Subgroups — C₁₃×#3551 #13112609

Order 1664.

1050 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#563	C₂	1	2	yes	maximal, complemented
2	C₁₃×#560	C₂	1	2	yes	maximal, complemented
3	C₁₃×#555	C₂	1	2	yes	maximal, complemented
4	C₁₃×#553	C₂	1	2	yes	maximal, complemented
5	C₁₃×#552	C₂	1	2	yes	maximal, complemented
6	C₁₃×#551	C₂	1	2	yes	maximal, complemented
7	C₁₃×#548	C₂	1	2	yes	maximal, complemented
8	C₁₃×#546	C₂	1	2	yes	maximal, complemented
9	C₁₃×#540	C₂	1	4	yes	maximal, complemented
10	C₁₃×#538	C₂	1	4	yes	maximal, complemented
11	C₁₃×#537	C₂	1	2	yes	maximal, complemented
12	C₁₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#529	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#41	C₂²	1	2	yes	—
18	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
19	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
20	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
23	C₁₃×#127	C₂²	1	1	yes	characteristic
24	C₁₃×#127	C₂²	1	2	yes	—
25	C₁₃×#126	C₂²	1	4	yes	—
26	C₁₃×#126	C₂²	1	4	yes	complemented
27	C₁₃×#126	C₂²	1	4	yes	complemented
28	C₁₃×#125	C₂²	1	2	yes	complemented
29	C₁₃×#125	C₂²	1	4	yes	complemented
30	C₁₃×#124	C₂²	1	2	yes	—
31	C₁₃×#124	C₂²	1	1	yes	characteristic
32	C₁₃×#124	C₂²	1	2	yes	—
33	C₁₃×#124	C₂²	1	2	yes	—
34	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#124	C₂²	1	4	yes	complemented
36	C₁₃×#123	C₂²	1	2	yes	—
37	C₁₃×#123	C₂²	1	4	yes	—
38	C₁₃×#123	C₂²	1	4	yes	—
39	C₁₃×#123	C₂²	1	4	yes	complemented
40	C₁₃×#123	C₂²	1	2	yes	complemented
41	C₁₃×#123	C₂²	1	4	yes	complemented
42	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
43	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
44	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
45	C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
46	C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
47	C₁₃×#121	C₂²	1	2	yes	—
48	C₁₃×#121	C₂²	1	2	yes	—
49	C₁₃×#121	C₂²	1	2	yes	—
50	C₁₃×#121	C₂²	1	2	yes	—
51	C₁₃×#121	C₂²	1	4	yes	—
52	C₁₃×#121	C₂²	1	2	yes	complemented
53	C₁₃×#121	C₂²	1	4	yes	complemented
54	C₁₃×#121	C₂²	1	4	yes	complemented
55	C₁₃×#121	C₂²	1	4	yes	complemented
56	C₁₃×#121	C₂²	1	4	yes	complemented
57	C₁₃×#121	C₂²	1	4	yes	complemented
58	C₁₃×#120	C₂²	1	2	yes	—
59	C₁₃×#120	C₂²	1	2	yes	—
60	C₁₃×#120	C₂²	1	4	yes	—
61	C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
62	C₄×D₄×C₁₃	C₂²	1	2	yes	—
63	C₄×D₄×C₁₃	C₂²	1	2	yes	—
64	C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
65	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
66	C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
67	C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
68	C₁₃×#117	C₂²	1	1	yes	characteristic
69	C₁₃×#117	C₂²	1	4	yes	complemented
70	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
71	C₁₃×#117	C₂²	1	4	yes	complemented
72	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
73	C₂×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
74	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
75	C₂⁴×C₁₃	C₂³	1	2	yes	—
76	C₁₃×#41	—	4	2	no	—
77	C₁₃×#41	—	4	2	no	—
78	C₁₃×#41	—	4	4	no	—
79	C₂×Q₈×C₁₃	—	4	2	no	—
80	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
81	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
83	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₂×D₄×C₁₃	—	4	2	no	—
85	C₂×D₄×C₁₃	C₂³	1	2	yes	—
86	C₂×D₄×C₁₃	C₂³	1	2	yes	—
87	C₂×D₄×C₁₃	C₂³	1	4	yes	—
88	C₂×D₄×C₁₃	C₂³	1	4	yes	—
89	C₂×D₄×C₁₃	C₂³	1	4	yes	—
90	C₂×D₄×C₁₃	C₂³	1	2	yes	—
91	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂×D₄×C₁₃	C₂³	1	4	yes	—
94	C₂×D₄×C₁₃	C₂³	1	2	yes	—
95	C₂×D₄×C₁₃	C₂³	1	2	yes	—
96	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
