Subgroups — C₂×C₁₃×#2563 #15721278

Order 3328.

3222 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2563	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#393	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×#390	C₂	1	2	yes	maximal
6	C₂×C₁₃×#382	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#380	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
10	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
12	C₂×C₁₃×C₄⋊Q₈	—	2	8	no	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	8	yes	complemented
14	C₂×C₄×D₄×C₁₃	—	2	8	no	—
15	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
22	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
23	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#393	C₂²	1	32	yes	complemented
25	C₁₃×#390	C₂²	1	16	yes	—
26	C₁₃×#382	C₂²	1	16	yes	complemented
27	C₁₃×#380	C₂²	1	32	yes	complemented
28	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
29	C₂×C₁₃×#95	C₂²	1	2	yes	—
30	C₂×C₁₃×#95	C₂²	1	8	yes	—
31	C₂⁵×C₁₃	C₂³	1	2	yes	—
32	C₂²×Q₈×C₁₃	—	2	8	no	—
33	C₂²×Q₈×C₁₃	—	4	8	no	—
34	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
35	C₂²×D₄×C₁₃	—	2	4	no	—
36	C₂²×D₄×C₁₃	—	2	4	no	—
37	C₂²×D₄×C₁₃	Q₈	1	8	yes	complemented
38	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
39	C₂³×C₄×C₁₃	—	2	8	no	—
40	C₂³×C₄×C₁₃	—	2	16	no	—
41	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
42	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
43	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
44	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₁₃×C₄⋊Q₈	—	2	32	no	—
49	C₄×D₄×C₁₃	—	2	32	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
54	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
56	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
57	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
58	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	4	16	no	—
60	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
61	C₂×C₁₃×C₂²⋊C₄	C₂³	1	32	yes	—
62	C₂×C₄²×C₁₃	—	2	8	no	—
63	C₂×C₄²×C₁₃	D₄	1	8	yes	—
64	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
65	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
66	C₁₃×#95	C₂³	1	8	yes	—
67	C₁₃×#95	C₂³	1	32	yes	—
68	C₂×#2563	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
69	C₂⁴×C₁₃	—	2	4	no	—
70	C₂⁴×C₁₃	—	2	8	no	—
71	C₂⁴×C₁₃	—	2	4	no	—
72	C₂⁴×C₁₃	—	2	8	no	—
73	C₂⁴×C₁₃	C₂×Q₈	1	8	yes	—
74	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
75	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
76	C₂×Q₈×C₁₃	—	2	16	no	—
77	C₂×Q₈×C₁₃	—	4	16	no	—
78	C₂×Q₈×C₁₃	—	4	32	no	—
79	C₂×D₄×C₁₃	—	2	32	no	—
80	C₂×D₄×C₁₃	—	2	8	no	—
81	C₂×D₄×C₁₃	—	2	8	no	—
82	C₂×D₄×C₁₃	C₂×Q₈	1	16	yes	complemented
83	C₂²×C₄×C₁₃	—	2	4	no	—
84	C₂²×C₄×C₁₃	—	2	4	no	—
85	C₂²×C₄×C₁₃	—	2	8	no	—
86	C₂²×C₄×C₁₃	—	2	8	no	—
87	C₂²×C₄×C₁₃	—	2	8	no	—
88	C₂²×C₄×C₁₃	—	2	8	no	—
89	C₂²×C₄×C₁₃	—	2	8	no	—
90	C₂²×C₄×C₁₃	—	2	16	no	—
91	C₂²×C₄×C₁₃	—	2	16	no	—
92	C₂²×C₄×C₁₃	—	2	32	no	—
93	C₂²×C₄×C₁₃	—	4	32	no	—
94	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
95	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
97	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
98	C₂²×C₄×C₁₃	#41	1	4	yes	—
99	C₂²×C₄×C₁₃	#41	1	8	yes	—
100	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
101	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
102	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
103	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
104	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
105	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
