Subgroups — C₁₃×#35057 #15721396

Order 3328.

2898 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#525	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2849	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2849	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2627	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2618	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2591	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2583	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2579	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2484	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2413	C₂	1	4	yes	maximal, complemented
12	C₁₃×#2406	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2322	C₂	1	4	yes	maximal, complemented
14	C₁₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#525	—	2	8	no	—
20	C₂×C₁₃×#123	C₂²	1	4	yes	—
21	C₂×C₁₃×#123	C₂²	1	2	yes	—
22	C₂×C₁₃×#123	C₂²	1	4	yes	—
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#120	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
30	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#117	C₂²	1	2	yes	—
32	C₂²×C₁₃×C₄⋊C₄	—	2	8	no	—
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
35	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
36	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
37	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
38	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
39	C₁₃×#400	C₂²	1	4	yes	complemented
40	C₁₃×#398	C₂²	1	8	yes	complemented
41	C₁₃×#398	C₂²	1	4	yes	complemented
42	C₁₃×#396	C₂²	1	8	yes	complemented
43	C₁₃×#395	C₂²	1	4	yes	complemented
44	C₁₃×#394	C₂²	1	4	yes	complemented
45	C₁₃×#389	C₂²	1	8	yes	complemented
46	C₁₃×#388	C₂²	1	8	yes	complemented
47	C₁₃×#387	C₂²	1	8	yes	complemented
48	C₁₃×#386	C₂²	1	4	yes	—
49	C₁₃×#386	C₂²	1	4	yes	—
50	C₁₃×#386	C₂²	1	4	yes	—
51	C₁₃×#386	C₂²	1	4	yes	—
52	C₁₃×#385	C₂²	1	4	yes	—
53	C₁₃×#385	C₂²	1	4	yes	—
54	C₁₃×#385	C₂²	1	4	yes	—
55	C₁₃×#385	C₂²	1	4	yes	—
56	C₁₃×#385	C₂²	1	8	yes	complemented
57	C₁₃×#381	C₂²	1	2	yes	—
58	C₁₃×#381	C₂²	1	4	yes	—
59	C₁₃×#381	C₂²	1	4	yes	—
60	C₁₃×#380	C₂²	1	2	yes	—
61	C₁₃×#380	C₂²	1	2	yes	—
62	C₁₃×#379	C₂²	1	2	yes	—
63	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
64	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
65	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×#41	—	2	4	no	—
67	C₂×C₁₃×#41	—	4	4	no	—
68	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
71	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
72	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	—	2	4	no	—
74	C₂³×C₄×C₁₃	—	2	8	no	—
75	C₂³×C₄×C₁₃	—	2	4	no	—
76	C₂³×C₄×C₁₃	—	4	4	no	—
77	C₂³×C₄×C₁₃	—	4	4	no	—
78	C₂³×C₄×C₁₃	D₄	1	8	yes	—
79	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
80	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
81	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
82	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
85	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
86	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
87	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
88	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₁₃×#123	—	2	8	no	—
93	C₁₃×#123	—	2	16	no	—
94	C₁₃×#123	—	4	8	no	—
95	C₁₃×C₂²⋊Q₈	—	2	4	no	—
96	C₁₃×C₂²⋊Q₈	—	2	4	no	—
97	C₁₃×#121	—	2	4	no	—
98	C₁₃×#121	—	2	4	no	—
99	C₁₃×#120	—	2	8	no	—
100	C₄×D₄×C₁₃	—	2	8	no	—
101	C₄×D₄×C₁₃	—	2	8	no	—
102	C₁₃×#117	—	2	4	no	—
103	C₁₃×#117	—	4	4	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
