Subgroups — C₄×D₁₃×M₃₂ #16015546

Order 3328.

918 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃×M₃₂	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
3	C₄×#88052	C₂	1	1	yes	maximal, characteristic, complemented
4	#13116429	C₂	1	2	yes	maximal, complemented
5	M₃₂×Dic₁₃	C₂	1	2	yes	maximal, complemented
6	C₄×#88038	C₂	1	2	yes	maximal, complemented
7	D₁₃×#346	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₆×D₁₃	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₈×D₁₃	C₄	1	1	yes	characteristic
11	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₄²×D₁₃	C₄	1	1	yes	characteristic
13	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
16	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
17	C₂×#88052	C₂²	1	2	yes	—
18	C₂×C₄×#1055	C₄	1	1	yes	characteristic
19	D₁₃×M₃₂	C₄	1	16	yes	direct product factor
20	C₂×#88038	C₂²	1	4	yes	—
21	C₂×C₁₆×D₁₃	C₂²	1	4	yes	—
22	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
23	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
24	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
25	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
26	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
27	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
28	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
29	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#346	C₂²	1	2	yes	complemented
31	C₄×C₁₃×C₁₆	C₂²	1	2	yes	complemented
32	#11718094	C₂²	1	4	yes	complemented
33	C₁₆×Dic₁₃	C₂²	1	4	yes	complemented
34	#11718053	C₂²	1	2	yes	complemented
35	C₄×#6090	C₂²	1	2	yes	complemented
36	C₂²×C₄×D₁₃	C₈	1	2	yes	—
37	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
40	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄×Dic₁₃	C₈	1	2	yes	—
42	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
44	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₁₃	C₈	1	8	yes	—
46	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₁₃	C₂×C₄	1	8	yes	—
49	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
54	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
55	C₄²×D₁₃	C₈	1	2	yes	—
56	C₄²×D₁₃	C₈	1	2	yes	—
57	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
61	C₁₃×M₃₂	C₂×C₄	1	8	yes	complemented
62	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
63	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
64	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
65	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
68	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
69	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
70	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
71	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
72	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
73	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
74	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
75	#88052	C₂×C₄	1	8	yes	complemented
76	C₂×#6090	C₂³	1	4	yes	—
77	C₄×#1055	C₂×C₄	1	1	yes	characteristic
78	C₄×#1055	C₂×C₄	1	1	yes	characteristic
79	C₄×#1055	C₂×C₄	1	1	yes	characteristic
80	C₄×#1055	C₂×C₄	1	1	yes	characteristic
81	#88038	C₂×C₄	1	16	yes	complemented
82	C₁₆×D₁₃	C₂×C₄	1	16	yes	complemented
83	C₂×C₄×M₃₂	—	13	1	no	maximal, Sylow
84	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
86	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
88	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
89	C₂×C₄×D₁₃	—	2	8	no	—
