Subgroups — C₁₃×#62860 #15749199

Order 3328.

6866 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3510	C₂	1	8	yes	maximal, complemented
2	C₁₃×#3509	C₂	1	8	yes	maximal, complemented
3	C₁₃×#3507	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3495	C₂	1	16	yes	maximal, complemented
5	C₁₃×#3491	C₂	1	8	yes	maximal, complemented
6	C₁₃×#3461	C₂	1	8	yes	maximal, complemented
7	C₁₃×#3458	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3449	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₃×#536	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3428	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#519	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	2	yes	—
13	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#559	C₂²	1	16	yes	complemented
15	C₁₃×#557	C₂²	1	16	yes	complemented
16	C₁₃×#556	C₂²	1	16	yes	complemented
17	C₁₃×#556	C₂²	1	32	yes	complemented
18	C₁₃×#554	C₂²	1	16	yes	complemented
19	C₁₃×#552	C₂²	1	64	yes	complemented
20	C₁₃×#552	C₂²	1	32	yes	complemented
21	C₁₃×#551	C₂²	1	64	yes	complemented
22	C₁₃×#544	C₂²	1	4	yes	complemented
23	C₁₃×#544	C₂²	1	8	yes	complemented
24	C₁₃×#543	C₂²	1	4	yes	—
25	C₁₃×#542	C₂²	1	32	yes	complemented
26	C₁₃×#541	C₂²	1	32	yes	complemented
27	C₁₃×#539	C₂²	1	32	yes	complemented
28	C₁₃×#537	C₂²	1	4	yes	—
29	C₁₃×#536	C₂²	1	8	yes	—
30	C₁₃×#536	C₂²	1	8	yes	—
31	C₁₃×#536	C₂²	1	4	yes	—
32	C₁₃×#536	C₂²	1	8	yes	complemented
33	C₁₃×#536	C₂²	1	8	yes	complemented
34	C₁₃×#535	C₂²	1	4	yes	—
35	C₁₃×#534	C₂²	1	4	yes	—
36	C₁₃×#533	C₂²	1	4	yes	complemented
37	C₁₃×#533	C₂²	1	8	yes	complemented
38	C₁₃×#533	C₂²	1	32	yes	complemented
39	C₁₃×#532	C₂²	1	4	yes	—
40	C₂×C₁₃×C₄⋊Q₈	C₂²	1	4	yes	complemented
41	C₁₃×#529	C₂²	1	32	yes	complemented
42	C₁₃×#529	C₂²	1	32	yes	complemented
43	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
44	C₁₃×#525	C₂²	1	8	yes	—
45	C₂×C₁₃×#123	C₂²	1	8	yes	—
46	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
47	C₁₃×#520	C₂²	1	8	yes	—
48	C₁₃×#520	C₂²	1	8	yes	complemented
49	C₁₃×#519	C₂²	1	8	yes	complemented
50	C₁₃×#519	C₂²	1	8	yes	complemented
51	C₁₃×#519	C₂²	1	4	yes	complemented
52	C₁₃×#518	C₂²	1	8	yes	—
53	C₁₃×#518	C₂²	1	4	yes	complemented
54	C₄×C₁₃×#41	C₂²	1	8	yes	—
55	C₄×C₁₃×#41	C₂²	1	8	yes	complemented
56	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
57	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
58	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#117	C₂²	1	4	yes	—
61	C₂×C₁₃×#117	C₂²	1	2	yes	—
62	C₂×C₁₃×#117	C₂²	1	8	yes	complemented
63	C₂×C₁₃×#41	—	2	16	no	—
64	C₂×C₁₃×#41	C₂³	1	4	yes	—
65	C₂×C₁₃×#41	C₂³	1	4	yes	—
66	C₂×C₁₃×#41	C₂³	1	4	yes	—
67	C₂×C₁₃×#41	C₂³	1	4	yes	—
68	C₂²×Q₈×C₁₃	—	2	8	no	—
69	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
70	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
71	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
72	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
73	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
74	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
75	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
77	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
78	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
80	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
81	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
82	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
83	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
