Subgroups — C₁₃×#3505 #13112563

Order 1664.

1152 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#553	C₂	1	2	yes	maximal, complemented
2	C₁₃×#553	C₂	1	4	yes	maximal, complemented
3	C₁₃×#552	C₂	1	2	yes	maximal, complemented
4	C₁₃×#551	C₂	1	4	yes	maximal, complemented
5	C₁₃×#548	C₂	1	2	yes	maximal, complemented
6	C₁₃×#546	C₂	1	2	yes	maximal, complemented
7	C₁₃×#539	C₂	1	2	yes	maximal, complemented
8	C₁₃×#538	C₂	1	2	yes	maximal, complemented
9	C₁₃×#534	C₂	1	2	yes	maximal, complemented
10	C₁₃×#529	C₂	1	2	yes	maximal, complemented
11	C₁₃×#525	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#518	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#41	C₂²	1	2	yes	complemented
17	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂²×D₄×C₁₃	C₂²	1	2	yes	—
20	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
21	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×#126	C₂²	1	4	yes	complemented
24	C₁₃×#126	C₂²	1	4	yes	complemented
25	C₁₃×#126	C₂²	1	4	yes	complemented
26	C₁₃×#125	C₂²	1	2	yes	complemented
27	C₁₃×#125	C₂²	1	4	yes	complemented
28	C₁₃×#124	C₂²	1	2	yes	complemented
29	C₁₃×#124	C₂²	1	4	yes	complemented
30	C₁₃×#123	C₂²	1	4	yes	—
31	C₁₃×#123	C₂²	1	4	yes	complemented
32	C₁₃×#123	C₂²	1	4	yes	complemented
33	C₁₃×#123	C₂²	1	4	yes	complemented
34	C₁₃×#123	C₂²	1	4	yes	complemented
35	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
38	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
39	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
40	C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
41	C₁₃×#121	C₂²	1	2	yes	—
42	C₁₃×#121	C₂²	1	2	yes	—
43	C₁₃×#121	C₂²	1	2	yes	complemented
44	C₁₃×#121	C₂²	1	2	yes	complemented
45	C₁₃×#121	C₂²	1	2	yes	complemented
46	C₁₃×#121	C₂²	1	4	yes	complemented
47	C₁₃×#121	C₂²	1	4	yes	complemented
48	C₁₃×#121	C₂²	1	4	yes	complemented
49	C₁₃×#120	C₂²	1	4	yes	—
50	C₁₃×#120	C₂²	1	4	yes	complemented
51	C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
52	C₄×D₄×C₁₃	C₂²	1	2	yes	—
53	C₄×D₄×C₁₃	C₂²	1	2	yes	—
54	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
55	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
56	C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
57	C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
58	C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
59	C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
60	C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
61	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
62	C₁₃×#117	C₂²	1	4	yes	complemented
63	C₁₃×#117	C₂²	1	2	yes	complemented
64	C₁₃×#117	C₂²	1	4	yes	complemented
65	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
67	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
69	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
70	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
71	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
73	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
74	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
75	C₂⁴×C₁₃	C₂³	1	2	yes	—
76	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
77	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
82	C₂×D₄×C₁₃	—	2	4	no	—
83	C₂×D₄×C₁₃	—	2	8	no	—
84	C₂×D₄×C₁₃	—	4	2	no	—
85	C₂×D₄×C₁₃	C₂³	1	2	yes	—
86	C₂×D₄×C₁₃	C₂³	1	4	yes	—
87	C₂×D₄×C₁₃	C₂³	1	2	yes	—
88	C₂×D₄×C₁₃	C₂³	1	4	yes	—
89	C₂×D₄×C₁₃	C₂³	1	2	yes	—
90	C₂×D₄×C₁₃	C₂³	1	4	yes	—
91	C₂×D₄×C₁₃	C₂³	1	4	yes	—
92	C₂×D₄×C₁₃	C₂³	1	2	yes	—
93	C₂²×C₄×C₁₃	—	4	2	no	—
94	C₂²×C₄×C₁₃	—	4	2	no	—
95	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
103	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
105	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
108	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
109	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	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	2	yes	—
115	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
116	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
