Subgroups — C₂×#13127938 #16769387

Order 3328.

2074 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	C₂²×#88155	C₂	1	1	yes	maximal, characteristic
2	#13127938	C₂	1	16	yes	maximal, direct product factor
3	C₂×#11718568	C₂	1	4	yes	maximal, complemented
4	C₂×#11718562	C₂	1	4	yes	maximal, complemented
5	C₂²×#88052	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₃×M₃₂	C₂	1	4	yes	maximal, complemented
7	C₂²×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#6127	C₄	1	1	yes	characteristic
9	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²×#6099	C₄	1	1	yes	characteristic
11	C₂×#88155	C₄	1	2	yes	—
12	C₂×#88155	C₄	1	8	yes	—
13	C₂×#88155	C₄	1	2	yes	—
14	C₂×#88155	C₂²	1	2	yes	—
15	C₂×#88155	C₂²	1	8	yes	—
16	C₂×#88155	C₂²	1	2	yes	—
17	C₂²×#6094	C₄	1	2	yes	—
18	C₂²×C₈×D₁₃	C₂²	1	2	yes	—
19	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
20	C₂×C₁₃×M₃₂	C₂²	1	2	yes	complemented
21	C₂×C₁₃×M₃₂	C₂²	1	8	yes	complemented
22	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	complemented
23	C₂×#88052	C₂²	1	2	yes	—
24	C₂×#88052	C₂²	1	2	yes	complemented
25	C₂×#88052	C₂²	1	8	yes	complemented
26	C₂²×#6090	C₂²	1	2	yes	complemented
27	#11718568	C₂²	1	32	yes	complemented
28	D₁₃×M₃₂	C₂²	1	32	yes	complemented
29	#11718562	C₂²	1	32	yes	complemented
30	C₂×#88038	C₂²	1	8	yes	complemented
31	C₂×C₁₆×D₁₃	C₂²	1	8	yes	complemented
32	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₂²⋊D₁₃	C₈	1	2	yes	—
34	C₂×#6127	C₈	1	2	yes	—
35	C₂×#6127	C₈	1	2	yes	—
36	C₂×#6127	C₈	1	8	yes	—
37	C₂×#6127	C₂×C₄	1	2	yes	—
38	C₂×#6127	C₂×C₄	1	8	yes	—
39	C₂×#6127	C₂×C₄	1	2	yes	—
40	C₂²×D₅₂	C₈	1	1	yes	characteristic
41	C₂²×C₄×D₁₃	C₂×C₄	1	2	yes	—
42	C₂²×Dic₂₆	C₈	1	1	yes	characteristic
43	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
51	C₂×#6099	C₂×C₄	1	2	yes	—
52	C₂×#6099	C₂×C₄	1	8	yes	—
53	C₂×#6099	C₂×C₄	1	2	yes	—
54	C₂²×#1055	C₂×C₄	1	2	yes	—
55	#88155	C₂×C₄	1	8	yes	—
56	#88155	C₂×C₄	1	16	yes	—
57	#88155	C₂×C₄	1	16	yes	—
58	#88155	C₂×C₄	1	8	yes	—
59	#88155	C₂³	1	8	yes	—
60	#88155	C₂³	1	8	yes	—
61	C₂×#6094	C₂×C₄	1	4	yes	—
62	C₂×#6094	C₂×C₄	1	16	yes	—
63	C₂×#6094	C₂×C₄	1	4	yes	—
64	C₂×C₈×D₁₃	C₂×C₄	1	8	yes	—
65	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
66	C₂×C₈×D₁₃	C₂³	1	4	yes	—
67	C₂×C₈×D₁₃	C₂³	1	8	yes	—
68	C₁₃×M₃₂	C₂³	1	8	yes	—
69	C₁₃×M₃₂	C₂³	1	8	yes	complemented
70	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
71	C₂×C₁₃×C₁₆	C₂³	1	8	yes	complemented
72	#88052	C₂³	1	8	yes	—
73	#88052	C₂³	1	8	yes	complemented
74	C₂×#6090	C₂³	1	4	yes	—
75	C₂×#6090	C₂³	1	8	yes	complemented
76	#88038	C₂³	1	32	yes	complemented
77	C₁₆×D₁₃	C₂³	1	32	yes	complemented
78	C₂×#3407	—	13	1	no	maximal, Sylow
79	C₂⁴×C₁₃	C₂×C₈	1	1	yes	characteristic
80	C₂³×D₁₃	C₂×C₈	1	2	yes	—
81	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
