Subgroups — C₁₃×#34954 #15721293

Order 3328.

1948 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2593	C₂	1	4	yes	maximal, complemented
2	C₁₃×#2582	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2571	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2548	C₂	1	2	yes	maximal
5	C₁₃×#2513	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2448	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2395	C₂	1	4	yes	maximal, complemented
8	C₄×C₁₃×#127	C₂	1	1	yes	maximal, characteristic
9	C₄×C₁₃×#124	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2293	C₂	1	4	yes	maximal, complemented
11	C₄²×Q₈×C₁₃	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#124	C₂²	1	4	yes	—
14	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
18	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
19	C₂×C₁₃×#117	C₂²	1	4	yes	—
20	C₁₃×#400	C₂²	1	4	yes	—
21	C₁₃×#399	C₂²	1	4	yes	—
22	C₁₃×#398	C₂²	1	4	yes	—
23	C₁₃×#397	C₂²	1	4	yes	—
24	C₁₃×#397	C₂²	1	8	yes	—
25	C₁₃×#394	C₂²	1	8	yes	—
26	C₁₃×#391	C₂²	1	4	yes	—
27	C₁₃×#390	C₂²	1	4	yes	—
28	C₁₃×#390	C₂²	1	4	yes	—
29	C₁₃×#390	C₂²	1	4	yes	—
30	C₁₃×#390	C₂²	1	4	yes	—
31	C₁₃×#390	C₂²	1	2	yes	—
32	C₁₃×#389	C₂²	1	4	yes	—
33	C₁₃×#389	C₂²	1	4	yes	—
34	C₁₃×#388	C₂²	1	8	yes	—
35	C₁₃×#388	C₂²	1	8	yes	—
36	C₁₃×#388	C₂²	1	8	yes	—
37	C₁₃×#388	C₂²	1	8	yes	—
38	C₁₃×#384	C₂²	1	1	yes	characteristic
39	C₁₃×#382	C₂²	1	4	yes	—
40	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
41	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
42	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
43	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
44	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
45	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
46	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
47	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
48	C₄³×C₁₃	C₂²	1	1	yes	characteristic
49	C₄³×C₁₃	C₂²	1	4	yes	—
50	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
51	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
52	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
54	C₁₃×#127	—	2	4	no	—
55	C₁₃×#124	—	2	16	no	—
56	C₄×Q₈×C₁₃	—	2	8	no	—
57	C₄×Q₈×C₁₃	—	2	8	no	—
58	C₄×Q₈×C₁₃	—	2	8	no	—
59	C₄×D₄×C₁₃	—	2	16	no	—
60	C₄×D₄×C₁₃	—	4	4	no	—
61	C₁₃×#117	—	4	8	no	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
72	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
73	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
74	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
75	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
76	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
77	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
78	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
79	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
80	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
81	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
82	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
83	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
84	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
89	C₁₃×#95	C₂³	1	4	yes	—
90	C₁₃×#95	C₂³	1	8	yes	—
91	C₁₃×#95	C₂³	1	8	yes	—
92	C₁₃×#95	C₂³	1	4	yes	—
93	C₁₃×#95	C₂³	1	4	yes	—
94	C₁₃×#95	C₂³	1	4	yes	—
95	C₁₃×#95	C₂³	1	4	yes	—
96	#34954	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
98	C₂×Q₈×C₁₃	—	2	4	no	—
99	C₂×Q₈×C₁₃	—	2	4	no	—
100	C₂×Q₈×C₁₃	#41	1	8	yes	—
101	C₂×D₄×C₁₃	—	2	8	no	—
102	C₂×D₄×C₁₃	—	2	8	no	—
103	C₂×D₄×C₁₃	—	2	4	no	—
104	C₂×D₄×C₁₃	—	2	8	no	—
105	C₂×D₄×C₁₃	—	4	2	no	—
106	C₂×D₄×C₁₃	—	4	2	no	—