117	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
118	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
119	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
120	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
121	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
122	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
123	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
124	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
126	C₁₃×C₂²⋊C₄	C₂³	1	4	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	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₄²×C₁₃	C₂³	1	2	yes	—
138	C₄²×C₁₃	C₂³	1	2	yes	—
139	C₄²×C₁₃	C₂³	1	4	yes	—
140	C₄²×C₁₃	C₂³	1	4	yes	—
141	#3505	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂³×C₁₃	—	2	2	no	—
143	C₂³×C₁₃	—	2	4	no	—
144	C₂³×C₁₃	—	4	1	no	—
145	C₂³×C₁₃	—	4	1	no	—
146	C₂³×C₁₃	—	4	1	no	—
147	C₂³×C₁₃	—	4	1	no	—
148	C₂³×C₁₃	—	4	2	no	—
149	C₂³×C₁₃	—	4	2	no	—
150	C₂³×C₁₃	#41	1	4	yes	complemented
151	C₂³×C₁₃	C₂⁴	1	2	yes	—
152	C₂³×C₁₃	C₂⁴	1	4	yes	—
153	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
154	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
155	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
156	Q₈×C₁₃	—	2	4	no	—
157	Q₈×C₁₃	—	4	2	no	—
158	D₄×C₁₃	—	2	4	no	—
159	D₄×C₁₃	—	2	8	no	—
160	D₄×C₁₃	—	2	4	no	—
161	D₄×C₁₃	—	2	8	no	—
162	D₄×C₁₃	—	2	4	no	—
163	D₄×C₁₃	—	4	2	no	—
164	D₄×C₁₃	—	4	4	no	—
165	D₄×C₁₃	—	4	4	no	—
166	C₂×C₄×C₁₃	—	2	4	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	4	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	4	1	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	4	4	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	4	no	—
182	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
183	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
184	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
185	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
187	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
188	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
189	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
192	#553	C₂×C₁₃	1	2	yes	complemented
193	#553	C₂×C₁₃	1	4	yes	complemented
194	#552	C₂×C₁₃	1	2	yes	complemented
195	#551	C₂×C₁₃	1	4	yes	complemented
196	#548	C₂×C₁₃	1	2	yes	complemented
197	#546	C₂×C₁₃	1	2	yes	complemented
198	#539	C₂×C₁₃	1	2	yes	complemented
199	#538	C₂×C₁₃	1	2	yes	complemented
200	#534	C₂×C₁₃	1	2	yes	complemented
201	#529	C₂×C₁₃	1	2	yes	complemented
202	#525	C₂×C₁₃	1	2	yes	complemented
203	C₂×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
204	C₂×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#518	C₂×C₁₃	1	2	yes	complemented
206	C₂×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
207	C₂²×C₁₃	—	2	1	no	—
208	C₂²×C₁₃	—	2	1	no	—
209	C₂²×C₁₃	—	2	1	no	—
210	C₂²×C₁₃	—	2	1	no	—
211	C₂²×C₁₃	—	2	1	no	—
212	C₂²×C₁₃	—	2	1	no	—
213	C₂²×C₁₃	—	2	2	no	—
214	C₂²×C₁₃	—	2	4	no	—
215	C₂²×C₁₃	—	2	2	no	—
216	C₂²×C₁₃	—	2	4	no	—
217	C₂²×C₁₃	—	2	4	no	—
218	C₂²×C₁₃	—	2	2	no	—
219	C₂²×C₁₃	—	4	4	no	—
220	C₂²×C₁₃	—	4	4	no	—
221	C₂²×C₁₃	—	8	4	no	—
222	C₂²×C₁₃	C₂×#41	1	2	yes	—
223	C₂²×C₁₃	C₂×#41	1	2	yes	—
224	C₂²×C₁₃	C₂×#41	1	2	yes	—
225	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
226	C₄×C₁₃	—	2	4	no	—
227	C₄×C₁₃	—	2	2	no	—
228	C₄×C₁₃	—	2	1	no	—
229	C₄×C₁₃	—	2	2	no	—
230	C₄×C₁₃	—	2	1	no	—
231	C₄×C₁₃	—	2	1	no	—
232	C₄×C₁₃	—	2	4	no	—
233	C₄×C₁₃	—	2	2	no	—
234	C₄×C₁₃	—	2	4	no	—
235	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
236	C₂×#41	C₂²×C₁₃	1	2	yes	complemented
237	C₂²×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
238	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
239	C₂²×D₄	C₂²×C₁₃	1	2	yes	—
240	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
241	C₂³×C₄	C₂²×C₁₃	1	1	yes	characteristic
242	C₂³×C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
243	#126	C₂²×C₁₃	1	4	yes	complemented
244	#126	C₂²×C₁₃	1	4	yes	complemented
