Subgroups — C₁₃×#34992 #15721331

Order 3328.

4346 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×#120	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2849	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2622	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2483	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2412	C₂	1	8	yes	maximal, complemented
7	C₁₃×#2405	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2315	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2308	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#379	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	complemented
15	C₂×C₁₃×#123	C₂²	1	8	yes	complemented
16	C₂×C₁₃×#120	—	2	8	no	—
17	C₂×C₁₃×#120	C₂²	1	2	yes	—
18	C₂×C₁₃×#120	C₂²	1	2	yes	—
19	C₂×C₁₃×#120	C₂²	1	4	yes	—
20	C₂²×C₁₃×C₂²⋊C₄	—	2	8	no	—
21	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
29	C₁₃×#397	C₂²	1	16	yes	complemented
30	C₁₃×#394	C₂²	1	16	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×#385	C₂²	1	8	yes	complemented
35	C₁₃×#385	C₂²	1	8	yes	complemented
36	C₁₃×#385	C₂²	1	8	yes	complemented
37	C₁₃×#381	C₂²	1	4	yes	complemented
38	C₁₃×#381	C₂²	1	8	yes	complemented
39	C₁₃×#380	C₂²	1	8	yes	complemented
40	C₁₃×#379	C₂²	1	4	yes	—
41	C₁₃×#379	C₂²	1	2	yes	complemented
42	C₁₃×#379	C₂²	1	2	yes	complemented
43	C₁₃×#379	C₂²	1	4	yes	complemented
44	C₂⁵×C₁₃	—	2	8	no	—
45	C₂⁵×C₁₃	—	4	8	no	—
46	C₂⁵×C₁₃	D₄	1	8	yes	—
47	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
48	C₂⁵×C₁₃	C₂³	1	2	yes	—
49	C₂⁵×C₁₃	C₂³	1	2	yes	—
50	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
51	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
52	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₃	—	2	8	no	—
54	C₂²×D₄×C₁₃	—	2	4	no	—
55	C₂²×D₄×C₁₃	—	2	8	no	—
56	C₂²×D₄×C₁₃	—	4	8	no	—
57	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
58	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
59	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
60	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
61	C₂³×C₄×C₁₃	—	2	8	no	—
62	C₂³×C₄×C₁₃	—	4	8	no	—
63	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
65	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
66	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
68	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
69	C₁₃×#123	—	4	16	no	—
70	C₁₃×#120	—	2	8	no	—
71	C₁₃×#120	—	2	16	no	—
72	C₁₃×#120	—	2	8	no	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	complemented
74	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
81	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
82	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
83	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
84	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
85	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
86	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
90	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
91	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
92	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	complemented
94	C₁₃×#95	C₂³	1	16	yes	complemented
95	C₁₃×#95	C₂³	1	16	yes	complemented
96	#34992	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂⁴×C₁₃	—	2	4	no	—