84	C₁₃×#127	C₂³	1	4	yes	—
85	C₁₃×#126	C₂³	1	64	yes	—
86	C₁₃×#126	C₂³	1	64	yes	—
87	C₁₃×#125	C₂³	1	16	yes	—
88	C₁₃×#125	C₂³	1	32	yes	—
89	C₁₃×#125	C₂³	1	64	yes	—
90	C₁₃×#125	C₂³	1	8	yes	—
91	C₁₃×#124	C₂³	1	16	yes	—
92	C₁₃×#124	C₂³	1	16	yes	—
93	C₁₃×#124	C₂³	1	32	yes	—
94	C₁₃×#124	C₂³	1	8	yes	—
95	C₁₃×#123	C₂³	1	32	yes	—
96	C₁₃×#123	C₂³	1	32	yes	—
97	C₁₃×#123	C₂³	1	16	yes	—
98	C₁₃×#123	C₂³	1	64	yes	—
99	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
100	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
101	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
102	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
103	C₁₃×C₂²⋊Q₈	C₂³	1	64	yes	—
104	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
105	C₁₃×#121	C₂³	1	16	yes	—
106	C₁₃×#121	C₂³	1	16	yes	—
107	C₁₃×#120	C₂³	1	16	yes	—
108	C₄×Q₈×C₁₃	C₂³	1	32	yes	—
109	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
110	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
111	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
112	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
113	C₄×Q₈×C₁₃	C₂³	1	32	yes	—
114	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
115	C₄×D₄×C₁₃	C₂³	1	32	yes	—
116	C₄×D₄×C₁₃	C₂³	1	16	yes	—
117	C₄×D₄×C₁₃	C₂³	1	32	yes	—
118	C₄×D₄×C₁₃	C₂³	1	16	yes	—
119	C₄×D₄×C₁₃	C₂³	1	16	yes	—
120	C₄×D₄×C₁₃	C₂³	1	32	yes	—
121	C₁₃×#117	C₂³	1	4	yes	—
122	C₁₃×#117	C₂³	1	4	yes	—
123	C₁₃×#117	C₂³	1	4	yes	—
124	C₁₃×#117	C₂³	1	4	yes	—
125	C₁₃×#117	C₂³	1	4	yes	—
126	C₁₃×#117	C₂³	1	4	yes	—
127	C₁₃×#117	C₂³	1	4	yes	—
128	C₁₃×#117	C₂³	1	32	yes	—
129	C₁₃×#117	C₂³	1	4	yes	—
130	C₁₃×#117	C₂³	1	16	yes	—
131	C₁₃×#117	C₂³	1	16	yes	—
132	C₁₃×#117	C₂³	1	16	yes	—
133	C₁₃×#117	C₂³	1	64	yes	—
134	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
137	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
140	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
141	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
143	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
144	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
145	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
146	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
147	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
149	C₂×C₄²×C₁₃	C₂³	1	16	yes	—
150	#62860	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
152	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
153	C₁₃×#41	—	2	16	no	—
154	C₁₃×#41	—	2	16	no	—
155	C₁₃×#41	—	2	16	no	—
156	C₁₃×#41	—	2	16	no	—
157	C₂×Q₈×C₁₃	—	2	16	no	—
158	C₂×Q₈×C₁₃	—	2	16	no	—
159	C₂×Q₈×C₁₃	—	2	8	no	—
160	C₂×Q₈×C₁₃	—	2	8	no	—
161	C₂×Q₈×C₁₃	—	2	8	no	—
162	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
163	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
164	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
165	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
166	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
167	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
168	C₂×D₄×C₁₃	—	2	16	no	—
169	C₂×D₄×C₁₃	—	2	8	no	—
170	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
171	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
172	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
173	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
174	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
175	C₂²×C₄×C₁₃	—	2	8	no	—
176	C₂²×C₄×C₁₃	—	2	16	no	—
177	C₂²×C₄×C₁₃	#41	1	8	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