245	#126	C₂²×C₁₃	1	4	yes	complemented
246	#125	C₂²×C₁₃	1	2	yes	complemented
247	#125	C₂²×C₁₃	1	4	yes	complemented
248	#124	C₂²×C₁₃	1	2	yes	complemented
249	#124	C₂²×C₁₃	1	4	yes	complemented
250	#123	C₂²×C₁₃	1	4	yes	—
251	#123	C₂²×C₁₃	1	4	yes	complemented
252	#123	C₂²×C₁₃	1	4	yes	complemented
253	#123	C₂²×C₁₃	1	4	yes	complemented
254	#123	C₂²×C₁₃	1	4	yes	complemented
255	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
256	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
257	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
258	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
259	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
260	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
261	#121	C₂²×C₁₃	1	2	yes	—
262	#121	C₂²×C₁₃	1	2	yes	—
263	#121	C₂²×C₁₃	1	2	yes	complemented
264	#121	C₂²×C₁₃	1	2	yes	complemented
265	#121	C₂²×C₁₃	1	2	yes	complemented
266	#121	C₂²×C₁₃	1	4	yes	complemented
267	#121	C₂²×C₁₃	1	4	yes	complemented
268	#121	C₂²×C₁₃	1	4	yes	complemented
269	#120	C₂²×C₁₃	1	4	yes	—
270	#120	C₂²×C₁₃	1	4	yes	complemented
271	C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
272	C₄×D₄	C₂²×C₁₃	1	2	yes	—
273	C₄×D₄	C₂²×C₁₃	1	2	yes	—
274	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
275	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
276	C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
277	C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
278	C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
279	C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
280	C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
281	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
282	#117	C₂²×C₁₃	1	4	yes	complemented
283	#117	C₂²×C₁₃	1	2	yes	complemented
284	#117	C₂²×C₁₃	1	4	yes	complemented
285	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
286	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
287	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
288	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
289	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
291	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
292	C₂×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
293	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
294	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
295	C₂×C₁₃	—	2	2	no	—
296	C₂×C₁₃	—	2	2	no	—
297	C₂×C₁₃	—	2	2	no	—
298	C₂×C₁₃	—	4	2	no	—
299	C₂×C₁₃	—	4	4	no	—
300	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
301	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
302	C₂×C₁₃	#585	1	1	yes	characteristic
303	C₂⁴	C₂³×C₁₃	1	2	yes	—
304	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
305	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
306	#41	—	4	4	no	—
307	C₂×Q₈	—	4	2	no	—
308	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
309	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
310	C₂×D₄	—	2	4	no	—
311	C₂×D₄	—	2	8	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	C₂³×C₁₃	1	2	yes	—
314	C₂×D₄	C₂³×C₁₃	1	4	yes	—
315	C₂×D₄	C₂³×C₁₃	1	2	yes	—
316	C₂×D₄	C₂³×C₁₃	1	4	yes	—
317	C₂×D₄	C₂³×C₁₃	1	2	yes	—
318	C₂×D₄	C₂³×C₁₃	1	4	yes	—
319	C₂×D₄	C₂³×C₁₃	1	4	yes	—
320	C₂×D₄	C₂³×C₁₃	1	2	yes	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
324	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
325	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
326	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
327	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
328	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
329	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
330	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
331	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
332	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
333	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
334	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
335	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