98	C₂⁴×C₁₃	—	2	8	no	—
99	C₂⁴×C₁₃	—	2	32	no	—
100	C₂⁴×C₁₃	—	2	8	no	—
101	C₂⁴×C₁₃	—	2	8	no	—
102	C₂⁴×C₁₃	—	2	4	no	—
103	C₂⁴×C₁₃	—	2	8	no	—
104	C₂⁴×C₁₃	—	2	8	no	—
105	C₂⁴×C₁₃	—	2	2	no	—
106	C₂⁴×C₁₃	—	2	4	no	—
107	C₂⁴×C₁₃	—	4	32	no	—
108	C₂⁴×C₁₃	—	4	4	no	—
109	C₂⁴×C₁₃	—	4	4	no	—
110	C₂⁴×C₁₃	—	4	4	no	—
111	C₂⁴×C₁₃	—	4	4	no	—
112	C₂⁴×C₁₃	—	4	4	no	—
113	C₂⁴×C₁₃	—	4	64	no	—
114	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
115	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
116	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
117	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
118	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
119	C₂⁴×C₁₃	#41	1	8	yes	—
120	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
121	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
122	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
123	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
124	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
126	C₂×D₄×C₁₃	—	2	8	no	—
127	C₂×D₄×C₁₃	—	2	4	no	—
128	C₂×D₄×C₁₃	—	2	4	no	—
129	C₂×D₄×C₁₃	—	2	8	no	—
130	C₂×D₄×C₁₃	—	2	8	no	—
131	C₂×D₄×C₁₃	—	2	8	no	—
132	C₂×D₄×C₁₃	—	2	16	no	—
133	C₂×D₄×C₁₃	—	4	8	no	—
134	C₂×D₄×C₁₃	—	4	32	no	—
135	C₂×D₄×C₁₃	—	4	16	no	—
136	C₂²×C₄×C₁₃	—	2	8	no	—
137	C₂²×C₄×C₁₃	—	2	8	no	—
138	C₂²×C₄×C₁₃	—	2	8	no	—
139	C₂²×C₄×C₁₃	—	2	4	no	—
140	C₂²×C₄×C₁₃	—	2	2	no	—
141	C₂²×C₄×C₁₃	—	2	4	no	—
142	C₂²×C₄×C₁₃	—	2	16	no	—
143	C₂²×C₄×C₁₃	—	2	8	no	—
144	C₂²×C₄×C₁₃	—	4	8	no	—
145	C₂²×C₄×C₁₃	—	4	8	no	—
146	C₂²×C₄×C₁₃	—	4	4	no	—
147	C₂²×C₄×C₁₃	—	4	8	no	—
148	C₂²×C₄×C₁₃	—	4	32	no	—
149	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
151	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
153	C₁₃×C₄⋊C₄	—	4	16	no	—
154	C₁₃×C₂²⋊C₄	—	2	16	no	—
155	C₁₃×C₂²⋊C₄	—	2	8	no	—
156	C₁₃×C₂²⋊C₄	—	2	8	no	—
157	C₁₃×C₂²⋊C₄	—	2	8	no	—
158	C₁₃×C₂²⋊C₄	—	2	4	no	—
159	C₁₃×C₂²⋊C₄	—	2	4	no	—
160	C₁₃×C₂²⋊C₄	—	2	8	no	—
161	C₁₃×C₂²⋊C₄	—	2	8	no	—
162	C₁₃×C₂²⋊C₄	—	2	8	no	—
163	C₁₃×C₂²⋊C₄	—	2	16	no	—
164	C₁₃×C₂²⋊C₄	—	4	8	no	—
165	C₁₃×C₂²⋊C₄	—	4	16	no	—
166	C₂²×#120	C₂×C₁₃	1	1	yes	characteristic
167	C₂³×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#2849	C₂×C₁₃	1	4	yes	complemented
169	#2622	C₂×C₁₃	1	4	yes	complemented
170	#2483	C₂×C₁₃	1	4	yes	complemented
171	#2412	C₂×C₁₃	1	8	yes	complemented
172	#2405	C₂×C₁₃	1	4	yes	complemented
173	#2315	C₂×C₁₃	1	2	yes	complemented
174	#2308	C₂×C₁₃	1	2	yes	complemented
175	C₂×#379	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₂³×C₁₃	—	2	32	no	—
177	C₂³×C₁₃	—	2	8	no	—
178	C₂³×C₁₃	—	2	16	no	—
179	C₂³×C₁₃	—	2	4	no	—
180	C₂³×C₁₃	—	2	4	no	—
181	C₂³×C₁₃	—	2	4	no	—
182	C₂³×C₁₃	—	2	4	no	—
183	C₂³×C₁₃	—	2	4	no	—
184	C₂³×C₁₃	—	2	16	no	—
185	C₂³×C₁₃	—	2	16	no	—
186	C₂³×C₁₃	—	2	8	no	—
187	C₂³×C₁₃	—	2	16	no	—
188	C₂³×C₁₃	—	2	16	no	—
189	C₂³×C₁₃	—	2	4	no	—
190	C₂³×C₁₃	—	2	4	no	—
191	C₂³×C₁₃	—	2	4	no	—
192	C₂³×C₁₃	—	2	2	no	—
193	C₂³×C₁₃	—	2	4	no	—
194	C₂³×C₁₃	—	2	8	no	—
195	C₂³×C₁₃	—	4	8	no	—
196	C₂³×C₁₃	—	4	8	no	—
197	C₂³×C₁₃	—	4	8	no	—
198	C₂³×C₁₃	—	4	8	no	—
199	C₂³×C₁₃	—	4	16	no	—
200	C₂³×C₁₃	—	4	32	no	—
201	C₂³×C₁₃	—	4	32	no	—
202	C₂³×C₁₃	—	4	128	no	—
203	C₂³×C₁₃	—	4	16	no	—
204	C₂³×C₁₃	—	4	8	no	—