125	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
126	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
131	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
132	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
133	C₁₃×#95	C₂³	1	4	yes	—
134	C₁₃×#95	C₂³	1	4	yes	—
135	C₁₃×#95	C₂³	1	8	yes	—
136	C₁₃×#95	C₂³	1	8	yes	—
137	C₁₃×#95	C₂³	1	8	yes	—
138	C₁₃×#95	C₂³	1	8	yes	—
139	#35057	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂⁴×C₁₃	—	2	4	no	—
141	C₂⁴×C₁₃	—	2	4	no	—
142	C₂⁴×C₁₃	—	2	4	no	—
143	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
144	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
145	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
146	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
147	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₁₃×#41	—	4	16	no	—
149	C₂×Q₈×C₁₃	—	2	2	no	—
150	C₂×Q₈×C₁₃	—	4	2	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	8	no	—
155	C₂×D₄×C₁₃	—	2	8	no	—
156	C₂×D₄×C₁₃	—	2	8	no	—
157	C₂×D₄×C₁₃	—	2	2	no	—
158	C₂×D₄×C₁₃	—	4	2	no	—
159	C₂²×C₄×C₁₃	—	2	32	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	4	no	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	2	4	no	—
166	C₂²×C₄×C₁₃	—	2	8	no	—
167	C₂²×C₄×C₁₃	—	2	8	no	—
168	C₂²×C₄×C₁₃	—	2	4	no	—
169	C₂²×C₄×C₁₃	—	2	4	no	—
170	C₂²×C₄×C₁₃	—	2	4	no	—
171	C₂²×C₄×C₁₃	—	2	8	no	—
172	C₂²×C₄×C₁₃	—	2	4	no	—
173	C₂²×C₄×C₁₃	—	4	16	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	4	no	—
179	C₂²×C₄×C₁₃	—	4	4	no	—
180	C₂²×C₄×C₁₃	—	4	4	no	—
181	C₂²×C₄×C₁₃	—	4	16	no	—
182	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
183	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
184	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
185	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
186	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
187	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
188	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
189	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
191	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
199	C₁₃×C₄⋊C₄	—	2	8	no	—
200	C₁₃×C₄⋊C₄	—	2	8	no	—
201	C₁₃×C₄⋊C₄	—	2	8	no	—
202	C₁₃×C₄⋊C₄	—	2	8	no	—
203	C₁₃×C₄⋊C₄	—	2	2	no	—
204	C₁₃×C₄⋊C₄	—	2	2	no	—
205	C₁₃×C₄⋊C₄	—	2	4	no	—
206	C₁₃×C₄⋊C₄	—	2	4	no	—
207	C₁₃×C₄⋊C₄	—	2	16	no	—
208	C₁₃×C₄⋊C₄	—	4	4	no	—
209	C₁₃×C₄⋊C₄	—	4	8	no	—
210	C₁₃×C₂²⋊C₄	—	2	4	no	—
211	C₁₃×C₂²⋊C₄	—	2	4	no	—
212	C₁₃×C₂²⋊C₄	—	2	4	no	—
213	C₁₃×C₂²⋊C₄	—	2	8	no	—
214	C₁₃×C₂²⋊C₄	—	2	8	no	—
215	C₁₃×C₂²⋊C₄	—	2	8	no	—
216	C₁₃×C₂²⋊C₄	—	2	4	no	—
217	C₁₃×C₂²⋊C₄	—	2	4	no	—
218	C₁₃×C₂²⋊C₄	—	2	16	no	—
219	C₁₃×C₂²⋊C₄	—	4	8	no	—
220	C₄²×C₁₃	—	2	4	no	—
221	C₄²×C₁₃	—	4	4	no	—
222	C₂×#525	C₂×C₁₃	1	1	yes	characteristic
223	C₂³×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#2849	C₂×C₁₃	1	2	yes	complemented
225	#2849	C₂×C₁₃	1	2	yes	complemented
226	#2627	C₂×C₁₃	1	2	yes	complemented
227	#2618	C₂×C₁₃	1	2	yes	complemented
228	#2591	C₂×C₁₃	1	2	yes	complemented
229	#2583	C₂×C₁₃	1	2	yes	complemented
230	#2579	C₂×C₁₃	1	4	yes	complemented
231	#2484	C₂×C₁₃	1	2	yes	complemented
232	#2413	C₂×C₁₃	1	4	yes	complemented
233	#2406	C₂×C₁₃	1	2	yes	complemented
234	#2322	C₂×C₁₃	1	4	yes	complemented
235	#2280	C₂×C₁₃	1	1	yes	characteristic, complemented
236	C₂³×C₁₃	—	2	32	no	—
237	C₂³×C₁₃	—	2	8	no	—
238	C₂³×C₁₃	—	2	8	no	—
239	C₂³×C₁₃	—	2	8	no	—
240	C₂³×C₁₃	—	2	2	no	—
241	C₂³×C₁₃	—	2	2	no	—
242	C₂³×C₁₃	—	2	2	no	—
243	C₂³×C₁₃	—	2	2	no	—
244	C₂³×C₁₃	—	2	2	no	—
245	C₂³×C₁₃	—	2	2	no	—
246	C₂³×C₁₃	—	2	2	no	—
247	C₂³×C₁₃	—	2	4	no	—
248	C₂³×C₁₃	—	2	4	no	—
249	C₂³×C₁₃	—	2	4	no	—
