Subgroups — C₁₃×#34400 #15720739

Order 3328.

1990 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2376	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2373	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2357	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2353	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2346	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2343	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2337	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2336	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2333	C₂	1	2	yes	maximal
11	C₁₃×#2332	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2320	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2318	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#529	C₄	1	16	yes	complemented
17	C₂×C₁₃×#126	C₂²	1	2	yes	—
18	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#123	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
26	C₂×C₁₃×#117	C₂²	1	2	yes	—
27	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#391	C₂²	1	4	yes	—
29	C₁₃×#390	C₂²	1	4	yes	—
30	C₁₃×#389	C₂²	1	4	yes	—
31	C₁₃×#389	C₂²	1	4	yes	—
32	C₁₃×#388	C₂²	1	4	yes	—
33	C₁₃×#388	C₂²	1	4	yes	—
34	C₁₃×#388	C₂²	1	4	yes	—
35	C₁₃×#388	C₂²	1	4	yes	—
36	C₁₃×#388	C₂²	1	4	yes	—
37	C₁₃×#388	C₂²	1	4	yes	—
38	C₁₃×#387	C₂²	1	4	yes	—
39	C₁₃×#387	C₂²	1	4	yes	—
40	C₁₃×#387	C₂²	1	4	yes	—
41	C₁₃×#387	C₂²	1	4	yes	—
42	C₁₃×#387	C₂²	1	4	yes	—
43	C₁₃×#387	C₂²	1	4	yes	—
44	C₁₃×#386	C₂²	1	4	yes	—
45	C₁₃×#386	C₂²	1	4	yes	—
46	C₁₃×#385	C₂²	1	4	yes	—
47	C₁₃×#385	C₂²	1	4	yes	—
48	C₁₃×#383	C₂²	1	2	yes	—
49	C₁₃×#383	C₂²	1	2	yes	—
50	C₁₃×#383	C₂²	1	2	yes	—
51	C₁₃×#382	C₂²	1	2	yes	—
52	C₁₃×#382	C₂²	1	2	yes	—
53	C₁₃×#382	C₂²	1	2	yes	—
54	C₁₃×#381	C₂²	1	2	yes	—
55	C₁₃×#381	C₂²	1	2	yes	—
56	C₁₃×#381	C₂²	1	2	yes	—
57	C₁₃×#380	C₂²	1	2	yes	—
58	C₁₃×#380	C₂²	1	2	yes	—
59	C₁₃×#380	C₂²	1	2	yes	—
60	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
61	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
62	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
63	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
64	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
65	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
66	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
67	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
68	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
69	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
70	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
71	C₁₃×#376	C₂²	1	1	yes	characteristic
72	C₁₃×#376	C₂²	1	1	yes	characteristic
73	C₁₃×#376	C₂²	1	2	yes	—
74	C₁₃×#376	C₂²	1	2	yes	—
75	C₂×C₁₃×#95	C₂²	1	2	yes	—
76	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
80	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×#126	C₂×C₄	1	16	yes	complemented
85	C₁₃×#125	C₂×C₄	1	8	yes	complemented
86	C₁₃×#124	C₂×C₄	1	8	yes	—
87	C₁₃×#123	C₂×C₄	1	16	yes	complemented
88	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
89	C₁₃×#121	C₂×C₄	1	8	yes	—
90	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
91	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
92	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
93	C₁₃×#117	C₂×C₄	1	16	yes	complemented
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
111	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
113	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
117	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
119	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
120	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
122	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
123	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
124	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
127	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
129	C₁₃×#95	C₂³	1	2	yes	—
130	C₁₃×#95	C₂³	1	4	yes	—
131	C₁₃×#95	C₂³	1	4	yes	—
132	C₁₃×#95	C₂³	1	2	yes	—
133	C₁₃×#95	C₂³	1	2	yes	—
134	C₁₃×#95	C₂³	1	4	yes	—
135	C₁₃×#95	C₂³	1	4	yes	—
136	C₁₃×#95	C₂³	1	4	yes	—
137	C₁₃×#95	C₂³	1	2	yes	—
138	C₁₃×#95	C₂³	1	4	yes	—