90	C₂×C₄×D₁₃	C₄²	1	4	yes	—
91	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
92	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
93	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
94	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
95	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
96	C₂×C₄×D₁₃	C₂×C₈	1	4	yes	—
97	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
98	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
101	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
103	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
106	C₄²×C₁₃	C₂×C₈	1	2	yes	—
107	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
110	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
111	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
112	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
113	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
114	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×#1055	C₄²	1	4	yes	—
117	C₂×#1055	C₂×C₈	1	4	yes	—
118	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
119	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
120	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
121	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
122	C₈×D₁₃	C₄²	1	4	yes	—
123	C₈×D₁₃	C₄²	1	4	yes	—
124	C₈×D₁₃	C₂×C₈	1	4	yes	—
125	C₈×D₁₃	C₂×C₈	1	4	yes	—
126	C₈×D₁₃	C₂×C₈	1	4	yes	—
127	C₈×D₁₃	C₂×C₈	1	4	yes	—
128	C₈×D₁₃	C₂²×C₄	1	4	yes	—
129	C₈×D₁₃	C₂²×C₄	1	4	yes	—
130	C₁₃×C₁₆	C₂²×C₄	1	8	yes	complemented
131	#6090	C₂²×C₄	1	8	yes	complemented
132	C₂²×M₃₂	—	13	2	no	—
133	C₂²×C₄×C₈	—	13	1	no	—
134	C₄×M₃₂	—	13	2	no	—
135	C₄×M₃₂	—	13	1	no	—
136	C₄×M₃₂	—	13	2	no	—
137	C₄×M₃₂	—	13	2	no	—
138	C₄×M₃₂	D₁₃	1	1	yes	characteristic, direct product factor
139	C₂×#346	—	13	2	no	—
140	C₂×C₄×C₁₆	—	13	2	no	—
141	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
142	C₂²×D₁₃	—	2	4	no	—
143	C₂²×D₁₃	C₄×C₈	1	4	yes	—
144	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
145	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
146	C₂×C₄×C₁₃	—	2	4	no	—
147	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
148	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
149	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
150	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
152	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
153	C₂×Dic₁₃	—	2	4	no	—
154	C₂×Dic₁₃	C₄×C₈	1	4	yes	—
155	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
156	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
157	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
158	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
159	C₄×D₁₃	—	2	4	no	—
160	C₄×D₁₃	—	2	4	no	—
161	C₄×D₁₃	—	2	4	no	—
162	C₄×D₁₃	C₄×C₈	1	4	yes	—
163	C₄×D₁₃	C₄×C₈	1	4	yes	—
164	C₄×D₁₃	M₃₂	1	8	yes	direct product factor
165	C₄×D₁₃	C₂×C₄²	1	2	yes	—
166	C₄×D₁₃	C₂×C₄²	1	2	yes	—
167	C₄×D₁₃	C₂²×C₈	1	2	yes	—
168	C₄×D₁₃	C₂²×C₈	1	2	yes	—
169	C₈×C₁₃	C₂×C₄²	1	2	yes	—
170	C₈×C₁₃	C₂²×C₈	1	2	yes	—
171	C₈×C₁₃	C₂²×C₈	1	2	yes	—
172	C₈×C₁₃	C₂³×C₄	1	2	yes	—
173	#1055	C₂×C₄²	1	2	yes	—
174	#1055	C₂×C₄²	1	2	yes	—
175	#1055	C₂²×C₈	1	2	yes	—
176	#1055	C₂²×C₈	1	2	yes	—
177	C₂³×C₈	—	13	1	no	—
178	C₂³×C₈	—	13	1	no	—
179	C₂²×C₄²	—	13	1	no	—
180	C₂×M₃₂	—	13	2	no	—
181	C₂×M₃₂	—	13	16	no	—
182	C₂×M₃₂	—	13	4	no	—
183	C₂×M₃₂	C₂×D₁₃	1	2	yes	—
184	C₂²×C₁₆	—	13	4	no	—
185	C₂×C₄×C₈	—	13	1	no	—
186	C₂×C₄×C₈	—	13	1	no	—
187	C₂×C₄×C₈	—	13	1	no	—
