Subgroups — C₁₃×#15143 #15701482

Order 3328.

1934 conjugacy classes of subgroups.

The subgroup lattice has 374 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
2	C₂×C₁₃×#395	C₂	1	4	yes	maximal
3	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#384	C₂	1	2	yes	maximal
5	C₁₃×#1444	C₂	1	4	yes	maximal
6	C₁₃×C₄⋊#95	C₂	1	2	yes	maximal
7	C₄×C₁₃×#95	C₂	1	1	yes	maximal, characteristic
8	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
9	C₂×C₁₃×C₄⋊Q₈	—	2	8	no	—
10	C₂×C₁₃×C₄⋊Q₈	—	2	4	no	—
11	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂²×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
19	C₁₃×#395	—	2	16	no	—
20	C₁₃×#389	—	2	4	no	—
21	C₁₃×#384	—	2	8	no	—
22	C₂×C₁₃×#95	C₂²	1	2	yes	—
23	C₂×C₁₃×#95	C₂²	1	8	yes	—
24	C₂×C₁₃×#95	C₂²	1	2	yes	—
25	C₂×C₁₃×#95	C₂²	1	2	yes	—
26	C₂²×Q₈×C₁₃	—	2	8	no	—
27	C₂²×Q₈×C₁₃	—	2	4	no	—
28	C₂²×Q₈×C₁₃	—	2	8	no	—
29	C₂²×Q₈×C₁₃	—	4	4	no	—
30	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
31	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
32	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
33	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
34	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
36	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
37	C₁₃×C₄⋊Q₈	—	2	32	no	—
38	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
39	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
40	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
41	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
42	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
43	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
44	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
45	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
46	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
50	C₂×C₁₃×C₄⋊C₄	—	4	8	no	—
51	C₂×C₁₃×C₄⋊C₄	D₄	1	8	yes	—
52	C₂×C₁₃×C₄⋊C₄	Q₈	1	4	yes	complemented
53	C₂×C₄²×C₁₃	—	2	4	no	—
54	C₂×C₄²×C₁₃	—	2	4	no	—
55	C₂×C₄²×C₁₃	—	2	4	no	—
56	C₂×C₄²×C₁₃	D₄	1	4	yes	—
57	C₂×C₄²×C₁₃	Q₈	1	8	yes	complemented
58	C₁₃×#95	—	2	4	no	—
59	C₁₃×#95	—	2	16	no	—
60	C₁₃×#95	D₄	1	8	yes	—
61	C₁₃×#95	Q₈	1	8	yes	complemented
62	#15143	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
64	C₂×Q₈×C₁₃	—	2	16	no	—
65	C₂×Q₈×C₁₃	—	4	32	no	—
66	C₂×Q₈×C₁₃	—	4	8	no	—
67	C₂×Q₈×C₁₃	—	4	8	no	—
68	C₂²×C₄×C₁₃	—	2	2	no	—
69	C₂²×C₄×C₁₃	—	2	4	no	—
70	C₂²×C₄×C₁₃	—	2	2	no	—
71	C₂²×C₄×C₁₃	—	2	4	no	—
72	C₂²×C₄×C₁₃	—	2	4	no	—
73	C₂²×C₄×C₁₃	—	2	2	no	—
74	C₂²×C₄×C₁₃	—	2	2	no	—
75	C₂²×C₄×C₁₃	—	2	4	no	—
76	C₂²×C₄×C₁₃	—	2	4	no	—
77	C₂²×C₄×C₁₃	—	2	2	no	—
78	C₂²×C₄×C₁₃	—	2	8	no	—
79	C₂²×C₄×C₁₃	—	2	4	no	—
80	C₂²×C₄×C₁₃	—	2	4	no	—
81	C₂²×C₄×C₁₃	—	2	2	no	—
82	C₂²×C₄×C₁₃	—	2	8	no	—
83	C₂²×C₄×C₁₃	—	2	4	no	—
84	C₂²×C₄×C₁₃	—	2	2	no	—
85	C₂²×C₄×C₁₃	—	2	4	no	—
86	C₂²×C₄×C₁₃	—	2	4	no	—
87	C₂²×C₄×C₁₃	—	2	4	no	—
88	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
89	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
90	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
93	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
94	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
96	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
97	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
