Subgroups — C₁₃×#34972 #15721311

Order 3328.

2474 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2604	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2565	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2545	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2503	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2501	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#2436	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#2434	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2413	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2396	C₂	1	4	yes	maximal, complemented
12	C₄×C₁₃×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
13	C₄×C₁₃×#124	C₂	1	2	yes	maximal, complemented
14	C₄×C₁₃×#123	C₂	1	4	yes	maximal, complemented
15	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₁₃×#529	—	2	8	no	—
19	C₂×C₁₃×#126	C₂²	1	2	yes	—
20	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#124	C₂²	1	2	yes	—
23	C₂×C₁₃×#123	C₂²	1	4	yes	—
24	C₂×C₁₃×#123	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₃	—	2	8	no	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#117	C₂²	1	2	yes	—
36	C₂×C₁₃×#117	C₂²	1	2	yes	—
37	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
39	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
40	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#400	C₂²	1	4	yes	—
42	C₁₃×#399	C₂²	1	4	yes	—
43	C₁₃×#398	C₂²	1	8	yes	—
44	C₁₃×#396	C₂²	1	8	yes	—
45	C₁₃×#395	C₂²	1	4	yes	—
46	C₁₃×#393	C₂²	1	4	yes	—
47	C₁₃×#391	C₂²	1	2	yes	—
48	C₁₃×#391	C₂²	1	2	yes	—
49	C₁₃×#391	C₂²	1	2	yes	—
50	C₁₃×#390	C₂²	1	2	yes	—
51	C₁₃×#389	C₂²	1	8	yes	—
52	C₁₃×#388	C₂²	1	8	yes	—
53	C₁₃×#388	C₂²	1	8	yes	—
54	C₁₃×#387	C₂²	1	8	yes	—
55	C₁₃×#386	C₂²	1	4	yes	—
56	C₁₃×#385	C₂²	1	4	yes	—
57	C₁₃×#384	C₂²	1	2	yes	—
58	C₁₃×#382	C₂²	1	2	yes	—
59	C₁₃×#381	C₂²	1	4	yes	—
60	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
61	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
62	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
63	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
64	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
65	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
66	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
67	C₁₃×#376	C₂²	1	2	yes	—
68	C₄³×C₁₃	C₂²	1	2	yes	—
69	C₂²×Q₈×C₁₃	—	2	8	no	—
70	C₂²×Q₈×C₁₃	—	2	4	no	—
71	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
73	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
74	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
75	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
77	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
78	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₁₃×C₄⋊Q₈	—	2	8	no	—
83	C₁₃×#126	—	2	8	no	—
84	C₁₃×#125	—	2	4	no	—
85	C₁₃×#124	—	2	8	no	—
86	C₁₃×#124	—	2	4	no	—
87	C₁₃×#123	—	2	8	no	—
88	C₁₃×#123	—	2	16	no	—
89	C₁₃×C₂²⋊Q₈	—	2	4	no	—
90	C₁₃×#121	—	2	4	no	—
91	C₄×Q₈×C₁₃	—	2	8	no	—
92	C₄×Q₈×C₁₃	—	2	8	no	—
93	C₄×Q₈×C₁₃	—	2	8	no	—
94	C₄×Q₈×C₁₃	—	2	8	no	—
95	C₄×Q₈×C₁₃	—	2	4	no	—
96	C₄×D₄×C₁₃	—	2	8	no	—
97	C₄×D₄×C₁₃	—	2	4	no	—
98	C₁₃×#117	—	2	8	no	—
99	C₁₃×#117	—	2	8	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
116	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
117	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
118	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
119	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
120	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
123	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₃	—	2	8	no	—
125	C₂×C₄²×C₁₃	D₄	1	8	yes	—
126	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
127	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
128	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
129	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
130	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