188	C₂×C₄×C₈	—	13	1	no	—
189	C₂×C₄×C₈	—	13	1	no	—
190	C₂×C₄×C₈	—	13	1	no	—
191	C₂×C₄×C₈	—	13	1	no	—
192	C₂×C₄×C₈	—	13	1	no	—
193	C₂×C₄×C₈	—	13	1	no	—
194	C₂×C₄×C₈	—	13	1	no	—
195	C₂×C₄×C₈	—	13	1	no	—
196	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
197	#346	—	13	4	no	—
198	#346	—	13	2	no	—
199	#346	C₂×D₁₃	1	2	yes	complemented
200	C₄×C₁₆	—	13	4	no	—
201	C₄×C₁₆	—	13	2	no	—
202	C₄×C₁₆	C₂×D₁₃	1	2	yes	complemented
203	C₂²×C₁₃	—	2	2	no	—
204	C₂²×C₁₃	C₂×C₄×C₈	1	2	yes	—
205	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
206	C₂×D₁₃	—	2	2	no	—
207	C₂×D₁₃	—	2	8	no	—
208	C₂×D₁₃	C₂×C₄×C₈	1	2	yes	—
209	C₂×D₁₃	C₂×C₄×C₈	1	2	yes	—
210	C₂×D₁₃	C₂×M₃₂	1	4	yes	—
211	C₄×C₁₃	—	2	2	no	—
212	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
213	C₄×C₁₃	C₂×M₃₂	1	4	yes	complemented
214	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
215	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
216	Dic₁₃	—	2	2	no	—
217	Dic₁₃	C₂×C₄×C₈	1	2	yes	—
218	Dic₁₃	C₂×C₄×C₈	1	2	yes	—
219	Dic₁₃	C₂×M₃₂	1	4	yes	complemented
220	C₂³×C₄	—	13	1	no	—
221	C₂³×C₄	—	13	2	no	—
222	C₂²×C₈	—	13	1	no	—
223	C₂²×C₈	—	13	1	no	—
224	C₂²×C₈	—	13	8	no	—
225	C₂²×C₈	—	13	1	no	—
226	C₂²×C₈	—	13	1	no	—
227	C₂²×C₈	—	13	1	no	—
228	C₂²×C₈	—	13	1	no	—
229	C₂²×C₈	—	13	1	no	—
230	C₂²×C₈	—	13	1	no	—
231	C₂²×C₈	—	13	8	no	—
232	C₂²×C₈	—	13	1	no	—
233	C₂²×C₈	—	13	1	no	—
234	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
235	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
236	C₂×C₄²	—	13	2	no	—
237	C₂×C₄²	—	13	1	no	—
238	C₂×C₄²	—	13	2	no	—
239	C₂×C₄²	—	13	2	no	—
240	C₂×C₄²	—	13	1	no	—
241	C₂×C₄²	—	13	1	no	—
242	C₂×C₄²	—	13	1	no	—
243	C₂×C₄²	—	13	1	no	—
244	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
245	M₃₂	—	13	8	no	—
246	M₃₂	—	13	16	no	—
247	M₃₂	C₄×D₁₃	1	8	yes	direct product factor
248	C₂×C₁₆	—	13	4	no	—
249	C₂×C₁₆	—	13	16	no	—
250	C₂×C₁₆	C₂²×D₁₃	1	4	yes	—
251	C₄×C₈	—	13	1	no	—
252	C₄×C₈	—	13	1	no	—
253	C₄×C₈	—	13	1	no	—
254	C₄×C₈	—	13	1	no	—
255	C₄×C₈	—	13	1	no	—
256	C₄×C₈	—	13	1	no	—
257	C₄×C₈	—	13	1	no	—
258	C₄×C₈	—	13	1	no	—
259	C₄×C₈	—	13	1	no	—
260	C₄×C₈	—	13	1	no	—
261	C₄×C₈	—	13	1	no	—
262	C₄×C₈	—	13	1	no	—
263	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
264	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
265	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
266	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
267	C₂×C₁₃	—	2	2	no	—
268	C₂×C₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
269	C₂×C₁₃	C₂²×M₃₂	1	2	yes	—
270	D₁₃	—	2	2	no	—
271	D₁₃	C₄×M₃₂	1	4	yes	direct product factor
272	C₂⁴	—	13	1	no	—
273	C₂²×C₄	—	13	1	no	—
274	C₂²×C₄	—	13	4	no	—
275	C₂²×C₄	—	13	2	no	—
276	C₂²×C₄	—	13	1	no	—
277	C₂²×C₄	—	13	1	no	—
278	C₂²×C₄	—	13	4	no	—
279	C₂²×C₄	—	13	1	no	—
280	C₂²×C₄	—	13	1	no	—
281	C₂²×C₄	—	13	2	no	—
282	C₂²×C₄	—	13	2	no	—
283	C₂²×C₄	—	13	2	no	—
284	C₂²×C₄	—	13	2	no	—
285	C₂²×C₄	—	26	8	no	—
286	C₂²×C₄	C₈×D₁₃	1	2	yes	—
287	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
288	C₂×C₈	—	13	4	no	—
289	C₂×C₈	—	13	4	no	—
290	C₂×C₈	—	13	1	no	—
291	C₂×C₈	—	13	1	no	—
292	C₂×C₈	—	13	1	no	—
293	C₂×C₈	—	13	1	no	—
294	C₂×C₈	—	13	4	no	—
295	C₂×C₈	—	13	4	no	—
296	C₂×C₈	—	13	4	no	—
297	C₂×C₈	—	13	4	no	—
298	C₂×C₈	—	13	4	no	—
299	C₂×C₈	—	13	4	no	—
300	C₂×C₈	—	13	4	no	—
301	C₂×C₈	—	13	4	no	—
302	C₂×C₈	C₈×D₁₃	1	4	yes	—
303	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
304	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
