Subgroups — C₂×C₁₃×#3140 #15746954

Order 3328.

2246 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3140	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#489	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×#488	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#419	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#418	C₂	1	2	yes	maximal
8	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
12	C₁₃×#533	—	2	4	no	—
13	C₁₃×#533	C₂²	1	8	yes	complemented
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
15	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
16	C₂×C₁₃×#124	—	2	2	no	—
17	C₂×C₁₃×#124	—	2	4	no	—
18	C₂×C₁₃×#124	C₂²	1	2	yes	—
19	C₂×C₁₃×#124	C₂²	1	2	yes	—
20	C₂×C₁₃×#124	C₂²	1	8	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
22	C₂×C₄×Q₈×C₁₃	—	2	2	no	—
23	C₂×C₁₃×#117	C₂²	1	2	yes	—
24	C₂²×C₁₃×C₂²⋊C₄	—	2	2	no	—
25	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#489	C₂²	1	32	yes	complemented
27	C₁₃×#488	C₂²	1	32	yes	complemented
28	C₁₃×#419	C₂²	1	16	yes	complemented
29	C₁₃×#418	C₂²	1	16	yes	—
30	C₂×C₁₃×#103	C₂²	1	8	yes	complemented
31	C₂×C₁₃×#102	C₂²	1	8	yes	—
32	C₄×C₁₃×M₁₆	C₂²	1	8	yes	complemented
33	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
34	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	complemented
35	C₂⁵×C₁₃	—	2	1	no	—
36	C₂²×Q₈×C₁₃	—	2	2	no	—
37	C₂²×Q₈×C₁₃	—	2	2	no	—
38	C₂²×Q₈×C₁₃	—	2	1	no	—
39	C₂²×Q₈×C₁₃	—	2	8	no	—
40	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
41	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
42	C₂²×D₄×C₁₃	—	2	2	no	—
43	C₂²×D₄×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	—	2	8	no	—
45	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
46	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
47	C₂³×C₄×C₁₃	—	2	1	no	—
48	C₂³×C₄×C₁₃	D₄	1	2	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂×C₁₃×M₁₆	—	2	8	no	—
51	C₂×C₁₃×M₁₆	C₂³	1	8	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
53	C₁₃×C₄⋊Q₈	—	2	4	no	—
54	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
55	C₁₃×#125	—	2	4	no	—
56	C₁₃×#125	C₂³	1	8	yes	complemented
57	C₁₃×#124	—	2	16	no	—
58	C₁₃×#124	—	2	4	no	—
59	C₁₃×#124	—	2	4	no	—
60	C₁₃×#124	C₂³	1	8	yes	—
61	C₁₃×#124	C₂³	1	8	yes	—
62	C₁₃×C₂²⋊Q₈	—	2	16	no	—
63	C₄×Q₈×C₁₃	—	2	16	no	—
64	C₁₃×#117	—	2	4	no	—
65	C₁₃×#117	C₂³	1	8	yes	—
66	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
73	C₂×C₄²×C₁₃	—	2	2	no	—
74	C₂×C₄²×C₁₃	D₄	1	2	yes	—
75	C₂×C₄²×C₁₃	D₄	1	4	yes	—
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
79	C₁₃×#103	C₂³	1	32	yes	complemented
80	C₁₃×#102	C₂³	1	32	yes	—
81	C₁₃×#97	C₂³	1	8	yes	complemented
82	C₄×C₈×C₁₃	C₂³	1	8	yes	complemented
