Subgroups — C₁₃×#34189 #15720528

Order 3328.

2342 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2357	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2356	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2353	C₂	1	8	yes	maximal, complemented
5	C₁₃×#2314	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2311	C₂	1	2	yes	maximal
7	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2283	C₂	1	4	yes	maximal, complemented
9	C₂×C₁₃×#382	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2274	C₂	1	2	yes	maximal, complemented
11	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
12	C₄×C₁₃×#41	C₄	1	16	yes	complemented
13	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
15	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
16	C₂×C₁₃×#117	C₂²	1	2	yes	—
17	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#117	C₂²	1	2	yes	—
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
22	C₁₃×#391	C₂²	1	4	yes	—
23	C₁₃×#390	C₂²	1	4	yes	—
24	C₁₃×#388	C₂²	1	16	yes	—
25	C₁₃×#387	C₂²	1	16	yes	—
26	C₁₃×#386	C₂²	1	8	yes	—
27	C₁₃×#384	C₂²	1	2	yes	—
28	C₁₃×#383	C₂²	1	8	yes	—
29	C₁₃×#382	C₂²	1	2	yes	—
30	C₁₃×#382	C₂²	1	2	yes	—
31	C₁₃×#382	C₂²	1	4	yes	—
32	C₁₃×#382	C₂²	1	2	yes	—
33	C₁₃×#381	C₂²	1	8	yes	—
34	C₁₃×#380	C₂²	1	8	yes	—
35	C₁₃×#380	C₂²	1	4	yes	—
36	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
38	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
39	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
40	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
41	C₁₃×#376	C₂²	1	8	yes	—
42	C₂×C₁₃×#95	C₂²	1	4	yes	—
43	C₂×C₁₃×#41	—	2	4	no	—
44	C₂×C₁₃×#41	—	2	4	no	—
45	C₂×C₁₃×#41	C₂×C₄	1	8	yes	—
46	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
48	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
51	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₄×Q₈×C₁₃	C₂×C₄	1	16	yes	complemented
55	C₄×D₄×C₁₃	C₂×C₄	1	32	yes	—
56	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
57	C₁₃×#117	—	2	8	no	—
58	C₁₃×#117	C₂×C₄	1	8	yes	—
59	C₁₃×#117	C₂×C₄	1	16	yes	complemented
60	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
67	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
68	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
69	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
70	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
71	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	—
72	C₂×C₄²×C₁₃	C₂×C₄	1	16	yes	complemented
73	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
74	C₂×C₄²×C₁₃	C₂³	1	16	yes	—
75	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
76	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
80	C₁₃×#95	C₂³	1	4	yes	—
81	C₁₃×#95	C₂³	1	16	yes	—
82	C₁₃×#95	C₂³	1	8	yes	—
83	C₁₃×#95	C₂³	1	4	yes	—
84	C₁₃×#95	C₂³	1	16	yes	—
85	C₁₃×#95	C₂³	1	8	yes	—
86	#34189	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
88	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
89	C₁₃×#41	—	2	32	no	—
90	C₂×Q₈×C₁₃	—	2	2	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
93	C₂×D₄×C₁₃	—	2	4	no	—
94	C₂×D₄×C₁₃	—	2	4	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
98	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₁₃	—	2	4	no	—
100	C₂²×C₄×C₁₃	—	2	4	no	—
101	C₂²×C₄×C₁₃	—	2	8	no	—
102	C₂²×C₄×C₁₃	—	4	8	no	—
103	C₂²×C₄×C₁₃	—	4	4	no	—
104	C₂²×C₄×C₁₃	—	4	8	no	—
105	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
106	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
107	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
108	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
109	C₂²×C₄×C₁₃	#41	1	4	yes	—
110	C₂²×C₄×C₁₃	#41	1	4	yes	—
111	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
112	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
113	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