131	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
132	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
137	C₁₃×#95	C₂³	1	4	yes	—
138	C₁₃×#95	C₂³	1	2	yes	—
139	C₁₃×#95	C₂³	1	2	yes	—
140	C₁₃×#95	C₂³	1	8	yes	—
141	C₁₃×#95	C₂³	1	8	yes	—
142	C₁₃×#95	C₂³	1	8	yes	—
143	C₁₃×#95	C₂³	1	8	yes	—
144	#34972	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
146	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
147	C₂×Q₈×C₁₃	—	2	32	no	—
148	C₂×Q₈×C₁₃	—	2	4	no	—
149	C₂×Q₈×C₁₃	—	2	4	no	—
150	C₂×Q₈×C₁₃	—	2	2	no	—
151	C₂×Q₈×C₁₃	—	2	8	no	—
152	C₂×Q₈×C₁₃	—	2	4	no	—
153	C₂×Q₈×C₁₃	—	2	4	no	—
154	C₂×Q₈×C₁₃	#41	1	8	yes	—
155	C₂×D₄×C₁₃	—	2	4	no	—
156	C₂×D₄×C₁₃	—	2	8	no	—
157	C₂×D₄×C₁₃	—	2	2	no	—
158	C₂×D₄×C₁₃	—	2	4	no	—
159	C₂²×C₄×C₁₃	—	2	4	no	—
160	C₂²×C₄×C₁₃	—	2	4	no	—
161	C₂²×C₄×C₁₃	—	2	8	no	—
162	C₂²×C₄×C₁₃	—	2	4	no	—
163	C₂²×C₄×C₁₃	—	2	4	no	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	2	8	no	—
166	C₂²×C₄×C₁₃	—	2	4	no	—
167	C₂²×C₄×C₁₃	—	2	8	no	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
170	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
184	C₁₃×C₄⋊C₄	—	2	8	no	—
185	C₁₃×C₄⋊C₄	—	2	8	no	—
186	C₁₃×C₄⋊C₄	—	2	4	no	—
187	C₁₃×C₄⋊C₄	—	2	4	no	—
188	C₁₃×C₄⋊C₄	—	2	4	no	—
189	C₁₃×C₄⋊C₄	—	2	4	no	—
190	C₁₃×C₄⋊C₄	—	2	2	no	—
191	C₁₃×C₄⋊C₄	—	2	4	no	—
192	C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₁₃×C₄⋊C₄	—	2	4	no	—
194	C₁₃×C₄⋊C₄	—	2	8	no	—
195	C₁₃×C₄⋊C₄	—	2	16	no	—
196	C₁₃×C₄⋊C₄	—	2	16	no	—
197	C₁₃×C₂²⋊C₄	—	2	4	no	—
198	C₁₃×C₂²⋊C₄	—	2	4	no	—
199	C₁₃×C₂²⋊C₄	—	2	4	no	—
200	C₁₃×C₂²⋊C₄	—	2	4	no	—
201	C₁₃×C₂²⋊C₄	—	2	4	no	—
202	C₁₃×C₂²⋊C₄	—	2	4	no	—
203	C₁₃×C₂²⋊C₄	—	2	16	no	—
204	C₁₃×C₂²⋊C₄	—	2	16	no	—
205	C₁₃×C₂²⋊C₄	#41	1	8	yes	—
206	C₄²×C₁₃	—	2	8	no	—
207	C₄²×C₁₃	—	2	8	no	—
208	C₄²×C₁₃	—	2	4	no	—
209	C₄²×C₁₃	—	2	8	no	—
210	C₄²×C₁₃	—	2	4	no	—
211	C₄²×C₁₃	—	2	4	no	—
212	C₄²×C₁₃	—	2	8	no	—
213	C₄²×C₁₃	C₂×D₄	1	4	yes	—
214	C₄²×C₁₃	C₂×D₄	1	4	yes	—
215	C₄²×C₁₃	C₂×D₄	1	4	yes	—
216	C₄²×C₁₃	C₂×D₄	1	4	yes	—
217	C₂×#529	C₂×C₁₃	1	1	yes	characteristic
218	C₂²×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#2604	C₂×C₁₃	1	4	yes	complemented
220	#2565	C₂×C₁₃	1	2	yes	complemented
221	#2545	C₂×C₁₃	1	2	yes	complemented
222	#2503	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#2501	C₂×C₁₃	1	1	yes	characteristic
224	#2436	C₂×C₁₃	1	1	yes	characteristic
225	#2434	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#2413	C₂×C₁₃	1	4	yes	complemented
227	#2396	C₂×C₁₃	1	4	yes	complemented
228	C₄×C₄⋊Q₈	C₂×C₁₃	1	2	yes	complemented
229	C₄×#124	C₂×C₁₃	1	2	yes	complemented
230	C₄×#123	C₂×C₁₃	1	4	yes	complemented
231	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
232	C₂³×C₁₃	—	2	2	no	—
233	C₂³×C₁₃	—	2	2	no	—
234	C₂³×C₁₃	—	2	2	no	—
235	C₂³×C₁₃	—	2	4	no	—
236	C₂³×C₁₃	—	2	4	no	—
237	C₂³×C₁₃	—	2	4	no	—
238	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
239	C₂³×C₁₃	C₂×#41	1	4	yes	—
240	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
241	Q₈×C₁₃	—	2	16	no	—
242	Q₈×C₁₃	—	2	16	no	—
243	Q₈×C₁₃	—	4	4	no	—
244	D₄×C₁₃	—	4	8	no	—
245	D₄×C₁₃	—	4	4	no	—
246	C₂×C₄×C₁₃	—	2	16	no	—
247	C₂×C₄×C₁₃	—	2	8	no	—
248	C₂×C₄×C₁₃	—	2	4	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	8	no	—
257	C₂×C₄×C₁₃	—	2	8	no	—
258	C₂×C₄×C₁₃	—	2	4	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	2	no	—
262	C₂×C₄×C₁₃	—	2	4	no	—
263	C₂×C₄×C₁₃	—	2	4	no	—
264	C₂×C₄×C₁₃	—	2	8	no	—
265	C₂×C₄×C₁₃	—	2	4	no	—
266	C₂×C₄×C₁₃	—	2	4	no	—
267	C₂×C₄×C₁₃	—	2	4	no	—
268	C₂×C₄×C₁₃	—	2	4	no	—
269	C₂×C₄×C₁₃	—	4	8	no	—
270	C₂×C₄×C₁₃	—	4	8	no	—
271	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
272	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
273	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
274	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
275	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
276	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