205	C₂³×C₁₃	—	4	4	no	—
206	C₂³×C₁₃	—	8	8	no	—
207	C₂³×C₁₃	#123	1	16	yes	complemented
208	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
209	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
210	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
211	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
212	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
213	C₂³×C₁₃	C₂×#41	1	4	yes	—
214	C₂³×C₁₃	C₂×#41	1	4	yes	—
215	C₂³×C₁₃	C₂×#41	1	4	yes	—
216	C₂³×C₁₃	H(5,𝔽₂)	1	8	yes	—
217	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
218	D₄×C₁₃	—	4	16	no	—
219	D₄×C₁₃	—	4	8	no	—
220	D₄×C₁₃	—	4	8	no	—
221	D₄×C₁₃	—	4	16	no	—
222	C₂×C₄×C₁₃	—	2	8	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	8	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	16	no	—
228	C₂×C₄×C₁₃	—	2	16	no	—
229	C₂×C₄×C₁₃	—	2	8	no	—
230	C₂×C₄×C₁₃	—	4	16	no	—
231	C₂×C₄×C₁₃	—	4	16	no	—
232	C₂×C₄×C₁₃	—	4	8	no	—
233	C₂×C₄×C₁₃	—	4	4	no	—
234	C₂×C₄×C₁₃	—	4	16	no	—
235	C₂×C₄×C₁₃	—	8	8	no	—
236	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
237	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
238	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
239	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	complemented
240	C₂×#123	C₂²×C₁₃	1	8	yes	complemented
241	C₂×#120	—	2	8	no	—
242	C₂×#120	C₂²×C₁₃	1	2	yes	—
243	C₂×#120	C₂²×C₁₃	1	2	yes	—
244	C₂×#120	C₂²×C₁₃	1	4	yes	—
245	C₂²×C₂²⋊C₄	—	2	8	no	—
246	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
247	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
248	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
249	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
250	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
251	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
252	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
253	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
254	#397	C₂²×C₁₃	1	16	yes	complemented
255	#394	C₂²×C₁₃	1	16	yes	complemented
256	#386	C₂²×C₁₃	1	8	yes	complemented
257	#386	C₂²×C₁₃	1	8	yes	complemented
258	#386	C₂²×C₁₃	1	8	yes	complemented
259	#385	C₂²×C₁₃	1	8	yes	complemented
260	#385	C₂²×C₁₃	1	8	yes	complemented
261	#385	C₂²×C₁₃	1	8	yes	complemented
262	#381	C₂²×C₁₃	1	4	yes	complemented
263	#381	C₂²×C₁₃	1	8	yes	complemented
264	#380	C₂²×C₁₃	1	8	yes	complemented
265	#379	C₂²×C₁₃	1	4	yes	—
266	#379	C₂²×C₁₃	1	2	yes	complemented
267	#379	C₂²×C₁₃	1	2	yes	complemented
268	#379	C₂²×C₁₃	1	4	yes	complemented
269	C₂²×C₁₃	—	2	32	no	—
270	C₂²×C₁₃	—	2	4	no	—
271	C₂²×C₁₃	—	2	4	no	—
272	C₂²×C₁₃	—	2	4	no	—
273	C₂²×C₁₃	—	2	4	no	—
274	C₂²×C₁₃	—	2	4	no	—
275	C₂²×C₁₃	—	2	8	no	—
276	C₂²×C₁₃	—	2	8	no	—
277	C₂²×C₁₃	—	2	16	no	—
278	C₂²×C₁₃	—	2	8	no	—
279	C₂²×C₁₃	—	2	4	no	—
280	C₂²×C₁₃	—	2	4	no	—
281	C₂²×C₁₃	—	2	4	no	—
282	C₂²×C₁₃	—	4	16	no	—
283	C₂²×C₁₃	—	4	32	no	—
284	C₂²×C₁₃	—	4	32	no	—
285	C₂²×C₁₃	—	4	16	no	—
286	C₂²×C₁₃	—	4	8	no	—
287	C₂²×C₁₃	—	4	2	no	—
288	C₂²×C₁₃	—	4	4	no	—
289	C₂²×C₁₃	—	4	8	no	—
290	C₂²×C₁₃	—	8	8	no	—
291	C₂²×C₁₃	C₂×#123	1	4	yes	—
292	C₂²×C₁₃	C₂×#123	1	4	yes	—
293	C₂²×C₁₃	C₂×#123	1	4	yes	—
294	C₂²×C₁₃	#534	1	8	yes	—
295	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
296	C₂²×C₁₃	C₂²×#41	1	2	yes	—