181	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
191	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
192	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
193	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
194	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
195	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
196	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
197	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
198	C₁₃×C₄⋊C₄	C₂⁴	1	64	yes	—
199	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
200	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
201	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
202	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
203	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
204	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
205	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
206	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
207	C₁₃×C₂²⋊C₄	C₂⁴	1	64	yes	—
208	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
209	C₄²×C₁₃	C₂⁴	1	8	yes	—
210	C₄²×C₁₃	C₂⁴	1	8	yes	—
211	C₄²×C₁₃	C₂⁴	1	32	yes	—
212	C₄²×C₁₃	C₂⁴	1	32	yes	—
213	C₄²×C₁₃	C₂⁴	1	4	yes	—
214	C₄²×C₁₃	C₂⁴	1	8	yes	—
215	C₄²×C₁₃	C₂⁴	1	4	yes	—
216	#3510	C₂×C₁₃	1	8	yes	complemented
217	#3509	C₂×C₁₃	1	8	yes	complemented
218	#3507	C₂×C₁₃	1	8	yes	complemented
219	#3495	C₂×C₁₃	1	16	yes	complemented
220	#3491	C₂×C₁₃	1	8	yes	complemented
221	#3461	C₂×C₁₃	1	8	yes	complemented
222	#3458	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#3449	C₂×C₁₃	1	1	yes	characteristic
224	C₂×#536	C₂×C₁₃	1	2	yes	complemented
225	#3428	C₂×C₁₃	1	2	yes	complemented
226	C₂×#519	C₂×C₁₃	1	1	yes	characteristic, complemented
227	C₂³×C₁₃	—	2	8	no	—
228	C₂³×C₁₃	—	4	2	no	—
229	C₂³×C₁₃	—	4	8	no	—
230	C₂³×C₁₃	C₂×#41	1	4	yes	—
231	C₂³×C₁₃	C₂⁵	1	8	yes	—
232	C₂³×C₁₃	C₂⁵	1	2	yes	—
233	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
234	Q₈×C₁₃	—	2	8	no	—
235	Q₈×C₁₃	—	2	16	no	—
236	Q₈×C₁₃	—	2	8	no	—
237	Q₈×C₁₃	—	2	8	no	—
238	Q₈×C₁₃	—	2	8	no	—
239	Q₈×C₁₃	—	4	16	no	—
240	D₄×C₁₃	—	2	16	no	—
241	D₄×C₁₃	—	2	16	no	—
242	D₄×C₁₃	—	2	8	no	—
243	D₄×C₁₃	—	2	8	no	—
244	D₄×C₁₃	—	4	16	no	—
245	C₂×C₄×C₁₃	—	2	8	no	—
246	C₂×C₄×C₁₃	—	2	16	no	—
247	C₂×C₄×C₁₃	—	2	8	no	—
248	C₂×C₄×C₁₃	—	2	16	no	—
249	C₂×C₄×C₁₃	—	2	16	no	—
250	C₂×C₄×C₁₃	—	4	4	no	—
251	C₂×C₄×C₁₃	—	4	32	no	—
252	C₂×C₄×C₁₃	—	4	8	no	—
253	C₂×C₄×C₁₃	—	4	4	no	—
254	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
255	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
256	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
257	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
258	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
259	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
260	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
261	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
262	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
263	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
265	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
266	C₂²×#41	C₂²×C₁₃	1	2	yes	—
267	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
268	#559	C₂²×C₁₃	1	16	yes	complemented
269	#557	C₂²×C₁₃	1	16	yes	complemented
270	#556	C₂²×C₁₃	1	16	yes	complemented
271	#556	C₂²×C₁₃	1	32	yes	complemented
272	#554	C₂²×C₁₃	1	16	yes	complemented
273	#552	C₂²×C₁₃	1	64	yes	complemented
274	#552	C₂²×C₁₃	1	32	yes	complemented
