Subgroups — C₁₃×#34358 #15720697

Order 3328.

2982 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2377	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2364	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2342	C₂	1	4	yes	maximal, complemented
5	D₄×C₁₃×C₂²⋊C₄	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2333	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2325	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2313	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2308	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#381	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#121	C₄	1	16	yes	complemented
16	C₂×C₁₃×#121	C₂²	1	2	yes	—
17	C₂×C₁₃×#121	C₂²	1	2	yes	—
18	C₂×C₁₃×#121	C₂²	1	2	yes	—
19	C₂×C₁₃×#121	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
21	C₂×C₁₃×#117	C₂²	1	2	yes	—
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₁₃×#390	C₂²	1	8	yes	complemented
27	C₁₃×#388	C₂²	1	8	yes	complemented
28	C₁₃×#388	C₂²	1	8	yes	complemented
29	C₁₃×#387	C₂²	1	8	yes	complemented
30	C₁₃×#387	C₂²	1	8	yes	complemented
31	C₁₃×#386	C₂²	1	8	yes	complemented
32	C₁₃×#386	C₂²	1	8	yes	complemented
33	C₁₃×#386	C₂²	1	8	yes	complemented
34	C₁₃×#386	C₂²	1	8	yes	complemented
35	C₁₃×#385	C₂²	1	8	yes	complemented
36	C₁₃×#381	C₂²	1	2	yes	—
37	C₁₃×#381	C₂²	1	2	yes	—
38	C₁₃×#381	C₂²	1	2	yes	—
39	C₁₃×#381	C₂²	1	2	yes	complemented
40	C₁₃×#381	C₂²	1	2	yes	complemented
41	C₁₃×#380	C₂²	1	4	yes	—
42	C₁₃×#380	C₂²	1	2	yes	complemented
43	C₁₃×#380	C₂²	1	2	yes	complemented
44	C₁₃×#379	C₂²	1	2	yes	—
45	C₁₃×#379	C₂²	1	4	yes	—
46	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
47	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
48	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
49	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
50	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
51	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
52	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
53	C₂⁵×C₁₃	C₂³	1	2	yes	—
54	C₂²×D₄×C₁₃	—	4	4	no	—
55	C₂²×D₄×C₁₃	—	4	8	no	—
56	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
57	C₂²×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
58	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
59	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
60	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
61	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
62	C₂³×C₄×C₁₃	—	4	4	no	—
63	C₂³×C₄×C₁₃	C₂×C₄	1	8	yes	complemented
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
68	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
69	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×#121	C₂×C₄	1	16	yes	complemented
74	C₁₃×#121	C₂×C₄	1	16	yes	complemented
75	C₁₃×#121	C₂×C₄	1	16	yes	complemented
76	C₁₃×#121	C₂×C₄	1	16	yes	complemented
77	C₄×D₄×C₁₃	—	4	16	no	—
78	C₁₃×#117	—	4	4	no	—
79	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
85	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
86	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
87	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
88	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
89	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
90	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
91	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
92	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
97	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
98	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
99	C₁₃×#95	C₂³	1	8	yes	—