103	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
104	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
105	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
106	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
107	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
108	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
109	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
110	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
111	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
112	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
113	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
116	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
117	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
118	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
119	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
123	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
124	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
127	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
128	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
130	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₄²×C₁₃	C₂³	1	1	yes	characteristic
134	C₄²×C₁₃	C₂³	1	2	yes	—
135	C₄²×C₁₃	C₂³	1	1	yes	characteristic
136	C₄²×C₁₃	C₂³	1	2	yes	—
137	C₄²×C₁₃	C₂³	1	4	yes	—
138	C₄²×C₁₃	C₂³	1	2	yes	—
139	#3551	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₁₃	—	4	2	no	—
141	C₂³×C₁₃	—	4	4	no	—
142	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₂³×C₁₃	C₂⁴	1	4	yes	—
144	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
145	C₂³×C₁₃	C₂⁴	1	2	yes	—
146	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
147	Q₈×C₁₃	—	2	4	no	—
148	Q₈×C₁₃	—	4	2	no	—
149	Q₈×C₁₃	—	4	1	no	—
150	Q₈×C₁₃	—	4	1	no	—
151	D₄×C₁₃	—	2	4	no	—
152	D₄×C₁₃	—	4	2	no	—
153	D₄×C₁₃	—	4	4	no	—
154	D₄×C₁₃	—	4	2	no	—
155	D₄×C₁₃	—	4	4	no	—
156	D₄×C₁₃	—	4	4	no	—
157	D₄×C₁₃	—	4	2	no	—
158	D₄×C₁₃	—	4	2	no	—
159	D₄×C₁₃	—	4	1	no	—
160	D₄×C₁₃	—	4	1	no	—
161	D₄×C₁₃	—	4	1	no	—
162	D₄×C₁₃	—	4	1	no	—
163	D₄×C₁₃	—	4	4	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	4	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	4	4	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	—	4	4	no	—
171	C₂×C₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	—	4	4	no	—
173	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
174	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
176	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
177	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
180	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
181	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
182	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
183	#563	C₂×C₁₃	1	2	yes	complemented
184	#560	C₂×C₁₃	1	2	yes	complemented
185	#555	C₂×C₁₃	1	2	yes	complemented
186	#553	C₂×C₁₃	1	2	yes	complemented
187	#552	C₂×C₁₃	1	2	yes	complemented
188	#551	C₂×C₁₃	1	2	yes	complemented
189	#548	C₂×C₁₃	1	2	yes	complemented
190	#546	C₂×C₁₃	1	2	yes	complemented
191	#540	C₂×C₁₃	1	4	yes	complemented
192	#538	C₂×C₁₃	1	4	yes	complemented
193	#537	C₂×C₁₃	1	2	yes	complemented
194	#536	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#535	C₂×C₁₃	1	1	yes	characteristic, complemented
196	#532	C₂×C₁₃	1	1	yes	characteristic, complemented
197	#529	C₂×C₁₃	1	2	yes	complemented
198	C₂²×C₁₃	—	2	1	no	—
199	C₂²×C₁₃	—	2	2	no	—
200	C₂²×C₁₃	—	2	1	no	—
201	C₂²×C₁₃	—	2	1	no	—
202	C₂²×C₁₃	—	2	4	no	—
203	C₂²×C₁₃	—	2	2	no	—
204	C₂²×C₁₃	—	2	2	no	—
205	C₂²×C₁₃	—	2	4	no	—
206	C₂²×C₁₃	—	2	2	no	—
207	C₂²×C₁₃	—	2	2	no	—
208	C₂²×C₁₃	—	2	4	no	—
209	C₂²×C₁₃	—	2	2	no	—
210	C₂²×C₁₃	—	8	4	no	—
211	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