85	C₂²×C₄×C₁₃	C₂²×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	4	yes	—
89	C₂×C₂²⋊D₁₃	C₂×C₈	1	4	yes	—
90	C₂×C₂²⋊D₁₃	C₂×C₈	1	4	yes	—
91	C₂×C₂²⋊D₁₃	C₂×C₈	1	16	yes	—
92	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
93	#6127	C₂×C₈	1	8	yes	—
94	#6127	C₂×C₈	1	16	yes	—
95	#6127	C₂×C₈	1	16	yes	—
96	#6127	C₂×C₈	1	8	yes	—
97	#6127	C₂²×C₄	1	8	yes	—
98	#6127	C₂²×C₄	1	8	yes	—
99	C₂×D₅₂	C₂×C₈	1	2	yes	—
100	C₂×D₅₂	C₂×C₈	1	2	yes	—
101	C₂×D₅₂	C₂×C₈	1	8	yes	—
102	C₂×C₄×D₁₃	C₂×C₈	1	4	yes	—
103	C₂×C₄×D₁₃	C₂×C₈	1	8	yes	—
104	C₂×C₄×D₁₃	C₂²×C₄	1	4	yes	—
105	C₂×C₄×D₁₃	C₂²×C₄	1	8	yes	—
106	C₂×Dic₂₆	C₂×C₈	1	8	yes	—
107	C₂×Dic₂₆	C₂×C₈	1	2	yes	—
108	C₂×Dic₂₆	C₂×C₈	1	2	yes	—
109	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
111	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
114	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
117	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
118	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
119	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
120	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
121	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
122	#6099	C₂²×C₄	1	8	yes	—
123	#6099	C₂²×C₄	1	8	yes	—
124	C₂×#1055	C₂²×C₄	1	4	yes	—
125	C₂×#1055	C₂²×C₄	1	8	yes	—
126	#6094	C₂²×C₄	1	16	yes	—
127	#6094	C₂²×C₄	1	16	yes	—
128	C₈×D₁₃	C₂²×C₄	1	8	yes	—
129	C₈×D₁₃	C₂²×C₄	1	16	yes	—
130	C₈×D₁₃	C₂⁴	1	8	yes	—
131	C₁₃×C₁₆	C₂⁴	1	8	yes	—
132	#6090	C₂⁴	1	8	yes	—
133	C₂²×#131	—	13	1	no	—
134	#3407	—	13	16	no	—
135	C₂×#504	—	13	4	no	—
136	C₂×#504	—	13	4	no	—
137	C₂²×M₃₂	—	13	4	no	—
138	C₂²×M₃₂	—	13	1	no	—
139	C₂²×M₃₂	D₁₃	1	1	yes	characteristic, complemented
140	C₂³×C₁₃	—	4	2	no	—
141	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
142	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
143	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
144	C₂³×C₁₃	C₂²×C₈	1	4	yes	—
145	C₂²×D₁₃	—	4	4	no	—
146	C₂²×D₁₃	C₂²×C₈	1	4	yes	—
147	C₂²×D₁₃	C₂²×C₈	1	8	yes	—
148	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
149	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
152	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
154	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
155	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
156	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
157	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
158	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
160	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
161	C₂²⋊D₁₃	C₂²×C₈	1	16	yes	—
162	C₂²⋊D₁₃	C₂²×C₈	1	16	yes	—
163	C₂×Dic₁₃	C₂²×C₈	1	8	yes	—
164	C₂×Dic₁₃	C₂²×C₈	1	4	yes	—
165	D₅₂	C₂²×C₈	1	8	yes	—
166	D₅₂	C₂²×C₈	1	8	yes	—
167	C₄×D₁₃	C₂²×C₈	1	16	yes	—
168	C₄×D₁₃	C₂²×C₈	1	8	yes	—
169	C₄×D₁₃	C₂³×C₄	1	8	yes	—
170	Dic₂₆	C₂²×C₈	1	8	yes	—