100	C₁₃×#95	C₂³	1	4	yes	—
101	C₁₃×#95	C₂³	1	8	yes	—
102	C₁₃×#95	C₂³	1	4	yes	—
103	C₁₃×#95	C₂³	1	4	yes	—
104	C₁₃×#95	C₂³	1	4	yes	—
105	C₁₃×#95	C₂³	1	4	yes	—
106	C₁₃×#95	C₂³	1	4	yes	—
107	#34358	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂⁴×C₁₃	—	2	4	no	—
109	C₂⁴×C₁₃	—	2	4	no	—
110	C₂⁴×C₁₃	—	2	8	no	—
111	C₂⁴×C₁₃	—	4	2	no	—
112	C₂⁴×C₁₃	—	4	4	no	—
113	C₂⁴×C₁₃	—	4	4	no	—
114	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
115	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
116	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
117	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
118	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
120	C₂×D₄×C₁₃	—	2	16	no	—
121	C₂×D₄×C₁₃	—	4	16	no	—
122	C₂×D₄×C₁₃	—	4	8	no	—
123	C₂×D₄×C₁₃	—	4	2	no	—
124	C₂×D₄×C₁₃	—	4	4	no	—
125	C₂×D₄×C₁₃	—	4	2	no	—
126	C₂×D₄×C₁₃	—	4	32	no	—
127	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
128	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
129	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
130	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
131	C₂²×C₄×C₁₃	—	2	4	no	—
132	C₂²×C₄×C₁₃	—	2	4	no	—
133	C₂²×C₄×C₁₃	—	2	8	no	—
134	C₂²×C₄×C₁₃	—	4	16	no	—
135	C₂²×C₄×C₁₃	—	4	2	no	—
136	C₂²×C₄×C₁₃	—	4	2	no	—
137	C₂²×C₄×C₁₃	—	4	2	no	—
138	C₂²×C₄×C₁₃	—	4	2	no	—
139	C₂²×C₄×C₁₃	—	4	4	no	—
140	C₂²×C₄×C₁₃	—	4	8	no	—
141	C₂²×C₄×C₁₃	—	4	4	no	—
142	C₂²×C₄×C₁₃	—	4	8	no	—
143	C₂²×C₄×C₁₃	—	4	8	no	—
144	C₂²×C₄×C₁₃	—	4	4	no	—
145	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
146	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
147	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
148	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
149	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
150	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
151	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
159	C₁₃×C₄⋊C₄	—	4	4	no	—
160	C₁₃×C₄⋊C₄	—	4	8	no	—
161	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
162	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
163	C₁₃×C₂²⋊C₄	—	2	8	no	—
164	C₁₃×C₂²⋊C₄	—	2	8	no	—
165	C₁₃×C₂²⋊C₄	—	2	8	no	—
166	C₁₃×C₂²⋊C₄	—	4	8	no	—
167	C₁₃×C₂²⋊C₄	—	4	4	no	—
168	C₁₃×C₂²⋊C₄	—	4	4	no	—
169	C₁₃×C₂²⋊C₄	—	4	8	no	—
170	C₁₃×C₂²⋊C₄	—	4	8	no	—
171	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
172	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
173	C₄²×C₁₃	—	4	4	no	—
174	C₄²×C₁₃	—	4	8	no	—
175	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic
176	#2377	C₂×C₁₃	1	4	yes	complemented
177	#2364	C₂×C₁₃	1	4	yes	complemented
178	#2342	C₂×C₁₃	1	4	yes	complemented
179	D₄×C₂²⋊C₄	C₂×C₁₃	1	4	yes	complemented
180	#2333	C₂×C₁₃	1	4	yes	complemented
181	#2325	C₂×C₁₃	1	4	yes	complemented
182	#2313	C₂×C₁₃	1	2	yes	complemented
183	#2308	C₂×C₁₃	1	2	yes	complemented
184	#2280	C₂×C₁₃	1	1	yes	characteristic, complemented
185	C₂×#381	C₂×C₁₃	1	1	yes	characteristic, complemented
186	C₂³×C₁₃	—	2	2	no	—
187	C₂³×C₁₃	—	2	2	no	—
188	C₂³×C₁₃	—	2	2	no	—
189	C₂³×C₁₃	—	2	2	no	—
190	C₂³×C₁₃	—	2	8	no	—
191	C₂³×C₁₃	—	2	8	no	—
192	C₂³×C₁₃	—	2	2	no	—
193	C₂³×C₁₃	—	2	4	no	—
194	C₂³×C₁₃	—	2	8	no	—
195	C₂³×C₁₃	—	2	4	no	—
196	C₂³×C₁₃	—	2	2	no	—
197	C₂³×C₁₃	—	2	2	no	—
198	C₂³×C₁₃	—	2	8	no	—
199	C₂³×C₁₃	—	2	16	no	—
200	C₂³×C₁₃	—	4	4	no	—
201	C₂³×C₁₃	—	4	8	no	—
202	C₂³×C₁₃	—	4	8	no	—
203	C₂³×C₁₃	—	4	16	no	—
204	C₂³×C₁₃	—	8	16	no	—
205	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
206	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
207	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