212	C₄×C₁₃	—	2	2	no	—
213	C₄×C₁₃	—	2	1	no	—
214	C₄×C₁₃	—	2	1	no	—
215	C₄×C₁₃	—	2	1	no	—
216	C₄×C₁₃	—	2	4	no	—
217	C₄×C₁₃	—	2	2	no	—
218	C₄×C₁₃	—	2	4	no	—
219	C₄×C₁₃	—	2	2	no	—
220	C₄×C₁₃	—	2	4	no	—
221	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
222	C₂×#41	C₂²×C₁₃	1	1	yes	characteristic
223	C₂×#41	C₂²×C₁₃	1	2	yes	—
224	C₂×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
225	C₂²×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
226	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
227	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
228	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
229	#127	C₂²×C₁₃	1	1	yes	characteristic
230	#127	C₂²×C₁₃	1	2	yes	—
231	#126	C₂²×C₁₃	1	4	yes	—
232	#126	C₂²×C₁₃	1	4	yes	complemented
233	#126	C₂²×C₁₃	1	4	yes	complemented
234	#125	C₂²×C₁₃	1	2	yes	complemented
235	#125	C₂²×C₁₃	1	4	yes	complemented
236	#124	C₂²×C₁₃	1	2	yes	—
237	#124	C₂²×C₁₃	1	1	yes	characteristic
238	#124	C₂²×C₁₃	1	2	yes	—
239	#124	C₂²×C₁₃	1	2	yes	—
240	#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
241	#124	C₂²×C₁₃	1	4	yes	complemented
242	#123	C₂²×C₁₃	1	2	yes	—
243	#123	C₂²×C₁₃	1	4	yes	—
244	#123	C₂²×C₁₃	1	4	yes	—
245	#123	C₂²×C₁₃	1	4	yes	complemented
246	#123	C₂²×C₁₃	1	2	yes	complemented
247	#123	C₂²×C₁₃	1	4	yes	complemented
248	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
249	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
250	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
251	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
252	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
253	#121	C₂²×C₁₃	1	2	yes	—
254	#121	C₂²×C₁₃	1	2	yes	—
255	#121	C₂²×C₁₃	1	2	yes	—
256	#121	C₂²×C₁₃	1	2	yes	—
257	#121	C₂²×C₁₃	1	4	yes	—
258	#121	C₂²×C₁₃	1	2	yes	complemented
259	#121	C₂²×C₁₃	1	4	yes	complemented
260	#121	C₂²×C₁₃	1	4	yes	complemented
261	#121	C₂²×C₁₃	1	4	yes	complemented
262	#121	C₂²×C₁₃	1	4	yes	complemented
263	#121	C₂²×C₁₃	1	4	yes	complemented
264	#120	C₂²×C₁₃	1	2	yes	—
265	#120	C₂²×C₁₃	1	2	yes	—
266	#120	C₂²×C₁₃	1	4	yes	—
267	C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
268	C₄×D₄	C₂²×C₁₃	1	2	yes	—
269	C₄×D₄	C₂²×C₁₃	1	2	yes	—
270	C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
271	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
272	C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
273	C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
274	#117	C₂²×C₁₃	1	1	yes	characteristic
275	#117	C₂²×C₁₃	1	4	yes	complemented
276	#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
277	#117	C₂²×C₁₃	1	4	yes	complemented
278	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
279	C₂×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
280	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
281	C₂×C₁₃	—	4	1	no	—
282	C₂×C₁₃	—	4	2	no	—
283	C₂×C₁₃	—	4	1	no	—
284	C₂×C₁₃	—	4	4	no	—
285	C₂×C₁₃	—	4	1	no	—
286	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
287	C₂×C₁₃	#585	1	2	yes	—
288	C₂⁴	C₂³×C₁₃	1	2	yes	—
289	#41	—	4	2	no	—
290	#41	—	4	2	no	—
291	#41	—	4	4	no	—
292	C₂×Q₈	—	4	2	no	—
293	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
294	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
295	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
296	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	C₂³×C₁₃	1	2	yes	—
299	C₂×D₄	C₂³×C₁₃	1	2	yes	—
300	C₂×D₄	C₂³×C₁₃	1	4	yes	—
301	C₂×D₄	C₂³×C₁₃	1	4	yes	—
302	C₂×D₄	C₂³×C₁₃	1	4	yes	—
303	C₂×D₄	C₂³×C₁₃	1	2	yes	—
304	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
305	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
306	C₂×D₄	C₂³×C₁₃	1	4	yes	—
307	C₂×D₄	C₂³×C₁₃	1	2	yes	—