336	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
337	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
338	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
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	2	yes	—
344	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
345	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
346	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
347	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
348	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
349	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
350	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
351	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
352	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
353	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
354	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
355	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
356	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
357	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
358	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
359	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
360	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
361	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
362	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
363	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
364	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
365	C₄²	C₂³×C₁₃	1	2	yes	—
366	C₄²	C₂³×C₁₃	1	2	yes	—
367	C₄²	C₂³×C₁₃	1	4	yes	—
368	C₄²	C₂³×C₁₃	1	4	yes	—
369	C₁₃	#3505	1	1	yes	characteristic, direct product factor, Sylow
370	C₂³	—	2	2	no	—
371	C₂³	—	2	4	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	4	2	no	—
378	C₂³	C₁₃×#41	1	4	yes	complemented
379	C₂³	C₂⁴×C₁₃	1	2	yes	—
380	C₂³	C₂⁴×C₁₃	1	4	yes	—
381	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
382	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
383	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
384	Q₈	—	2	4	no	—
385	Q₈	—	4	2	no	—
386	D₄	—	2	4	no	—
387	D₄	—	2	8	no	—
388	D₄	—	2	4	no	—
389	D₄	—	2	8	no	—
390	D₄	—	2	4	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	4	no	—
393	D₄	—	4	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
411	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
412	C₂×C₄	C₂⁴×C₁₃	1	4	yes	—
413	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
414	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
415	C₂×C₄	C₂⁴×C₁₃	1	4	yes	—
416	C₂×C₄	C₂⁴×C₁₃	1	4	yes	—
417	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
418	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
419	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	8	4	no	—
435	C₂²	C₂×C₁₃×#41	1	2	yes	—
436	C₂²	C₂×C₁₃×#41	1	2	yes	—
437	C₂²	C₂×C₁₃×#41	1	2	yes	—
438	C₂²	C₂⁵×C₁₃	1	1	yes	characteristic
439	C₄	—	2	4	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	2	no	—
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	2	4	no	—
446	C₄	—	2	2	no	—
447	C₄	—	2	4	no	—
448	C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
449	C₂	—	2	2	no	—
450	C₂	—	2	2	no	—
451	C₂	—	2	2	no	—
452	C₂	—	4	2	no	—
453	C₂	—	4	4	no	—
454	C₂	C₂²×C₁₃×#41	1	1	yes	characteristic
455	C₂	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
456	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×#553	C₂	semidirect
2. C₁₃×#553	C₂	semidirect
3. C₁₃×#552	C₂	semidirect
4. C₁₃×#551	C₂	semidirect
5. C₁₃×#548	C₂	semidirect
6. C₁₃×#546	C₂	semidirect
7. C₁₃×#539	C₂	semidirect
8. C₁₃×#538	C₂	semidirect
9. C₁₃×#534	C₂	semidirect
10. C₁₃×#529	C₂	semidirect
11. C₁₃×#525	C₂	semidirect
12. C₂×C₁₃×C₂²⋊Q₈	C₂	semidirect
13. C₂×C₁₃×#121	C₂	semidirect
14. C₁₃×#518	C₂	semidirect
15. C₂×C₄×D₄×C₁₃	C₂	semidirect
16. C₂×C₁₃×#41	C₂²	semidirect
17. C₂²×Q₈×C₁₃	C₂²	semidirect
20. C₂²×D₄×C₁₃	C₂²	semidirect
22. C₂³×C₄×C₁₃	C₂²	semidirect
23. C₁₃×#126	C₂²	semidirect
24. C₁₃×#126	C₂²	semidirect