297	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
298	C₄×C₁₃	—	4	2	no	—
299	C₄×C₁₃	—	4	8	no	—
300	C₄×C₁₃	—	4	4	no	—
301	C₄×C₁₃	—	4	8	no	—
302	C₂⁵	—	2	8	no	—
303	C₂⁵	—	4	8	no	—
304	C₂⁵	D₄×C₁₃	1	8	yes	—
305	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
306	C₂⁵	C₂³×C₁₃	1	2	yes	—
307	C₂⁵	C₂³×C₁₃	1	2	yes	—
308	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
309	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
310	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
311	C₂²×D₄	—	2	8	no	—
312	C₂²×D₄	—	2	4	no	—
313	C₂²×D₄	—	2	8	no	—
314	C₂²×D₄	—	4	8	no	—
315	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
316	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
317	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
318	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
319	C₂³×C₄	—	2	8	no	—
320	C₂³×C₄	—	4	8	no	—
321	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
323	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
324	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
325	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
326	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
327	#123	—	4	16	no	—
328	#120	—	2	8	no	—
329	#120	—	2	16	no	—
330	#120	—	2	8	no	—
331	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	complemented
332	C₂×C₂²⋊C₄	—	2	16	no	—
333	C₂×C₂²⋊C₄	—	2	8	no	—
334	C₂×C₂²⋊C₄	—	2	16	no	—
335	C₂×C₂²⋊C₄	—	2	8	no	—
336	C₂×C₂²⋊C₄	—	2	8	no	—
337	C₂×C₂²⋊C₄	—	2	4	no	—
338	C₂×C₂²⋊C₄	—	2	8	no	—
339	C₂×C₂²⋊C₄	—	4	8	no	—
340	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
341	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
342	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
343	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
344	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
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	8	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	complemented
352	#95	C₂³×C₁₃	1	16	yes	complemented
353	#95	C₂³×C₁₃	1	16	yes	complemented
354	C₂×C₁₃	—	2	4	no	—
355	C₂×C₁₃	—	2	8	no	—
356	C₂×C₁₃	—	2	4	no	—
357	C₂×C₁₃	—	2	4	no	—
358	C₂×C₁₃	—	4	4	no	—
359	C₂×C₁₃	—	8	2	no	—
360	C₂×C₁₃	C₂²×#123	1	1	yes	characteristic
361	C₂×C₁₃	C₂×#534	1	2	yes	—
362	C₂×C₁₃	#3490	1	4	yes	—
363	C₂⁴	—	2	4	no	—
364	C₂⁴	—	2	8	no	—
365	C₂⁴	—	2	32	no	—
366	C₂⁴	—	2	8	no	—
367	C₂⁴	—	2	8	no	—
368	C₂⁴	—	2	4	no	—
369	C₂⁴	—	2	8	no	—
370	C₂⁴	—	2	8	no	—
371	C₂⁴	—	2	2	no	—
372	C₂⁴	—	2	4	no	—
373	C₂⁴	—	4	32	no	—
374	C₂⁴	—	4	4	no	—
375	C₂⁴	—	4	4	no	—
376	C₂⁴	—	4	4	no	—
377	C₂⁴	—	4	4	no	—
378	C₂⁴	—	4	4	no	—
379	C₂⁴	—	4	64	no	—
380	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
381	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
382	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
383	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
384	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
385	C₂⁴	C₁₃×#41	1	8	yes	—
386	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
387	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
388	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
389	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
390	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