308	C₂×D₄	C₂³×C₁₃	1	2	yes	—
309	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
310	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
311	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
312	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
313	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
314	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
315	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
316	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
317	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
318	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
319	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
320	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
321	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
322	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
323	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
324	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
325	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
326	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
327	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
328	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
329	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
330	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
331	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
332	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
333	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
334	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
335	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
336	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
337	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
338	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
339	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
340	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
341	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
342	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
343	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
344	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
345	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
346	C₄²	C₂³×C₁₃	1	1	yes	characteristic
347	C₄²	C₂³×C₁₃	1	2	yes	—
348	C₄²	C₂³×C₁₃	1	1	yes	characteristic
349	C₄²	C₂³×C₁₃	1	2	yes	—
350	C₄²	C₂³×C₁₃	1	4	yes	—
351	C₄²	C₂³×C₁₃	1	2	yes	—
352	C₁₃	#3551	1	1	yes	characteristic, direct product factor, Sylow
353	C₂³	—	4	2	no	—
354	C₂³	—	4	4	no	—
355	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
356	C₂³	C₂⁴×C₁₃	1	4	yes	—
357	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
358	C₂³	C₂⁴×C₁₃	1	2	yes	—
359	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
360	Q₈	—	2	4	no	—
361	Q₈	—	4	2	no	—
362	Q₈	—	4	1	no	—
363	Q₈	—	4	1	no	—
364	D₄	—	2	4	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	4	no	—
367	D₄	—	4	2	no	—
368	D₄	—	4	4	no	—
369	D₄	—	4	4	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	1	no	—
373	D₄	—	4	1	no	—
374	D₄	—	4	1	no	—
375	D₄	—	4	1	no	—
376	D₄	—	4	4	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
387	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
388	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
389	C₂×C₄	C₂⁴×C₁₃	1	4	yes	—
390	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
391	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
392	C₂×C₄	C₂⁴×C₁₃	1	4	yes	—
393	C₂×C₄	C₂⁴×C₁₃	1	4	yes	—
394	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
395	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
396	C₂²	—	2	1	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	4	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	8	4	no	—
