1	4	yes	—
238	C₂²⋊C₈	—	26	2	no	—
239	C₂²⋊C₈	—	26	2	no	—
240	C₂²⋊C₈	—	26	2	no	—
241	C₂²⋊C₈	—	26	2	no	—
242	C₂²⋊C₈	C₂×Dic₁₃	1	2	yes	—
243	C₂²⋊C₈	C₂×Dic₁₃	1	2	yes	—
244	C₂²⋊C₈	C₂×Dic₁₃	1	4	yes	—
245	#97	—	26	2	no	—
246	C₄×C₈	—	26	2	no	—
247	C₄×C₈	—	26	2	no	—
248	C₄×C₈	—	26	2	no	—
249	C₄×C₈	C₂×Dic₁₃	1	4	yes	—
250	C₄×C₈	C₂²×D₁₃	1	2	yes	—
251	C₄×C₈	C₂²×D₁₃	1	2	yes	—
252	C₂×C₁₃	—	2	2	no	—
253	C₂×C₁₃	—	2	2	no	—
254	C₂×C₁₃	—	4	1	no	—
255	C₂×C₁₃	C₂×#424	1	1	yes	characteristic
256	C₂×C₁₃	C₂×#427	1	1	yes	characteristic
257	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
258	C₂⁴	C₄⋊Dic₁₃	1	1	yes	characteristic
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
263	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
264	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
265	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
266	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
267	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
268	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
269	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
270	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
271	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
272	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
273	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
277	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
278	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
279	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
280	M₁₆	—	52	4	no	—
281	C₂×C₈	—	2	8	no	—
282	C₂×C₈	—	26	4	no	—
283	C₂×C₈	—	26	4	no	—
284	C₂×C₈	—	52	4	no	—
285	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
286	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
287	C₄²	C₄⋊Dic₁₃	1	1	yes	characteristic
288	C₄²	C₄⋊Dic₁₃	1	1	yes	characteristic
289	C₄²	C₄⋊Dic₁₃	1	1	yes	characteristic
290	C₄²	C₄⋊Dic₁₃	1	1	yes	characteristic
291	C₄²	C₄⋊Dic₁₃	1	1	yes	characteristic
292	C₄²	C₄⋊Dic₁₃	1	1	yes	characteristic
293	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
294	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
295	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
296	C₄²	C₂×D₅₂	1	1	yes	characteristic
297	C₄²	C₂×D₅₂	1	1	yes	characteristic
298	C₄²	C₂×D₅₂	1	1	yes	characteristic
299	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
300	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
301	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
302	C₄²	C₂³×D₁₃	1	1	yes	characteristic
303	C₁₃	#17803	1	1	yes	characteristic, complemented, Sylow
304	C₂³	—	2	2	no	—
305	C₂³	—	2	2	no	—
306	C₂³	—	4	1	no	—
307	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
308	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
309	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	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	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	#88158	1	4	yes	—
327	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
328	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
329	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
330	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
331	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
332	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
333	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
334	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
335	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
336	C₂×C₄	#88202	1	4	yes	—
337	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
338	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
339	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
340	C₈	—	2	4	no	—
341	C₈	—	2	4	no	—
342	C₈	—	52	4	no	—
343	C₈	—	52	4	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	4	4	no	—
352	C₂²	#11718660	1	2	yes	—
353	C₂²	#11718767	1	2	yes	—
354	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	#11718660	1	2	yes	—
363	C₄	#11718767	1	2	yes	—
364	C₄	#11718786	1	2	yes	—
365	C₄	C₂×#88158	1	2	yes	—
366	C₄	C₂×#88202	1	2	yes	—
367	C₂	—	2	2	no	—
368	C₂	—	2	2	no	—
369	C₂	—	4	1	no	—
370	C₂	C₂×#11718660	1	1	yes	characteristic
371	C₂	C₂×#11718767	1	1	yes	characteristic
372	C₂	C₂×#11718786	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×D₅₂
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₂×C₁₃×#431	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₃	C₄⋊C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₂×#431	D₁₃
hypocenter	C₁₃	#17803
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #13113616	C₂	semidirect
4. #13113611	C₂	semidirect
5. #13113607	C₂	semidirect
6. #13113584	C₂	semidirect
31. #11718050	C₂²	semidirect
32. #11718049	C₂²	semidirect
303. C₁₃	#17803	semidirect

Maximal subgroups

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

subgroup	index
#13123469	2
C₂×#11718586	2
#13113616	2
#13113611	2
#13113607	2
#13113584	2
C₂×C₁₃×#431	2
#17803	13