107	C₂²×C₄×C₁₃	—	2	16	no	—
108	C₂²×C₄×C₁₃	—	2	8	no	—
109	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
110	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
111	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
112	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
114	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
115	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₁₃×C₄⋊C₄	—	2	8	no	—
120	C₁₃×C₄⋊C₄	—	2	8	no	—
121	C₁₃×C₄⋊C₄	—	2	8	no	—
122	C₁₃×C₄⋊C₄	—	2	8	no	—
123	C₁₃×C₄⋊C₄	—	2	4	no	—
124	C₁₃×C₄⋊C₄	—	2	4	no	—
125	C₁₃×C₄⋊C₄	—	2	4	no	—
126	C₁₃×C₄⋊C₄	—	4	4	no	—
127	C₁₃×C₄⋊C₄	—	4	4	no	—
128	C₁₃×C₄⋊C₄	—	4	2	no	—
129	C₁₃×C₂²⋊C₄	—	2	16	no	—
130	C₁₃×C₂²⋊C₄	—	2	16	no	—
131	C₁₃×C₂²⋊C₄	—	2	16	no	—
132	C₁₃×C₂²⋊C₄	—	4	8	no	—
133	C₁₃×C₂²⋊C₄	—	4	8	no	—
134	C₁₃×C₂²⋊C₄	—	4	4	no	—
135	C₄²×C₁₃	—	2	8	no	—
136	C₄²×C₁₃	—	2	4	no	—
137	C₄²×C₁₃	—	2	8	no	—
138	C₄²×C₁₃	—	2	8	no	—
139	C₄²×C₁₃	—	2	8	no	—
140	C₄²×C₁₃	—	2	8	no	—
141	C₄²×C₁₃	—	2	2	no	—
142	C₄²×C₁₃	—	4	1	no	—
143	C₄²×C₁₃	—	4	4	no	—
144	C₄²×C₁₃	#41	1	8	yes	—
145	C₄²×C₁₃	#41	1	4	yes	—
146	#2593	C₂×C₁₃	1	4	yes	complemented
147	#2582	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#2571	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#2548	C₂×C₁₃	1	2	yes	—
150	#2513	C₂×C₁₃	1	4	yes	complemented
151	#2448	C₂×C₁₃	1	4	yes	complemented
152	#2395	C₂×C₁₃	1	4	yes	complemented
153	C₄×#127	C₂×C₁₃	1	1	yes	characteristic
154	C₄×#124	C₂×C₁₃	1	4	yes	complemented
155	#2293	C₂×C₁₃	1	4	yes	complemented
156	C₄²×Q₈	C₂×C₁₃	1	2	yes	complemented
157	C₂³×C₁₃	—	2	8	no	—
158	C₂³×C₁₃	—	2	8	no	—
159	C₂³×C₁₃	—	2	4	no	—
160	C₂³×C₁₃	—	2	4	no	—
161	C₂³×C₁₃	—	2	4	no	—
162	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
163	Q₈×C₁₃	—	2	16	no	—
164	D₄×C₁₃	—	4	8	no	—
165	D₄×C₁₃	—	4	16	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	4	no	—
168	C₂×C₄×C₁₃	—	2	4	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	4	no	—
173	C₂×C₄×C₁₃	—	2	4	no	—
174	C₂×C₄×C₁₃	—	2	4	no	—
175	C₂×C₄×C₁₃	—	2	4	no	—
176	C₂×C₄×C₁₃	—	2	4	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	8	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	4	no	—
181	C₂×C₄×C₁₃	—	2	4	no	—
182	C₂×C₄×C₁₃	—	2	4	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	4	16	no	—
186	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
187	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
188	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
189	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
190	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
191	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
192	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
193	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
194	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×#124	C₂²×C₁₃	1	4	yes	—
196	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
197	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
198	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
199	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
200	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
201	C₂×#117	C₂²×C₁₃	1	4	yes	—
202	#400	C₂²×C₁₃	1	4	yes	—
203	#399	C₂²×C₁₃	1	4	yes	—
204	#398	C₂²×C₁₃	1	4	yes	—
205	#397	C₂²×C₁₃	1	8	yes	—
206	#397	C₂²×C₁₃	1	4	yes	—
207	#394	C₂²×C₁₃	1	8	yes	—
208	#391	C₂²×C₁₃	1	4	yes	—
209	#390	C₂²×C₁₃	1	2	yes	—
210	#390	C₂²×C₁₃	1	4	yes	—
211	#390	C₂²×C₁₃	1	4	yes	—
212	#390	C₂²×C₁₃	1	4	yes	—
213	#390	C₂²×C₁₃	1	4	yes	—
214	#389	C₂²×C₁₃	1	4	yes	—
215	#389	C₂²×C₁₃	1	4	yes	—
216	#388	C₂²×C₁₃	1	8	yes	—
217	#388	C₂²×C₁₃	1	8	yes	—