275	#551	C₂²×C₁₃	1	64	yes	complemented
276	#544	C₂²×C₁₃	1	4	yes	complemented
277	#544	C₂²×C₁₃	1	8	yes	complemented
278	#543	C₂²×C₁₃	1	4	yes	—
279	#542	C₂²×C₁₃	1	32	yes	complemented
280	#541	C₂²×C₁₃	1	32	yes	complemented
281	#539	C₂²×C₁₃	1	32	yes	complemented
282	#537	C₂²×C₁₃	1	4	yes	—
283	#536	C₂²×C₁₃	1	8	yes	—
284	#536	C₂²×C₁₃	1	8	yes	—
285	#536	C₂²×C₁₃	1	4	yes	—
286	#536	C₂²×C₁₃	1	8	yes	complemented
287	#536	C₂²×C₁₃	1	8	yes	complemented
288	#535	C₂²×C₁₃	1	4	yes	—
289	#534	C₂²×C₁₃	1	4	yes	—
290	#533	C₂²×C₁₃	1	4	yes	complemented
291	#533	C₂²×C₁₃	1	8	yes	complemented
292	#533	C₂²×C₁₃	1	32	yes	complemented
293	#532	C₂²×C₁₃	1	4	yes	—
294	C₂×C₄⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
295	#529	C₂²×C₁₃	1	32	yes	complemented
296	#529	C₂²×C₁₃	1	32	yes	complemented
297	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
298	#525	C₂²×C₁₃	1	8	yes	—
299	C₂×#123	C₂²×C₁₃	1	8	yes	—
300	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
301	#520	C₂²×C₁₃	1	8	yes	—
302	#520	C₂²×C₁₃	1	8	yes	complemented
303	#519	C₂²×C₁₃	1	8	yes	complemented
304	#519	C₂²×C₁₃	1	8	yes	complemented
305	#519	C₂²×C₁₃	1	4	yes	complemented
306	#518	C₂²×C₁₃	1	8	yes	—
307	#518	C₂²×C₁₃	1	4	yes	complemented
308	C₄×#41	C₂²×C₁₃	1	8	yes	—
309	C₄×#41	C₂²×C₁₃	1	8	yes	complemented
310	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
311	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
312	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
313	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
314	C₂×#117	C₂²×C₁₃	1	4	yes	—
315	C₂×#117	C₂²×C₁₃	1	2	yes	—
316	C₂×#117	C₂²×C₁₃	1	8	yes	complemented
317	C₂²×C₁₃	—	2	2	no	—
318	C₂²×C₁₃	—	2	4	no	—
319	C₂²×C₁₃	—	2	8	no	—
320	C₂²×C₁₃	—	2	16	no	—
321	C₂²×C₁₃	—	4	4	no	—
322	C₂²×C₁₃	—	8	8	no	—
323	C₂²×C₁₃	C₂²×#41	1	4	yes	—
324	C₂²×C₁₃	C₂²×#41	1	2	yes	—
325	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
326	C₄×C₁₃	—	2	8	no	—
327	C₄×C₁₃	—	2	8	no	—
328	C₄×C₁₃	—	2	8	no	—
329	C₄×C₁₃	—	2	16	no	—
330	C₄×C₁₃	—	2	8	no	—
331	C₄×C₁₃	C₂²×#41	1	2	yes	—
332	C₄×C₁₃	C₂²×#41	1	4	yes	—
333	C₄×C₁₃	C₂²×#41	1	2	yes	—
334	C₂×#41	—	2	16	no	—
335	C₂×#41	C₂³×C₁₃	1	4	yes	—
336	C₂×#41	C₂³×C₁₃	1	4	yes	—
337	C₂×#41	C₂³×C₁₃	1	4	yes	—
338	C₂×#41	C₂³×C₁₃	1	4	yes	—
339	C₂²×Q₈	—	2	8	no	—
340	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
341	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
342	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
343	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
344	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
345	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
346	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
347	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
348	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
349	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
350	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
351	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
352	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
353	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
354	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
355	#127	C₂³×C₁₃	1	4	yes	—
356	#126	C₂³×C₁₃	1	64	yes	—
357	#126	C₂³×C₁₃	1	64	yes	—
358	#125	C₂³×C₁₃	1	16	yes	—
359	#125	C₂³×C₁₃	1	32	yes	—
360	#125	C₂³×C₁₃	1	64	yes	—
361	#125	C₂³×C₁₃	1	8	yes	—
362	#124	C₂³×C₁₃	1	16	yes	—
363	#124	C₂³×C₁₃	1	16	yes	—
364	#124	C₂³×C₁₃	1	32	yes	—