250	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
251	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
252	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
253	C₂³×C₁₃	C₂×#41	1	4	yes	—
254	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
255	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
256	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
257	Q₈×C₁₃	—	4	4	no	—
258	D₄×C₁₃	—	4	4	no	—
259	D₄×C₁₃	—	4	8	no	—
260	D₄×C₁₃	—	4	8	no	—
261	D₄×C₁₃	—	4	8	no	—
262	C₂×C₄×C₁₃	—	2	16	no	—
263	C₂×C₄×C₁₃	—	2	16	no	—
264	C₂×C₄×C₁₃	—	2	16	no	—
265	C₂×C₄×C₁₃	—	2	8	no	—
266	C₂×C₄×C₁₃	—	2	8	no	—
267	C₂×C₄×C₁₃	—	2	4	no	—
268	C₂×C₄×C₁₃	—	2	4	no	—
269	C₂×C₄×C₁₃	—	2	2	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	2	2	no	—
273	C₂×C₄×C₁₃	—	2	2	no	—
274	C₂×C₄×C₁₃	—	2	2	no	—
275	C₂×C₄×C₁₃	—	2	2	no	—
276	C₂×C₄×C₁₃	—	2	4	no	—
277	C₂×C₄×C₁₃	—	2	8	no	—
278	C₂×C₄×C₁₃	—	2	4	no	—
279	C₂×C₄×C₁₃	—	2	8	no	—
280	C₂×C₄×C₁₃	—	2	8	no	—
281	C₂×C₄×C₁₃	—	2	4	no	—
282	C₂×C₄×C₁₃	—	2	8	no	—
283	C₂×C₄×C₁₃	—	2	4	no	—
284	C₂×C₄×C₁₃	—	4	4	no	—
285	C₂×C₄×C₁₃	—	4	4	no	—
286	C₂×C₄×C₁₃	—	4	4	no	—
287	C₂×C₄×C₁₃	—	4	4	no	—
288	C₂×C₄×C₁₃	—	4	8	no	—
289	C₂×C₄×C₁₃	—	4	8	no	—
290	C₂×C₄×C₁₃	—	4	8	no	—
291	C₂×C₄×C₁₃	—	4	8	no	—
292	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
293	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
294	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
295	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
296	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
297	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
298	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
299	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
300	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
301	#525	—	2	8	no	—
302	C₂×#123	C₂²×C₁₃	1	4	yes	—
303	C₂×#123	C₂²×C₁₃	1	2	yes	—
304	C₂×#123	C₂²×C₁₃	1	4	yes	—
305	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×#120	C₂²×C₁₃	1	2	yes	—
310	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
311	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
312	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
313	C₂×#117	C₂²×C₁₃	1	2	yes	—
314	C₂²×C₄⋊C₄	—	2	8	no	—
315	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
316	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
317	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
318	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
319	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
320	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
321	#400	C₂²×C₁₃	1	4	yes	complemented
322	#398	C₂²×C₁₃	1	8	yes	complemented
323	#398	C₂²×C₁₃	1	4	yes	complemented
324	#396	C₂²×C₁₃	1	8	yes	complemented
325	#395	C₂²×C₁₃	1	4	yes	complemented
326	#394	C₂²×C₁₃	1	4	yes	complemented
327	#389	C₂²×C₁₃	1	8	yes	complemented
328	#388	C₂²×C₁₃	1	8	yes	complemented
329	#387	C₂²×C₁₃	1	8	yes	complemented
330	#386	C₂²×C₁₃	1	4	yes	—
331	#386	C₂²×C₁₃	1	4	yes	—
332	#386	C₂²×C₁₃	1	4	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	—
337	#385	C₂²×C₁₃	1	4	yes	—
338	#385	C₂²×C₁₃	1	8	yes	complemented
339	#381	C₂²×C₁₃	1	4	yes	—
340	#381	C₂²×C₁₃	1	4	yes	—
341	#381	C₂²×C₁₃	1	2	yes	—
342	#380	C₂²×C₁₃	1	2	yes	—
343	#380	C₂²×C₁₃	1	2	yes	—
344	#379	C₂²×C₁₃	1	2	yes	—
345	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
346	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
347	C₂²×C₁₃	—	2	32	no	—
348	C₂²×C₁₃	—	2	2	no	—
349	C₂²×C₁₃	—	2	2	no	—
350	C₂²×C₁₃	—	2	2	no	—
351	C₂²×C₁₃	—	2	2	no	—
352	C₂²×C₁₃	—	2	2	no	—
