Subgroups — C₁₃×#34995 #15721334

Order 3328.

2214 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2852	C₂	1	4	yes	maximal, complemented
2	C₁₃×#2643	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2510	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2493	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2481	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2480	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2315	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2315	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2308	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#2308	C₂	1	1	yes	maximal, characteristic
11	C₂×C₁₃×#386	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#126	C₂²	1	4	yes	complemented
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
18	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
25	C₁₃×#401	C₂²	1	4	yes	complemented
26	C₁₃×#400	C₂²	1	4	yes	complemented
27	C₁₃×#400	C₂²	1	4	yes	complemented
28	C₁₃×#400	C₂²	1	4	yes	complemented
29	C₁₃×#397	C₂²	1	4	yes	complemented
30	C₁₃×#397	C₂²	1	4	yes	complemented
31	C₁₃×#397	C₂²	1	4	yes	complemented
32	C₁₃×#396	C₂²	1	4	yes	complemented
33	C₁₃×#388	C₂²	1	4	yes	complemented
34	C₁₃×#388	C₂²	1	4	yes	complemented
35	C₁₃×#388	C₂²	1	4	yes	complemented
36	C₁₃×#387	C₂²	1	4	yes	complemented
37	C₁₃×#387	C₂²	1	4	yes	complemented
38	C₁₃×#387	C₂²	1	4	yes	complemented
39	C₁₃×#386	C₂²	1	2	yes	—
40	C₁₃×#386	C₂²	1	4	yes	—
41	C₁₃×#386	C₂²	1	4	yes	—
42	C₁₃×#386	C₂²	1	2	yes	—
43	C₁₃×#386	C₂²	1	2	yes	—
44	C₁₃×#386	C₂²	1	4	yes	—
45	C₁₃×#386	C₂²	1	4	yes	—
46	C₁₃×#386	C₂²	1	2	yes	—
47	C₁₃×#385	C₂²	1	4	yes	—
48	C₁₃×#385	C₂²	1	4	yes	—
49	C₁₃×#385	C₂²	1	4	yes	complemented
50	C₁₃×#385	C₂²	1	2	yes	complemented
51	C₁₃×#385	C₂²	1	2	yes	complemented
52	C₁₃×#385	C₂²	1	4	yes	complemented
53	C₁₃×#385	C₂²	1	4	yes	complemented
54	C₁₃×#383	C₂²	1	4	yes	complemented
55	C₁₃×#381	C₂²	1	2	yes	—
56	C₁₃×#381	C₂²	1	2	yes	—
57	C₁₃×#380	C₂²	1	4	yes	—
58	C₁₃×#380	C₂²	1	2	yes	complemented
59	C₁₃×#380	C₂²	1	2	yes	complemented
60	C₁₃×#379	C₂²	1	2	yes	—
61	C₁₃×#379	C₂²	1	2	yes	—
62	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
63	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
64	C₂×C₁₃×#95	C₂²	1	2	yes	—
65	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
66	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
67	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
68	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₃	—	2	4	no	—
70	C₂²×D₄×C₁₃	—	2	4	no	—
71	C₂²×D₄×C₁₃	—	2	4	no	—
72	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
73	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
74	C₂³×C₄×C₁₃	—	2	4	no	—
75	C₂³×C₄×C₁₃	—	4	4	no	—