409	C₂²	C₂⁵×C₁₃	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	4	no	—
415	C₄	—	2	2	no	—
416	C₄	—	2	4	no	—
417	C₄	—	2	2	no	—
418	C₄	—	2	4	no	—
419	C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
420	C₂	—	4	1	no	—
421	C₂	—	4	4	no	—
422	C₂	—	4	1	no	—
423	C₂	—	4	2	no	—
424	C₂	—	4	1	no	—
425	C₂	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
426	C₂	C₁₃×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#563	C₂	semidirect
2. C₁₃×#560	C₂	semidirect
3. C₁₃×#555	C₂	semidirect
4. C₁₃×#553	C₂	semidirect
5. C₁₃×#552	C₂	semidirect
6. C₁₃×#551	C₂	semidirect
7. C₁₃×#548	C₂	semidirect
8. C₁₃×#546	C₂	semidirect
9. C₁₃×#540	C₂	semidirect
10. C₁₃×#538	C₂	semidirect
11. C₁₃×#537	C₂	semidirect
12. C₁₃×#536	C₂	semidirect
13. C₁₃×#535	C₂	semidirect
14. C₁₃×#532	C₂	semidirect
15. C₁₃×#529	C₂	semidirect
18. C₂×C₁₃×#41	C₂²	semidirect
19. C₂²×Q₈×C₁₃	C₂²	semidirect
21. C₁₃×C₄⋊Q₈	C₂²	semidirect
22. C₁₃×C₄⋊Q₈	C₂²	semidirect
26. C₁₃×#126	C₂²	semidirect
27. C₁₃×#126	C₂²	semidirect
28. C₁₃×#125	C₂²	semidirect
29. C₁₃×#125	C₂²	semidirect
34. C₁₃×#124	C₂²	semidirect
35. C₁₃×#124	C₂²	semidirect
39. C₁₃×#123	C₂²	semidirect
40. C₁₃×#123	C₂²	semidirect
41. C₁₃×#123	C₂²	semidirect
43. C₁₃×C₂²⋊Q₈	C₂²	semidirect
44. C₁₃×C₂²⋊Q₈	C₂²	semidirect
45. C₁₃×C₂²⋊Q₈	C₂²	semidirect
46. C₁₃×C₂²⋊Q₈	C₂²	semidirect
52. C₁₃×#121	C₂²	semidirect
53. C₁₃×#121	C₂²	semidirect
54. C₁₃×#121	C₂²	semidirect
55. C₁₃×#121	C₂²	semidirect
56. C₁₃×#121	C₂²	semidirect
57. C₁₃×#121	C₂²	semidirect
61. C₄×Q₈×C₁₃	C₂²	semidirect
64. C₄×D₄×C₁₃	C₂²	semidirect
65. C₄×D₄×C₁₃	C₂²	semidirect
66. C₄×D₄×C₁₃	C₂²	semidirect
67. C₄×D₄×C₁₃	C₂²	semidirect
69. C₁₃×#117	C₂²	semidirect
70. C₁₃×#117	C₂²	semidirect
71. C₁₃×#117	C₂²	semidirect
72. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
74. C₂×C₄²×C₁₃	C₂²	semidirect
139. #3551	C₁₃	direct (N × H)
183. #563	C₂×C₁₃	semidirect
184. #560	C₂×C₁₃	semidirect
185. #555	C₂×C₁₃	semidirect
186. #553	C₂×C₁₃	semidirect
187. #552	C₂×C₁₃	semidirect
188. #551	C₂×C₁₃	semidirect
189. #548	C₂×C₁₃	semidirect
190. #546	C₂×C₁₃	semidirect
191. #540	C₂×C₁₃	semidirect
192. #538	C₂×C₁₃	semidirect
193. #537	C₂×C₁₃	semidirect
194. #536	C₂×C₁₃	semidirect
195. #535	C₂×C₁₃	semidirect
196. #532	C₂×C₁₃	semidirect
197. #529	C₂×C₁₃	semidirect
224. C₂×#41	C₂²×C₁₃	semidirect
225. C₂²×Q₈	C₂²×C₁₃	semidirect
227. C₄⋊Q₈	C₂²×C₁₃	semidirect
228. C₄⋊Q₈	C₂²×C₁₃	semidirect
232. #126	C₂²×C₁₃	semidirect
233. #126	C₂²×C₁₃	semidirect
234. #125	C₂²×C₁₃	semidirect
235. #125	C₂²×C₁₃	semidirect
240. #124	C₂²×C₁₃	semidirect
241. #124	C₂²×C₁₃	semidirect
245. #123	C₂²×C₁₃	semidirect
246. #123	C₂²×C₁₃	semidirect
247. #123	C₂²×C₁₃	semidirect
249. C₂²⋊Q₈	C₂²×C₁₃	semidirect
250. C₂²⋊Q₈	C₂²×C₁₃	semidirect
251. C₂²⋊Q₈	C₂²×C₁₃	semidirect
252. C₂²⋊Q₈	C₂²×C₁₃	semidirect
258. #121	C₂²×C₁₃	semidirect
259. #121	C₂²×C₁₃	semidirect
260. #121	C₂²×C₁₃	semidirect
261. #121	C₂²×C₁₃	semidirect
262. #121	C₂²×C₁₃	semidirect
263. #121	C₂²×C₁₃	semidirect
267. C₄×Q₈	C₂²×C₁₃	semidirect
270. C₄×D₄	C₂²×C₁₃	semidirect
271. C₄×D₄	C₂²×C₁₃	semidirect
272. C₄×D₄	C₂²×C₁₃	semidirect
273. C₄×D₄	C₂²×C₁₃	semidirect
275. #117	C₂²×C₁₃	semidirect
276. #117	C₂²×C₁₃	semidirect
277. #117	C₂²×C₁₃	semidirect
278. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
280. C₂×C₄²	C₂²×C₁₃	semidirect
352. C₁₃	#3551	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×#563	2
C₁₃×#560	2
C₁₃×#555	2
C₁₃×#553	2
C₁₃×#552	2
C₁₃×#551	2
C₁₃×#548	2
C₁₃×#546	2
C₁₃×#540	2
C₁₃×#538	2
C₁₃×#537	2
C₁₃×#536	2
C₁₃×#535	2
C₁₃×#532	2
C₁₃×#529	2
#3551	13

Subgroups — C13×#3551 #13112609

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3551 #13112609