208	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
209	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
210	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
211	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
212	D₄×C₁₃	—	2	32	no	—
213	D₄×C₁₃	—	4	8	no	—
214	D₄×C₁₃	—	4	8	no	—
215	D₄×C₁₃	—	4	16	no	—
216	C₂×C₄×C₁₃	—	2	8	no	—
217	C₂×C₄×C₁₃	—	2	8	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	8	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	8	no	—
224	C₂×C₄×C₁₃	—	2	8	no	—
225	C₂×C₄×C₁₃	—	2	8	no	—
226	C₂×C₄×C₁₃	—	2	8	no	—
227	C₂×C₄×C₁₃	—	2	8	no	—
228	C₂×C₄×C₁₃	—	2	8	no	—
229	C₂×C₄×C₁₃	—	4	4	no	—
230	C₂×C₄×C₁₃	—	4	4	no	—
231	C₂×C₄×C₁₃	—	4	4	no	—
232	C₂×C₄×C₁₃	—	4	4	no	—
233	C₂×C₄×C₁₃	—	4	8	no	—
234	C₂×C₄×C₁₃	—	8	8	no	—
235	C₂×C₄×C₁₃	—	8	16	no	—
236	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
237	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
238	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
239	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
240	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
241	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
242	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
243	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×#121	C₄×C₁₃	1	16	yes	complemented
245	C₂×#121	C₂²×C₁₃	1	2	yes	—
246	C₂×#121	C₂²×C₁₃	1	2	yes	—
247	C₂×#121	C₂²×C₁₃	1	2	yes	—
248	C₂×#121	C₂²×C₁₃	1	2	yes	—
249	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
250	C₂×#117	C₂²×C₁₃	1	2	yes	—
251	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
252	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
253	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
254	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
255	#390	C₂²×C₁₃	1	8	yes	complemented
256	#388	C₂²×C₁₃	1	8	yes	complemented
257	#388	C₂²×C₁₃	1	8	yes	complemented
258	#387	C₂²×C₁₃	1	8	yes	complemented
259	#387	C₂²×C₁₃	1	8	yes	complemented
260	#386	C₂²×C₁₃	1	8	yes	complemented
261	#386	C₂²×C₁₃	1	8	yes	complemented
262	#386	C₂²×C₁₃	1	8	yes	complemented
263	#386	C₂²×C₁₃	1	8	yes	complemented
264	#385	C₂²×C₁₃	1	8	yes	complemented
265	#381	C₂²×C₁₃	1	2	yes	—
266	#381	C₂²×C₁₃	1	2	yes	—
267	#381	C₂²×C₁₃	1	2	yes	—
268	#381	C₂²×C₁₃	1	2	yes	complemented
269	#381	C₂²×C₁₃	1	2	yes	complemented
270	#380	C₂²×C₁₃	1	4	yes	—
271	#380	C₂²×C₁₃	1	2	yes	complemented
272	#380	C₂²×C₁₃	1	2	yes	complemented
273	#379	C₂²×C₁₃	1	4	yes	—
274	#379	C₂²×C₁₃	1	2	yes	—
275	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
276	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
277	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
278	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
279	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
280	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
281	C₂²×C₁₃	—	2	2	no	—
282	C₂²×C₁₃	—	2	2	no	—
283	C₂²×C₁₃	—	2	2	no	—
284	C₂²×C₁₃	—	2	2	no	—
285	C₂²×C₁₃	—	2	8	no	—
286	C₂²×C₁₃	—	2	8	no	—
287	C₂²×C₁₃	—	2	2	no	—
288	C₂²×C₁₃	—	2	8	no	—
289	C₂²×C₁₃	—	2	2	no	—
290	C₂²×C₁₃	—	2	8	no	—
291	C₂²×C₁₃	—	2	2	no	—
292	C₂²×C₁₃	—	2	8	no	—
293	C₂²×C₁₃	—	4	16	no	—
294	C₂²×C₁₃	—	4	8	no	—
295	C₂²×C₁₃	—	4	4	no	—
296	C₂²×C₁₃	—	4	8	no	—
297	C₂²×C₁₃	—	8	16	no	—
298	C₂²×C₁₃	#518	1	4	yes	—
299	C₂²×C₁₃	#518	1	4	yes	—
300	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
301	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
302	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
303	C₂²×C₁₃	#585	1	2	yes	—
304	C₄×C₁₃	—	2	2	no	—
305	C₄×C₁₃	—	2	2	no	—
