Subgroups — C₁₃×#3515 #13112573

Order 1664.

1014 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#553	C₂	1	2	yes	maximal, complemented
5	C₁₃×#552	C₂	1	2	yes	maximal, complemented
6	C₁₃×#552	C₂	1	4	yes	maximal, complemented
7	C₁₃×#552	C₂	1	2	yes	maximal, complemented
8	C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#547	C₂	1	2	yes	maximal, complemented
10	C₁₃×#541	C₂	1	2	yes	maximal, complemented
11	C₁₃×#539	C₂	1	4	yes	maximal, complemented
12	C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#529	C₂	1	2	yes	maximal, complemented
14	C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#125	C₂	1	2	yes	maximal, complemented
16	C₁₃×#520	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#41	C₂²	1	2	yes	—
20	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₁₃×#126	C₂²	1	4	yes	—
24	C₁₃×#126	C₂²	1	2	yes	—
25	C₁₃×#126	C₂²	1	4	yes	—
26	C₁₃×#126	C₂²	1	4	yes	—
27	C₁₃×#125	C₂²	1	1	yes	characteristic
28	C₁₃×#125	C₂²	1	2	yes	—
29	C₁₃×#125	C₂²	1	4	yes	—
30	C₁₃×#125	C₂²	1	4	yes	—
31	C₁₃×#125	C₂²	1	2	yes	—
32	C₁₃×#125	C₂²	1	2	yes	—
33	C₁₃×#125	C₂²	1	4	yes	—
34	C₁₃×#125	C₂²	1	4	yes	—
35	C₁₃×#125	C₂²	1	2	yes	—
36	C₁₃×#124	C₂²	1	1	yes	characteristic
37	C₁₃×#123	C₂²	1	2	yes	—
38	C₁₃×#123	C₂²	1	4	yes	—
39	C₁₃×#123	C₂²	1	4	yes	—
40	C₁₃×#123	C₂²	1	4	yes	—
41	C₁₃×#123	C₂²	1	4	yes	—
42	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
44	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
45	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
46	C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
47	C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
48	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
49	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
50	C₁₃×#121	C₂²	1	2	yes	—
51	C₁₃×#121	C₂²	1	1	yes	characteristic
52	C₁₃×#121	C₂²	1	4	yes	—
53	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
54	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
55	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
56	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
57	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
58	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
59	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
60	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
61	C₄×D₄×C₁₃	C₂²	1	2	yes	—
62	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
63	C₄×D₄×C₁₃	C₂²	1	2	yes	—
64	C₄×D₄×C₁₃	C₂²	1	4	yes	—
65	C₄×D₄×C₁₃	C₂²	1	2	yes	—
66	C₄×D₄×C₁₃	C₂²	1	4	yes	—
67	C₄×D₄×C₁₃	C₂²	1	2	yes	—
68	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
69	C₄×D₄×C₁₃	C₂²	1	2	yes	—
70	C₁₃×#117	C₂²	1	1	yes	characteristic
71	C₁₃×#117	C₂²	1	2	yes	—
72	C₁₃×#117	C₂²	1	2	yes	—
73	C₁₃×#117	C₂²	1	4	yes	—
74	C₁₃×#117	C₂²	1	4	yes	—
75	C₁₃×#117	C₂²	1	2	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
77	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
78	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
81	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
82	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
83	C₁₃×#41	—	2	4	no	—
84	C₁₃×#41	—	2	8	no	—
85	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
88	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
89	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂×D₄×C₁₃	C₂³	1	2	yes	—
91	C₂×D₄×C₁₃	C₂³	1	4	yes	—
92	C₂×D₄×C₁₃	C₂³	1	2	yes	—
93	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
95	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
96	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
99	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
103	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
104	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
106	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
107	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
109	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
113	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₁₃×C₄⋊C₄	C₂³	1	4	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×C₄⋊C₄	C₂³	1	4	yes	—
119	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
120	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
122	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