76	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
80	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
81	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
85	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×#126	—	4	8	no	—
88	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
100	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
103	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
110	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
112	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
113	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
114	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
115	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
116	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
117	C₂×C₄²×C₁₃	—	4	4	no	—
118	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
119	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
120	C₁₃×#95	C₂³	1	4	yes	—
121	C₁₃×#95	C₂³	1	4	yes	—
122	C₁₃×#95	C₂³	1	4	yes	—
123	C₁₃×#95	C₂³	1	4	yes	—
124	C₁₃×#95	C₂³	1	4	yes	—
125	C₁₃×#95	C₂³	1	4	yes	—
126	C₁₃×#95	C₂³	1	4	yes	—
127	C₁₃×#95	C₂³	1	4	yes	—
128	C₁₃×#95	C₂³	1	4	yes	—
129	C₁₃×#95	C₂³	1	4	yes	—
130	C₁₃×#95	C₂³	1	4	yes	—
131	C₁₃×#95	C₂³	1	4	yes	—
132	C₁₃×#95	C₂³	1	4	yes	—
133	C₁₃×#95	C₂³	1	4	yes	—
134	#34995	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂⁴×C₁₃	—	2	2	no	—
136	C₂⁴×C₁₃	—	2	2	no	—
137	C₂⁴×C₁₃	—	2	2	no	—
138	C₂⁴×C₁₃	—	4	2	no	—
139	C₂⁴×C₁₃	—	4	2	no	—
140	C₂⁴×C₁₃	—	4	2	no	—
141	C₂⁴×C₁₃	—	4	2	no	—
142	C₂⁴×C₁₃	#41	1	4	yes	—
143	C₂⁴×C₁₃	#41	1	4	yes	—
144	C₂⁴×C₁₃	#41	1	4	yes	—
145	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
146	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
147	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	4	no	—
151	C₂×D₄×C₁₃	—	2	4	no	—
152	C₂×D₄×C₁₃	—	2	4	no	—
153	C₂×D₄×C₁₃	—	2	4	no	—
154	C₂×D₄×C₁₃	—	2	4	no	—
155	C₂×D₄×C₁₃	—	4	16	no	—
156	C₂²×C₄×C₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₃	—	2	4	no	—
158	C₂²×C₄×C₁₃	—	2	4	no	—
159	C₂²×C₄×C₁₃	—	2	4	no	—
160	C₂²×C₄×C₁₃	—	2	4	no	—
161	C₂²×C₄×C₁₃	—	2	4	no	—
162	C₂²×C₄×C₁₃	—	2	4	no	—
163	C₂²×C₄×C₁₃	—	2	2	no	—
164	C₂²×C₄×C₁₃	—	2	2	no	—
165	C₂²×C₄×C₁₃	—	2	2	no	—
166	C₂²×C₄×C₁₃	—	2	2	no	—
167	C₂²×C₄×C₁₃	—	2	4	no	—
168	C₂²×C₄×C₁₃	—	2	2	no	—
169	C₂²×C₄×C₁₃	—	2	2	no	—
170	C₂²×C₄×C₁₃	—	2	4	no	—
171	C₂²×C₄×C₁₃	—	2	4	no	—
172	C₂²×C₄×C₁₃	—	4	2	no	—
173	C₂²×C₄×C₁₃	—	4	2	no	—
174	C₂²×C₄×C₁₃	—	4	2	no	—
175	C₂²×C₄×C₁₃	—	4	2	no	—
176	C₂²×C₄×C₁₃	—	4	2	no	—
177	C₂²×C₄×C₁₃	—	4	2	no	—
178	C₂²×C₄×C₁₃	—	4	2	no	—
179	C₂²×C₄×C₁₃	—	4	2	no	—
180	C₂²×C₄×C₁₃	—	4	2	no	—
181	C₂²×C₄×C₁₃	—	4	2	no	—
182	C₂²×C₄×C₁₃	—	4	2	no	—
183	C₂²×C₄×C₁₃	—	4	2	no	—
184	C₂²×C₄×C₁₃	—	4	2	no	—
185	C₂²×C₄×C₁₃	—	4	16	no	—