98	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
99	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
100	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
101	C₂²×C₄×C₁₃	#41	1	2	yes	—
102	C₁₃×C₄⋊C₄	—	2	16	no	—
103	C₁₃×C₄⋊C₄	—	2	16	no	—
104	C₁₃×C₄⋊C₄	—	2	8	no	—
105	C₁₃×C₄⋊C₄	—	4	32	no	—
106	C₁₃×C₄⋊C₄	—	4	4	no	—
107	C₁₃×C₄⋊C₄	—	4	8	no	—
108	C₄²×C₁₃	—	2	8	no	—
109	C₄²×C₁₃	—	2	16	no	—
110	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
111	C₂×#395	C₂×C₁₃	1	4	yes	—
112	C₂×#389	C₂×C₁₃	1	1	yes	characteristic
113	C₂×#384	C₂×C₁₃	1	2	yes	—
114	#1444	C₂×C₁₃	1	4	yes	—
115	C₄⋊#95	C₂×C₁₃	1	2	yes	—
116	C₄×#95	C₂×C₁₃	1	1	yes	characteristic
117	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
118	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
119	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
120	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
121	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
122	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
123	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
124	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
125	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
126	Q₈×C₁₃	—	4	32	no	—
127	C₂×C₄×C₁₃	—	2	2	no	—
128	C₂×C₄×C₁₃	—	2	2	no	—
129	C₂×C₄×C₁₃	—	2	8	no	—
130	C₂×C₄×C₁₃	—	2	2	no	—
131	C₂×C₄×C₁₃	—	2	2	no	—
132	C₂×C₄×C₁₃	—	2	8	no	—
133	C₂×C₄×C₁₃	—	2	8	no	—
134	C₂×C₄×C₁₃	—	2	8	no	—
135	C₂×C₄×C₁₃	—	2	8	no	—
136	C₂×C₄×C₁₃	—	2	8	no	—
137	C₂×C₄×C₁₃	—	2	8	no	—
138	C₂×C₄×C₁₃	—	2	8	no	—
139	C₂×C₄×C₁₃	—	2	8	no	—
140	C₂×C₄×C₁₃	—	2	4	no	—
141	C₂×C₄×C₁₃	—	2	16	no	—
142	C₂×C₄×C₁₃	—	2	8	no	—
143	C₂×C₄×C₁₃	—	4	2	no	—
144	C₂×C₄×C₁₃	—	4	4	no	—
145	C₂×C₄×C₁₃	—	4	4	no	—
146	C₂×C₄×C₁₃	—	4	2	no	—
147	C₂×C₄×C₁₃	—	4	8	no	—
148	C₂×C₄×C₁₃	—	4	4	no	—
149	C₂×C₄×C₁₃	—	4	2	no	—
150	C₂×C₄×C₁₃	—	4	2	no	—
151	C₂×C₄×C₁₃	—	4	2	no	—
152	C₂×C₄×C₁₃	—	4	8	no	—
153	C₂×C₄×C₁₃	#120	1	4	yes	—
154	C₂×C₄×C₁₃	C₂²⋊Q₈	1	8	yes	—
155	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
156	C₂×C₄×C₁₃	#127	1	4	yes	—
157	C₂×C₄×C₁₃	C₄⋊Q₈	1	4	yes	—
158	C₂×C₄×C₁₃	C₄⋊Q₈	1	4	yes	—
159	C₂×C₄×C₁₃	C₄⋊Q₈	1	8	yes	—
160	C₂×C₄×C₁₃	C₄⋊Q₈	1	16	yes	complemented
161	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
162	C₂×C₄⋊Q₈	—	2	8	no	—
163	C₂×C₄⋊Q₈	—	2	4	no	—
164	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
165	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
166	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
167	C₂²×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
168	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
169	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
170	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
171	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
172	#395	—	2	16	no	—
173	#389	—	2	4	no	—
174	#384	—	2	8	no	—
175	C₂×#95	C₂²×C₁₃	1	8	yes	—
176	C₂×#95	C₂²×C₁₃	1	2	yes	—
177	C₂×#95	C₂²×C₁₃	1	2	yes	—
178	C₂×#95	C₂²×C₁₃	1	2	yes	—
179	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
180	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
181	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
182	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
183	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