391	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
392	C₂×D₄	—	2	8	no	—
393	C₂×D₄	—	2	4	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	8	no	—
396	C₂×D₄	—	2	8	no	—
397	C₂×D₄	—	2	8	no	—
398	C₂×D₄	—	2	16	no	—
399	C₂×D₄	—	4	8	no	—
400	C₂×D₄	—	4	32	no	—
401	C₂×D₄	—	4	16	no	—
402	C₂²×C₄	—	2	8	no	—
403	C₂²×C₄	—	2	8	no	—
404	C₂²×C₄	—	2	8	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	16	no	—
409	C₂²×C₄	—	2	8	no	—
410	C₂²×C₄	—	4	8	no	—
411	C₂²×C₄	—	4	8	no	—
412	C₂²×C₄	—	4	4	no	—
413	C₂²×C₄	—	4	8	no	—
414	C₂²×C₄	—	4	32	no	—
415	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
416	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
417	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
418	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
419	C₄⋊C₄	—	4	16	no	—
420	C₂²⋊C₄	—	2	16	no	—
421	C₂²⋊C₄	—	2	8	no	—
422	C₂²⋊C₄	—	2	8	no	—
423	C₂²⋊C₄	—	2	8	no	—
424	C₂²⋊C₄	—	2	4	no	—
425	C₂²⋊C₄	—	2	4	no	—
426	C₂²⋊C₄	—	2	8	no	—
427	C₂²⋊C₄	—	2	8	no	—
428	C₂²⋊C₄	—	2	8	no	—
429	C₂²⋊C₄	—	2	16	no	—
430	C₂²⋊C₄	—	4	8	no	—
431	C₂²⋊C₄	—	4	16	no	—
432	C₁₃	#34992	1	1	yes	characteristic, direct product factor, Sylow
433	C₂³	—	2	32	no	—
434	C₂³	—	2	8	no	—
435	C₂³	—	2	16	no	—
436	C₂³	—	2	4	no	—
437	C₂³	—	2	4	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	4	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	2	16	no	—
442	C₂³	—	2	16	no	—
443	C₂³	—	2	8	no	—
444	C₂³	—	2	16	no	—
445	C₂³	—	2	16	no	—
446	C₂³	—	2	4	no	—
447	C₂³	—	2	4	no	—
448	C₂³	—	2	4	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	2	4	no	—
451	C₂³	—	2	8	no	—
452	C₂³	—	4	8	no	—
453	C₂³	—	4	8	no	—
454	C₂³	—	4	8	no	—
455	C₂³	—	4	8	no	—
456	C₂³	—	4	16	no	—
457	C₂³	—	4	32	no	—
458	C₂³	—	4	32	no	—
459	C₂³	—	4	128	no	—
460	C₂³	—	4	16	no	—
461	C₂³	—	4	8	no	—
462	C₂³	—	4	4	no	—
463	C₂³	—	8	8	no	—
464	C₂³	C₁₃×#123	1	16	yes	complemented
465	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
466	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
467	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
468	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
469	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
470	C₂³	C₂×C₁₃×#41	1	4	yes	—
471	C₂³	C₂×C₁₃×#41	1	4	yes	—
472	C₂³	C₂×C₁₃×#41	1	4	yes	—
473	C₂³	C₁₃×H(5,𝔽₂)	1	8	yes	—
474	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
475	D₄	—	4	16	no	—
476	D₄	—	4	8	no	—
477	D₄	—	4	8	no	—
478	D₄	—	4	16	no	—
479	C₂×C₄	—	2	8	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	8	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	16	no	—
485	C₂×C₄	—	2	16	no	—
486	C₂×C₄	—	2	8	no	—
487	C₂×C₄	—	4	16	no	—
488	C₂×C₄	—	4	16	no	—
489	C₂×C₄	—	4	8	no	—
490	C₂×C₄	—	4	4	no	—
491	C₂×C₄	—	4	16	no	—
492	C₂×C₄	—	8	8	no	—
493	C₂²	—	2	32	no	—
494	C₂²	—	2	4	no	—
495	C₂²	—	2	4	no	—
496	C₂²	—	2	4	no	—
497	C₂²	—	2	4	no	—
498	C₂²	—	2	4	no	—
499	C₂²	—	2	8	no	—
500	C₂²	—	2	8	no	—
501	C₂²	—	2	16	no	—
502	C₂²	—	2	8	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	2	4	no	—
505	C₂²	—	2	4	no	—
506	C₂²	—	4	16	no	—
507	C₂²	—	4	32	no	—
508	C₂²	—	4	32	no	—
509	C₂²	—	4	16	no	—
510	C₂²	—	4	8	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	4	no	—
513	C₂²	—	4	8	no	—
514	C₂²	—	8	8	no	—
515	C₂²	C₂×C₁₃×#123	1	4	yes	—