365	#124	C₂³×C₁₃	1	8	yes	—
366	#123	C₂³×C₁₃	1	32	yes	—
367	#123	C₂³×C₁₃	1	32	yes	—
368	#123	C₂³×C₁₃	1	16	yes	—
369	#123	C₂³×C₁₃	1	64	yes	—
370	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
371	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
372	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
373	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
374	C₂²⋊Q₈	C₂³×C₁₃	1	64	yes	—
375	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
376	#121	C₂³×C₁₃	1	16	yes	—
377	#121	C₂³×C₁₃	1	16	yes	—
378	#120	C₂³×C₁₃	1	16	yes	—
379	C₄×Q₈	C₂³×C₁₃	1	32	yes	—
380	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
381	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
382	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
383	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
384	C₄×Q₈	C₂³×C₁₃	1	32	yes	—
385	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
386	C₄×D₄	C₂³×C₁₃	1	32	yes	—
387	C₄×D₄	C₂³×C₁₃	1	16	yes	—
388	C₄×D₄	C₂³×C₁₃	1	32	yes	—
389	C₄×D₄	C₂³×C₁₃	1	16	yes	—
390	C₄×D₄	C₂³×C₁₃	1	16	yes	—
391	C₄×D₄	C₂³×C₁₃	1	32	yes	—
392	#117	C₂³×C₁₃	1	4	yes	—
393	#117	C₂³×C₁₃	1	4	yes	—
394	#117	C₂³×C₁₃	1	4	yes	—
395	#117	C₂³×C₁₃	1	4	yes	—
396	#117	C₂³×C₁₃	1	4	yes	—
397	#117	C₂³×C₁₃	1	4	yes	—
398	#117	C₂³×C₁₃	1	4	yes	—
399	#117	C₂³×C₁₃	1	32	yes	—
400	#117	C₂³×C₁₃	1	4	yes	—
401	#117	C₂³×C₁₃	1	16	yes	—
402	#117	C₂³×C₁₃	1	16	yes	—
403	#117	C₂³×C₁₃	1	16	yes	—
404	#117	C₂³×C₁₃	1	64	yes	—
405	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
407	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
408	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
409	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
410	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
416	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
417	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
418	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
419	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
420	C₂×C₄²	C₂³×C₁₃	1	16	yes	—
421	C₂×C₁₃	—	2	4	no	—
422	C₂×C₁₃	—	2	2	no	—
423	C₂×C₁₃	—	4	8	no	—
424	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
425	C₂×C₁₃	2₋¹⁺⁶	1	2	yes	—
426	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
427	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
428	#41	—	2	16	no	—
429	#41	—	2	16	no	—
430	#41	—	2	16	no	—
431	#41	—	2	16	no	—
432	C₂×Q₈	—	2	16	no	—
433	C₂×Q₈	—	2	16	no	—
434	C₂×Q₈	—	2	8	no	—
435	C₂×Q₈	—	2	8	no	—
436	C₂×Q₈	—	2	8	no	—
437	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
438	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
439	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
440	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
441	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
442	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
443	C₂×D₄	—	2	16	no	—
444	C₂×D₄	—	2	8	no	—
445	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
446	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
447	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
448	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
449	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
450	C₂²×C₄	—	2	8	no	—
451	C₂²×C₄	—	2	16	no	—
452	C₂²×C₄	C₁₃×#41	1	8	yes	—
453	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
454	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
455	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
456	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