123	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
125	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
126	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
127	C₁₃×C₄⋊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	2	yes	—
131	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
133	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
134	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₄²×C₁₃	C₂³	1	1	yes	characteristic
141	C₄²×C₁₃	C₂³	1	2	yes	—
142	C₄²×C₁₃	C₂³	1	1	yes	characteristic
143	C₄²×C₁₃	C₂³	1	1	yes	characteristic
144	C₄²×C₁₃	C₂³	1	2	yes	—
145	C₄²×C₁₃	C₂³	1	1	yes	characteristic
146	C₄²×C₁₃	C₂³	1	2	yes	—
147	C₄²×C₁₃	C₂³	1	4	yes	—
148	C₄²×C₁₃	C₂³	1	4	yes	—
149	C₄²×C₁₃	C₂³	1	2	yes	—
150	#3515	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
152	C₂³×C₁₃	C₂⁴	1	2	yes	—
153	C₂³×C₁₃	C₂⁴	1	2	yes	—
154	Q₈×C₁₃	—	2	2	no	—
155	Q₈×C₁₃	—	2	4	no	—
156	Q₈×C₁₃	—	2	2	no	—
157	Q₈×C₁₃	—	4	2	no	—
158	D₄×C₁₃	—	2	4	no	—
159	D₄×C₁₃	—	2	8	no	—
160	D₄×C₁₃	—	2	2	no	—
161	D₄×C₁₃	—	4	2	no	—
162	D₄×C₁₃	#41	1	4	yes	—
163	C₂×C₄×C₁₃	—	2	4	no	—
164	C₂×C₄×C₁₃	—	2	8	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	4	no	—
167	C₂×C₄×C₁₃	—	2	4	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	—	4	4	no	—
171	C₂×C₄×C₁₃	—	4	1	no	—
172	C₂×C₄×C₁₃	—	4	4	no	—
173	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
177	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
178	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
179	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
181	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
182	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
183	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
184	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
185	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
187	#557	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#554	C₂×C₁₃	1	1	yes	characteristic, complemented
189	#554	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#553	C₂×C₁₃	1	2	yes	complemented
191	#552	C₂×C₁₃	1	2	yes	complemented
192	#552	C₂×C₁₃	1	4	yes	complemented
193	#552	C₂×C₁₃	1	2	yes	complemented
194	#547	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#547	C₂×C₁₃	1	2	yes	complemented
196	#541	C₂×C₁₃	1	2	yes	complemented
197	#539	C₂×C₁₃	1	4	yes	complemented
198	#533	C₂×C₁₃	1	1	yes	characteristic, complemented
199	#529	C₂×C₁₃	1	2	yes	complemented
200	#529	C₂×C₁₃	1	1	yes	characteristic, complemented
201	C₂×#125	C₂×C₁₃	1	2	yes	complemented
202	#520	C₂×C₁₃	1	2	yes	complemented
203	C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
204	C₂²×C₁₃	—	2	2	no	—
205	C₂²×C₁₃	—	2	2	no	—
206	C₂²×C₁₃	—	2	1	no	—
207	C₂²×C₁₃	—	2	2	no	—
208	C₂²×C₁₃	—	2	1	no	—
209	C₂²×C₁₃	—	2	2	no	—
210	C₂²×C₁₃	—	2	2	no	—
211	C₂²×C₁₃	—	2	1	no	—
212	C₂²×C₁₃	C₂×#41	1	4	yes	—
213	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
214	C₄×C₁₃	—	2	1	no	—
215	C₄×C₁₃	—	2	2	no	—
216	C₄×C₁₃	—	2	2	no	—
217	C₄×C₁₃	—	2	4	no	—
218	C₄×C₁₃	—	2	1	no	—
219	C₄×C₁₃	—	2	2	no	—
220	C₄×C₁₃	—	2	2	no	—
221	C₄×C₁₃	—	2	1	no	—
222	C₄×C₁₃	—	2	2	no	—
223	C₄×C₁₃	—	2	2	no	—
224	C₄×C₁₃	—	2	4	no	—
225	C₄×C₁₃	—	2	1	no	—
226	C₄×C₁₃	C₂×#41	1	2	yes	—
227	C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
228	C₂×#41	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×#41	C₂²×C₁₃	1	2	yes	—
230	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
231	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
232	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
233	#126	C₂²×C₁₃	1	4	yes	—
234	#126	C₂²×C₁₃	1	2	yes	—
235	#126	C₂²×C₁₃	1	4	yes	—
236	#126	C₂²×C₁₃	1	4	yes	—
237	#125	C₂²×C₁₃	1	1	yes	characteristic
238	#125	C₂²×C₁₃	1	2	yes	—
239	#125	C₂²×C₁₃	1	4	yes	—
240	#125	C₂²×C₁₃	1	4	yes	—
241	#125	C₂²×C₁₃	1	2	yes	—
242	#125	C₂²×C₁₃	1	2	yes	—
243	#125	C₂²×C₁₃	1	4	yes	—
244	#125	C₂²×C₁₃	1	4	yes	—
245	#125	C₂²×C₁₃	1	2	yes	—
246	#124	C₂²×C₁₃	1	1	yes	characteristic
247	#123	C₂²×C₁₃	1	2	yes	—
248	#123	C₂²×C₁₃	1	4	yes	—
249	#123	C₂²×C₁₃	1	4	yes	—
250	#123	C₂²×C₁₃	1	4	yes	—
251	#123	C₂²×C₁₃	1	4	yes	—
252	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
253	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