83	C₂×#3140	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂⁴×C₁₃	—	2	4	no	—
85	C₂⁴×C₁₃	—	2	2	no	—
86	C₂⁴×C₁₃	—	4	8	no	—
87	C₂⁴×C₁₃	—	4	4	no	—
88	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
89	C₂×Q₈×C₁₃	—	2	8	no	—
90	C₂×Q₈×C₁₃	—	2	4	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	2	8	no	—
93	C₂×Q₈×C₁₃	—	2	16	no	—
94	C₂×Q₈×C₁₃	—	4	8	no	—
95	C₂×Q₈×C₁₃	—	4	8	no	—
96	C₂×Q₈×C₁₃	—	4	4	no	—
97	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
98	C₂×D₄×C₁₃	—	2	4	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	8	no	—
101	C₂×D₄×C₁₃	—	2	16	no	—
102	C₂×D₄×C₁₃	—	4	8	no	—
103	C₂×D₄×C₁₃	—	4	4	no	—
104	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
105	C₂²×C₄×C₁₃	—	2	4	no	—
106	C₂²×C₄×C₁₃	—	2	4	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	4	4	no	—
109	C₂²×C₄×C₁₃	—	4	4	no	—
110	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	#41	1	8	yes	—
116	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₁₃×M₁₆	—	2	16	no	—
119	C₂×C₈×C₁₃	—	2	8	no	—
120	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
121	C₁₃×C₄⋊C₄	—	2	16	no	—
122	C₁₃×C₄⋊C₄	—	2	8	no	—
123	C₁₃×C₄⋊C₄	—	2	4	no	—
124	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
125	C₁₃×C₂²⋊C₄	—	2	8	no	—
126	C₁₃×C₂²⋊C₄	—	2	16	no	—
127	C₁₃×C₂²⋊C₄	—	2	16	no	—
128	C₄²×C₁₃	—	2	8	no	—
129	C₄²×C₁₃	C₂×D₄	1	8	yes	—
130	C₄²×C₁₃	C₂×D₄	1	2	yes	—
131	C₄²×C₁₃	C₂×D₄	1	2	yes	—
132	C₄²×C₁₃	C₂⁴	1	2	yes	—
133	C₄²×C₁₃	C₂⁴	1	2	yes	—
134	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
135	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic
136	#3140	C₂×C₁₃	1	16	yes	direct product factor
137	C₂×#489	C₂×C₁₃	1	4	yes	complemented
138	C₂×#488	C₂×C₁₃	1	4	yes	complemented
139	C₂×#419	C₂×C₁₃	1	2	yes	complemented
140	C₂×#418	C₂×C₁₃	1	2	yes	—
141	C₂×C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
142	C₂³×C₁₃	—	2	4	no	—
143	C₂³×C₁₃	—	2	4	no	—
144	C₂³×C₁₃	—	4	16	no	—
145	C₂³×C₁₃	—	4	8	no	—
146	C₂³×C₁₃	—	4	4	no	—
147	C₂³×C₁₃	—	4	8	no	—
148	C₂³×C₁₃	—	8	16	no	—
149	C₂³×C₁₃	#124	1	4	yes	—
150	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
151	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
152	Q₈×C₁₃	—	2	8	no	—
153	Q₈×C₁₃	—	4	16	no	—
154	Q₈×C₁₃	—	4	8	no	—
155	Q₈×C₁₃	—	4	4	no	—
156	D₄×C₁₃	—	2	8	no	—
157	D₄×C₁₃	—	4	8	no	—
158	D₄×C₁₃	—	4	4	no	—
159	C₂×C₄×C₁₃	—	2	4	no	—
160	C₂×C₄×C₁₃	—	2	4	no	—
161	C₂×C₄×C₁₃	—	2	8	no	—
162	C₂×C₄×C₁₃	—	2	4	no	—
163	C₂×C₄×C₁₃	—	4	8	no	—
164	C₂×C₄×C₁₃	—	4	8	no	—
165	C₂×C₄×C₁₃	—	4	4	no	—
166	C₂×C₄×C₁₃	—	4	8	no	—
167	C₂×C₄×C₁₃	#124	1	8	yes	—
168	C₂×C₄×C₁₃	#124	1	4	yes	—
169	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
170	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
171	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