139	C₁₃×#95	C₂³	1	4	yes	—
140	C₁₃×#95	C₂³	1	4	yes	—
141	C₁₃×#95	C₂³	1	2	yes	—
142	C₁₃×#95	C₂³	1	4	yes	—
143	C₁₃×#95	C₂³	1	2	yes	—
144	C₁₃×#95	C₂³	1	4	yes	—
145	C₁₃×#95	C₂³	1	4	yes	—
146	#34400	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
149	C₂×Q₈×C₁₃	—	4	2	no	—
150	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
151	C₂×D₄×C₁₃	—	4	2	no	—
152	C₂×D₄×C₁₃	—	4	2	no	—
153	C₂×D₄×C₁₃	—	4	2	no	—
154	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
155	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
156	C₂²×C₄×C₁₃	—	4	2	no	—
157	C₂²×C₄×C₁₃	—	4	2	no	—
158	C₂²×C₄×C₁₃	—	4	4	no	—
159	C₂²×C₄×C₁₃	—	4	2	no	—
160	C₂²×C₄×C₁₃	—	4	4	no	—
161	C₂²×C₄×C₁₃	—	4	4	no	—
162	C₂²×C₄×C₁₃	—	4	4	no	—
163	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
164	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
165	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
166	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
170	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₁₃×C₄⋊C₄	—	4	4	no	—
181	C₁₃×C₄⋊C₄	—	4	4	no	—
182	C₁₃×C₄⋊C₄	—	4	4	no	—
183	C₁₃×C₄⋊C₄	—	4	4	no	—
184	C₁₃×C₄⋊C₄	—	4	4	no	—
185	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
186	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
187	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
188	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
189	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
190	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
191	C₁₃×C₂²⋊C₄	—	4	4	no	—
192	C₁₃×C₂²⋊C₄	—	4	4	no	—
193	C₁₃×C₂²⋊C₄	—	4	4	no	—
194	C₁₃×C₂²⋊C₄	—	4	2	no	—
195	C₁₃×C₂²⋊C₄	—	4	2	no	—
196	C₁₃×C₂²⋊C₄	—	4	4	no	—
197	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
198	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
199	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
200	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
201	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
202	C₄²×C₁₃	—	4	2	no	—
203	C₄²×C₁₃	—	4	2	no	—
204	C₄²×C₁₃	—	4	2	no	—
205	C₄²×C₁₃	—	4	2	no	—
206	C₄²×C₁₃	—	4	4	no	—
207	C₄²×C₁₃	—	4	4	no	—
208	C₄²×C₁₃	—	4	4	no	—
209	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
210	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
211	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
212	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
213	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
214	C₂×#529	C₂×C₁₃	1	1	yes	characteristic
215	#2376	C₂×C₁₃	1	4	yes	complemented
216	#2373	C₂×C₁₃	1	4	yes	complemented
217	#2357	C₂×C₁₃	1	2	yes	complemented
218	#2353	C₂×C₁₃	1	2	yes	complemented
219	#2346	C₂×C₁₃	1	2	yes	complemented
220	#2343	C₂×C₁₃	1	2	yes	complemented
221	#2337	C₂×C₁₃	1	2	yes	complemented
222	#2336	C₂×C₁₃	1	2	yes	complemented
223	#2333	C₂×C₁₃	1	2	yes	—
224	#2332	C₂×C₁₃	1	2	yes	complemented
225	#2320	C₂×C₁₃	1	2	yes	complemented
226	#2318	C₂×C₁₃	1	2	yes	complemented
227	#2283	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#2283	C₂×C₁₃	1	1	yes	characteristic, complemented
229	C₂³×C₁₃	—	2	2	no	—
230	C₂³×C₁₃	—	2	2	no	—
231	C₂³×C₁₃	—	2	2	no	—
232	C₂³×C₁₃	—	2	4	no	—
233	C₂³×C₁₃	—	2	4	no	—
234	C₂³×C₁₃	—	2	2	no	—
235	C₂³×C₁₃	—	2	2	no	—
236	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
237	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
238	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
239	Q₈×C₁₃	—	4	4	no	—
240	D₄×C₁₃	—	4	4	no	—
241	D₄×C₁₃	—	4	8	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	4	no	—
246	C₂×C₄×C₁₃	—	2	4	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	2	4	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	4	no	—
258	C₂×C₄×C₁₃	—	2	4	no	—
259	C₂×C₄×C₁₃	—	2	4	no	—
260	C₂×C₄×C₁₃	—	2	4	no	—
261	C₂×C₄×C₁₃	—	2	4	no	—
262	C₂×C₄×C₁₃	—	2	4	no	—
263	C₂×C₄×C₁₃	—	2	4	no	—
264	C₂×C₄×C₁₃	—	4	4	no	—
265	C₂×C₄×C₁₃	—	4	8	no	—
266	C₂×C₄×C₁₃	—	4	4	no	—
267	C₂×C₄×C₁₃	—	4	4	no	—
268	C₂×C₄×C₁₃	—	8	8	no	—
269	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
270	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
271	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