254	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
255	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
256	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
257	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
258	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
259	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
260	#121	C₂²×C₁₃	1	2	yes	—
261	#121	C₂²×C₁₃	1	1	yes	characteristic
262	#121	C₂²×C₁₃	1	4	yes	—
263	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
264	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
265	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
266	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
267	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
268	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
269	C₄×Q₈	C₂²×C₁₃	1	2	yes	—
270	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
271	C₄×D₄	C₂²×C₁₃	1	2	yes	—
272	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
273	C₄×D₄	C₂²×C₁₃	1	2	yes	—
274	C₄×D₄	C₂²×C₁₃	1	4	yes	—
275	C₄×D₄	C₂²×C₁₃	1	2	yes	—
276	C₄×D₄	C₂²×C₁₃	1	4	yes	—
277	C₄×D₄	C₂²×C₁₃	1	2	yes	—
278	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
279	C₄×D₄	C₂²×C₁₃	1	2	yes	—
280	#117	C₂²×C₁₃	1	1	yes	characteristic
281	#117	C₂²×C₁₃	1	2	yes	—
282	#117	C₂²×C₁₃	1	2	yes	—
283	#117	C₂²×C₁₃	1	4	yes	—
284	#117	C₂²×C₁₃	1	4	yes	—
285	#117	C₂²×C₁₃	1	2	yes	—
286	C₂×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
287	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
288	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
289	C₂×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
290	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
291	C₂×C₄²	C₂²×C₁₃	1	2	yes	—
292	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×C₁₃	—	2	4	no	—
294	C₂×C₁₃	—	4	1	no	—
295	C₂×C₁₃	—	4	2	no	—
296	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
297	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
298	C₂×C₁₃	#585	1	1	yes	characteristic
299	#41	—	2	4	no	—
300	#41	—	2	8	no	—
301	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
302	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
303	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
304	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
305	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
306	C₂×D₄	C₂³×C₁₃	1	2	yes	—
307	C₂×D₄	C₂³×C₁₃	1	4	yes	—
308	C₂×D₄	C₂³×C₁₃	1	2	yes	—
309	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
310	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
311	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
312	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
313	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
314	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
315	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
316	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
317	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
318	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
319	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
320	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
321	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
322	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
323	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
324	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
325	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	2	yes	—
330	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
331	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
332	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
333	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
334	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
335	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
336	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
337	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
338	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
339	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
340	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
341	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
342	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
