Subgroups — C₂×C₁₃×#3396 #15747731

Order 3328.

2086 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#559	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3396	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#495	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#493	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#460	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#463	C₂	1	4	yes	maximal, complemented
7	C₂×C₈×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×C₁₃×D₈	C₂	1	2	yes	maximal, complemented
10	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	—
12	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
13	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
14	C₁₃×#559	—	2	8	no	—
15	C₁₃×#559	C₂²	1	16	yes	complemented
16	C₂×C₁₃×#127	C₂²	1	2	yes	—
17	C₂×C₁₃×#124	—	2	2	no	—
18	C₂×C₁₃×#124	C₂²	1	4	yes	—
19	C₂×C₁₃×#123	—	2	4	no	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	—	2	2	no	—
23	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
24	C₁₃×#495	C₂²	1	16	yes	complemented
25	C₁₃×#493	C₂²	1	8	yes	—
26	C₁₃×#463	C₂²	1	32	yes	complemented
27	C₁₃×#460	C₂²	1	16	yes	complemented
28	C₈×Q₈×C₁₃	C₂²	1	8	yes	complemented
29	C₄×C₁₃×Q₁₆	C₂²	1	8	yes	complemented
30	C₄×C₁₃×D₈	C₂²	1	16	yes	complemented
31	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
33	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#103	C₂²	1	2	yes	—
35	C₂×C₁₃×#102	C₂²	1	4	yes	—
36	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
38	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
39	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
40	C₂²×D₄×C₁₃	—	2	2	no	—
41	C₂²×D₄×C₁₃	—	2	2	no	—
42	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
43	C₂³×C₄×C₁₃	—	2	4	no	—
44	C₂×C₁₃×Q₁₆	—	2	4	no	—
45	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
46	C₂×C₁₃×SD₁₆	—	4	8	no	—
47	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
48	C₂×C₁₃×D₈	—	2	8	no	—
49	C₂×C₁₃×D₈	—	4	4	no	—
50	C₂×C₁₃×D₈	C₂³	1	8	yes	—
51	C₂×C₁₃×D₈	C₂³	1	8	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₁₃×#127	—	2	4	no	—
56	C₁₃×#127	C₂³	1	8	yes	—
57	C₁₃×#124	—	2	16	no	—
58	C₁₃×#124	—	2	8	no	—
59	C₁₃×#124	C₂³	1	16	yes	—
60	C₁₃×#123	—	2	32	no	—
61	C₄×Q₈×C₁₃	—	2	4	no	—
62	C₄×Q₈×C₁₃	D₄	1	4	yes	—
63	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
64	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
65	C₄×D₄×C₁₃	—	2	16	no	—
66	C₄×D₄×C₁₃	—	2	8	no	—
67	C₄×D₄×C₁₃	C₂³	1	16	yes	—
68	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
75	C₂×C₄²×C₁₃	—	2	2	no	—
76	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×#107	C₂³	1	4	yes	—
79	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
80	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
81	C₁₃×#103	C₂³	1	8	yes	—
82	C₁₃×#102	C₂³	1	16	yes	—
83	C₄×C₈×C₁₃	C₂³	1	8	yes	—
84	C₄×C₈×C₁₃	C₂³	1	4	yes	—
85	C₂×#3396	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₃	—	2	4	no	—
87	C₂×Q₈×C₁₃	—	2	4	no	—
88	C₂×Q₈×C₁₃	—	2	2	no	—
89	C₂×Q₈×C₁₃	—	2	4	no	—
90	C₂×Q₈×C₁₃	—	2	4	no	—
91	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
92	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
93	C₂×D₄×C₁₃	—	2	4	no	—
94	C₂×D₄×C₁₃	—	2	8	no	—
95	C₂×D₄×C₁₃	—	2	8	no	—
96	C₂×D₄×C₁₃	—	2	8	no	—
97	C₂×D₄×C₁₃	—	2	8	no	—
98	C₂×D₄×C₁₃	—	4	8	no	—
99	C₂×D₄×C₁₃	—	8	4	no	—
100	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	16	no	—
104	C₂²×C₄×C₁₃	—	8	8	no	—