171	Dic₂₆	C₂²×C₈	1	8	yes	—
172	C₈×C₁₃	C₂³×C₄	1	2	yes	—
173	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
174	C₈×C₁₃	C₂³×C₄	1	2	yes	—
175	C₈×C₁₃	C₂³×C₄	1	2	yes	—
176	C₈×C₁₃	C₂⁵	1	1	yes	characteristic
177	#1055	C₂³×C₄	1	8	yes	—
178	C₂²×#41	—	13	1	no	—
179	C₂×#131	—	13	2	no	—
180	C₂×#131	—	13	2	no	—
181	C₂×#131	—	13	8	no	—
182	C₂×#131	—	13	2	no	—
183	C₂×#131	—	13	2	no	—
184	C₂×#131	—	13	8	no	—
185	C₂²×M₁₆	—	13	1	no	—
186	C₂²×M₁₆	—	13	2	no	—
187	C₂³×C₈	—	13	2	no	—
188	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
189	#504	—	13	32	no	—
190	#504	—	13	32	no	—
191	C₂×M₃₂	—	13	2	no	—
192	C₂×M₃₂	—	13	2	no	—
193	C₂×M₃₂	—	13	8	no	—
194	C₂×M₃₂	—	13	32	no	—
195	C₂×M₃₂	—	13	8	no	—
196	C₂×M₃₂	C₂×D₁₃	1	2	yes	—
197	C₂×M₃₂	C₂×D₁₃	1	2	yes	complemented
198	C₂×M₃₂	C₂×D₁₃	1	8	yes	complemented
199	C₂²×C₁₆	—	13	2	no	—
200	C₂²×C₁₆	—	13	8	no	—
201	C₂²×C₁₆	C₂×D₁₃	1	2	yes	complemented
202	C₂²×C₁₃	—	2	2	no	—
203	C₂²×C₁₃	—	2	2	no	—
204	C₂²×C₁₃	—	2	2	no	—
205	C₂²×C₁₃	—	4	4	no	—
206	C₂²×C₁₃	C₂³×C₈	1	2	yes	—
207	C₂²×C₁₃	C₂³×C₈	1	2	yes	—
208	C₂²×C₁₃	C₂³×C₈	1	2	yes	—
209	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
210	C₂×D₁₃	—	2	8	no	—
211	C₂×D₁₃	—	4	8	no	—
212	C₂×D₁₃	C₂³×C₈	1	8	yes	—
213	C₄×C₁₃	C₂³×C₈	1	2	yes	—
214	C₄×C₁₃	C₂³×C₈	1	2	yes	—
215	C₄×C₁₃	C₂³×C₈	1	2	yes	—
216	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
217	C₄×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
218	Dic₁₃	C₂³×C₈	1	8	yes	—
219	C₂×#41	—	13	2	no	—
220	C₂×#41	—	13	2	no	—
221	C₂×#41	—	13	8	no	—
222	C₂×#41	—	13	2	no	—
223	C₂×#41	—	13	2	no	—
224	C₂×#41	—	13	8	no	—
225	C₂²×Q₈	—	13	1	no	—
226	C₂²×D₄	—	13	2	no	—
227	C₂²×D₄	—	13	1	no	—
228	C₂³×C₄	—	13	2	no	—
229	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
230	#131	—	13	8	no	—
231	#131	—	13	8	no	—
232	#131	—	13	16	no	—
233	#131	—	13	16	no	—
234	#131	—	13	8	no	—
235	#131	—	13	8	no	—
236	C₂×M₁₆	—	13	2	no	—
237	C₂×M₁₆	—	13	2	no	—
238	C₂×M₁₆	—	13	8	no	—
239	C₂×M₁₆	—	13	4	no	—
240	C₂×M₁₆	—	13	4	no	—
241	C₂×M₁₆	—	13	16	no	—
242	C₂²×C₈	—	13	2	no	—
243	C₂²×C₈	—	13	8	no	—
244	C₂²×C₈	—	13	4	no	—
245	C₂²×C₈	—	13	8	no	—
246	C₂²×C₈	—	13	4	no	—
247	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
248	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
249	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
250	C₂²×C₈	C₄×D₁₃	1	4	yes	—
251	C₂²×C₈	C₂²×D₁₃	1	4	yes	—
252	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
253	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
254	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
255	M₃₂	—	13	8	no	—
256	M₃₂	—	13	8	no	—
257	M₃₂	—	13	32	no	—
258	M₃₂	C₂²×D₁₃	1	8	yes	—
259	M₃₂	C₂²×D₁₃	1	8	yes	complemented
260	C₂×C₁₆	—	13	8	no	—
261	C₂×C₁₆	—	13	4	no	—
262	C₂×C₁₆	—	13	32	no	—
263	C₂×C₁₆	C₂²×D₁₃	1	4	yes	—