172	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
174	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
175	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
176	C₈×C₁₃	—	2	8	no	—
177	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
178	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
179	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
180	#533	—	2	4	no	—
181	#533	C₂²×C₁₃	1	8	yes	complemented
182	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
183	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
184	C₂×#124	—	2	2	no	—
185	C₂×#124	—	2	4	no	—
186	C₂×#124	C₂²×C₁₃	1	2	yes	—
187	C₂×#124	C₂²×C₁₃	1	2	yes	—
188	C₂×#124	C₂²×C₁₃	1	8	yes	—
189	C₂×C₂²⋊Q₈	—	2	2	no	—
190	C₂×C₄×Q₈	—	2	2	no	—
191	C₂×#117	C₂²×C₁₃	1	2	yes	—
192	C₂²×C₂²⋊C₄	—	2	2	no	—
193	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
194	#489	C₂²×C₁₃	1	32	yes	complemented
195	#488	C₂²×C₁₃	1	32	yes	complemented
196	#419	C₂²×C₁₃	1	16	yes	complemented
197	#418	C₂²×C₁₃	1	16	yes	—
198	C₂×#103	C₂²×C₁₃	1	8	yes	complemented
199	C₂×#102	C₂²×C₁₃	1	8	yes	—
200	C₄×M₁₆	C₂²×C₁₃	1	8	yes	complemented
201	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
202	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	complemented
203	C₂²×C₁₃	—	2	8	no	—
204	C₂²×C₁₃	—	2	4	no	—
205	C₂²×C₁₃	—	4	4	no	—
206	C₂²×C₁₃	—	4	8	no	—
207	C₂²×C₁₃	—	8	16	no	—
208	C₂²×C₁₃	—	8	8	no	—
209	C₂²×C₁₃	C₂×#124	1	4	yes	—
210	C₂²×C₁₃	C₂×#124	1	2	yes	—
211	C₂²×C₁₃	#575	1	4	yes	—
212	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
213	C₄×C₁₃	—	2	4	no	—
214	C₄×C₁₃	—	2	4	no	—
215	C₄×C₁₃	—	4	4	no	—
216	C₄×C₁₃	—	4	8	no	—
217	C₄×C₁₃	C₂×#124	1	4	yes	—
218	C₄×C₁₃	C₂×#124	1	2	yes	—
219	C₄×C₁₃	C₂²×#41	1	2	yes	—
220	C₂⁵	—	2	1	no	—
221	C₂²×Q₈	—	2	2	no	—
222	C₂²×Q₈	—	2	1	no	—
223	C₂²×Q₈	—	2	2	no	—
224	C₂²×Q₈	—	2	8	no	—
225	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
226	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
227	C₂²×D₄	—	2	1	no	—
228	C₂²×D₄	—	2	2	no	—
229	C₂²×D₄	—	2	8	no	—
230	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
231	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
232	C₂³×C₄	—	2	1	no	—
233	C₂³×C₄	D₄×C₁₃	1	2	yes	—
234	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
235	C₂×M₁₆	—	2	8	no	—
236	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
237	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
238	C₄⋊Q₈	—	2	4	no	—
239	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
240	#125	—	2	4	no	—
241	#125	C₂³×C₁₃	1	8	yes	complemented
242	#124	—	2	16	no	—
243	#124	—	2	4	no	—
244	#124	—	2	4	no	—
245	#124	C₂³×C₁₃	1	8	yes	—
246	#124	C₂³×C₁₃	1	8	yes	—
247	C₂²⋊Q₈	—	2	16	no	—
248	C₄×Q₈	—	2	16	no	—
249	#117	—	2	4	no	—
250	#117	C₂³×C₁₃	1	8	yes	—