106	C₁₃×C₄⋊C₄	—	2	8	no	—
107	C₁₃×C₄⋊C₄	—	2	16	no	—
108	C₁₃×C₄⋊C₄	—	2	16	no	—
109	C₁₃×C₄⋊C₄	—	2	16	no	—
110	C₁₃×C₂²⋊C₄	—	2	16	no	—
111	C₁₃×C₂²⋊C₄	—	4	32	no	—
112	C₄²×C₁₃	—	2	16	no	—
113	C₄²×C₁₃	C₂×D₄	1	16	yes	—
114	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
115	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic
116	#2563	C₂×C₁₃	1	16	yes	direct product factor
117	C₂×#393	C₂×C₁₃	1	4	yes	complemented
118	C₂×#390	C₂×C₁₃	1	2	yes	—
119	C₂×#382	C₂×C₁₃	1	2	yes	complemented
120	C₂×#380	C₂×C₁₃	1	4	yes	complemented
121	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
122	C₂³×C₁₃	—	2	16	no	—
123	C₂³×C₁₃	—	2	32	no	—
124	C₂³×C₁₃	—	2	4	no	—
125	C₂³×C₁₃	—	2	8	no	—
126	C₂³×C₁₃	—	2	4	no	—
127	C₂³×C₁₃	—	2	8	no	—
128	C₂³×C₁₃	—	4	8	no	—
129	C₂³×C₁₃	—	4	8	no	—
130	C₂³×C₁₃	—	4	16	no	—
131	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
132	C₂³×C₁₃	C₂²×Q₈	1	8	yes	—
133	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
134	C₂³×C₁₃	C₂×#41	1	2	yes	—
135	C₂³×C₁₃	C₂×#41	1	4	yes	—
136	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
137	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
138	Q₈×C₁₃	—	4	32	no	—
139	D₄×C₁₃	—	2	32	no	—
140	C₂×C₄×C₁₃	—	2	8	no	—
141	C₂×C₄×C₁₃	—	2	4	no	—
142	C₂×C₄×C₁₃	—	2	4	no	—
143	C₂×C₄×C₁₃	—	2	8	no	—
144	C₂×C₄×C₁₃	—	2	8	no	—
145	C₂×C₄×C₁₃	—	2	8	no	—
146	C₂×C₄×C₁₃	—	2	8	no	—
147	C₂×C₄×C₁₃	—	2	8	no	—
148	C₂×C₄×C₁₃	—	2	16	no	—
149	C₂×C₄×C₁₃	—	4	8	no	—
150	C₂×C₄×C₁₃	—	4	16	no	—
151	C₂×C₄×C₁₃	—	4	16	no	—
152	C₂×C₄×C₁₃	—	4	32	no	—
153	C₂×C₄×C₁₃	C₂²⋊Q₈	1	16	yes	—
154	C₂×C₄×C₁₃	#124	1	16	yes	—
155	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
156	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
157	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
158	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
159	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
160	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
161	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
162	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
163	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
164	C₂×C₄⋊Q₈	—	2	8	no	—
165	C₂×C₄⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
166	C₂×C₄×D₄	—	2	8	no	—
167	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
168	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
169	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
170	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
171	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
172	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
173	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
174	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
175	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
176	#393	C₂²×C₁₃	1	32	yes	complemented
177	#390	C₂²×C₁₃	1	16	yes	—
178	#382	C₂²×C₁₃	1	16	yes	complemented
179	#380	C₂²×C₁₃	1	32	yes	complemented
180	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
181	C₂×#95	C₂²×C₁₃	1	2	yes	—
182	C₂×#95	C₂²×C₁₃	1	8	yes	—
183	C₂²×C₁₃	—	2	8	no	—
184	C₂²×C₁₃	—	2	16	no	—
185	C₂²×C₁₃	—	4	32	no	—
186	C₂²×C₁₃	—	4	4	no	—
187	C₂²×C₁₃	—	4	4	no	—
188	C₂²×C₁₃	—	4	8	no	—
189	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
190	C₂²×C₁₃	C₂×#124	1	4	yes	—
191	C₂²×C₁₃	#535	1	4	yes	—
192	C₂²×C₁₃	#554	1	8	yes	—
193	C₂²×C₁₃	#555	1	8	yes	—
194	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
195	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
196	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
197	C₂²×C₁₃	C₂²×#41	1	2	yes	—
198	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