105	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
110	C₁₃×Q₁₆	—	2	8	no	—
111	C₁₃×SD₁₆	—	4	16	no	—
112	C₁₃×D₈	—	2	16	no	—
113	C₁₃×D₈	—	4	8	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	2	4	no	—
116	C₂×C₈×C₁₃	#41	1	4	yes	—
117	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
118	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
119	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
120	C₁₃×C₄⋊C₄	—	2	8	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
123	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
124	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
125	C₁₃×C₂²⋊C₄	—	2	16	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	4	yes	—
130	C₄²×C₁₃	C₂×D₄	1	2	yes	—
131	C₄²×C₁₃	C₂⁴	1	4	yes	—
132	C₄²×C₁₃	C₂⁴	1	2	yes	—
133	C₂×#559	C₂×C₁₃	1	2	yes	complemented
134	#3396	C₂×C₁₃	1	16	yes	direct product factor
135	C₂×#495	C₂×C₁₃	1	2	yes	complemented
136	C₂×#493	C₂×C₁₃	1	1	yes	characteristic
137	C₂×#460	C₂×C₁₃	1	2	yes	complemented
138	C₂×#463	C₂×C₁₃	1	4	yes	complemented
139	C₂×C₈×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
140	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
141	C₂×C₄×D₈	C₂×C₁₃	1	2	yes	complemented
142	C₂³×C₁₃	—	2	8	no	—
143	C₂³×C₁₃	—	4	8	no	—
144	C₂³×C₁₃	—	4	8	no	—
145	C₂³×C₁₃	—	4	8	no	—
146	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₁₃	—	2	8	no	—
148	Q₈×C₁₃	—	2	4	no	—
149	Q₈×C₁₃	—	2	4	no	—
150	Q₈×C₁₃	—	4	4	no	—
151	D₄×C₁₃	—	2	8	no	—
152	D₄×C₁₃	—	2	8	no	—
153	D₄×C₁₃	—	4	8	no	—
154	D₄×C₁₃	—	4	16	no	—
155	D₄×C₁₃	—	8	8	no	—
156	C₂×C₄×C₁₃	—	2	4	no	—
157	C₂×C₄×C₁₃	—	2	4	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	4	no	—
160	C₂×C₄×C₁₃	—	2	4	no	—
161	C₂×C₄×C₁₃	—	4	4	no	—
162	C₂×C₄×C₁₃	—	4	4	no	—
163	C₂×C₄×C₁₃	—	8	16	no	—
164	C₂×C₄×C₁₃	#135	1	4	yes	—
165	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
166	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
167	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
168	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
170	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
171	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
172	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
173	C₈×C₁₃	—	2	2	no	—
174	C₈×C₁₃	—	2	4	no	—
175	C₈×C₁₃	C₂×#41	1	4	yes	—
176	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
177	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	—
178	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
179	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
180	#559	—	2	8	no	—
181	#559	C₂²×C₁₃	1	16	yes	complemented
182	C₂×#127	C₂²×C₁₃	1	2	yes	—
183	C₂×#124	—	2	2	no	—
184	C₂×#124	C₂²×C₁₃	1	4	yes	—
185	C₂×#123	—	2	4	no	—
186	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
187	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
188	C₂×C₄×D₄	—	2	2	no	—
189	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
190	#495	C₂²×C₁₃	1	16	yes	complemented
191	#493	C₂²×C₁₃	1	8	yes	—
192	#463	C₂²×C₁₃	1	32	yes	complemented
193	#460	C₂²×C₁₃	1	16	yes	complemented
194	C₈×Q₈	C₂²×C₁₃	1	8	yes	complemented
195	C₄×Q₁₆	C₂²×C₁₃	1	8	yes	complemented
196	C₄×D₈	C₂²×C₁₃	1	16	yes	complemented
197	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
199	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×#103	C₂²×C₁₃	1	2	yes	—
201	C₂×#102	C₂²×C₁₃	1	4	yes	—
202	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
203	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
204	C₂²×C₁₃	—	4	8	no	—