277	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
278	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
279	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
280	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
281	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
283	#529	—	2	8	no	—
284	C₂×#126	C₂²×C₁₃	1	2	yes	—
285	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×#124	C₂²×C₁₃	1	2	yes	—
288	C₂×#123	C₂²×C₁₃	1	2	yes	—
289	C₂×#123	C₂²×C₁₃	1	4	yes	—
290	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×C₄×Q₈	—	2	8	no	—
293	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
295	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
296	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
297	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
298	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
299	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×#117	C₂²×C₁₃	1	2	yes	—
301	C₂×#117	C₂²×C₁₃	1	2	yes	—
302	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
303	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
304	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
305	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
306	#400	C₂²×C₁₃	1	4	yes	—
307	#399	C₂²×C₁₃	1	4	yes	—
308	#398	C₂²×C₁₃	1	8	yes	—
309	#396	C₂²×C₁₃	1	8	yes	—
310	#395	C₂²×C₁₃	1	4	yes	—
311	#393	C₂²×C₁₃	1	4	yes	—
312	#391	C₂²×C₁₃	1	2	yes	—
313	#391	C₂²×C₁₃	1	2	yes	—
314	#391	C₂²×C₁₃	1	2	yes	—
315	#390	C₂²×C₁₃	1	2	yes	—
316	#389	C₂²×C₁₃	1	8	yes	—
317	#388	C₂²×C₁₃	1	8	yes	—
318	#388	C₂²×C₁₃	1	8	yes	—
319	#387	C₂²×C₁₃	1	8	yes	—
320	#386	C₂²×C₁₃	1	4	yes	—
321	#385	C₂²×C₁₃	1	4	yes	—
322	#384	C₂²×C₁₃	1	2	yes	—
323	#382	C₂²×C₁₃	1	2	yes	—
324	#381	C₂²×C₁₃	1	4	yes	—
325	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
326	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
327	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
328	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
329	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
330	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
331	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
332	#376	C₂²×C₁₃	1	2	yes	—
333	C₄³	C₂²×C₁₃	1	2	yes	—
334	C₂²×C₁₃	—	2	2	no	—
335	C₂²×C₁₃	—	2	2	no	—
336	C₂²×C₁₃	—	2	8	no	—
337	C₂²×C₁₃	—	4	2	no	—
338	C₂²×C₁₃	—	4	2	no	—
339	C₂²×C₁₃	—	4	2	no	—
340	C₂²×C₁₃	—	4	8	no	—
341	C₂²×C₁₃	#532	1	4	yes	—
342	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
343	C₂²×C₁₃	C₂²×#41	1	2	yes	—
344	C₂²×C₁₃	C₂²×#41	1	2	yes	—
345	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
346	C₄×C₁₃	—	2	2	no	—
347	C₄×C₁₃	—	2	8	no	—
348	C₄×C₁₃	—	2	2	no	—
349	C₄×C₁₃	—	2	2	no	—
350	C₄×C₁₃	—	2	2	no	—
351	C₄×C₁₃	—	2	8	no	—
352	C₄×C₁₃	—	4	2	no	—
353	C₄×C₁₃	—	4	4	no	—
354	C₄×C₁₃	—	4	2	no	—
355	C₄×C₁₃	—	4	2	no	—
356	C₄×C₁₃	—	4	4	no	—
357	C₄×C₁₃	#525	1	4	yes	—
358	C₄×C₁₃	#536	1	4	yes	—
359	C₂²×Q₈	—	2	8	no	—
360	C₂²×Q₈	—	2	4	no	—
361	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
362	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
363	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
364	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
365	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
366	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
367	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
368	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
369	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
370	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
371	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
372	C₄⋊Q₈	—	2	8	no	—
373	#126	—	2	8	no	—
374	#125	—	2	4	no	—
375	#124	—	2	8	no	—
376	#124	—	2	4	no	—
377	#123	—	2	8	no	—
378	#123	—	2	16	no	—
379	C₂²⋊Q₈	—	2	4	no	—
380	#121	—	2	4	no	—
381	C₄×Q₈	—	2	8	no	—
382	C₄×Q₈	—	2	8	no	—
383	C₄×Q₈	—	2	8	no	—
384	C₄×Q₈	—	2	8	no	—
385	C₄×Q₈	—	2	4	no	—
386	C₄×D₄	—	2	8	no	—
387	C₄×D₄	—	2	4	no	—