186	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
191	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
192	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
195	C₁₃×C₄⋊C₄	—	2	8	no	—
196	C₁₃×C₄⋊C₄	—	4	4	no	—
197	C₁₃×C₄⋊C₄	—	4	4	no	—
198	C₁₃×C₄⋊C₄	—	4	4	no	—
199	C₁₃×C₄⋊C₄	—	4	4	no	—
200	C₁₃×C₄⋊C₄	—	4	4	no	—
201	C₁₃×C₂²⋊C₄	—	2	4	no	—
202	C₁₃×C₂²⋊C₄	—	2	4	no	—
203	C₁₃×C₂²⋊C₄	—	2	4	no	—
204	C₁₃×C₂²⋊C₄	—	2	4	no	—
205	C₁₃×C₂²⋊C₄	—	2	4	no	—
206	C₁₃×C₂²⋊C₄	—	2	4	no	—
207	C₁₃×C₂²⋊C₄	—	2	4	no	—
208	C₁₃×C₂²⋊C₄	—	2	4	no	—
209	C₁₃×C₂²⋊C₄	—	2	4	no	—
210	C₁₃×C₂²⋊C₄	—	2	4	no	—
211	C₁₃×C₂²⋊C₄	—	2	8	no	—
212	C₁₃×C₂²⋊C₄	—	4	4	no	—
213	C₁₃×C₂²⋊C₄	—	4	4	no	—
214	C₁₃×C₂²⋊C₄	—	4	4	no	—
215	C₁₃×C₂²⋊C₄	—	4	4	no	—
216	C₁₃×C₂²⋊C₄	—	4	4	no	—
217	C₄²×C₁₃	—	2	8	no	—
218	C₄²×C₁₃	—	4	4	no	—
219	#2852	C₂×C₁₃	1	4	yes	complemented
220	#2643	C₂×C₁₃	1	4	yes	complemented
221	#2510	C₂×C₁₃	1	4	yes	complemented
222	#2493	C₂×C₁₃	1	4	yes	complemented
223	#2481	C₂×C₁₃	1	4	yes	complemented
224	#2480	C₂×C₁₃	1	4	yes	complemented
225	#2315	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#2315	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#2308	C₂×C₁₃	1	1	yes	characteristic
228	#2308	C₂×C₁₃	1	1	yes	characteristic
229	C₂×#386	C₂×C₁₃	1	1	yes	characteristic
230	C₂×#385	C₂×C₁₃	1	1	yes	characteristic, complemented
231	C₂×C₄×C₂²⋊C₄	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	2	no	—
236	C₂³×C₁₃	—	2	2	no	—
237	C₂³×C₁₃	—	2	2	no	—
238	C₂³×C₁₃	—	2	2	no	—
239	C₂³×C₁₃	—	2	2	no	—
240	C₂³×C₁₃	—	2	2	no	—
241	C₂³×C₁₃	—	2	4	no	—
242	C₂³×C₁₃	—	2	4	no	—
243	C₂³×C₁₃	—	4	4	no	—
244	C₂³×C₁₃	—	4	8	no	—
245	C₂³×C₁₃	—	4	4	no	—
246	C₂³×C₁₃	—	4	8	no	—
247	C₂³×C₁₃	—	4	8	no	—
248	C₂³×C₁₃	—	4	4	no	—
249	C₂³×C₁₃	—	8	2	no	—
250	C₂³×C₁₃	—	8	2	no	—
251	C₂³×C₁₃	—	8	4	no	—
252	C₂³×C₁₃	#126	1	16	yes	complemented
253	C₂³×C₁₃	C₂×#41	1	2	yes	—
254	C₂³×C₁₃	C₂×#41	1	2	yes	—
255	C₂³×C₁₃	C₂×#41	1	2	yes	—
256	C₂³×C₁₃	C₂×#41	1	2	yes	—
257	C₂³×C₁₃	C₂×#41	1	2	yes	—
258	C₂³×C₁₃	C₂×#41	1	2	yes	—
259	C₂³×C₁₃	C₂×#41	1	2	yes	—
260	C₂³×C₁₃	C₂×#41	1	2	yes	—
261	C₂³×C₁₃	C₂×#41	1	2	yes	—
262	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
263	D₄×C₁₃	—	4	8	no	—
264	D₄×C₁₃	—	4	8	no	—
265	C₂×C₄×C₁₃	—	2	8	no	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	2	2	no	—
268	C₂×C₄×C₁₃	—	2	4	no	—
269	C₂×C₄×C₁₃	—	2	4	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	2	4	no	—
273	C₂×C₄×C₁₃	—	2	4	no	—
274	C₂×C₄×C₁₃	—	2	2	no	—
275	C₂×C₄×C₁₃	—	2	2	no	—
276	C₂×C₄×C₁₃	—	2	2	no	—
277	C₂×C₄×C₁₃	—	2	2	no	—
278	C₂×C₄×C₁₃	—	2	4	no	—
279	C₂×C₄×C₁₃	—	2	4	no	—
280	C₂×C₄×C₁₃	—	2	4	no	—
281	C₂×C₄×C₁₃	—	2	2	no	—
282	C₂×C₄×C₁₃	—	2	4	no	—
283	C₂×C₄×C₁₃	—	2	4	no	—
284	C₂×C₄×C₁₃	—	2	2	no	—