116	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	—	4	8	no	—
123	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
124	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
125	C₁₃×C₂²⋊C₄	—	2	8	no	—
126	C₁₃×C₂²⋊C₄	—	4	16	no	—
127	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
128	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
129	C₄²×C₁₃	—	2	8	no	—
130	C₄²×C₁₃	—	4	16	no	—
131	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
132	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
133	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
134	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
135	C₄²×C₁₃	C₂²×C₄	1	16	yes	—
136	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic
137	#2357	C₂×C₁₃	1	4	yes	complemented
138	#2356	C₂×C₁₃	1	4	yes	complemented
139	#2353	C₂×C₁₃	1	8	yes	complemented
140	#2314	C₂×C₁₃	1	4	yes	complemented
141	#2311	C₂×C₁₃	1	2	yes	—
142	#2285	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#2283	C₂×C₁₃	1	4	yes	complemented
144	C₂×#382	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#2274	C₂×C₁₃	1	2	yes	complemented
146	C₂³×C₁₃	—	2	4	no	—
147	C₂³×C₁₃	—	2	2	no	—
148	C₂³×C₁₃	—	2	2	no	—
149	C₂³×C₁₃	—	2	8	no	—
150	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
151	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
152	C₂³×C₁₃	C₂×#41	1	2	yes	—
153	C₂³×C₁₃	C₂×#41	1	2	yes	—
154	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
155	Q₈×C₁₃	—	2	8	no	—
156	D₄×C₁₃	—	2	16	no	—
157	D₄×C₁₃	—	2	8	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	8	no	—
161	C₂×C₄×C₁₃	—	2	4	no	—
162	C₂×C₄×C₁₃	—	2	4	no	—
163	C₂×C₄×C₁₃	—	2	16	no	—
164	C₂×C₄×C₁₃	—	2	8	no	—
165	C₂×C₄×C₁₃	—	2	8	no	—
166	C₂×C₄×C₁₃	—	2	8	no	—
167	C₂×C₄×C₁₃	—	2	16	no	—
168	C₂×C₄×C₁₃	—	2	8	no	—
169	C₂×C₄×C₁₃	—	4	8	no	—
170	C₂×C₄×C₁₃	—	4	16	no	—
171	C₂×C₄×C₁₃	—	8	8	no	—
172	C₂×C₄×C₁₃	#117	1	16	yes	—
173	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
174	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
175	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
176	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
177	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
178	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
179	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
180	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
181	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
182	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
183	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
184	C₄×#41	C₄×C₁₃	1	16	yes	complemented
185	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
186	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
187	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
188	C₂×#117	C₂²×C₁₃	1	2	yes	—
189	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
190	C₂×#117	C₂²×C₁₃	1	2	yes	—
191	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
192	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
193	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
194	#391	C₂²×C₁₃	1	4	yes	—
195	#390	C₂²×C₁₃	1	4	yes	—
196	#388	C₂²×C₁₃	1	16	yes	—
197	#387	C₂²×C₁₃	1	16	yes	—
198	#386	C₂²×C₁₃	1	8	yes	—
199	#384	C₂²×C₁₃	1	2	yes	—
200	#383	C₂²×C₁₃	1	8	yes	—
201	#382	C₂²×C₁₃	1	2	yes	—
202	#382	C₂²×C₁₃	1	4	yes	—
203	#382	C₂²×C₁₃	1	2	yes	—
204	#382	C₂²×C₁₃	1	2	yes	—
205	#381	C₂²×C₁₃	1	8	yes	—
206	#380	C₂²×C₁₃	1	8	yes	—
207	#380	C₂²×C₁₃	1	4	yes	—
208	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
209	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
210	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
211	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
212	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
213	#376	C₂²×C₁₃	1	8	yes	—
214	C₂×#95	C₂²×C₁₃	1	4	yes	—
215	C₂²×C₁₃	—	2	4	no	—
216	C₂²×C₁₃	—	2	4	no	—