388	#117	—	2	8	no	—
389	#117	—	2	8	no	—
390	C₂×C₄⋊C₄	—	2	8	no	—
391	C₂×C₄⋊C₄	—	2	4	no	—
392	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
393	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
394	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
395	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
396	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
397	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
398	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
399	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
401	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
403	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
404	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
405	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
406	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
414	C₂×C₄²	—	2	8	no	—
415	C₂×C₄²	D₄×C₁₃	1	8	yes	—
416	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
417	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
418	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
419	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
420	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
421	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
422	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
423	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
425	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
426	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
427	#95	C₂³×C₁₃	1	4	yes	—
428	#95	C₂³×C₁₃	1	2	yes	—
429	#95	C₂³×C₁₃	1	2	yes	—
430	#95	C₂³×C₁₃	1	8	yes	—
431	#95	C₂³×C₁₃	1	8	yes	—
432	#95	C₂³×C₁₃	1	8	yes	—
433	#95	C₂³×C₁₃	1	8	yes	—
434	C₂×C₁₃	—	2	4	no	—
435	C₂×C₁₃	—	8	2	no	—
436	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
437	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
438	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
439	C₂×C₁₃	#3482	1	4	yes	—
440	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
441	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
442	C₂×Q₈	—	2	32	no	—
443	C₂×Q₈	—	2	4	no	—
444	C₂×Q₈	—	2	4	no	—
445	C₂×Q₈	—	2	2	no	—
446	C₂×Q₈	—	2	8	no	—
447	C₂×Q₈	—	2	4	no	—
448	C₂×Q₈	—	2	4	no	—
449	C₂×Q₈	C₁₃×#41	1	8	yes	—
450	C₂×D₄	—	2	4	no	—
451	C₂×D₄	—	2	8	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	4	no	—
454	C₂²×C₄	—	2	4	no	—
455	C₂²×C₄	—	2	4	no	—
456	C₂²×C₄	—	2	8	no	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	8	no	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	8	no	—
463	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
464	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
465	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
466	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
467	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
468	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
469	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
470	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
471	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
472	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
473	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
474	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
475	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
476	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
477	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
478	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
479	C₄⋊C₄	—	2	8	no	—
480	C₄⋊C₄	—	2	8	no	—
481	C₄⋊C₄	—	2	4	no	—
482	C₄⋊C₄	—	2	4	no	—
483	C₄⋊C₄	—	2	4	no	—
484	C₄⋊C₄	—	2	4	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	4	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	4	no	—
489	C₄⋊C₄	—	2	8	no	—
490	C₄⋊C₄	—	2	16	no	—
491	C₄⋊C₄	—	2	16	no	—
492	C₂²⋊C₄	—	2	4	no	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	—	2	4	no	—
495	C₂²⋊C₄	—	2	4	no	—