285	C₂×C₄×C₁₃	—	2	4	no	—
286	C₂×C₄×C₁₃	—	2	4	no	—
287	C₂×C₄×C₁₃	—	2	4	no	—
288	C₂×C₄×C₁₃	—	2	4	no	—
289	C₂×C₄×C₁₃	—	2	4	no	—
290	C₂×C₄×C₁₃	—	4	8	no	—
291	C₂×C₄×C₁₃	—	4	8	no	—
292	C₂×C₄×C₁₃	—	4	8	no	—
293	C₂×C₄×C₁₃	—	4	8	no	—
294	C₂×C₄×C₁₃	—	4	8	no	—
295	C₂×C₄×C₁₃	—	4	4	no	—
296	C₂×C₄×C₁₃	—	4	4	no	—
297	C₂×C₄×C₁₃	—	8	2	no	—
298	C₂×C₄×C₁₃	—	8	2	no	—
299	C₂×C₄×C₁₃	—	8	4	no	—
300	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
301	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
302	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×#126	C₂²×C₁₃	1	4	yes	complemented
304	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
305	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
306	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
307	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
308	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
309	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
310	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
311	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
312	#401	C₂²×C₁₃	1	4	yes	complemented
313	#400	C₂²×C₁₃	1	4	yes	complemented
314	#400	C₂²×C₁₃	1	4	yes	complemented
315	#400	C₂²×C₁₃	1	4	yes	complemented
316	#397	C₂²×C₁₃	1	4	yes	complemented
317	#397	C₂²×C₁₃	1	4	yes	complemented
318	#397	C₂²×C₁₃	1	4	yes	complemented
319	#396	C₂²×C₁₃	1	4	yes	complemented
320	#388	C₂²×C₁₃	1	4	yes	complemented
321	#388	C₂²×C₁₃	1	4	yes	complemented
322	#388	C₂²×C₁₃	1	4	yes	complemented
323	#387	C₂²×C₁₃	1	4	yes	complemented
324	#387	C₂²×C₁₃	1	4	yes	complemented
325	#387	C₂²×C₁₃	1	4	yes	complemented
326	#386	C₂²×C₁₃	1	4	yes	—
327	#386	C₂²×C₁₃	1	4	yes	—
328	#386	C₂²×C₁₃	1	2	yes	—
329	#386	C₂²×C₁₃	1	4	yes	—
330	#386	C₂²×C₁₃	1	2	yes	—
331	#386	C₂²×C₁₃	1	2	yes	—
332	#386	C₂²×C₁₃	1	2	yes	—
333	#386	C₂²×C₁₃	1	4	yes	—
334	#385	C₂²×C₁₃	1	4	yes	—
335	#385	C₂²×C₁₃	1	4	yes	—
336	#385	C₂²×C₁₃	1	4	yes	complemented
337	#385	C₂²×C₁₃	1	4	yes	complemented
338	#385	C₂²×C₁₃	1	4	yes	complemented
339	#385	C₂²×C₁₃	1	2	yes	complemented
340	#385	C₂²×C₁₃	1	2	yes	complemented
341	#383	C₂²×C₁₃	1	4	yes	complemented
342	#381	C₂²×C₁₃	1	2	yes	—
343	#381	C₂²×C₁₃	1	2	yes	—
344	#380	C₂²×C₁₃	1	4	yes	—
345	#380	C₂²×C₁₃	1	2	yes	complemented
346	#380	C₂²×C₁₃	1	2	yes	complemented
347	#379	C₂²×C₁₃	1	2	yes	—
348	#379	C₂²×C₁₃	1	2	yes	—
349	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
350	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
351	C₂×#95	C₂²×C₁₃	1	2	yes	—
352	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
353	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
354	C₂²×C₁₃	—	2	4	no	—
355	C₂²×C₁₃	—	2	4	no	—
356	C₂²×C₁₃	—	2	4	no	—
357	C₂²×C₁₃	—	2	2	no	—
358	C₂²×C₁₃	—	2	2	no	—
359	C₂²×C₁₃	—	2	2	no	—