25. C₁₃×#126	C₂²	semidirect
26. C₁₃×#125	C₂²	semidirect
27. C₁₃×#125	C₂²	semidirect
28. C₁₃×#124	C₂²	semidirect
29. C₁₃×#124	C₂²	semidirect
31. C₁₃×#123	C₂²	semidirect
32. C₁₃×#123	C₂²	semidirect
33. C₁₃×#123	C₂²	semidirect
34. C₁₃×#123	C₂²	semidirect
35. C₁₃×C₂²⋊Q₈	C₂²	semidirect
36. C₁₃×C₂²⋊Q₈	C₂²	semidirect
37. C₁₃×C₂²⋊Q₈	C₂²	semidirect
38. C₁₃×C₂²⋊Q₈	C₂²	semidirect
39. C₁₃×C₂²⋊Q₈	C₂²	semidirect
40. C₁₃×C₂²⋊Q₈	C₂²	semidirect
43. C₁₃×#121	C₂²	semidirect
44. C₁₃×#121	C₂²	semidirect
45. C₁₃×#121	C₂²	semidirect
46. C₁₃×#121	C₂²	semidirect
47. C₁₃×#121	C₂²	semidirect
48. C₁₃×#121	C₂²	semidirect
50. C₁₃×#120	C₂²	semidirect
51. C₄×Q₈×C₁₃	C₂²	semidirect
54. C₄×D₄×C₁₃	C₂²	semidirect
55. C₄×D₄×C₁₃	C₂²	semidirect
56. C₄×D₄×C₁₃	C₂²	semidirect
57. C₄×D₄×C₁₃	C₂²	semidirect
58. C₄×D₄×C₁₃	C₂²	semidirect
59. C₄×D₄×C₁₃	C₂²	semidirect
60. C₄×D₄×C₁₃	C₂²	semidirect
61. C₄×D₄×C₁₃	C₂²	semidirect
62. C₁₃×#117	C₂²	semidirect
63. C₁₃×#117	C₂²	semidirect
64. C₁₃×#117	C₂²	semidirect
65. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
66. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
67. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
68. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
71. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
72. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
73. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
74. C₂×C₄²×C₁₃	C₂²	semidirect
141. #3505	C₁₃	direct (N × H)
150. C₂³×C₁₃	#41	semidirect
192. #553	C₂×C₁₃	semidirect
193. #553	C₂×C₁₃	semidirect
194. #552	C₂×C₁₃	semidirect
195. #551	C₂×C₁₃	semidirect
196. #548	C₂×C₁₃	semidirect
197. #546	C₂×C₁₃	semidirect
198. #539	C₂×C₁₃	semidirect
199. #538	C₂×C₁₃	semidirect
200. #534	C₂×C₁₃	semidirect
201. #529	C₂×C₁₃	semidirect
202. #525	C₂×C₁₃	semidirect
203. C₂×C₂²⋊Q₈	C₂×C₁₃	semidirect
204. C₂×#121	C₂×C₁₃	semidirect
205. #518	C₂×C₁₃	semidirect
206. C₂×C₄×D₄	C₂×C₁₃	semidirect
236. C₂×#41	C₂²×C₁₃	semidirect
237. C₂²×Q₈	C₂²×C₁₃	semidirect
240. C₂²×D₄	C₂²×C₁₃	semidirect
242. C₂³×C₄	C₂²×C₁₃	semidirect
243. #126	C₂²×C₁₃	semidirect
244. #126	C₂²×C₁₃	semidirect
245. #126	C₂²×C₁₃	semidirect
246. #125	C₂²×C₁₃	semidirect
247. #125	C₂²×C₁₃	semidirect
248. #124	C₂²×C₁₃	semidirect
249. #124	C₂²×C₁₃	semidirect
251. #123	C₂²×C₁₃	semidirect
252. #123	C₂²×C₁₃	semidirect
253. #123	C₂²×C₁₃	semidirect
254. #123	C₂²×C₁₃	semidirect
255. C₂²⋊Q₈	C₂²×C₁₃	semidirect
256. C₂²⋊Q₈	C₂²×C₁₃	semidirect
257. C₂²⋊Q₈	C₂²×C₁₃	semidirect
258. C₂²⋊Q₈	C₂²×C₁₃	semidirect
259. C₂²⋊Q₈	C₂²×C₁₃	semidirect
260. C₂²⋊Q₈	C₂²×C₁₃	semidirect
263. #121	C₂²×C₁₃	semidirect
264. #121	C₂²×C₁₃	semidirect
265. #121	C₂²×C₁₃	semidirect
266. #121	C₂²×C₁₃	semidirect
267. #121	C₂²×C₁₃	semidirect
268. #121	C₂²×C₁₃	semidirect
270. #120	C₂²×C₁₃	semidirect
271. C₄×Q₈	C₂²×C₁₃	semidirect
274. C₄×D₄	C₂²×C₁₃	semidirect
275. C₄×D₄	C₂²×C₁₃	semidirect
276. C₄×D₄	C₂²×C₁₃	semidirect
277. C₄×D₄	C₂²×C₁₃	semidirect
278. C₄×D₄	C₂²×C₁₃	semidirect
279. C₄×D₄	C₂²×C₁₃	semidirect
280. C₄×D₄	C₂²×C₁₃	semidirect
281. C₄×D₄	C₂²×C₁₃	semidirect
282. #117	C₂²×C₁₃	semidirect
283. #117	C₂²×C₁₃	semidirect
284. #117	C₂²×C₁₃	semidirect
285. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
286. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
287. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
288. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
291. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
292. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
293. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
294. C₂×C₄²	C₂²×C₁₃	semidirect
369. C₁₃	#3505	direct (N × H)
378. C₂³	C₁₃×#41	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#553	2
C₁₃×#552	2
C₁₃×#551	2
C₁₃×#548	2
C₁₃×#546	2
C₁₃×#539	2
C₁₃×#538	2
C₁₃×#534	2
C₁₃×#529	2
C₁₃×#525	2
C₂×C₁₃×C₂²⋊Q₈	2
C₂×C₁₃×#121	2
C₁₃×#518	2
C₂×C₄×D₄×C₁₃	2
#3505	13

Subgroups — C13×#3505 #13112563

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3505 #13112563