205	C₂²×C₁₃	—	4	8	no	—
206	C₂²×C₁₃	—	4	8	no	—
207	C₂²×C₁₃	—	8	16	no	—
208	C₂²×C₁₃	#550	1	2	yes	—
209	C₂²×C₁₃	C₂×#135	1	2	yes	—
210	C₂²×C₁₃	#576	1	2	yes	—
211	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
212	C₄×C₁₃	—	2	4	no	—
213	C₄×C₁₃	—	2	4	no	—
214	C₄×C₁₃	—	2	2	no	—
215	C₄×C₁₃	—	4	4	no	—
216	C₄×C₁₃	—	4	4	no	—
217	C₄×C₁₃	#550	1	2	yes	—
218	C₄×C₁₃	C₂×#135	1	4	yes	—
219	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
220	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
221	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
222	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
223	C₂²×D₄	—	2	2	no	—
224	C₂²×D₄	—	2	2	no	—
225	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
226	C₂³×C₄	—	2	4	no	—
227	C₂×Q₁₆	—	2	4	no	—
228	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
229	C₂×SD₁₆	—	4	8	no	—
230	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
231	C₂×D₈	—	2	8	no	—
232	C₂×D₈	—	4	4	no	—
233	C₂×D₈	C₂³×C₁₃	1	8	yes	—
234	C₂×D₈	C₂³×C₁₃	1	8	yes	—
235	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
236	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
237	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
238	#127	—	2	4	no	—
239	#127	C₂³×C₁₃	1	8	yes	—
240	#124	—	2	16	no	—
241	#124	—	2	8	no	—
242	#124	C₂³×C₁₃	1	16	yes	—
243	#123	—	2	32	no	—
244	C₄×Q₈	—	2	4	no	—
245	C₄×Q₈	D₄×C₁₃	1	4	yes	—
246	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
247	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
248	C₄×D₄	—	2	16	no	—
249	C₄×D₄	—	2	8	no	—
250	C₄×D₄	C₂³×C₁₃	1	16	yes	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
253	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
254	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
255	C₂×C₂²⋊C₄	—	2	4	no	—
256	C₂×C₂²⋊C₄	—	2	4	no	—
257	C₂×C₂²⋊C₄	—	2	4	no	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
260	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
261	#107	C₂³×C₁₃	1	4	yes	—
262	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
263	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
264	#103	C₂³×C₁₃	1	8	yes	—
265	#102	C₂³×C₁₃	1	16	yes	—
266	C₄×C₈	C₂³×C₁₃	1	8	yes	—
267	C₄×C₈	C₂³×C₁₃	1	4	yes	—
268	C₂×C₁₃	—	8	8	no	—
269	C₂×C₁₃	#3396	1	4	yes	direct product factor
270	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
271	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
272	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
273	C₂⁴	—	2	4	no	—
274	C₂×Q₈	—	2	4	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	2	4	no	—
277	C₂×Q₈	—	2	4	no	—
278	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
279	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	2	8	no	—
282	C₂×D₄	—	2	8	no	—
283	C₂×D₄	—	2	8	no	—
284	C₂×D₄	—	2	8	no	—
285	C₂×D₄	—	4	8	no	—
286	C₂×D₄	—	8	4	no	—
287	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	16	no	—
291	C₂²×C₄	—	8	8	no	—
292	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
293	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
296	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
297	Q₁₆	—	2	8	no	—
298	SD₁₆	—	4	16	no	—
299	D₈	—	2	16	no	—
300	D₈	—	4	8	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	C₁₃×#41	1	4	yes	—
304	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
305	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
306	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
307	C₄⋊C₄	—	2	8	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