217	C₂²×C₁₃	—	2	4	no	—
218	C₂²×C₁₃	—	2	4	no	—
219	C₂²×C₁₃	—	2	8	no	—
220	C₂²×C₁₃	—	4	4	no	—
221	C₂²×C₁₃	—	4	4	no	—
222	C₂²×C₁₃	C₂×#117	1	4	yes	—
223	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
224	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
225	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
226	C₂²×C₁₃	#585	1	4	yes	—
227	C₄×C₁₃	—	2	4	no	—
228	C₄×C₁₃	—	2	4	no	—
229	C₄×C₁₃	—	2	8	no	—
230	C₄×C₁₃	—	2	4	no	—
231	C₄×C₁₃	—	4	8	no	—
232	C₄×C₁₃	—	4	8	no	—
233	C₄×C₁₃	C₂×#117	1	4	yes	—
234	C₄×C₁₃	C₂×#117	1	4	yes	—
235	C₂×#41	—	2	4	no	—
236	C₂×#41	—	2	4	no	—
237	C₂×#41	C₂×C₄×C₁₃	1	8	yes	—
238	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
239	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
240	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
241	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
242	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
243	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
244	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
245	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
246	C₄×Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
247	C₄×D₄	C₂×C₄×C₁₃	1	32	yes	—
248	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
249	#117	—	2	8	no	—
250	#117	C₂×C₄×C₁₃	1	8	yes	—
251	#117	C₂×C₄×C₁₃	1	16	yes	complemented
252	C₂×C₄⋊C₄	—	2	8	no	—
253	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
254	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
255	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
256	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
257	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
258	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
259	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
260	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
261	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
262	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
263	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	—
264	C₂×C₄²	C₂×C₄×C₁₃	1	16	yes	complemented
265	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
266	C₂×C₄²	C₂³×C₁₃	1	16	yes	—
267	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
268	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
270	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
271	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
272	#95	C₂³×C₁₃	1	8	yes	—
273	#95	C₂³×C₁₃	1	8	yes	—
274	#95	C₂³×C₁₃	1	4	yes	—
275	#95	C₂³×C₁₃	1	16	yes	—
276	#95	C₂³×C₁₃	1	4	yes	—
277	#95	C₂³×C₁₃	1	16	yes	—
278	C₂×C₁₃	—	2	4	no	—
279	C₂×C₁₃	—	4	4	no	—
280	C₂×C₁₃	C₂²×#117	1	1	yes	characteristic
281	C₂×C₁₃	#3428	1	2	yes	—
282	C₂×C₁₃	#3510	1	2	yes	—
283	C₂×C₁₃	#3512	1	2	yes	—
284	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
285	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
286	#41	—	2	32	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
295	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	8	no	—
299	C₂²×C₄	—	4	8	no	—
300	C₂²×C₄	—	4	4	no	—
301	C₂²×C₄	—	4	8	no	—
302	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
303	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
304	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	—
305	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
306	C₂²×C₄	C₁₃×#41	1	4	yes	—
307	C₂²×C₄	C₁₃×#41	1	4	yes	—
308	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
309	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
310	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
311	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
312	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
313	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
314	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
315	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