516	C₂²	C₂×C₁₃×#123	1	4	yes	—
517	C₂²	C₂×C₁₃×#123	1	4	yes	—
518	C₂²	C₁₃×#534	1	8	yes	—
519	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
520	C₂²	C₂²×C₁₃×#41	1	2	yes	—
521	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
522	C₄	—	4	2	no	—
523	C₄	—	4	8	no	—
524	C₄	—	4	4	no	—
525	C₄	—	4	8	no	—
526	C₂	—	2	4	no	—
527	C₂	—	2	8	no	—
528	C₂	—	2	4	no	—
529	C₂	—	2	4	no	—
530	C₂	—	4	4	no	—
531	C₂	—	8	2	no	—
532	C₂	C₂²×C₁₃×#123	1	1	yes	characteristic
533	C₂	C₂×C₁₃×#534	1	2	yes	—
534	C₂	C₁₃×#3490	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#120	C₂
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
2. C₂³×C₁₃×C₂²⋊C₄	C₂	semidirect
3. C₁₃×#2849	C₂	semidirect
4. C₁₃×#2622	C₂	semidirect
5. C₁₃×#2483	C₂	semidirect
6. C₁₃×#2412	C₂	semidirect
7. C₁₃×#2405	C₂	semidirect
8. C₁₃×#2315	C₂	semidirect
9. C₁₃×#2308	C₂	semidirect
10. C₂×C₁₃×#379	C₂	semidirect
14. C₂⁴×C₄×C₁₃	C₂²	semidirect
15. C₂×C₁₃×#123	C₂²	semidirect
26. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
27. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
28. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
29. C₁₃×#397	C₂²	semidirect
30. C₁₃×#394	C₂²	semidirect
31. C₁₃×#386	C₂²	semidirect
32. C₁₃×#386	C₂²	semidirect
33. C₁₃×#386	C₂²	semidirect
34. C₁₃×#385	C₂²	semidirect
35. C₁₃×#385	C₂²	semidirect
36. C₁₃×#385	C₂²	semidirect
37. C₁₃×#381	C₂²	semidirect
38. C₁₃×#381	C₂²	semidirect
39. C₁₃×#380	C₂²	semidirect
41. C₁₃×#379	C₂²	semidirect
42. C₁₃×#379	C₂²	semidirect
43. C₁₃×#379	C₂²	semidirect
73. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
93. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
94. C₁₃×#95	C₂³	semidirect
95. C₁₃×#95	C₂³	semidirect
96. #34992	C₁₃	direct (N × H)
167. C₂³×C₂²⋊C₄	C₂×C₁₃	semidirect
168. #2849	C₂×C₁₃	semidirect
169. #2622	C₂×C₁₃	semidirect
170. #2483	C₂×C₁₃	semidirect
171. #2412	C₂×C₁₃	semidirect
172. #2405	C₂×C₁₃	semidirect
173. #2315	C₂×C₁₃	semidirect
174. #2308	C₂×C₁₃	semidirect
175. C₂×#379	C₂×C₁₃	semidirect
207. C₂³×C₁₃	#123	semidirect
239. C₂⁴×C₄	C₂²×C₁₃	semidirect
240. C₂×#123	C₂²×C₁₃	semidirect
251. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
252. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
253. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
254. #397	C₂²×C₁₃	semidirect
255. #394	C₂²×C₁₃	semidirect
256. #386	C₂²×C₁₃	semidirect
257. #386	C₂²×C₁₃	semidirect
258. #386	C₂²×C₁₃	semidirect
259. #385	C₂²×C₁₃	semidirect
260. #385	C₂²×C₁₃	semidirect
261. #385	C₂²×C₁₃	semidirect
262. #381	C₂²×C₁₃	semidirect
263. #381	C₂²×C₁₃	semidirect
264. #380	C₂²×C₁₃	semidirect
266. #379	C₂²×C₁₃	semidirect
267. #379	C₂²×C₁₃	semidirect
268. #379	C₂²×C₁₃	semidirect
331. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
351. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
352. #95	C₂³×C₁₃	semidirect
353. #95	C₂³×C₁₃	semidirect
432. C₁₃	#34992	direct (N × H)
464. C₂³	C₁₃×#123	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#120	2
C₂³×C₁₃×C₂²⋊C₄	2
C₁₃×#2849	2
C₁₃×#2622	2
C₁₃×#2483	2
C₁₃×#2412	2
C₁₃×#2405	2
C₁₃×#2315	2
C₁₃×#2308	2
C₂×C₁₃×#379	2
#34992	13

Subgroups — C13×#34992 #15721331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34992 #15721331