218	#388	C₂²×C₁₃	1	8	yes	—
219	#388	C₂²×C₁₃	1	8	yes	—
220	#384	C₂²×C₁₃	1	1	yes	characteristic
221	#382	C₂²×C₁₃	1	4	yes	—
222	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
223	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
224	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
225	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
226	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
227	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
228	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
229	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
230	C₄³	C₂²×C₁₃	1	1	yes	characteristic
231	C₄³	C₂²×C₁₃	1	4	yes	—
232	C₂²×C₁₃	—	4	8	no	—
233	C₂²×C₁₃	—	4	4	no	—
234	C₂²×C₁₃	—	4	4	no	—
235	C₂²×C₁₃	—	4	8	no	—
236	C₂²×C₁₃	—	4	4	no	—
237	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
238	C₂²×C₁₃	C₂²×#41	1	2	yes	—
239	C₂²×C₁₃	C₂²×#41	1	2	yes	—
240	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
241	C₂²×C₁₃	#585	1	1	yes	characteristic
242	C₄×C₁₃	—	2	8	no	—
243	C₄×C₁₃	—	2	2	no	—
244	C₄×C₁₃	—	2	4	no	—
245	C₄×C₁₃	—	4	4	no	—
246	C₄×C₁₃	—	4	4	no	—
247	C₄×C₁₃	—	4	4	no	—
248	C₄×C₁₃	—	4	4	no	—
249	C₄×C₁₃	—	4	1	no	—
250	C₄×C₁₃	#529	1	8	yes	—
251	C₄×C₁₃	#559	1	4	yes	—
252	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
253	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
254	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
255	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
256	#127	—	2	4	no	—
257	#124	—	2	16	no	—
258	C₄×Q₈	—	2	8	no	—
259	C₄×Q₈	—	2	8	no	—
260	C₄×Q₈	—	2	8	no	—
261	C₄×D₄	—	2	16	no	—
262	C₄×D₄	—	4	4	no	—
263	#117	—	4	8	no	—
264	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
265	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
267	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
270	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
271	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
274	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
275	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
276	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
277	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
278	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
279	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
280	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
281	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
283	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
284	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
285	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
286	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
287	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
288	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
289	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
290	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
291	#95	C₂³×C₁₃	1	4	yes	—
292	#95	C₂³×C₁₃	1	8	yes	—
293	#95	C₂³×C₁₃	1	8	yes	—
294	#95	C₂³×C₁₃	1	4	yes	—
295	#95	C₂³×C₁₃	1	4	yes	—
296	#95	C₂³×C₁₃	1	4	yes	—
297	#95	C₂³×C₁₃	1	4	yes	—
298	C₂×C₁₃	—	8	4	no	—
299	C₂×C₁₃	C₂×#529	1	2	yes	—
300	C₂×C₁₃	#3460	1	1	yes	characteristic
301	C₂×C₁₃	C₂×#559	1	1	yes	characteristic
302	C₂×C₁₃	#3480	1	2	yes	—
303	C₂×C₁₃	#3483	1	1	yes	characteristic
304	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	—	2	4	no	—
307	C₂×Q₈	C₁₃×#41	1	8	yes	—
308	C₂×D₄	—	2	8	no	—
309	C₂×D₄	—	2	8	no	—
310	C₂×D₄	—	2	4	no	—
311	C₂×D₄	—	2	8	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂²×C₄	—	2	16	no	—
315	C₂²×C₄	—	2	8	no	—