360	C₂²×C₁₃	—	2	2	no	—
361	C₂²×C₁₃	—	2	2	no	—
362	C₂²×C₁₃	—	2	2	no	—
363	C₂²×C₁₃	—	2	4	no	—
364	C₂²×C₁₃	—	2	4	no	—
365	C₂²×C₁₃	—	2	4	no	—
366	C₂²×C₁₃	—	4	16	no	—
367	C₂²×C₁₃	—	4	2	no	—
368	C₂²×C₁₃	—	4	4	no	—
369	C₂²×C₁₃	—	4	2	no	—
370	C₂²×C₁₃	—	4	2	no	—
371	C₂²×C₁₃	—	4	4	no	—
372	C₂²×C₁₃	—	8	8	no	—
373	C₂²×C₁₃	C₂×#126	1	4	yes	—
374	C₂²×C₁₃	C₂×#126	1	4	yes	—
375	C₂²×C₁₃	C₂×#126	1	4	yes	—
376	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
377	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
378	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
379	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
380	C₂²×C₁₃	#585	1	2	yes	—
381	C₄×C₁₃	—	2	4	no	—
382	C₄×C₁₃	—	4	2	no	—
383	C₄×C₁₃	—	4	4	no	—
384	C₄×C₁₃	—	4	4	no	—
385	C₄×C₁₃	—	4	2	no	—
386	C₄×C₁₃	—	4	2	no	—
387	C₄×C₁₃	—	4	2	no	—
388	C₄×C₁₃	—	4	4	no	—
389	C₄×C₁₃	—	4	4	no	—
390	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
391	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
392	C₂²×D₄	—	2	4	no	—
393	C₂²×D₄	—	2	4	no	—
394	C₂²×D₄	—	2	4	no	—
395	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
396	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
397	C₂³×C₄	—	2	4	no	—
398	C₂³×C₄	—	4	4	no	—
399	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
400	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
401	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
402	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
403	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
404	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
405	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
406	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
407	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
408	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
409	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
410	#126	—	4	8	no	—
411	C₂×C₄⋊C₄	—	4	4	no	—
412	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
413	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
414	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
415	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
416	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
417	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
418	C₂×C₂²⋊C₄	—	2	4	no	—
419	C₂×C₂²⋊C₄	—	2	4	no	—
420	C₂×C₂²⋊C₄	—	2	4	no	—
421	C₂×C₂²⋊C₄	—	2	4	no	—
422	C₂×C₂²⋊C₄	—	2	4	no	—
423	C₂×C₂²⋊C₄	—	4	4	no	—
424	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
440	C₂×C₄²	—	4	4	no	—
441	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
442	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
443	#95	C₂³×C₁₃	1	4	yes	—
444	#95	C₂³×C₁₃	1	4	yes	—
445	#95	C₂³×C₁₃	1	4	yes	—
446	#95	C₂³×C₁₃	1	4	yes	—