184	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
185	C₂²×C₁₃	C₂×C₄⋊Q₈	1	4	yes	—
186	C₂²×C₁₃	C₂×C₄⋊Q₈	1	2	yes	—
187	C₂²×C₁₃	#535	1	1	yes	characteristic
188	C₂²×C₁₃	#536	1	1	yes	characteristic
189	C₂²×C₁₃	#544	1	4	yes	—
190	C₂²×C₁₃	D₄²	1	4	yes	—
191	C₂²×C₁₃	#547	1	2	yes	—
192	C₂²×C₁₃	D₄×Q₈	1	4	yes	—
193	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
194	C₂²×C₁₃	#554	1	2	yes	—
195	C₂²×C₁₃	Q₈²	1	2	yes	—
196	C₄×C₁₃	—	2	4	no	—
197	C₄×C₁₃	—	2	4	no	—
198	C₄×C₁₃	—	2	16	no	—
199	C₄×C₁₃	—	4	8	no	—
200	C₄×C₁₃	—	4	4	no	—
201	C₄×C₁₃	—	8	2	no	—
202	C₄×C₁₃	#395	1	8	yes	complemented
203	C₂²×Q₈	—	2	8	no	—
204	C₂²×Q₈	—	2	4	no	—
205	C₂²×Q₈	—	2	8	no	—
206	C₂²×Q₈	—	4	4	no	—
207	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
208	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
209	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
210	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
211	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
212	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
213	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
214	C₄⋊Q₈	—	2	32	no	—
215	C₂×C₄⋊C₄	—	2	8	no	—
216	C₂×C₄⋊C₄	—	2	4	no	—
217	C₂×C₄⋊C₄	—	2	4	no	—
218	C₂×C₄⋊C₄	—	2	4	no	—
219	C₂×C₄⋊C₄	—	2	2	no	—
220	C₂×C₄⋊C₄	—	2	2	no	—
221	C₂×C₄⋊C₄	—	2	16	no	—
222	C₂×C₄⋊C₄	—	2	4	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	—	2	4	no	—
225	C₂×C₄⋊C₄	—	2	16	no	—
226	C₂×C₄⋊C₄	—	2	8	no	—
227	C₂×C₄⋊C₄	—	4	8	no	—
228	C₂×C₄⋊C₄	D₄×C₁₃	1	8	yes	—
229	C₂×C₄⋊C₄	Q₈×C₁₃	1	4	yes	complemented
230	C₂×C₄²	—	2	4	no	—
231	C₂×C₄²	—	2	4	no	—
232	C₂×C₄²	—	2	4	no	—
233	C₂×C₄²	D₄×C₁₃	1	4	yes	—
234	C₂×C₄²	Q₈×C₁₃	1	8	yes	complemented
235	#95	—	2	4	no	—
236	#95	—	2	16	no	—
237	#95	D₄×C₁₃	1	8	yes	—
238	#95	Q₈×C₁₃	1	8	yes	complemented
239	C₂×C₁₃	C₂×#395	1	1	yes	characteristic
240	C₂×C₁₃	#2433	1	1	yes	characteristic
241	C₂×C₁₃	#2434	1	1	yes	characteristic
242	C₂×C₁₃	#2440	1	4	yes	—
243	C₂×C₁₃	#2542	1	1	yes	characteristic
244	C₂×C₁₃	#2551	1	4	yes	—
245	C₂×C₁₃	#2567	1	1	yes	characteristic
246	C₂×C₁₃	#2660	1	1	yes	characteristic
247	C₂×C₁₃	#2868	1	1	yes	characteristic
248	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
249	C₂×Q₈	—	2	16	no	—
250	C₂×Q₈	—	4	32	no	—
251	C₂×Q₈	—	4	8	no	—
252	C₂×Q₈	—	4	8	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	8	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	8	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
274	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
275	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
276	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
277	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
278	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
279	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
280	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
281	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
282	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
283	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
284	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
285	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
286	C₂²×C₄	C₁₃×#41	1	2	yes	—
287	C₄⋊C₄	—	2	16	no	—
288	C₄⋊C₄	—	2	16	no	—
289	C₄⋊C₄	—	2	8	no	—
290	C₄⋊C₄	—	4	32	no	—