272	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
273	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
274	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
275	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
276	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
277	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
278	#529	C₄×C₁₃	1	16	yes	complemented
279	C₂×#126	C₂²×C₁₃	1	2	yes	—
280	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
281	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×#123	C₂²×C₁₃	1	2	yes	—
283	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
288	C₂×#117	C₂²×C₁₃	1	2	yes	—
289	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
290	#391	C₂²×C₁₃	1	4	yes	—
291	#390	C₂²×C₁₃	1	4	yes	—
292	#389	C₂²×C₁₃	1	4	yes	—
293	#389	C₂²×C₁₃	1	4	yes	—
294	#388	C₂²×C₁₃	1	4	yes	—
295	#388	C₂²×C₁₃	1	4	yes	—
296	#388	C₂²×C₁₃	1	4	yes	—
297	#388	C₂²×C₁₃	1	4	yes	—
298	#388	C₂²×C₁₃	1	4	yes	—
299	#388	C₂²×C₁₃	1	4	yes	—
300	#387	C₂²×C₁₃	1	4	yes	—
301	#387	C₂²×C₁₃	1	4	yes	—
302	#387	C₂²×C₁₃	1	4	yes	—
303	#387	C₂²×C₁₃	1	4	yes	—
304	#387	C₂²×C₁₃	1	4	yes	—
305	#387	C₂²×C₁₃	1	4	yes	—
306	#386	C₂²×C₁₃	1	4	yes	—
307	#386	C₂²×C₁₃	1	4	yes	—
308	#385	C₂²×C₁₃	1	4	yes	—
309	#385	C₂²×C₁₃	1	4	yes	—
310	#383	C₂²×C₁₃	1	2	yes	—
311	#383	C₂²×C₁₃	1	2	yes	—
312	#383	C₂²×C₁₃	1	2	yes	—
313	#382	C₂²×C₁₃	1	2	yes	—
314	#382	C₂²×C₁₃	1	2	yes	—
315	#382	C₂²×C₁₃	1	2	yes	—
316	#381	C₂²×C₁₃	1	2	yes	—
317	#381	C₂²×C₁₃	1	2	yes	—
318	#381	C₂²×C₁₃	1	2	yes	—
319	#380	C₂²×C₁₃	1	2	yes	—
320	#380	C₂²×C₁₃	1	2	yes	—
321	#380	C₂²×C₁₃	1	2	yes	—
322	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
323	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
324	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
325	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
326	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
327	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
328	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
329	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
330	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
331	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
332	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
333	#376	C₂²×C₁₃	1	2	yes	—
334	#376	C₂²×C₁₃	1	1	yes	characteristic
335	#376	C₂²×C₁₃	1	1	yes	characteristic
336	#376	C₂²×C₁₃	1	2	yes	—
337	C₂×#95	C₂²×C₁₃	1	2	yes	—
338	C₂²×C₁₃	—	2	2	no	—
339	C₂²×C₁₃	—	2	2	no	—
340	C₂²×C₁₃	—	2	2	no	—
341	C₂²×C₁₃	—	2	4	no	—
342	C₂²×C₁₃	—	2	4	no	—
343	C₂²×C₁₃	—	2	4	no	—
344	C₂²×C₁₃	—	4	4	no	—
345	C₂²×C₁₃	—	4	4	no	—
346	C₂²×C₁₃	—	4	4	no	—
347	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
348	C₂²×C₁₃	#585	1	2	yes	—
349	C₂²×C₁₃	#585	1	2	yes	—
350	C₂²×C₁₃	#585	1	2	yes	—
351	C₄×C₁₃	—	2	2	no	—
352	C₄×C₁₃	—	2	2	no	—
353	C₄×C₁₃	—	2	2	no	—
354	C₄×C₁₃	—	2	4	no	—
355	C₄×C₁₃	—	2	2	no	—
356	C₄×C₁₃	—	2	2	no	—
357	C₄×C₁₃	—	2	2	no	—
358	C₄×C₁₃	—	2	4	no	—
359	C₄×C₁₃	—	2	4	no	—
360	C₄×C₁₃	—	4	4	no	—
361	C₄×C₁₃	—	4	4	no	—
362	C₄×C₁₃	—	4	4	no	—
363	C₄×C₁₃	—	4	4	no	—
364	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
365	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
366	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
367	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
368	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
369	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
370	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
371	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
372	#126	C₂×C₄×C₁₃	1	16	yes	complemented
373	#125	C₂×C₄×C₁₃	1	8	yes	complemented
374	#124	C₂×C₄×C₁₃	1	8	yes	—
375	#123	C₂×C₄×C₁₃	1	16	yes	complemented
376	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
377	#121	C₂×C₄×C₁₃	1	8	yes	—
378	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
379	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
380	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
381	#117	C₂×C₄×C₁₃	1	16	yes	complemented
382	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
384	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