306	C₄×C₁₃	—	2	2	no	—
307	C₄×C₁₃	—	2	2	no	—
308	C₄×C₁₃	—	2	8	no	—
309	C₄×C₁₃	—	4	8	no	—
310	C₄×C₁₃	—	4	8	no	—
311	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
312	C₂⁵	C₂³×C₁₃	1	2	yes	—
313	C₂²×D₄	—	4	4	no	—
314	C₂²×D₄	—	4	8	no	—
315	C₂²×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
316	C₂²×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
317	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
318	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
319	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
320	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
321	C₂³×C₄	—	4	4	no	—
322	C₂³×C₄	C₂×C₄×C₁₃	1	8	yes	complemented
323	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
324	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
325	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
326	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
327	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
328	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
329	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
330	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
331	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
332	#121	C₂×C₄×C₁₃	1	16	yes	complemented
333	#121	C₂×C₄×C₁₃	1	16	yes	complemented
334	#121	C₂×C₄×C₁₃	1	16	yes	complemented
335	#121	C₂×C₄×C₁₃	1	16	yes	complemented
336	C₄×D₄	—	4	16	no	—
337	#117	—	4	4	no	—
338	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	complemented
339	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
340	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
341	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
342	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
343	C₂×C₂²⋊C₄	—	4	4	no	—
344	C₂×C₂²⋊C₄	—	4	8	no	—
345	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	16	yes	complemented
346	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
356	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
357	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
358	#95	C₂³×C₁₃	1	4	yes	—
359	#95	C₂³×C₁₃	1	4	yes	—
360	#95	C₂³×C₁₃	1	4	yes	—
361	#95	C₂³×C₁₃	1	4	yes	—
362	#95	C₂³×C₁₃	1	8	yes	—
363	#95	C₂³×C₁₃	1	8	yes	—
364	#95	C₂³×C₁₃	1	4	yes	—
365	#95	C₂³×C₁₃	1	4	yes	—
366	C₂×C₁₃	—	2	4	no	—
367	C₂×C₁₃	—	2	4	no	—
368	C₂×C₁₃	—	4	2	no	—
369	C₂×C₁₃	—	4	8	no	—
370	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
371	C₂×C₁₃	C₂×#518	1	1	yes	characteristic
372	C₂×C₁₃	#3428	1	1	yes	characteristic
373	C₂×C₁₃	#3534	1	4	yes	—
374	C₂⁴	—	2	4	no	—
375	C₂⁴	—	2	4	no	—
376	C₂⁴	—	2	8	no	—
377	C₂⁴	—	4	2	no	—
378	C₂⁴	—	4	4	no	—
379	C₂⁴	—	4	4	no	—
380	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
381	C₂⁴	C₂²×C₄×C₁₃	1	8	yes	—
382	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
383	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
384	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
385	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
386	C₂×D₄	—	2	16	no	—
387	C₂×D₄	—	4	16	no	—
388	C₂×D₄	—	4	8	no	—
389	C₂×D₄	—	4	2	no	—
390	C₂×D₄	—	4	4	no	—
391	C₂×D₄	—	4	2	no	—
392	C₂×D₄	—	4	32	no	—
393	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
394	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
395	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
396	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	8	no	—
400	C₂²×C₄	—	4	16	no	—
401	C₂²×C₄	—	4	2	no	—
402	C₂²×C₄	—	4	2	no	—
403	C₂²×C₄	—	4	2	no	—
404	C₂²×C₄	—	4	2	no	—
405	C₂²×C₄	—	4	4	no	—
406	C₂²×C₄	—	4	8	no	—
407	C₂²×C₄	—	4	4	no	—