199	C₄×C₁₃	—	2	4	no	—
200	C₄×C₁₃	—	4	4	no	—
201	C₄×C₁₃	—	4	8	no	—
202	C₄×C₁₃	—	4	8	no	—
203	C₄×C₁₃	C₂×C₂²⋊Q₈	1	8	yes	—
204	C₄×C₁₃	C₂×#124	1	8	yes	—
205	C₂⁵	C₂³×C₁₃	1	2	yes	—
206	C₂²×Q₈	—	2	8	no	—
207	C₂²×Q₈	—	4	8	no	—
208	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
209	C₂²×D₄	—	2	4	no	—
210	C₂²×D₄	—	2	4	no	—
211	C₂²×D₄	Q₈×C₁₃	1	8	yes	complemented
212	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
213	C₂³×C₄	—	2	8	no	—
214	C₂³×C₄	—	2	16	no	—
215	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
216	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
217	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
218	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
219	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
220	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
221	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
222	C₄⋊Q₈	—	2	32	no	—
223	C₄×D₄	—	2	32	no	—
224	C₂×C₄⋊C₄	—	2	4	no	—
225	C₂×C₄⋊C₄	—	2	8	no	—
226	C₂×C₄⋊C₄	—	2	8	no	—
227	C₂×C₄⋊C₄	—	2	8	no	—
228	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
229	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
230	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
231	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
232	C₂×C₂²⋊C₄	—	2	8	no	—
233	C₂×C₂²⋊C₄	—	4	16	no	—
234	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
235	C₂×C₂²⋊C₄	C₂³×C₁₃	1	32	yes	—
236	C₂×C₄²	—	2	8	no	—
237	C₂×C₄²	D₄×C₁₃	1	8	yes	—
238	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
239	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
240	#95	C₂³×C₁₃	1	8	yes	—
241	#95	C₂³×C₁₃	1	32	yes	—
242	C₂×C₁₃	—	4	8	no	—
243	C₂×C₁₃	#2563	1	8	yes	direct product factor
244	C₂×C₁₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
245	C₂×C₁₃	C₂²×#124	1	1	yes	characteristic
246	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
247	C₂×C₁₃	C₂×#554	1	2	yes	—
248	C₂×C₁₃	C₂×#555	1	2	yes	—
249	C₂⁴	—	2	4	no	—
250	C₂⁴	—	2	8	no	—
251	C₂⁴	—	2	4	no	—
252	C₂⁴	—	2	8	no	—
253	C₂⁴	C₂×Q₈×C₁₃	1	8	yes	—
254	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
255	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
256	C₂×Q₈	—	2	16	no	—
257	C₂×Q₈	—	4	16	no	—
258	C₂×Q₈	—	4	32	no	—
259	C₂×D₄	—	2	32	no	—
260	C₂×D₄	—	2	8	no	—
261	C₂×D₄	—	2	8	no	—
262	C₂×D₄	C₂×Q₈×C₁₃	1	16	yes	complemented
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	8	no	—
266	C₂²×C₄	—	2	8	no	—
267	C₂²×C₄	—	2	8	no	—
268	C₂²×C₄	—	2	8	no	—
269	C₂²×C₄	—	2	8	no	—
270	C₂²×C₄	—	2	16	no	—
271	C₂²×C₄	—	2	16	no	—
272	C₂²×C₄	—	2	32	no	—
273	C₂²×C₄	—	4	32	no	—
274	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
275	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
276	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
277	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
278	C₂²×C₄	C₁₃×#41	1	4	yes	—
279	C₂²×C₄	C₁₃×#41	1	8	yes	—
280	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
281	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
282	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
283	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
284	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
285	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
286	C₄⋊C₄	—	2	8	no	—
287	C₄⋊C₄	—	2	16	no	—
288	C₄⋊C₄	—	2	16	no	—
289	C₄⋊C₄	—	2	16	no	—
290	C₂²⋊C₄	—	2	16	no	—
291	C₂²⋊C₄	—	4	32	no	—
292	C₄²	—	2	16	no	—
293	C₄²	C₂×D₄×C₁₃	1	16	yes	—
294	C₁₃	C₂×#2563	1	1	yes	characteristic, direct product factor, Sylow
295	C₂³	—	2	16	no	—
296	C₂³	—	2	32	no	—
297	C₂³	—	2	4	no	—
298	C₂³	—	2	8	no	—