251	C₂×C₄⋊C₄	—	2	4	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₂²⋊C₄	—	2	4	no	—
256	C₂×C₂²⋊C₄	—	2	4	no	—
257	C₂×C₂²⋊C₄	—	2	16	no	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	D₄×C₁₃	1	2	yes	—
260	C₂×C₄²	D₄×C₁₃	1	4	yes	—
261	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
263	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
264	#103	C₂³×C₁₃	1	32	yes	complemented
265	#102	C₂³×C₁₃	1	32	yes	—
266	#97	C₂³×C₁₃	1	8	yes	complemented
267	C₄×C₈	C₂³×C₁₃	1	8	yes	complemented
268	C₂×C₁₃	—	2	4	no	—
269	C₂×C₁₃	—	8	4	no	—
270	C₂×C₁₃	#3140	1	4	yes	direct product factor
271	C₂×C₁₃	C₂²×#124	1	1	yes	characteristic
272	C₂×C₁₃	C₂×#575	1	2	yes	—
273	C₂⁴	—	2	4	no	—
274	C₂⁴	—	2	2	no	—
275	C₂⁴	—	4	8	no	—
276	C₂⁴	—	4	4	no	—
277	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
278	C₂×Q₈	—	2	8	no	—
279	C₂×Q₈	—	2	4	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	2	8	no	—
282	C₂×Q₈	—	2	16	no	—
283	C₂×Q₈	—	4	8	no	—
284	C₂×Q₈	—	4	8	no	—
285	C₂×Q₈	—	4	4	no	—
286	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	8	no	—
290	C₂×D₄	—	2	16	no	—
291	C₂×D₄	—	4	8	no	—
292	C₂×D₄	—	4	4	no	—
293	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	4	4	no	—
298	C₂²×C₄	—	4	4	no	—
299	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
300	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
302	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
304	C₂²×C₄	C₁₃×#41	1	8	yes	—
305	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
306	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
307	M₁₆	—	2	16	no	—
308	C₂×C₈	—	2	8	no	—
309	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
310	C₄⋊C₄	—	2	16	no	—
311	C₄⋊C₄	—	2	8	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
314	C₂²⋊C₄	—	2	8	no	—
315	C₂²⋊C₄	—	2	16	no	—
316	C₂²⋊C₄	—	2	16	no	—
317	C₄²	—	2	8	no	—
318	C₄²	C₂×D₄×C₁₃	1	8	yes	—
319	C₄²	C₂×D₄×C₁₃	1	2	yes	—
320	C₄²	C₂×D₄×C₁₃	1	2	yes	—
321	C₄²	C₂⁴×C₁₃	1	2	yes	—
322	C₄²	C₂⁴×C₁₃	1	2	yes	—
323	C₁₃	C₂×#3140	1	1	yes	characteristic, direct product factor, Sylow
324	C₂³	—	2	4	no	—
325	C₂³	—	2	4	no	—
326	C₂³	—	4	16	no	—
327	C₂³	—	4	8	no	—
328	C₂³	—	4	4	no	—
329	C₂³	—	4	8	no	—
330	C₂³	—	8	16	no	—
331	C₂³	C₁₃×#124	1	4	yes	—
332	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
333	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
334	Q₈	—	2	8	no	—
335	Q₈	—	4	16	no	—
336	Q₈	—	4	8	no	—
337	Q₈	—	4	4	no	—
338	D₄	—	2	8	no	—
339	D₄	—	4	8	no	—
340	D₄	—	4	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	4	8	no	—
346	C₂×C₄	—	4	8	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	8	no	—
349	C₂×C₄	C₁₃×#124	1	8	yes	—
350	C₂×C₄	C₁₃×#124	1	4	yes	—
351	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