353	C₂²×C₁₃	—	2	2	no	—
354	C₂²×C₁₃	—	2	8	no	—
355	C₂²×C₁₃	—	2	8	no	—
356	C₂²×C₁₃	—	2	8	no	—
357	C₂²×C₁₃	—	4	2	no	—
358	C₂²×C₁₃	—	4	2	no	—
359	C₂²×C₁₃	—	4	2	no	—
360	C₂²×C₁₃	—	4	8	no	—
361	C₂²×C₁₃	#525	1	4	yes	—
362	C₂²×C₁₃	#534	1	4	yes	—
363	C₂²×C₁₃	#536	1	4	yes	—
364	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
365	C₂²×C₁₃	C₂²×#41	1	2	yes	—
366	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
367	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
368	C₄×C₁₃	—	2	8	no	—
369	C₄×C₁₃	—	2	2	no	—
370	C₄×C₁₃	—	2	2	no	—
371	C₄×C₁₃	—	2	2	no	—
372	C₄×C₁₃	—	2	2	no	—
373	C₄×C₁₃	—	4	2	no	—
374	C₄×C₁₃	—	4	4	no	—
375	C₄×C₁₃	—	4	2	no	—
376	C₄×C₁₃	—	4	2	no	—
377	C₄×C₁₃	—	4	8	no	—
378	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
379	C₂×#41	—	2	4	no	—
380	C₂×#41	—	4	4	no	—
381	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
382	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
383	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
384	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
385	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
386	C₂³×C₄	—	2	4	no	—
387	C₂³×C₄	—	2	8	no	—
388	C₂³×C₄	—	2	4	no	—
389	C₂³×C₄	—	4	4	no	—
390	C₂³×C₄	—	4	4	no	—
391	C₂³×C₄	D₄×C₁₃	1	8	yes	—
392	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
393	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
394	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
395	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
396	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
397	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
398	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
399	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
400	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
401	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
402	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
403	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
404	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
405	#123	—	2	8	no	—
406	#123	—	2	16	no	—
407	#123	—	4	8	no	—
408	C₂²⋊Q₈	—	2	4	no	—
409	C₂²⋊Q₈	—	2	4	no	—
410	#121	—	2	4	no	—
411	#121	—	2	4	no	—
412	#120	—	2	8	no	—
413	C₄×D₄	—	2	8	no	—
414	C₄×D₄	—	2	8	no	—
415	#117	—	2	4	no	—
416	#117	—	4	4	no	—
417	C₂×C₄⋊C₄	—	2	8	no	—
418	C₂×C₄⋊C₄	—	2	8	no	—
419	C₂×C₄⋊C₄	—	2	8	no	—
420	C₂×C₄⋊C₄	—	2	8	no	—
421	C₂×C₄⋊C₄	—	2	8	no	—
422	C₂×C₄⋊C₄	—	2	8	no	—
423	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
424	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
425	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
426	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
427	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
430	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
431	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
432	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
433	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	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	2	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
444	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
445	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
446	#95	C₂³×C₁₃	1	4	yes	—
447	#95	C₂³×C₁₃	1	4	yes	—
448	#95	C₂³×C₁₃	1	8	yes	—
449	#95	C₂³×C₁₃	1	8	yes	—
450	#95	C₂³×C₁₃	1	8	yes	—
451	#95	C₂³×C₁₃	1	8	yes	—
452	C₂×C₁₃	—	2	4	no	—
453	C₂×C₁₃	—	2	4	no	—
454	C₂×C₁₃	—	2	4	no	—
455	C₂×C₁₃	—	8	2	no	—
456	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
457	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