299	C₂³	—	2	4	no	—
300	C₂³	—	2	8	no	—
301	C₂³	—	4	8	no	—
302	C₂³	—	4	8	no	—
303	C₂³	—	4	16	no	—
304	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
305	C₂³	C₂²×Q₈×C₁₃	1	8	yes	—
306	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
307	C₂³	C₂×C₁₃×#41	1	2	yes	—
308	C₂³	C₂×C₁₃×#41	1	4	yes	—
309	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
310	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
311	Q₈	—	4	32	no	—
312	D₄	—	2	32	no	—
313	C₂×C₄	—	2	8	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	2	8	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	8	no	—
321	C₂×C₄	—	2	16	no	—
322	C₂×C₄	—	4	8	no	—
323	C₂×C₄	—	4	16	no	—
324	C₂×C₄	—	4	16	no	—
325	C₂×C₄	—	4	32	no	—
326	C₂×C₄	C₁₃×C₂²⋊Q₈	1	16	yes	—
327	C₂×C₄	C₁₃×#124	1	16	yes	—
328	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
329	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
330	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
331	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
332	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
333	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
334	C₂²	—	2	8	no	—
335	C₂²	—	2	16	no	—
336	C₂²	—	4	32	no	—
337	C₂²	—	4	4	no	—
338	C₂²	—	4	4	no	—
339	C₂²	—	4	8	no	—
340	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
341	C₂²	C₂×C₁₃×#124	1	4	yes	—
342	C₂²	C₁₃×#535	1	4	yes	—
343	C₂²	C₁₃×#554	1	8	yes	—
344	C₂²	C₁₃×#555	1	8	yes	—
345	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
346	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
347	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
348	C₂²	C₂²×C₁₃×#41	1	2	yes	—
349	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
350	C₄	—	2	4	no	—
351	C₄	—	4	4	no	—
352	C₄	—	4	8	no	—
353	C₄	—	4	8	no	—
354	C₄	C₂×C₁₃×C₂²⋊Q₈	1	8	yes	—
355	C₄	C₂×C₁₃×#124	1	8	yes	—
356	C₂	—	4	8	no	—
357	C₂	C₁₃×#2563	1	8	yes	direct product factor
358	C₂	C₂²×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
359	C₂	C₂²×C₁₃×#124	1	1	yes	characteristic
360	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
361	C₂	C₂×C₁₃×#554	1	2	yes	—
362	C₂	C₂×C₁₃×#555	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
3. C₁₃×#2563	C₂	direct (N × H)
4. C₂×C₁₃×#393	C₂	semidirect
6. C₂×C₁₃×#382	C₂	semidirect
7. C₂×C₁₃×#380	C₂	semidirect
8. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
13. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
24. C₁₃×#393	C₂²	semidirect
26. C₁₃×#382	C₂²	semidirect
27. C₁₃×#380	C₂²	semidirect
28. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
37. C₂²×D₄×C₁₃	Q₈	semidirect
68. C₂×#2563	C₁₃	direct (N × H)
82. C₂×D₄×C₁₃	C₂×Q₈	semidirect
114. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
116. #2563	C₂×C₁₃	direct (N × H)
117. C₂×#393	C₂×C₁₃	semidirect
119. C₂×#382	C₂×C₁₃	semidirect
120. C₂×#380	C₂×C₁₃	semidirect
121. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
165. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
176. #393	C₂²×C₁₃	semidirect
178. #382	C₂²×C₁₃	semidirect
179. #380	C₂²×C₁₃	semidirect
180. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
211. C₂²×D₄	Q₈×C₁₃	semidirect
243. C₂×C₁₃	#2563	direct (N × H)
262. C₂×D₄	C₂×Q₈×C₁₃	semidirect
294. C₁₃	C₂×#2563	direct (N × H)
357. C₂	C₁₃×#2563	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×C₁₃×C₄⋊Q₈	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2563	2
C₂×C₁₃×#393	2
C₂×C₁₃×#390	2
C₂×C₁₃×#382	2
C₂×C₁₃×#380	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×#2563	13

Subgroups — C2×C13×#2563 #15721278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2563 #15721278