291	C₄⋊C₄	—	4	4	no	—
292	C₄⋊C₄	—	4	8	no	—
293	C₄²	—	2	8	no	—
294	C₄²	—	2	16	no	—
295	C₁₃	#15143	1	1	yes	characteristic, direct product factor, Sylow
296	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
297	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
298	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
299	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
300	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
301	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
302	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
303	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
304	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
305	Q₈	—	4	32	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	8	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	2	8	no	—
314	C₂×C₄	—	2	8	no	—
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	2	8	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	16	no	—
321	C₂×C₄	—	2	8	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	8	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	8	no	—
332	C₂×C₄	C₁₃×#120	1	4	yes	—
333	C₂×C₄	C₁₃×C₂²⋊Q₈	1	8	yes	—
334	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
335	C₂×C₄	C₁₃×#127	1	4	yes	—
336	C₂×C₄	C₁₃×C₄⋊Q₈	1	4	yes	—
337	C₂×C₄	C₁₃×C₄⋊Q₈	1	8	yes	—
338	C₂×C₄	C₁₃×C₄⋊Q₈	1	4	yes	—
339	C₂×C₄	C₁₃×C₄⋊Q₈	1	16	yes	complemented
340	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
341	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
342	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	2	yes	—
343	C₂²	C₂×C₁₃×#127	1	1	yes	characteristic
344	C₂²	C₂×C₁₃×C₄⋊Q₈	1	2	yes	—
345	C₂²	C₂×C₁₃×C₄⋊Q₈	1	4	yes	—
346	C₂²	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
347	C₂²	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
348	C₂²	C₁₃×#535	1	1	yes	characteristic
349	C₂²	C₁₃×#536	1	1	yes	characteristic
350	C₂²	C₁₃×#544	1	4	yes	—
351	C₂²	D₄²×C₁₃	1	4	yes	—
352	C₂²	C₁₃×#547	1	2	yes	—
353	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
354	C₂²	D₄×Q₈×C₁₃	1	4	yes	—
355	C₂²	C₁₃×#554	1	2	yes	—
356	C₂²	Q₈²×C₁₃	1	2	yes	—
357	C₄	—	2	4	no	—
358	C₄	—	2	4	no	—
359	C₄	—	2	16	no	—
360	C₄	—	4	4	no	—
361	C₄	—	4	8	no	—
362	C₄	—	8	2	no	—
363	C₄	C₁₃×#395	1	8	yes	complemented
364	C₂	C₂×C₁₃×#395	1	1	yes	characteristic
365	C₂	C₁₃×#2433	1	1	yes	characteristic
366	C₂	C₁₃×#2434	1	1	yes	characteristic
367	C₂	C₁₃×#2440	1	4	yes	—
368	C₂	C₁₃×#2542	1	1	yes	characteristic
369	C₂	C₁₃×#2551	1	4	yes	—
370	C₂	C₁₃×#2567	1	1	yes	characteristic
371	C₂	C₁₃×#2660	1	1	yes	characteristic
372	C₂	C₁₃×#2868	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
52. C₂×C₁₃×C₄⋊C₄	Q₈	semidirect
57. C₂×C₄²×C₁₃	Q₈	semidirect
61. C₁₃×#95	Q₈	semidirect
62. #15143	C₁₃	direct (N × H)
160. C₂×C₄×C₁₃	C₄⋊Q₈	semidirect
202. C₄×C₁₃	#395	semidirect
229. C₂×C₄⋊C₄	Q₈×C₁₃	semidirect
234. C₂×C₄²	Q₈×C₁₃	semidirect
238. #95	Q₈×C₁₃	semidirect
295. C₁₃	#15143	direct (N × H)
339. C₂×C₄	C₁₃×C₄⋊Q₈	semidirect
363. C₄	C₁₃×#395	semidirect

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
C₂×C₁₃×#395	2
C₂×C₁₃×#389	2
C₂×C₁₃×#384	2
C₁₃×#1444	2
C₁₃×C₄⋊#95	2
C₄×C₁₃×#95	2
#15143	13

Subgroups — C13×#15143 #15701482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#15143 #15701482