264	C₂×C₁₆	C₂²×D₁₃	1	8	yes	complemented
265	C₂×C₁₃	—	2	2	no	—
266	C₂×C₁₃	—	2	2	no	—
267	C₂×C₁₃	—	2	2	no	—
268	C₂×C₁₃	#3407	1	2	yes	complemented
269	C₂×C₁₃	C₂⁴×C₈	1	1	yes	characteristic
270	D₁₃	—	2	8	no	—
271	C₂⁴	—	13	2	no	—
272	C₂⁴	C₈×D₁₃	1	1	yes	characteristic
273	#41	—	13	8	no	—
274	#41	—	13	8	no	—
275	#41	—	13	16	no	—
276	#41	—	13	16	no	—
277	#41	—	13	8	no	—
278	#41	—	13	8	no	—
279	C₂×Q₈	—	13	8	no	—
280	C₂×Q₈	—	13	2	no	—
281	C₂×Q₈	—	13	2	no	—
282	C₂×D₄	—	13	4	no	—
283	C₂×D₄	—	13	4	no	—
284	C₂×D₄	—	13	16	no	—
285	C₂×D₄	—	13	2	no	—
286	C₂×D₄	—	13	2	no	—
287	C₂×D₄	—	13	8	no	—
288	C₂²×C₄	—	13	2	no	—
289	C₂²×C₄	—	13	4	no	—
290	C₂²×C₄	—	13	8	no	—
291	C₂²×C₄	—	13	8	no	—
292	C₂²×C₄	—	13	4	no	—
293	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
294	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
295	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
296	C₂²×C₄	C₈×D₁₃	1	4	yes	—
297	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₄×D₁₃	1	4	yes	—
299	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
301	M₁₆	—	13	8	no	—
302	M₁₆	—	13	8	no	—
303	M₁₆	—	13	16	no	—
304	M₁₆	—	13	16	no	—
305	C₂×C₈	—	13	8	no	—
306	C₂×C₈	—	13	4	no	—
307	C₂×C₈	—	13	16	no	—
308	C₂×C₈	—	13	8	no	—
309	C₂×C₈	—	13	8	no	—
310	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
311	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
312	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
313	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
314	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
315	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
316	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
317	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
318	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
319	C₂×C₈	C₂³×D₁₃	1	2	yes	—
320	C₂×C₈	C₂³×D₁₃	1	2	yes	—
321	C₂×C₈	C₂³×D₁₃	1	2	yes	—
322	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
323	C₁₆	—	13	8	no	—
324	C₁₆	C₂³×D₁₃	1	8	yes	—
325	C₁₃	C₂×#3407	1	1	yes	characteristic, complemented, Sylow
326	C₂³	—	4	2	no	—
327	C₂³	—	13	4	no	—
328	C₂³	—	13	8	no	—
329	C₂³	—	52	4	no	—
330	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
331	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
332	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
333	C₂³	C₂×C₈×D₁₃	1	4	yes	—
334	Q₈	—	13	8	no	—
335	Q₈	—	13	8	no	—
336	D₄	—	13	16	no	—
337	D₄	—	13	16	no	—
338	D₄	—	13	8	no	—
339	D₄	—	13	8	no	—
340	C₂×C₄	—	13	8	no	—
341	C₂×C₄	—	13	4	no	—
342	C₂×C₄	—	13	16	no	—
343	C₂×C₄	—	13	8	no	—
344	C₂×C₄	—	13	8	no	—
345	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
346	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
347	C₂×C₄	C₂×C₈×D₁₃	1	4	yes	—
348	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
349	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