316	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
317	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
318	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
319	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
320	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
321	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
322	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
323	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
324	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
325	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
326	C₄⋊C₄	—	2	8	no	—
327	C₄⋊C₄	—	2	8	no	—
328	C₄⋊C₄	—	2	8	no	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	4	4	no	—
334	C₄⋊C₄	—	4	4	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	2	16	no	—
337	C₂²⋊C₄	—	2	16	no	—
338	C₂²⋊C₄	—	2	16	no	—
339	C₂²⋊C₄	—	4	8	no	—
340	C₂²⋊C₄	—	4	4	no	—
341	C₂²⋊C₄	—	4	8	no	—
342	C₄²	—	2	8	no	—
343	C₄²	—	2	4	no	—
344	C₄²	—	2	8	no	—
345	C₄²	—	2	8	no	—
346	C₄²	—	2	8	no	—
347	C₄²	—	2	8	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	4	1	no	—
350	C₄²	—	4	4	no	—
351	C₄²	C₁₃×#41	1	8	yes	—
352	C₄²	C₁₃×#41	1	4	yes	—
353	C₁₃	#34954	1	1	yes	characteristic, direct product factor, Sylow
354	C₂³	—	2	8	no	—
355	C₂³	—	2	8	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	4	no	—
358	C₂³	—	2	4	no	—
359	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
360	Q₈	—	2	16	no	—
361	D₄	—	4	8	no	—
362	D₄	—	4	16	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	4	16	no	—
383	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
384	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
385	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
386	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
387	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
388	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
389	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
390	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
391	C₂²	—	4	8	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	8	no	—
395	C₂²	—	4	4	no	—
396	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
397	C₂²	C₂²×C₁₃×#41	1	2	yes	—
398	C₂²	C₂²×C₁₃×#41	1	2	yes	—
399	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
400	C₂²	C₁₃×#585	1	1	yes	characteristic
401	C₄	—	2	8	no	—
402	C₄	—	2	2	no	—
403	C₄	—	2	4	no	—
404	C₄	—	4	4	no	—
405	C₄	—	4	4	no	—
406	C₄	—	4	4	no	—
407	C₄	—	4	4	no	—
408	C₄	—	4	1	no	—
409	C₄	C₁₃×#529	1	8	yes	—
410	C₄	C₁₃×#559	1	4	yes	—
411	C₂	—	8	4	no	—
412	C₂	C₂×C₁₃×#529	1	2	yes	—
413	C₂	C₁₃×#3460	1	1	yes	characteristic
414	C₂	C₂×C₁₃×#559	1	1	yes	characteristic
415	C₂	C₁₃×#3480	1	2	yes	—
416	C₂	C₁₃×#3483	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2593	C₂	semidirect
2. C₁₃×#2582	C₂	semidirect
3. C₁₃×#2571	C₂	semidirect
5. C₁₃×#2513	C₂	semidirect
6. C₁₃×#2448	C₂	semidirect
7. C₁₃×#2395	C₂	semidirect
9. C₄×C₁₃×#124	C₂	semidirect
10. C₁₃×#2293	C₂	semidirect
11. C₄²×Q₈×C₁₃	C₂	semidirect
96. #34954	C₁₃	direct (N × H)
146. #2593	C₂×C₁₃	semidirect
147. #2582	C₂×C₁₃	semidirect
148. #2571	C₂×C₁₃	semidirect
150. #2513	C₂×C₁₃	semidirect
151. #2448	C₂×C₁₃	semidirect
152. #2395	C₂×C₁₃	semidirect
154. C₄×#124	C₂×C₁₃	semidirect
155. #2293	C₂×C₁₃	semidirect
156. C₄²×Q₈	C₂×C₁₃	semidirect
353. C₁₃	#34954	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#2593	2
C₁₃×#2582	2
C₁₃×#2571	2
C₁₃×#2548	2
C₁₃×#2513	2
C₁₃×#2448	2
C₁₃×#2395	2
C₄×C₁₃×#127	2
C₄×C₁₃×#124	2
C₁₃×#2293	2
C₄²×Q₈×C₁₃	2
#34954	13

Subgroups — C13×#34954 #15721293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34954 #15721293