316	C₄⋊C₄	—	2	8	no	—
317	C₄⋊C₄	—	2	8	no	—
318	C₄⋊C₄	—	2	8	no	—
319	C₄⋊C₄	—	4	8	no	—
320	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
321	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
322	C₂²⋊C₄	—	2	8	no	—
323	C₂²⋊C₄	—	4	16	no	—
324	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
325	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
326	C₄²	—	2	8	no	—
327	C₄²	—	4	16	no	—
328	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
329	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
330	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
331	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
332	C₄²	C₂²×C₄×C₁₃	1	16	yes	—
333	C₁₃	#34189	1	1	yes	characteristic, direct product factor, Sylow
334	C₂³	—	2	4	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	8	no	—
338	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
339	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
340	C₂³	C₂×C₁₃×#41	1	2	yes	—
341	C₂³	C₂×C₁₃×#41	1	2	yes	—
342	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
343	Q₈	—	2	8	no	—
344	D₄	—	2	16	no	—
345	D₄	—	2	8	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	16	no	—
352	C₂×C₄	—	2	8	no	—
353	C₂×C₄	—	2	8	no	—
354	C₂×C₄	—	2	8	no	—
355	C₂×C₄	—	2	16	no	—
356	C₂×C₄	—	2	8	no	—
357	C₂×C₄	—	4	8	no	—
358	C₂×C₄	—	4	16	no	—
359	C₂×C₄	—	8	8	no	—
360	C₂×C₄	C₁₃×#117	1	16	yes	—
361	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
362	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
363	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
364	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
365	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
366	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
367	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
368	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
369	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
370	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
371	C₂²	—	2	4	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	4	no	—
375	C₂²	—	2	8	no	—
376	C₂²	—	4	4	no	—
377	C₂²	—	4	4	no	—
378	C₂²	C₂×C₁₃×#117	1	4	yes	—
379	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
380	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
381	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
382	C₂²	C₁₃×#585	1	4	yes	—
383	C₄	—	2	4	no	—
384	C₄	—	2	4	no	—
385	C₄	—	2	8	no	—
386	C₄	—	2	4	no	—
387	C₄	—	4	8	no	—
388	C₄	—	4	8	no	—
389	C₄	C₂×C₁₃×#117	1	4	yes	—
390	C₄	C₂×C₁₃×#117	1	4	yes	—
391	C₂	—	2	4	no	—
392	C₂	—	4	4	no	—
393	C₂	C₂²×C₁₃×#117	1	1	yes	characteristic
394	C₂	C₁₃×#3428	1	2	yes	—
395	C₂	C₁₃×#3510	1	2	yes	—
396	C₂	C₁₃×#3512	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2357	C₂	semidirect
3. C₁₃×#2356	C₂	semidirect
4. C₁₃×#2353	C₂	semidirect
5. C₁₃×#2314	C₂	semidirect
7. C₁₃×#2285	C₂	semidirect
8. C₁₃×#2283	C₂	semidirect
9. C₂×C₁₃×#382	C₂	semidirect
10. C₁₃×#2274	C₂	semidirect
12. C₄×C₁₃×#41	C₄	semidirect
54. C₄×Q₈×C₁₃	C₂×C₄	semidirect
56. C₄×D₄×C₁₃	C₂×C₄	semidirect
59. C₁₃×#117	C₂×C₄	semidirect
72. C₂×C₄²×C₁₃	C₂×C₄	semidirect
86. #34189	C₁₃	direct (N × H)
137. #2357	C₂×C₁₃	semidirect
138. #2356	C₂×C₁₃	semidirect
139. #2353	C₂×C₁₃	semidirect
140. #2314	C₂×C₁₃	semidirect
142. #2285	C₂×C₁₃	semidirect
143. #2283	C₂×C₁₃	semidirect
144. C₂×#382	C₂×C₁₃	semidirect
145. #2274	C₂×C₁₃	semidirect
184. C₄×#41	C₄×C₁₃	semidirect
246. C₄×Q₈	C₂×C₄×C₁₃	semidirect
248. C₄×D₄	C₂×C₄×C₁₃	semidirect
251. #117	C₂×C₄×C₁₃	semidirect
264. C₂×C₄²	C₂×C₄×C₁₃	semidirect
333. C₁₃	#34189	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×C₄×C₁₃×#41	2
C₁₃×#2357	2
C₁₃×#2356	2
C₁₃×#2353	2
C₁₃×#2314	2
C₁₃×#2311	2
C₁₃×#2285	2
C₁₃×#2283	2
C₂×C₁₃×#382	2
C₁₃×#2274	2
#34189	13

Subgroups — C13×#34189 #15720528

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34189 #15720528