457	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
458	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
459	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
460	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
461	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
462	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
463	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
464	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
465	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
466	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
467	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
468	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
469	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
470	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
471	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
472	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
473	C₄⋊C₄	C₂⁴×C₁₃	1	64	yes	—
474	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
475	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
476	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
477	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
478	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
479	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
480	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
481	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
482	C₂²⋊C₄	C₂⁴×C₁₃	1	64	yes	—
483	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
484	C₄²	C₂⁴×C₁₃	1	8	yes	—
485	C₄²	C₂⁴×C₁₃	1	8	yes	—
486	C₄²	C₂⁴×C₁₃	1	32	yes	—
487	C₄²	C₂⁴×C₁₃	1	32	yes	—
488	C₄²	C₂⁴×C₁₃	1	4	yes	—
489	C₄²	C₂⁴×C₁₃	1	8	yes	—
490	C₄²	C₂⁴×C₁₃	1	4	yes	—
491	C₁₃	#62860	1	1	yes	characteristic, direct product factor, Sylow
492	C₂³	—	2	8	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	8	no	—
495	C₂³	C₂×C₁₃×#41	1	4	yes	—
496	C₂³	C₂⁵×C₁₃	1	8	yes	—
497	C₂³	C₂⁵×C₁₃	1	2	yes	—
498	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
499	Q₈	—	2	8	no	—
500	Q₈	—	2	16	no	—
501	Q₈	—	2	8	no	—
502	Q₈	—	2	8	no	—
503	Q₈	—	2	8	no	—
504	Q₈	—	4	16	no	—
505	D₄	—	2	16	no	—
506	D₄	—	2	16	no	—
507	D₄	—	2	8	no	—
508	D₄	—	2	8	no	—
509	D₄	—	4	16	no	—
510	C₂×C₄	—	2	8	no	—
511	C₂×C₄	—	2	16	no	—
512	C₂×C₄	—	2	8	no	—
513	C₂×C₄	—	2	16	no	—
514	C₂×C₄	—	2	16	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	—	4	32	no	—
517	C₂×C₄	—	4	8	no	—
518	C₂×C₄	—	4	4	no	—
519	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
520	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
521	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
522	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
523	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
524	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
525	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
526	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
527	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
528	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
529	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
530	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
531	C₂²	—	2	2	no	—
532	C₂²	—	2	4	no	—
533	C₂²	—	2	8	no	—
534	C₂²	—	2	16	no	—
535	C₂²	—	4	4	no	—
536	C₂²	—	8	8	no	—
537	C₂²	C₂²×C₁₃×#41	1	4	yes	—
538	C₂²	C₂²×C₁₃×#41	1	2	yes	—
539	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
540	C₄	—	2	8	no	—
541	C₄	—	2	8	no	—