310	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
311	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
312	C₂²⋊C₄	—	2	16	no	—
313	C₂²⋊C₄	—	2	16	no	—
314	C₂²⋊C₄	—	2	16	no	—
315	C₄²	—	2	8	no	—
316	C₄²	C₂×D₄×C₁₃	1	4	yes	—
317	C₄²	C₂×D₄×C₁₃	1	2	yes	—
318	C₄²	C₂⁴×C₁₃	1	4	yes	—
319	C₄²	C₂⁴×C₁₃	1	2	yes	—
320	C₁₃	C₂×#3396	1	1	yes	characteristic, direct product factor, Sylow
321	C₂³	—	2	8	no	—
322	C₂³	—	4	8	no	—
323	C₂³	—	4	8	no	—
324	C₂³	—	4	8	no	—
325	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
326	Q₈	—	2	8	no	—
327	Q₈	—	2	4	no	—
328	Q₈	—	2	4	no	—
329	Q₈	—	4	4	no	—
330	D₄	—	2	8	no	—
331	D₄	—	2	8	no	—
332	D₄	—	4	8	no	—
333	D₄	—	4	16	no	—
334	D₄	—	8	8	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	8	16	no	—
343	C₂×C₄	C₁₃×#135	1	4	yes	—
344	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
345	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
346	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
347	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
349	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
350	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
351	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
352	C₈	—	2	2	no	—
353	C₈	—	2	4	no	—
354	C₈	C₂×C₁₃×#41	1	4	yes	—
355	C₂²	—	4	8	no	—
356	C₂²	—	4	8	no	—
357	C₂²	—	4	8	no	—
358	C₂²	—	8	16	no	—
359	C₂²	C₁₃×#550	1	2	yes	—
360	C₂²	C₂×C₁₃×#135	1	2	yes	—
361	C₂²	C₁₃×#576	1	2	yes	—
362	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
363	C₄	—	2	4	no	—
364	C₄	—	2	4	no	—
365	C₄	—	2	2	no	—
366	C₄	—	4	4	no	—
367	C₄	—	4	4	no	—
368	C₄	C₁₃×#550	1	2	yes	—
369	C₄	C₂×C₁₃×#135	1	4	yes	—
370	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
371	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
372	C₂	—	8	8	no	—
373	C₂	C₁₃×#3396	1	4	yes	direct product factor
374	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
375	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
376	C₂	C₂×C₁₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#493	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#559	C₂	semidirect
2. C₁₃×#3396	C₂	direct (N × H)
3. C₂×C₁₃×#495	C₂	semidirect
5. C₂×C₁₃×#460	C₂	semidirect
6. C₂×C₁₃×#463	C₂	semidirect
7. C₂×C₈×Q₈×C₁₃	C₂	semidirect
8. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
9. C₂×C₄×C₁₃×D₈	C₂	semidirect
15. C₁₃×#559	C₂²	semidirect
24. C₁₃×#495	C₂²	semidirect
26. C₁₃×#463	C₂²	semidirect
27. C₁₃×#460	C₂²	semidirect
28. C₈×Q₈×C₁₃	C₂²	semidirect
29. C₄×C₁₃×Q₁₆	C₂²	semidirect
30. C₄×C₁₃×D₈	C₂²	semidirect
85. C₂×#3396	C₁₃	direct (N × H)
133. C₂×#559	C₂×C₁₃	semidirect
134. #3396	C₂×C₁₃	direct (N × H)
135. C₂×#495	C₂×C₁₃	semidirect
137. C₂×#460	C₂×C₁₃	semidirect
138. C₂×#463	C₂×C₁₃	semidirect
139. C₂×C₈×Q₈	C₂×C₁₃	semidirect
140. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
141. C₂×C₄×D₈	C₂×C₁₃	semidirect
181. #559	C₂²×C₁₃	semidirect
190. #495	C₂²×C₁₃	semidirect
192. #463	C₂²×C₁₃	semidirect
193. #460	C₂²×C₁₃	semidirect
194. C₈×Q₈	C₂²×C₁₃	semidirect
195. C₄×Q₁₆	C₂²×C₁₃	semidirect
196. C₄×D₈	C₂²×C₁₃	semidirect
269. C₂×C₁₃	#3396	direct (N × H)
320. C₁₃	C₂×#3396	direct (N × H)
373. C₂	C₁₃×#3396	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×#559	2
C₁₃×#3396	2
C₂×C₁₃×#495	2
C₂×C₁₃×#493	2
C₂×C₁₃×#460	2
C₂×C₁₃×#463	2
C₂×C₈×Q₈×C₁₃	2
C₂×C₄×C₁₃×Q₁₆	2
C₂×C₄×C₁₃×D₈	2
C₂×#3396	13

Subgroups — C2×C13×#3396 #15747731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3396 #15747731