385	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
387	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
388	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
389	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
391	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
404	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	complemented
405	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
406	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
407	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
408	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
409	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
410	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
411	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
412	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
413	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
414	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
415	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
416	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
417	#95	C₂³×C₁₃	1	2	yes	—
418	#95	C₂³×C₁₃	1	2	yes	—
419	#95	C₂³×C₁₃	1	4	yes	—
420	#95	C₂³×C₁₃	1	2	yes	—
421	#95	C₂³×C₁₃	1	4	yes	—
422	#95	C₂³×C₁₃	1	2	yes	—
423	#95	C₂³×C₁₃	1	4	yes	—
424	#95	C₂³×C₁₃	1	2	yes	—
425	#95	C₂³×C₁₃	1	4	yes	—
426	#95	C₂³×C₁₃	1	2	yes	—
427	#95	C₂³×C₁₃	1	4	yes	—
428	#95	C₂³×C₁₃	1	4	yes	—
429	#95	C₂³×C₁₃	1	4	yes	—
430	#95	C₂³×C₁₃	1	4	yes	—
431	#95	C₂³×C₁₃	1	4	yes	—
432	#95	C₂³×C₁₃	1	4	yes	—
433	#95	C₂³×C₁₃	1	4	yes	—
434	C₂×C₁₃	—	4	2	no	—
435	C₂×C₁₃	—	4	4	no	—
436	C₂×C₁₃	#3428	1	1	yes	characteristic
437	C₂×C₁₃	#3428	1	1	yes	characteristic
438	C₂×C₁₃	#3428	1	1	yes	characteristic
439	C₂×C₁₃	#3566	1	4	yes	—
440	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
441	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
442	C₂×Q₈	—	4	2	no	—
443	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
444	C₂×D₄	—	4	2	no	—
445	C₂×D₄	—	4	2	no	—
446	C₂×D₄	—	4	2	no	—
447	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
448	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
449	C₂²×C₄	—	4	2	no	—
450	C₂²×C₄	—	4	2	no	—
451	C₂²×C₄	—	4	4	no	—
452	C₂²×C₄	—	4	2	no	—
453	C₂²×C₄	—	4	4	no	—
454	C₂²×C₄	—	4	4	no	—
455	C₂²×C₄	—	4	4	no	—
456	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
457	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
458	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
459	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
460	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
461	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
462	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
463	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
464	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
465	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
466	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
467	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
468	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
469	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
470	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
471	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
472	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
473	C₄⋊C₄	—	4	4	no	—
474	C₄⋊C₄	—	4	4	no	—
475	C₄⋊C₄	—	4	4	no	—
476	C₄⋊C₄	—	4	4	no	—
477	C₄⋊C₄	—	4	4	no	—
478	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
479	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
480	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
481	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
482	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
483	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
484	C₂²⋊C₄	—	4	4	no	—
485	C₂²⋊C₄	—	4	4	no	—
486	C₂²⋊C₄	—	4	4	no	—
487	C₂²⋊C₄	—	4	2	no	—
488	C₂²⋊C₄	—	4	2	no	—
489	C₂²⋊C₄	—	4	4	no	—
490	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
491	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
492	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
493	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