542	C₄	—	2	8	no	—
543	C₄	—	2	16	no	—
544	C₄	—	2	8	no	—
545	C₄	C₂²×C₁₃×#41	1	2	yes	—
546	C₄	C₂²×C₁₃×#41	1	4	yes	—
547	C₄	C₂²×C₁₃×#41	1	2	yes	—
548	C₂	—	2	4	no	—
549	C₂	—	2	2	no	—
550	C₂	—	4	8	no	—
551	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
552	C₂	C₁₃×2₋¹⁺⁶	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
prime radical	C₁₃×#3449	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3510	C₂	semidirect
2. C₁₃×#3509	C₂	semidirect
3. C₁₃×#3507	C₂	semidirect
4. C₁₃×#3495	C₂	semidirect
5. C₁₃×#3491	C₂	semidirect
6. C₁₃×#3461	C₂	semidirect
7. C₁₃×#3458	C₂	semidirect
9. C₂×C₁₃×#536	C₂	semidirect
10. C₁₃×#3428	C₂	semidirect
11. C₂×C₁₃×#519	C₂	semidirect
14. C₁₃×#559	C₂²	semidirect
15. C₁₃×#557	C₂²	semidirect
16. C₁₃×#556	C₂²	semidirect
17. C₁₃×#556	C₂²	semidirect
18. C₁₃×#554	C₂²	semidirect
19. C₁₃×#552	C₂²	semidirect
20. C₁₃×#552	C₂²	semidirect
21. C₁₃×#551	C₂²	semidirect
22. C₁₃×#544	C₂²	semidirect
23. C₁₃×#544	C₂²	semidirect
25. C₁₃×#542	C₂²	semidirect
26. C₁₃×#541	C₂²	semidirect
27. C₁₃×#539	C₂²	semidirect
32. C₁₃×#536	C₂²	semidirect
33. C₁₃×#536	C₂²	semidirect
36. C₁₃×#533	C₂²	semidirect
37. C₁₃×#533	C₂²	semidirect
38. C₁₃×#533	C₂²	semidirect
40. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
41. C₁₃×#529	C₂²	semidirect
42. C₁₃×#529	C₂²	semidirect
43. C₂×C₁₃×#124	C₂²	semidirect
46. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
48. C₁₃×#520	C₂²	semidirect
49. C₁₃×#519	C₂²	semidirect
50. C₁₃×#519	C₂²	semidirect
51. C₁₃×#519	C₂²	semidirect
53. C₁₃×#518	C₂²	semidirect
55. C₄×C₁₃×#41	C₂²	semidirect
56. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
57. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
62. C₂×C₁₃×#117	C₂²	semidirect
150. #62860	C₁₃	direct (N × H)
216. #3510	C₂×C₁₃	semidirect
217. #3509	C₂×C₁₃	semidirect
218. #3507	C₂×C₁₃	semidirect
219. #3495	C₂×C₁₃	semidirect
220. #3491	C₂×C₁₃	semidirect
221. #3461	C₂×C₁₃	semidirect
222. #3458	C₂×C₁₃	semidirect
224. C₂×#536	C₂×C₁₃	semidirect
225. #3428	C₂×C₁₃	semidirect
226. C₂×#519	C₂×C₁₃	semidirect
268. #559	C₂²×C₁₃	semidirect
269. #557	C₂²×C₁₃	semidirect
270. #556	C₂²×C₁₃	semidirect
271. #556	C₂²×C₁₃	semidirect
272. #554	C₂²×C₁₃	semidirect
273. #552	C₂²×C₁₃	semidirect
274. #552	C₂²×C₁₃	semidirect
275. #551	C₂²×C₁₃	semidirect
276. #544	C₂²×C₁₃	semidirect
277. #544	C₂²×C₁₃	semidirect
279. #542	C₂²×C₁₃	semidirect
280. #541	C₂²×C₁₃	semidirect
281. #539	C₂²×C₁₃	semidirect
286. #536	C₂²×C₁₃	semidirect
287. #536	C₂²×C₁₃	semidirect
290. #533	C₂²×C₁₃	semidirect
291. #533	C₂²×C₁₃	semidirect
292. #533	C₂²×C₁₃	semidirect
294. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
295. #529	C₂²×C₁₃	semidirect
296. #529	C₂²×C₁₃	semidirect
297. C₂×#124	C₂²×C₁₃	semidirect
300. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
302. #520	C₂²×C₁₃	semidirect
303. #519	C₂²×C₁₃	semidirect
304. #519	C₂²×C₁₃	semidirect
305. #519	C₂²×C₁₃	semidirect
307. #518	C₂²×C₁₃	semidirect
309. C₄×#41	C₂²×C₁₃	semidirect
310. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
311. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
316. C₂×#117	C₂²×C₁₃	semidirect
491. C₁₃	#62860	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3510	2
C₁₃×#3509	2
C₁₃×#3507	2
C₁₃×#3495	2
C₁₃×#3491	2
C₁₃×#3461	2
C₁₃×#3458	2
C₁₃×#3449	2
C₂×C₁₃×#536	2
C₁₃×#3428	2
C₂×C₁₃×#519	2
#62860	13

Subgroups — C13×#62860 #15749199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62860 #15749199