352	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
353	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
354	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
355	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
356	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
357	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
358	C₈	—	2	8	no	—
359	C₂²	—	2	4	no	—
360	C₂²	—	2	8	no	—
361	C₂²	—	4	8	no	—
362	C₂²	—	4	4	no	—
363	C₂²	—	8	16	no	—
364	C₂²	—	8	8	no	—
365	C₂²	C₂×C₁₃×#124	1	4	yes	—
366	C₂²	C₂×C₁₃×#124	1	2	yes	—
367	C₂²	C₁₃×#575	1	4	yes	—
368	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
369	C₄	—	2	4	no	—
370	C₄	—	2	4	no	—
371	C₄	—	4	8	no	—
372	C₄	—	4	4	no	—
373	C₄	C₂×C₁₃×#124	1	4	yes	—
374	C₄	C₂×C₁₃×#124	1	2	yes	—
375	C₄	C₂²×C₁₃×#41	1	2	yes	—
376	C₂	—	2	4	no	—
377	C₂	—	8	4	no	—
378	C₂	C₁₃×#3140	1	4	yes	direct product factor
379	C₂	C₂²×C₁₃×#124	1	1	yes	characteristic
380	C₂	C₂×C₁₃×#575	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#533	C₂	semidirect
3. C₁₃×#3140	C₂	direct (N × H)
4. C₂×C₁₃×#489	C₂	semidirect
5. C₂×C₁₃×#488	C₂	semidirect
6. C₂×C₁₃×#419	C₂	semidirect
8. C₂×C₄×C₁₃×M₁₆	C₂	semidirect
13. C₁₃×#533	C₂²	semidirect
14. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
15. C₂×C₁₃×#125	C₂²	semidirect
26. C₁₃×#489	C₂²	semidirect
27. C₁₃×#488	C₂²	semidirect
28. C₁₃×#419	C₂²	semidirect
30. C₂×C₁₃×#103	C₂²	semidirect
32. C₄×C₁₃×M₁₆	C₂²	semidirect
33. C₂×C₁₃×#97	C₂²	semidirect
34. C₂×C₄×C₈×C₁₃	C₂²	semidirect
54. C₁₃×C₄⋊Q₈	C₂³	semidirect
56. C₁₃×#125	C₂³	semidirect
79. C₁₃×#103	C₂³	semidirect
81. C₁₃×#97	C₂³	semidirect
82. C₄×C₈×C₁₃	C₂³	semidirect
83. C₂×#3140	C₁₃	direct (N × H)
134. C₂×#533	C₂×C₁₃	semidirect
136. #3140	C₂×C₁₃	direct (N × H)
137. C₂×#489	C₂×C₁₃	semidirect
138. C₂×#488	C₂×C₁₃	semidirect
139. C₂×#419	C₂×C₁₃	semidirect
141. C₂×C₄×M₁₆	C₂×C₁₃	semidirect
181. #533	C₂²×C₁₃	semidirect
182. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
183. C₂×#125	C₂²×C₁₃	semidirect
194. #489	C₂²×C₁₃	semidirect
195. #488	C₂²×C₁₃	semidirect
196. #419	C₂²×C₁₃	semidirect
198. C₂×#103	C₂²×C₁₃	semidirect
200. C₄×M₁₆	C₂²×C₁₃	semidirect
201. C₂×#97	C₂²×C₁₃	semidirect
202. C₂×C₄×C₈	C₂²×C₁₃	semidirect
239. C₄⋊Q₈	C₂³×C₁₃	semidirect
241. #125	C₂³×C₁₃	semidirect
264. #103	C₂³×C₁₃	semidirect
266. #97	C₂³×C₁₃	semidirect
267. C₄×C₈	C₂³×C₁₃	semidirect
270. C₂×C₁₃	#3140	direct (N × H)
323. C₁₃	C₂×#3140	direct (N × H)
378. C₂	C₁₃×#3140	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×C₁₃×#533	2
C₂²×C₁₃×#124	2
C₁₃×#3140	2
C₂×C₁₃×#489	2
C₂×C₁₃×#488	2
C₂×C₁₃×#419	2
C₂×C₁₃×#418	2
C₂×C₄×C₁₃×M₁₆	2
C₂×#3140	13

Subgroups — C2×C13×#3140 #15746954

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3140 #15746954