447	#95	C₂³×C₁₃	1	4	yes	—
448	#95	C₂³×C₁₃	1	4	yes	—
449	#95	C₂³×C₁₃	1	4	yes	—
450	#95	C₂³×C₁₃	1	4	yes	—
451	#95	C₂³×C₁₃	1	4	yes	—
452	#95	C₂³×C₁₃	1	4	yes	—
453	#95	C₂³×C₁₃	1	4	yes	—
454	#95	C₂³×C₁₃	1	4	yes	—
455	#95	C₂³×C₁₃	1	4	yes	—
456	#95	C₂³×C₁₃	1	4	yes	—
457	C₂×C₁₃	—	2	4	no	—
458	C₂×C₁₃	—	2	4	no	—
459	C₂×C₁₃	—	2	4	no	—
460	C₂×C₁₃	—	8	2	no	—
461	C₂×C₁₃	C₂²×#126	1	1	yes	characteristic
462	C₂×C₁₃	#3459	1	2	yes	—
463	C₂×C₁₃	#3490	1	1	yes	characteristic
464	C₂×C₁₃	#3491	1	1	yes	characteristic
465	C₂×C₁₃	#3505	1	2	yes	—
466	C₂⁴	—	2	2	no	—
467	C₂⁴	—	2	2	no	—
468	C₂⁴	—	2	2	no	—
469	C₂⁴	—	4	2	no	—
470	C₂⁴	—	4	2	no	—
471	C₂⁴	—	4	2	no	—
472	C₂⁴	—	4	2	no	—
473	C₂⁴	C₁₃×#41	1	4	yes	—
474	C₂⁴	C₁₃×#41	1	4	yes	—
475	C₂⁴	C₁₃×#41	1	4	yes	—
476	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
477	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
478	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
479	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
480	C₂×D₄	—	2	4	no	—
481	C₂×D₄	—	2	4	no	—
482	C₂×D₄	—	2	4	no	—
483	C₂×D₄	—	2	4	no	—
484	C₂×D₄	—	2	4	no	—
485	C₂×D₄	—	2	4	no	—
486	C₂×D₄	—	4	16	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	4	no	—
489	C₂²×C₄	—	2	4	no	—
490	C₂²×C₄	—	2	4	no	—
491	C₂²×C₄	—	2	4	no	—
492	C₂²×C₄	—	2	4	no	—
493	C₂²×C₄	—	2	4	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	4	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	4	no	—
502	C₂²×C₄	—	2	4	no	—
503	C₂²×C₄	—	4	2	no	—
504	C₂²×C₄	—	4	2	no	—
505	C₂²×C₄	—	4	2	no	—
506	C₂²×C₄	—	4	2	no	—
507	C₂²×C₄	—	4	2	no	—
508	C₂²×C₄	—	4	2	no	—
509	C₂²×C₄	—	4	2	no	—
510	C₂²×C₄	—	4	2	no	—
511	C₂²×C₄	—	4	2	no	—
512	C₂²×C₄	—	4	2	no	—
513	C₂²×C₄	—	4	2	no	—
514	C₂²×C₄	—	4	2	no	—
515	C₂²×C₄	—	4	2	no	—
516	C₂²×C₄	—	4	16	no	—
517	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
518	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
519	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
520	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
521	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
522	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
523	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
524	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
525	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
526	C₄⋊C₄	—	2	8	no	—
527	C₄⋊C₄	—	4	4	no	—
528	C₄⋊C₄	—	4	4	no	—
529	C₄⋊C₄	—	4	4	no	—
530	C₄⋊C₄	—	4	4	no	—
531	C₄⋊C₄	—	4	4	no	—
532	C₂²⋊C₄	—	2	4	no	—
533	C₂²⋊C₄	—	2	4	no	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	4	no	—
536	C₂²⋊C₄	—	2	4	no	—
537	C₂²⋊C₄	—	2	4	no	—
538	C₂²⋊C₄	—	2	4	no	—
539	C₂²⋊C₄	—	2	4	no	—
540	C₂²⋊C₄	—	2	4	no	—
541	C₂²⋊C₄	—	2	4	no	—
542	C₂²⋊C₄	—	2	8	no	—
543	C₂²⋊C₄	—	4	4	no	—