458	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
459	C₂×C₁₃	#3492	1	4	yes	—
460	C₂⁴	—	2	4	no	—
461	C₂⁴	—	2	4	no	—
462	C₂⁴	—	2	4	no	—
463	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
464	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
465	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
466	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
467	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
468	#41	—	4	16	no	—
469	C₂×Q₈	—	2	2	no	—
470	C₂×Q₈	—	4	2	no	—
471	C₂×D₄	—	2	4	no	—
472	C₂×D₄	—	2	4	no	—
473	C₂×D₄	—	2	4	no	—
474	C₂×D₄	—	2	8	no	—
475	C₂×D₄	—	2	8	no	—
476	C₂×D₄	—	2	8	no	—
477	C₂×D₄	—	2	2	no	—
478	C₂×D₄	—	4	2	no	—
479	C₂²×C₄	—	2	32	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	4	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	8	no	—
487	C₂²×C₄	—	2	8	no	—
488	C₂²×C₄	—	2	4	no	—
489	C₂²×C₄	—	2	4	no	—
490	C₂²×C₄	—	2	4	no	—
491	C₂²×C₄	—	2	8	no	—
492	C₂²×C₄	—	2	4	no	—
493	C₂²×C₄	—	4	16	no	—
494	C₂²×C₄	—	4	2	no	—
495	C₂²×C₄	—	4	2	no	—
496	C₂²×C₄	—	4	2	no	—
497	C₂²×C₄	—	4	2	no	—
498	C₂²×C₄	—	4	4	no	—
499	C₂²×C₄	—	4	4	no	—
500	C₂²×C₄	—	4	4	no	—
501	C₂²×C₄	—	4	16	no	—
502	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
503	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
504	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
505	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
506	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
507	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
508	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
509	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
510	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
511	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
512	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
513	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
514	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
515	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
516	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
517	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
518	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
519	C₄⋊C₄	—	2	8	no	—
520	C₄⋊C₄	—	2	8	no	—
521	C₄⋊C₄	—	2	8	no	—
522	C₄⋊C₄	—	2	8	no	—
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	2	2	no	—
525	C₄⋊C₄	—	2	4	no	—
526	C₄⋊C₄	—	2	4	no	—
527	C₄⋊C₄	—	2	16	no	—
528	C₄⋊C₄	—	4	4	no	—
529	C₄⋊C₄	—	4	8	no	—
530	C₂²⋊C₄	—	2	4	no	—
531	C₂²⋊C₄	—	2	4	no	—
532	C₂²⋊C₄	—	2	4	no	—
533	C₂²⋊C₄	—	2	8	no	—
534	C₂²⋊C₄	—	2	8	no	—
535	C₂²⋊C₄	—	2	8	no	—
536	C₂²⋊C₄	—	2	4	no	—
537	C₂²⋊C₄	—	2	4	no	—
538	C₂²⋊C₄	—	2	16	no	—
539	C₂²⋊C₄	—	4	8	no	—
540	C₄²	—	2	4	no	—
541	C₄²	—	4	4	no	—
542	C₁₃	#35057	1	1	yes	characteristic, direct product factor, Sylow
543	C₂³	—	2	32	no	—
544	C₂³	—	2	8	no	—
545	C₂³	—	2	8	no	—
546	C₂³	—	2	8	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	2	no	—
550	C₂³	—	2	2	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	2	2	no	—
553	C₂³	—	2	2	no	—
554	C₂³	—	2	4	no	—
555	C₂³	—	2	4	no	—
556	C₂³	—	2	4	no	—
557	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
558	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
559	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
560	C₂³	C₂×C₁₃×#41	1	4	yes	—
561	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
562	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
563	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
564	Q₈	—	4	4	no	—
565	D₄	—	4	4	no	—
566	D₄	—	4	8	no	—
567	D₄	—	4	8	no	—
568	D₄	—	4	8	no	—
569	C₂×C₄	—	2	16	no	—
570	C₂×C₄	—	2	16	no	—
571	C₂×C₄	—	2	16	no	—