408	C₂²×C₄	—	4	8	no	—
409	C₂²×C₄	—	4	8	no	—
410	C₂²×C₄	—	4	4	no	—
411	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
412	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
413	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
414	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
415	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
416	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
417	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
418	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
419	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
420	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
421	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
422	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
424	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
425	C₄⋊C₄	—	4	4	no	—
426	C₄⋊C₄	—	4	8	no	—
427	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
428	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
429	C₂²⋊C₄	—	2	8	no	—
430	C₂²⋊C₄	—	2	8	no	—
431	C₂²⋊C₄	—	2	8	no	—
432	C₂²⋊C₄	—	4	8	no	—
433	C₂²⋊C₄	—	4	4	no	—
434	C₂²⋊C₄	—	4	8	no	—
435	C₂²⋊C₄	—	4	4	no	—
436	C₂²⋊C₄	—	4	8	no	—
437	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
438	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
439	C₄²	—	4	4	no	—
440	C₄²	—	4	8	no	—
441	C₁₃	#34358	1	1	yes	characteristic, direct product factor, Sylow
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	2	8	no	—
447	C₂³	—	2	8	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	4	no	—
450	C₂³	—	2	8	no	—
451	C₂³	—	2	4	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	8	no	—
455	C₂³	—	2	16	no	—
456	C₂³	—	4	4	no	—
457	C₂³	—	4	8	no	—
458	C₂³	—	4	8	no	—
459	C₂³	—	4	16	no	—
460	C₂³	—	8	16	no	—
461	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
462	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
463	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
464	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
465	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
466	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
467	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
468	D₄	—	2	32	no	—
469	D₄	—	4	8	no	—
470	D₄	—	4	8	no	—
471	D₄	—	4	16	no	—
472	C₂×C₄	—	2	8	no	—
473	C₂×C₄	—	2	8	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	8	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	8	no	—
480	C₂×C₄	—	2	8	no	—
481	C₂×C₄	—	2	8	no	—
482	C₂×C₄	—	2	8	no	—
483	C₂×C₄	—	2	8	no	—
484	C₂×C₄	—	2	8	no	—
485	C₂×C₄	—	4	4	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	—	4	8	no	—
490	C₂×C₄	—	8	8	no	—
491	C₂×C₄	—	8	16	no	—
492	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
493	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
494	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
495	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
496	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
497	C₂²	—	2	8	no	—
498	C₂²	—	2	8	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	2	2	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	2	8	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	8	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	8	no	—
509	C₂²	—	4	16	no	—
510	C₂²	—	4	8	no	—
511	C₂²	—	4	4	no	—
512	C₂²	—	4	8	no	—
513	C₂²	—	8	16	no	—
514	C₂²	C₁₃×#518	1	4	yes	—
515	C₂²	C₁₃×#518	1	4	yes	—
516	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
517	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
518	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