544	C₂²⋊C₄	—	4	4	no	—
545	C₂²⋊C₄	—	4	4	no	—
546	C₂²⋊C₄	—	4	4	no	—
547	C₂²⋊C₄	—	4	4	no	—
548	C₄²	—	2	8	no	—
549	C₄²	—	4	4	no	—
550	C₁₃	#34995	1	1	yes	characteristic, direct product factor, Sylow
551	C₂³	—	2	2	no	—
552	C₂³	—	2	2	no	—
553	C₂³	—	2	2	no	—
554	C₂³	—	2	2	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	2	2	no	—
557	C₂³	—	2	2	no	—
558	C₂³	—	2	2	no	—
559	C₂³	—	2	2	no	—
560	C₂³	—	2	4	no	—
561	C₂³	—	2	4	no	—
562	C₂³	—	4	4	no	—
563	C₂³	—	4	8	no	—
564	C₂³	—	4	4	no	—
565	C₂³	—	4	8	no	—
566	C₂³	—	4	8	no	—
567	C₂³	—	4	4	no	—
568	C₂³	—	8	2	no	—
569	C₂³	—	8	2	no	—
570	C₂³	—	8	4	no	—
571	C₂³	C₁₃×#126	1	16	yes	complemented
572	C₂³	C₂×C₁₃×#41	1	2	yes	—
573	C₂³	C₂×C₁₃×#41	1	2	yes	—
574	C₂³	C₂×C₁₃×#41	1	2	yes	—
575	C₂³	C₂×C₁₃×#41	1	2	yes	—
576	C₂³	C₂×C₁₃×#41	1	2	yes	—
577	C₂³	C₂×C₁₃×#41	1	2	yes	—
578	C₂³	C₂×C₁₃×#41	1	2	yes	—
579	C₂³	C₂×C₁₃×#41	1	2	yes	—
580	C₂³	C₂×C₁₃×#41	1	2	yes	—
581	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
582	D₄	—	4	8	no	—
583	D₄	—	4	8	no	—
584	C₂×C₄	—	2	8	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	4	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	4	8	no	—
610	C₂×C₄	—	4	8	no	—
611	C₂×C₄	—	4	4	no	—
612	C₂×C₄	—	4	8	no	—
613	C₂×C₄	—	4	8	no	—
614	C₂×C₄	—	4	8	no	—
615	C₂×C₄	—	4	4	no	—
616	C₂×C₄	—	8	2	no	—
617	C₂×C₄	—	8	2	no	—
618	C₂×C₄	—	8	4	no	—
619	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
620	C₂²	—	2	4	no	—
621	C₂²	—	2	4	no	—
622	C₂²	—	2	4	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	2	no	—
625	C₂²	—	2	2	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	4	no	—
630	C₂²	—	2	4	no	—
631	C₂²	—	2	4	no	—
632	C₂²	—	4	16	no	—
633	C₂²	—	4	2	no	—
634	C₂²	—	4	4	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	4	2	no	—
637	C₂²	—	4	4	no	—
638	C₂²	—	8	8	no	—
639	C₂²	C₂×C₁₃×#126	1	4	yes	—
640	C₂²	C₂×C₁₃×#126	1	4	yes	—
641	C₂²	C₂×C₁₃×#126	1	4	yes	—
642	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
643	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
644	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
645	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
646	C₂²	C₁₃×#585	1	2	yes	—
647	C₄	—	2	4	no	—
648	C₄	—	4	2	no	—
649	C₄	—	4	4	no	—
650	C₄	—	4	4	no	—
651	C₄	—	4	2	no	—
652	C₄	—	4	2	no	—
653	C₄	—	4	2	no	—
654	C₄	—	4	4	no	—
655	C₄	—	4	4	no	—
656	C₂	—	2	4	no	—
657	C₂	—	2	4	no	—
658	C₂	—	2	4	no	—
659	C₂	—	8	2	no	—
660	C₂	C₂²×C₁₃×#126	1	1	yes	characteristic
661	C₂	C₁₃×#3459	1	2	yes	—
662	C₂	C₁₃×#3490	1	1	yes	characteristic
663	C₂	C₁₃×#3491	1	1	yes	characteristic
664	C₂	C₁₃×#3505	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2852	C₂	semidirect
2. C₁₃×#2643	C₂	semidirect
3. C₁₃×#2510	C₂	semidirect
4. C₁₃×#2493	C₂	semidirect
5. C₁₃×#2481	C₂	semidirect