343	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
344	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
345	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
346	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
347	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
348	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
349	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
350	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
351	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
352	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
353	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
354	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
355	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
356	C₄²	C₂³×C₁₃	1	1	yes	characteristic
357	C₄²	C₂³×C₁₃	1	2	yes	—
358	C₄²	C₂³×C₁₃	1	1	yes	characteristic
359	C₄²	C₂³×C₁₃	1	1	yes	characteristic
360	C₄²	C₂³×C₁₃	1	2	yes	—
361	C₄²	C₂³×C₁₃	1	1	yes	characteristic
362	C₄²	C₂³×C₁₃	1	2	yes	—
363	C₄²	C₂³×C₁₃	1	4	yes	—
364	C₄²	C₂³×C₁₃	1	4	yes	—
365	C₄²	C₂³×C₁₃	1	2	yes	—
366	C₁₃	#3515	1	1	yes	characteristic, direct product factor, Sylow
367	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
368	C₂³	C₂⁴×C₁₃	1	2	yes	—
369	C₂³	C₂⁴×C₁₃	1	2	yes	—
370	Q₈	—	2	2	no	—
371	Q₈	—	2	4	no	—
372	Q₈	—	2	2	no	—
373	Q₈	—	4	2	no	—
374	D₄	—	2	4	no	—
375	D₄	—	2	8	no	—
376	D₄	—	2	2	no	—
377	D₄	—	4	2	no	—
378	D₄	C₁₃×#41	1	4	yes	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	8	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
390	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
391	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
392	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
393	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
394	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
395	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
396	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
397	C₂×C₄	C₂⁴×C₁₃	1	4	yes	—
398	C₂×C₄	C₂⁴×C₁₃	1	4	yes	—
399	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
400	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
401	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
402	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	1	no	—
411	C₂²	C₂×C₁₃×#41	1	4	yes	—
412	C₂²	C₂⁵×C₁₃	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	2	4	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	2	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	1	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	4	no	—
424	C₄	—	2	1	no	—
425	C₄	C₂×C₁₃×#41	1	2	yes	—
426	C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
427	C₂	—	2	4	no	—
428	C₂	—	4	1	no	—
429	C₂	—	4	2	no	—
430	C₂	C₂²×C₁₃×#41	1	1	yes	characteristic
431	C₂	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
432	C₂	C₁₃×#585	1	1	yes	characteristic

	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×#557	C₂	semidirect
2. C₁₃×#554	C₂	semidirect
3. C₁₃×#554	C₂	semidirect
4. C₁₃×#553	C₂	semidirect
5. C₁₃×#552	C₂	semidirect
6. C₁₃×#552	C₂	semidirect
7. C₁₃×#552	C₂	semidirect
8. C₁₃×#547	C₂	semidirect
9. C₁₃×#547	C₂	semidirect
10. C₁₃×#541	C₂	semidirect
11. C₁₃×#539	C₂	semidirect
12. C₁₃×#533	C₂	semidirect
13. C₁₃×#529	C₂	semidirect
14. C₁₃×#529	C₂	semidirect
15. C₂×C₁₃×#125	C₂	semidirect
16. C₁₃×#520	C₂	semidirect
17. C₄×C₁₃×#41	C₂	semidirect
150. #3515	C₁₃	direct (N × H)
187. #557	C₂×C₁₃	semidirect
188. #554	C₂×C₁₃	semidirect
189. #554	C₂×C₁₃	semidirect
190. #553	C₂×C₁₃	semidirect
191. #552	C₂×C₁₃	semidirect
192. #552	C₂×C₁₃	semidirect
193. #552	C₂×C₁₃	semidirect
194. #547	C₂×C₁₃	semidirect
195. #547	C₂×C₁₃	semidirect
196. #541	C₂×C₁₃	semidirect
197. #539	C₂×C₁₃	semidirect
198. #533	C₂×C₁₃	semidirect
199. #529	C₂×C₁₃	semidirect
200. #529	C₂×C₁₃	semidirect
201. C₂×#125	C₂×C₁₃	semidirect
202. #520	C₂×C₁₃	semidirect
203. C₄×#41	C₂×C₁₃	semidirect
366. C₁₃	#3515	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×#557	2
C₁₃×#554	2
C₁₃×#553	2
C₁₃×#552	2
C₁₃×#547	2
C₁₃×#541	2
C₁₃×#539	2
C₁₃×#533	2
C₁₃×#529	2
C₂×C₁₃×#125	2
C₁₃×#520	2
C₄×C₁₃×#41	2
#3515	13

Subgroups — C13×#3515 #13112573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3515 #13112573