305	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
306	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
307	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
308	C₄²	—	13	2	no	—
309	C₄²	—	13	2	no	—
310	C₄²	—	13	2	no	—
311	C₄²	—	13	2	no	—
312	C₄²	—	13	2	no	—
313	C₄²	—	13	1	no	—
314	C₄²	—	13	1	no	—
315	C₄²	C₈×D₁₃	1	2	yes	—
316	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
317	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
318	C₁₆	—	13	8	no	—
319	C₁₆	C₂×C₄×D₁₃	1	8	yes	complemented
320	C₁₃	C₂×C₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
321	C₂³	—	13	1	no	—
322	C₂³	—	13	1	no	—
323	C₂³	—	13	4	no	—
324	C₂³	—	26	4	no	—
325	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	13	1	no	—
328	C₂×C₄	—	13	1	no	—
329	C₂×C₄	—	13	2	no	—
330	C₂×C₄	—	13	4	no	—
331	C₂×C₄	—	13	2	no	—
332	C₂×C₄	—	13	2	no	—
333	C₂×C₄	—	13	2	no	—
334	C₂×C₄	—	13	2	no	—
335	C₂×C₄	—	13	8	no	—
336	C₂×C₄	—	13	4	no	—
337	C₂×C₄	—	13	4	no	—
338	C₂×C₄	—	13	2	no	—
339	C₂×C₄	—	26	4	no	—
340	C₂×C₄	—	26	4	no	—
341	C₂×C₄	—	26	4	no	—
342	C₂×C₄	—	26	4	no	—
343	C₂×C₄	C₄²×D₁₃	1	2	yes	—
344	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
345	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
346	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
347	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
348	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
349	C₈	—	13	2	no	—
350	C₈	—	13	2	no	—
351	C₈	—	13	2	no	—
352	C₈	—	13	2	no	—
353	C₈	C₄²×D₁₃	1	2	yes	—
354	C₈	C₂×C₈×D₁₃	1	2	yes	—
355	C₈	C₂×C₈×D₁₃	1	2	yes	—
356	C₈	C₂²×C₄×D₁₃	1	2	yes	—
357	C₂²	—	2	2	no	—
358	C₂²	—	13	2	no	—
359	C₂²	—	13	4	no	—
360	C₂²	—	13	2	no	—
361	C₂²	—	26	8	no	—
362	C₂²	—	26	2	no	—
363	C₂²	C₄×C₈×D₁₃	1	2	yes	—
364	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
365	C₄	—	2	2	no	—
366	C₄	—	13	2	no	—
367	C₄	—	13	2	no	—
368	C₄	—	13	4	no	—
369	C₄	—	26	2	no	—
370	C₄	C₄×C₈×D₁₃	1	2	yes	—
371	C₄	D₁₃×M₃₂	1	4	yes	direct product factor
372	C₄	C₂×C₄²×D₁₃	1	1	yes	characteristic
373	C₄	C₂²×C₈×D₁₃	1	1	yes	characteristic
374	C₂	—	2	2	no	—
375	C₂	—	13	4	no	—
376	C₂	—	26	2	no	—
377	C₂	C₂×C₄×C₈×D₁₃	1	1	yes	characteristic
378	C₂	C₂×D₁₃×M₃₂	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₄×#88052	C₂	semidirect
4. #13116429	C₂	semidirect
5. M₃₂×Dic₁₃	C₂	semidirect
6. C₄×#88038	C₂	semidirect
7. D₁₃×#346	C₂	semidirect
8. C₄×C₁₆×D₁₃	C₂	semidirect
9. C₄×C₁₃×M₃₂	C₂	semidirect
19. D₁₃×M₃₂	C₄	direct (N × H)
30. C₁₃×#346	C₂²	semidirect
31. C₄×C₁₃×C₁₆	C₂²	semidirect
32. #11718094	C₂²	semidirect
33. C₁₆×Dic₁₃	C₂²	semidirect
34. #11718053	C₂²	semidirect
35. C₄×#6090	C₂²	semidirect
61. C₁₃×M₃₂	C₂×C₄	semidirect
75. #88052	C₂×C₄	semidirect
81. #88038	C₂×C₄	semidirect
82. C₁₆×D₁₃	C₂×C₄	semidirect
130. C₁₃×C₁₆	C₂²×C₄	semidirect
131. #6090	C₂²×C₄	semidirect
138. C₄×M₃₂	D₁₃	direct (N × H)
164. C₄×D₁₃	M₃₂	direct (N × H)
199. #346	C₂×D₁₃	semidirect
202. C₄×C₁₆	C₂×D₁₃	semidirect
213. C₄×C₁₃	C₂×M₃₂	semidirect
219. Dic₁₃	C₂×M₃₂	semidirect
247. M₃₂	C₄×D₁₃	direct (N × H)
271. D₁₃	C₄×M₃₂	direct (N × H)
319. C₁₆	C₂×C₄×D₁₃	semidirect
320. C₁₃	C₂×C₄×M₃₂	semidirect
371. C₄	D₁₃×M₃₂	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×D₁₃×M₃₂	2
C₂×C₄×C₈×D₁₃	2
C₄×#88052	2
#13116429	2
M₃₂×Dic₁₃	2
C₄×#88038	2
D₁₃×#346	2
C₄×C₁₆×D₁₃	2
C₄×C₁₃×M₃₂	2
C₂×C₄×M₃₂	13

Subgroups — C4×D13×M32 #16015546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₁₃×M₃₂ #16015546