572	C₂×C₄	—	2	8	no	—
573	C₂×C₄	—	2	8	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	8	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	8	no	—
587	C₂×C₄	—	2	8	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	8	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	4	4	no	—
592	C₂×C₄	—	4	4	no	—
593	C₂×C₄	—	4	4	no	—
594	C₂×C₄	—	4	4	no	—
595	C₂×C₄	—	4	8	no	—
596	C₂×C₄	—	4	8	no	—
597	C₂×C₄	—	4	8	no	—
598	C₂×C₄	—	4	8	no	—
599	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
600	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
601	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
602	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
603	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
604	C₂²	—	2	32	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	8	no	—
612	C₂²	—	2	8	no	—
613	C₂²	—	2	8	no	—
614	C₂²	—	4	2	no	—
615	C₂²	—	4	2	no	—
616	C₂²	—	4	2	no	—
617	C₂²	—	4	8	no	—
618	C₂²	C₁₃×#525	1	4	yes	—
619	C₂²	C₁₃×#534	1	4	yes	—
620	C₂²	C₁₃×#536	1	4	yes	—
621	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
622	C₂²	C₂²×C₁₃×#41	1	2	yes	—
623	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
624	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
625	C₄	—	2	8	no	—
626	C₄	—	2	2	no	—
627	C₄	—	2	2	no	—
628	C₄	—	2	2	no	—
629	C₄	—	2	2	no	—
630	C₄	—	4	2	no	—
631	C₄	—	4	4	no	—
632	C₄	—	4	2	no	—
633	C₄	—	4	2	no	—
634	C₄	—	4	8	no	—
635	C₂	—	2	4	no	—
636	C₂	—	2	4	no	—
637	C₂	—	2	4	no	—
638	C₂	—	8	2	no	—
639	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
640	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
641	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
642	C₂	C₁₃×#3492	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#525	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×C₄⋊C₄	C₂	semidirect
3. C₁₃×#2849	C₂	semidirect
4. C₁₃×#2849	C₂	semidirect
5. C₁₃×#2627	C₂	semidirect
6. C₁₃×#2618	C₂	semidirect
7. C₁₃×#2591	C₂	semidirect
8. C₁₃×#2583	C₂	semidirect
9. C₁₃×#2579	C₂	semidirect
10. C₁₃×#2484	C₂	semidirect
11. C₁₃×#2413	C₂	semidirect
12. C₁₃×#2406	C₂	semidirect
13. C₁₃×#2322	C₂	semidirect
14. C₁₃×#2280	C₂	semidirect
39. C₁₃×#400	C₂²	semidirect
40. C₁₃×#398	C₂²	semidirect
41. C₁₃×#398	C₂²	semidirect
42. C₁₃×#396	C₂²	semidirect
43. C₁₃×#395	C₂²	semidirect
44. C₁₃×#394	C₂²	semidirect
45. C₁₃×#389	C₂²	semidirect
46. C₁₃×#388	C₂²	semidirect
47. C₁₃×#387	C₂²	semidirect
56. C₁₃×#385	C₂²	semidirect
139. #35057	C₁₃	direct (N × H)
188. C₂²×C₄×C₁₃	#41	semidirect
223. C₂³×C₄⋊C₄	C₂×C₁₃	semidirect
224. #2849	C₂×C₁₃	semidirect
225. #2849	C₂×C₁₃	semidirect
226. #2627	C₂×C₁₃	semidirect
227. #2618	C₂×C₁₃	semidirect
228. #2591	C₂×C₁₃	semidirect
229. #2583	C₂×C₁₃	semidirect
230. #2579	C₂×C₁₃	semidirect
231. #2484	C₂×C₁₃	semidirect
232. #2413	C₂×C₁₃	semidirect
233. #2406	C₂×C₁₃	semidirect
234. #2322	C₂×C₁₃	semidirect
235. #2280	C₂×C₁₃	semidirect
321. #400	C₂²×C₁₃	semidirect
322. #398	C₂²×C₁₃	semidirect
323. #398	C₂²×C₁₃	semidirect
324. #396	C₂²×C₁₃	semidirect
325. #395	C₂²×C₁₃	semidirect
326. #394	C₂²×C₁₃	semidirect
327. #389	C₂²×C₁₃	semidirect
328. #388	C₂²×C₁₃	semidirect
329. #387	C₂²×C₁₃	semidirect
338. #385	C₂²×C₁₃	semidirect
508. C₂²×C₄	C₁₃×#41	semidirect
542. C₁₃	#35057	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#525	2
C₂³×C₁₃×C₄⋊C₄	2
C₁₃×#2849	2
C₁₃×#2627	2
C₁₃×#2618	2
C₁₃×#2591	2
C₁₃×#2583	2
C₁₃×#2579	2
C₁₃×#2484	2
C₁₃×#2413	2
C₁₃×#2406	2
C₁₃×#2322	2
C₁₃×#2280	2
#35057	13

Subgroups — C13×#35057 #15721396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#35057 #15721396