494	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
495	C₄²	—	4	2	no	—
496	C₄²	—	4	2	no	—
497	C₄²	—	4	2	no	—
498	C₄²	—	4	2	no	—
499	C₄²	—	4	4	no	—
500	C₄²	—	4	4	no	—
501	C₄²	—	4	4	no	—
502	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
503	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
504	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
505	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
506	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
507	C₁₃	#34400	1	1	yes	characteristic, direct product factor, Sylow
508	C₂³	—	2	2	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	4	no	—
512	C₂³	—	2	4	no	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	2	no	—
515	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
516	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
517	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
518	Q₈	—	4	4	no	—
519	D₄	—	4	4	no	—
520	D₄	—	4	8	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	4	4	no	—
544	C₂×C₄	—	4	8	no	—
545	C₂×C₄	—	4	4	no	—
546	C₂×C₄	—	4	4	no	—
547	C₂×C₄	—	8	8	no	—
548	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
549	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
550	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
551	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
552	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
553	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
554	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
555	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
556	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	2	4	no	—
561	C₂²	—	2	4	no	—
562	C₂²	—	2	4	no	—
563	C₂²	—	4	4	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	4	4	no	—
566	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
567	C₂²	C₁₃×#585	1	2	yes	—
568	C₂²	C₁₃×#585	1	2	yes	—
569	C₂²	C₁₃×#585	1	2	yes	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	4	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	4	no	—
578	C₄	—	2	4	no	—
579	C₄	—	4	4	no	—
580	C₄	—	4	4	no	—
581	C₄	—	4	4	no	—
582	C₄	—	4	4	no	—
583	C₂	—	4	2	no	—
584	C₂	—	4	4	no	—
585	C₂	C₁₃×#3428	1	1	yes	characteristic
586	C₂	C₁₃×#3428	1	1	yes	characteristic
587	C₂	C₁₃×#3428	1	1	yes	characteristic
588	C₂	C₁₃×#3566	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
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×#2376	C₂	semidirect
3. C₁₃×#2373	C₂	semidirect
4. C₁₃×#2357	C₂	semidirect
5. C₁₃×#2353	C₂	semidirect
6. C₁₃×#2346	C₂	semidirect
7. C₁₃×#2343	C₂	semidirect
8. C₁₃×#2337	C₂	semidirect
9. C₁₃×#2336	C₂	semidirect
11. C₁₃×#2332	C₂	semidirect
12. C₁₃×#2320	C₂	semidirect
13. C₁₃×#2318	C₂	semidirect
14. C₁₃×#2283	C₂	semidirect
15. C₁₃×#2283	C₂	semidirect
16. C₁₃×#529	C₄	semidirect
84. C₁₃×#126	C₂×C₄	semidirect
85. C₁₃×#125	C₂×C₄	semidirect
87. C₁₃×#123	C₂×C₄	semidirect
88. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
90. C₄×Q₈×C₁₃	C₂×C₄	semidirect
92. C₄×D₄×C₁₃	C₂×C₄	semidirect
93. C₁₃×#117	C₂×C₄	semidirect
116. C₂×C₄²×C₁₃	C₂×C₄	semidirect
146. #34400	C₁₃	direct (N × H)
215. #2376	C₂×C₁₃	semidirect
216. #2373	C₂×C₁₃	semidirect
217. #2357	C₂×C₁₃	semidirect
218. #2353	C₂×C₁₃	semidirect
219. #2346	C₂×C₁₃	semidirect
220. #2343	C₂×C₁₃	semidirect
221. #2337	C₂×C₁₃	semidirect
222. #2336	C₂×C₁₃	semidirect
224. #2332	C₂×C₁₃	semidirect
225. #2320	C₂×C₁₃	semidirect
226. #2318	C₂×C₁₃	semidirect
227. #2283	C₂×C₁₃	semidirect
228. #2283	C₂×C₁₃	semidirect
278. #529	C₄×C₁₃	semidirect
372. #126	C₂×C₄×C₁₃	semidirect
373. #125	C₂×C₄×C₁₃	semidirect
375. #123	C₂×C₄×C₁₃	semidirect
376. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
378. C₄×Q₈	C₂×C₄×C₁₃	semidirect
380. C₄×D₄	C₂×C₄×C₁₃	semidirect
381. #117	C₂×C₄×C₁₃	semidirect
404. C₂×C₄²	C₂×C₄×C₁₃	semidirect
507. C₁₃	#34400	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×#529	2
C₁₃×#2376	2
C₁₃×#2373	2
C₁₃×#2357	2
C₁₃×#2353	2
C₁₃×#2346	2
C₁₃×#2343	2
C₁₃×#2337	2
C₁₃×#2336	2
C₁₃×#2333	2
C₁₃×#2332	2
C₁₃×#2320	2
C₁₃×#2318	2
C₁₃×#2283	2
#34400	13

Subgroups — C13×#34400 #15720739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34400 #15720739