6. C₁₃×#2480	C₂	semidirect
7. C₁₃×#2315	C₂	semidirect
8. C₁₃×#2315	C₂	semidirect
12. C₂×C₁₃×#385	C₂	semidirect
13. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
16. C₂×C₁₃×#126	C₂²	semidirect
17. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
24. C₂²×C₄²×C₁₃	C₂²	semidirect
25. C₁₃×#401	C₂²	semidirect
26. C₁₃×#400	C₂²	semidirect
27. C₁₃×#400	C₂²	semidirect
28. C₁₃×#400	C₂²	semidirect
29. C₁₃×#397	C₂²	semidirect
30. C₁₃×#397	C₂²	semidirect
31. C₁₃×#397	C₂²	semidirect
32. C₁₃×#396	C₂²	semidirect
33. C₁₃×#388	C₂²	semidirect
34. C₁₃×#388	C₂²	semidirect
35. C₁₃×#388	C₂²	semidirect
36. C₁₃×#387	C₂²	semidirect
37. C₁₃×#387	C₂²	semidirect
38. C₁₃×#387	C₂²	semidirect
49. C₁₃×#385	C₂²	semidirect
50. C₁₃×#385	C₂²	semidirect
51. C₁₃×#385	C₂²	semidirect
52. C₁₃×#385	C₂²	semidirect
53. C₁₃×#385	C₂²	semidirect
54. C₁₃×#383	C₂²	semidirect
58. C₁₃×#380	C₂²	semidirect
59. C₁₃×#380	C₂²	semidirect
63. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
65. C₂×C₁₃×#95	C₂²	semidirect
66. C₂×C₁₃×#95	C₂²	semidirect
134. #34995	C₁₃	direct (N × H)
219. #2852	C₂×C₁₃	semidirect
220. #2643	C₂×C₁₃	semidirect
221. #2510	C₂×C₁₃	semidirect
222. #2493	C₂×C₁₃	semidirect
223. #2481	C₂×C₁₃	semidirect
224. #2480	C₂×C₁₃	semidirect
225. #2315	C₂×C₁₃	semidirect
226. #2315	C₂×C₁₃	semidirect
230. C₂×#385	C₂×C₁₃	semidirect
231. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
252. C₂³×C₁₃	#126	semidirect
303. C₂×#126	C₂²×C₁₃	semidirect
304. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
311. C₂²×C₄²	C₂²×C₁₃	semidirect
312. #401	C₂²×C₁₃	semidirect
313. #400	C₂²×C₁₃	semidirect
314. #400	C₂²×C₁₃	semidirect
315. #400	C₂²×C₁₃	semidirect
316. #397	C₂²×C₁₃	semidirect
317. #397	C₂²×C₁₃	semidirect
318. #397	C₂²×C₁₃	semidirect
319. #396	C₂²×C₁₃	semidirect
320. #388	C₂²×C₁₃	semidirect
321. #388	C₂²×C₁₃	semidirect
322. #388	C₂²×C₁₃	semidirect
323. #387	C₂²×C₁₃	semidirect
324. #387	C₂²×C₁₃	semidirect
325. #387	C₂²×C₁₃	semidirect
336. #385	C₂²×C₁₃	semidirect
337. #385	C₂²×C₁₃	semidirect
338. #385	C₂²×C₁₃	semidirect
339. #385	C₂²×C₁₃	semidirect
340. #385	C₂²×C₁₃	semidirect
341. #383	C₂²×C₁₃	semidirect
345. #380	C₂²×C₁₃	semidirect
346. #380	C₂²×C₁₃	semidirect
350. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
352. C₂×#95	C₂²×C₁₃	semidirect
353. C₂×#95	C₂²×C₁₃	semidirect
550. C₁₃	#34995	direct (N × H)
571. C₂³	C₁₃×#126	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#2852	2
C₁₃×#2643	2
C₁₃×#2510	2
C₁₃×#2493	2
C₁₃×#2481	2
C₁₃×#2480	2
C₁₃×#2315	2
C₁₃×#2308	2
C₂×C₁₃×#386	2
C₂×C₁₃×#385	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
#34995	13

Subgroups — C13×#34995 #15721334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34995 #15721334