496	C₂²⋊C₄	—	2	4	no	—
497	C₂²⋊C₄	—	2	4	no	—
498	C₂²⋊C₄	—	2	16	no	—
499	C₂²⋊C₄	—	2	16	no	—
500	C₂²⋊C₄	C₁₃×#41	1	8	yes	—
501	C₄²	—	2	8	no	—
502	C₄²	—	2	8	no	—
503	C₄²	—	2	4	no	—
504	C₄²	—	2	8	no	—
505	C₄²	—	2	4	no	—
506	C₄²	—	2	4	no	—
507	C₄²	—	2	8	no	—
508	C₄²	C₂×D₄×C₁₃	1	4	yes	—
509	C₄²	C₂×D₄×C₁₃	1	4	yes	—
510	C₄²	C₂×D₄×C₁₃	1	4	yes	—
511	C₄²	C₂×D₄×C₁₃	1	4	yes	—
512	C₁₃	#34972	1	1	yes	characteristic, direct product factor, Sylow
513	C₂³	—	2	2	no	—
514	C₂³	—	2	2	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	2	4	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	2	4	no	—
519	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
520	C₂³	C₂×C₁₃×#41	1	4	yes	—
521	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
522	Q₈	—	2	16	no	—
523	Q₈	—	2	16	no	—
524	Q₈	—	4	4	no	—
525	D₄	—	4	8	no	—
526	D₄	—	4	4	no	—
527	C₂×C₄	—	2	16	no	—
528	C₂×C₄	—	2	8	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	8	no	—
538	C₂×C₄	—	2	8	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	8	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	4	8	no	—
551	C₂×C₄	—	4	8	no	—
552	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
553	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
554	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
555	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
556	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
557	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
558	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
559	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
560	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
561	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
562	C₂²	—	2	2	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	2	8	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	8	no	—
569	C₂²	C₁₃×#532	1	4	yes	—
570	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
571	C₂²	C₂²×C₁₃×#41	1	2	yes	—
572	C₂²	C₂²×C₁₃×#41	1	2	yes	—
573	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
574	C₄	—	2	2	no	—
575	C₄	—	2	8	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	2	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	8	no	—
580	C₄	—	4	2	no	—
581	C₄	—	4	4	no	—
582	C₄	—	4	2	no	—
583	C₄	—	4	2	no	—
584	C₄	—	4	4	no	—
585	C₄	C₁₃×#525	1	4	yes	—
586	C₄	C₁₃×#536	1	4	yes	—
587	C₂	—	2	4	no	—
588	C₂	—	8	2	no	—
589	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
590	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
591	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
592	C₂	C₁₃×#3482	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂×C₁₃×#121	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
2. C₂²×C₄×Q₈×C₁₃	C₂	semidirect
3. C₁₃×#2604	C₂	semidirect
4. C₁₃×#2565	C₂	semidirect
5. C₁₃×#2545	C₂	semidirect
6. C₁₃×#2503	C₂	semidirect
9. C₁₃×#2434	C₂	semidirect
10. C₁₃×#2413	C₂	semidirect
11. C₁₃×#2396	C₂	semidirect
12. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
13. C₄×C₁₃×#124	C₂	semidirect
14. C₄×C₁₃×#123	C₂	semidirect
15. C₄×C₁₃×#117	C₂	semidirect
144. #34972	C₁₃	direct (N × H)
218. C₂²×C₄×Q₈	C₂×C₁₃	semidirect
219. #2604	C₂×C₁₃	semidirect
220. #2565	C₂×C₁₃	semidirect
221. #2545	C₂×C₁₃	semidirect
222. #2503	C₂×C₁₃	semidirect
225. #2434	C₂×C₁₃	semidirect
226. #2413	C₂×C₁₃	semidirect
227. #2396	C₂×C₁₃	semidirect
228. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
229. C₄×#124	C₂×C₁₃	semidirect
230. C₄×#123	C₂×C₁₃	semidirect
231. C₄×#117	C₂×C₁₃	semidirect
512. C₁₃	#34972	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×#529	2
C₂²×C₄×Q₈×C₁₃	2
C₁₃×#2604	2
C₁₃×#2565	2
C₁₃×#2545	2
C₁₃×#2503	2
C₁₃×#2501	2
C₁₃×#2436	2
C₁₃×#2434	2
C₁₃×#2413	2
C₁₃×#2396	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×#124	2
C₄×C₁₃×#123	2
C₄×C₁₃×#117	2
#34972	13

Subgroups — C13×#34972 #15721311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34972 #15721311