350	C₂×C₄	C₂×C₈×D₁₃	1	4	yes	—
351	C₂×C₄	C₂×C₈×D₁₃	1	4	yes	—
352	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
353	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
354	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
355	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
356	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
357	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
358	C₈	—	13	8	no	—
359	C₈	C₂²×C₄×D₁₃	1	2	yes	—
360	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
361	C₈	C₂²×C₄×D₁₃	1	2	yes	—
362	C₈	C₂²×C₄×D₁₃	1	2	yes	—
363	C₈	C₂⁴×D₁₃	1	1	yes	characteristic
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	13	8	no	—
369	C₂²	—	26	8	no	—
370	C₂²	—	52	8	no	—
371	C₂²	C₂²×C₈×D₁₃	1	2	yes	—
372	C₂²	C₂²×C₈×D₁₃	1	2	yes	—
373	C₂²	C₂²×C₈×D₁₃	1	2	yes	—
374	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
375	C₄	—	13	8	no	—
376	C₄	C₂²×C₈×D₁₃	1	2	yes	—
377	C₄	C₂²×C₈×D₁₃	1	1	yes	characteristic
378	C₄	C₂²×C₈×D₁₃	1	2	yes	—
379	C₄	C₂²×C₈×D₁₃	1	2	yes	—
380	C₄	C₂³×C₄×D₁₃	1	1	yes	characteristic
381	C₂	—	2	2	no	—
382	C₂	—	2	2	no	—
383	C₂	—	2	2	no	—
384	C₂	—	26	8	no	—
385	C₂	#13127938	1	2	yes	direct product factor
386	C₂	C₂³×C₈×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂³×D₁₃
commutator	C₂×C₁₃	C₂⁴×C₈
Frattini	C₈	C₂⁴×D₁₃
Fitting	C₂²×C₁₃×M₃₂	C₂
socle	C₂²×C₁₃	C₂³×C₈
prime radical	C₂²×#6127	C₄
cosocle	C₈×C₁₃	C₂⁵
hypercenter	C₂²×M₃₂	D₁₃
hypocenter	C₁₃	C₂×#3407
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×M₃₂

Complements

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

N	H ≅ G/N	type
2. #13127938	C₂	direct (N × H)
3. C₂×#11718568	C₂	semidirect
4. C₂×#11718562	C₂	semidirect
5. C₂²×#88052	C₂	semidirect
6. C₂×D₁₃×M₃₂	C₂	semidirect
7. C₂²×C₁₃×M₃₂	C₂	semidirect
20. C₂×C₁₃×M₃₂	C₂²	semidirect
21. C₂×C₁₃×M₃₂	C₂²	semidirect
22. C₂²×C₁₃×C₁₆	C₂²	semidirect
24. C₂×#88052	C₂²	semidirect
25. C₂×#88052	C₂²	semidirect
26. C₂²×#6090	C₂²	semidirect
27. #11718568	C₂²	semidirect
28. D₁₃×M₃₂	C₂²	semidirect
29. #11718562	C₂²	semidirect
30. C₂×#88038	C₂²	semidirect
31. C₂×C₁₆×D₁₃	C₂²	semidirect
69. C₁₃×M₃₂	C₂³	semidirect
71. C₂×C₁₃×C₁₆	C₂³	semidirect
73. #88052	C₂³	semidirect
75. C₂×#6090	C₂³	semidirect
76. #88038	C₂³	semidirect
77. C₁₆×D₁₃	C₂³	semidirect
139. C₂²×M₃₂	D₁₃	semidirect
197. C₂×M₃₂	C₂×D₁₃	semidirect
198. C₂×M₃₂	C₂×D₁₃	semidirect
201. C₂²×C₁₆	C₂×D₁₃	semidirect
259. M₃₂	C₂²×D₁₃	semidirect
264. C₂×C₁₆	C₂²×D₁₃	semidirect
268. C₂×C₁₃	#3407	semidirect
325. C₁₃	C₂×#3407	semidirect
385. C₂	#13127938	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×#88155	2
#13127938	2
C₂×#11718568	2
C₂×#11718562	2
C₂²×#88052	2
C₂×D₁₃×M₃₂	2
C₂²×C₁₃×M₃₂	2
C₂×#3407	13

Subgroups — C2×#13127938 #16769387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13127938 #16769387