519	C₂²	C₁₃×#585	1	2	yes	—
520	C₄	—	2	2	no	—
521	C₄	—	2	2	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	2	8	no	—
525	C₄	—	4	8	no	—
526	C₄	—	4	8	no	—
527	C₂	—	2	4	no	—
528	C₂	—	2	4	no	—
529	C₂	—	4	2	no	—
530	C₂	—	4	8	no	—
531	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
532	C₂	C₂×C₁₃×#518	1	1	yes	characteristic
533	C₂	C₁₃×#3428	1	1	yes	characteristic
534	C₂	C₁₃×#3534	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#121	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2377	C₂	semidirect
3. C₁₃×#2364	C₂	semidirect
4. C₁₃×#2342	C₂	semidirect
5. D₄×C₁₃×C₂²⋊C₄	C₂	semidirect
6. C₁₃×#2333	C₂	semidirect
7. C₁₃×#2325	C₂	semidirect
8. C₁₃×#2313	C₂	semidirect
9. C₁₃×#2308	C₂	semidirect
10. C₁₃×#2280	C₂	semidirect
11. C₂×C₁₃×#381	C₂	semidirect
15. C₂×C₁₃×#121	C₄	semidirect
20. C₂×C₄×D₄×C₁₃	C₂²	semidirect
26. C₁₃×#390	C₂²	semidirect
27. C₁₃×#388	C₂²	semidirect
28. C₁₃×#388	C₂²	semidirect
29. C₁₃×#387	C₂²	semidirect
30. C₁₃×#387	C₂²	semidirect
31. C₁₃×#386	C₂²	semidirect
32. C₁₃×#386	C₂²	semidirect
33. C₁₃×#386	C₂²	semidirect
34. C₁₃×#386	C₂²	semidirect
35. C₁₃×#385	C₂²	semidirect
39. C₁₃×#381	C₂²	semidirect
40. C₁₃×#381	C₂²	semidirect
42. C₁₃×#380	C₂²	semidirect
43. C₁₃×#380	C₂²	semidirect
47. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
48. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
49. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
50. C₂×C₁₃×#95	C₂²	semidirect
51. C₂×C₁₃×#95	C₂²	semidirect
56. C₂²×D₄×C₁₃	C₂×C₄	semidirect
57. C₂²×D₄×C₁₃	C₂×C₄	semidirect
63. C₂³×C₄×C₁₃	C₂×C₄	semidirect
73. C₁₃×#121	C₂×C₄	semidirect
74. C₁₃×#121	C₂×C₄	semidirect
75. C₁₃×#121	C₂×C₄	semidirect
76. C₁₃×#121	C₂×C₄	semidirect
79. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
86. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
107. #34358	C₁₃	direct (N × H)
176. #2377	C₂×C₁₃	semidirect
177. #2364	C₂×C₁₃	semidirect
178. #2342	C₂×C₁₃	semidirect
179. D₄×C₂²⋊C₄	C₂×C₁₃	semidirect
180. #2333	C₂×C₁₃	semidirect
181. #2325	C₂×C₁₃	semidirect
182. #2313	C₂×C₁₃	semidirect
183. #2308	C₂×C₁₃	semidirect
184. #2280	C₂×C₁₃	semidirect
185. C₂×#381	C₂×C₁₃	semidirect
244. C₂×#121	C₄×C₁₃	semidirect
249. C₂×C₄×D₄	C₂²×C₁₃	semidirect
255. #390	C₂²×C₁₃	semidirect
256. #388	C₂²×C₁₃	semidirect
257. #388	C₂²×C₁₃	semidirect
258. #387	C₂²×C₁₃	semidirect
259. #387	C₂²×C₁₃	semidirect
260. #386	C₂²×C₁₃	semidirect
261. #386	C₂²×C₁₃	semidirect
262. #386	C₂²×C₁₃	semidirect
263. #386	C₂²×C₁₃	semidirect
264. #385	C₂²×C₁₃	semidirect
268. #381	C₂²×C₁₃	semidirect
269. #381	C₂²×C₁₃	semidirect
271. #380	C₂²×C₁₃	semidirect
272. #380	C₂²×C₁₃	semidirect
276. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
277. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
278. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
279. C₂×#95	C₂²×C₁₃	semidirect
280. C₂×#95	C₂²×C₁₃	semidirect
315. C₂²×D₄	C₂×C₄×C₁₃	semidirect
316. C₂²×D₄	C₂×C₄×C₁₃	semidirect
322. C₂³×C₄	C₂×C₄×C₁₃	semidirect
332. #121	C₂×C₄×C₁₃	semidirect
333. #121	C₂×C₄×C₁₃	semidirect
334. #121	C₂×C₄×C₁₃	semidirect
335. #121	C₂×C₄×C₁₃	semidirect
338. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
345. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
441. C₁₃	#34358	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#121	2
C₁₃×#2377	2
C₁₃×#2364	2
C₁₃×#2342	2
D₄×C₁₃×C₂²⋊C₄	2
C₁₃×#2333	2
C₁₃×#2325	2
C₁₃×#2313	2
C₁₃×#2308	2
C₁₃×#2280	2
C₂×C₁₃×#381	2
#34358	13

Subgroups — C13×#34358 #15720697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34358 #15720697