Subgroups — C₁₃×#62850 #15749189

Order 3328.

6846 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3524	C₂	1	8	yes	maximal, complemented
2	C₁₃×#3523	C₂	1	8	yes	maximal, complemented
3	C₁₃×#3518	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3516	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3507	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3497	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3493	C₂	1	6	yes	maximal, complemented
9	C₁₃×#3486	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3461	C₂	1	6	yes	maximal, complemented
11	C₁₃×#3455	C₂	1	6	yes	maximal, complemented
12	C₄×C₁₃×2₋¹⁺⁴	C₂	1	2	yes	maximal, complemented
13	C₂×C₁₃×#519	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
15	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#559	C₂²	1	12	yes	complemented
17	Q₈²×C₁₃	C₂²	1	4	yes	complemented
18	C₁₃×#557	C₂²	1	12	yes	complemented
19	C₁₃×#557	C₂²	1	8	yes	complemented
20	C₁₃×#557	C₂²	1	4	yes	complemented
21	C₁₃×#556	C₂²	1	24	yes	—
22	C₁₃×#556	C₂²	1	12	yes	complemented
23	C₁₃×#556	C₂²	1	24	yes	complemented
24	C₁₃×#555	C₂²	1	24	yes	—
25	C₁₃×#554	C₂²	1	12	yes	complemented
26	C₁₃×#553	C₂²	1	24	yes	—
27	C₁₃×#552	C₂²	1	24	yes	—
28	C₁₃×#552	C₂²	1	24	yes	complemented
29	C₁₃×#550	C₂²	1	4	yes	complemented
30	D₄×Q₈×C₁₃	C₂²	1	8	yes	—
31	D₄×Q₈×C₁₃	C₂²	1	8	yes	—
32	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
33	C₁₃×#548	C₂²	1	8	yes	—
34	C₁₃×#548	C₂²	1	8	yes	—
35	C₁₃×#548	C₂²	1	8	yes	complemented
36	C₁₃×#544	C₂²	1	6	yes	—
37	C₁₃×#542	C₂²	1	12	yes	—
38	C₁₃×#542	C₂²	1	12	yes	—
39	C₁₃×#542	C₂²	1	24	yes	complemented
40	C₁₃×#541	C₂²	1	12	yes	—
41	C₁₃×#541	C₂²	1	24	yes	complemented
42	C₁₃×#540	C₂²	1	12	yes	—
43	C₁₃×#539	C₂²	1	12	yes	—
44	C₁₃×#539	C₂²	1	12	yes	—
45	C₁₃×#538	C₂²	1	4	yes	—
46	C₁₃×#538	C₂²	1	12	yes	—
47	C₁₃×#537	C₂²	1	6	yes	—
48	C₁₃×#536	C₂²	1	12	yes	—
49	C₁₃×#533	C₂²	1	6	yes	—
50	C₁₃×#533	C₂²	1	24	yes	complemented
51	C₁₃×#532	C₂²	1	6	yes	—
52	C₁₃×#529	C₂²	1	24	yes	—
53	C₁₃×#529	C₂²	1	24	yes	—
54	C₁₃×#529	C₂²	1	24	yes	—
55	C₁₃×#529	C₂²	1	24	yes	complemented
56	C₁₃×#525	C₂²	1	12	yes	—
57	C₁₃×#520	C₂²	1	12	yes	—
58	C₁₃×#520	C₂²	1	8	yes	complemented
59	C₁₃×#519	C₂²	1	8	yes	—
60	C₁₃×#519	C₂²	1	8	yes	—
61	C₁₃×#519	C₂²	1	2	yes	—
62	C₁₃×#519	C₂²	1	8	yes	complemented
63	C₄×C₁₃×#41	C₂²	1	12	yes	—
64	C₄×C₁₃×#41	C₂²	1	8	yes	complemented
65	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
66	C₂×C₄×Q₈×C₁₃	C₂²	1	3	yes	—
67	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
68	C₂×C₄×Q₈×C₁₃	C₂²	1	3	yes	—
69	C₂×C₄×Q₈×C₁₃	C₂²	1	8	yes	complemented
70	C₂×C₁₃×#117	C₂²	1	3	yes	—
71	C₂×C₁₃×#117	C₂²	1	3	yes	—
72	C₁₃×2₋¹⁺⁴	—	2	16	no	—
73	C₂×C₁₃×#41	C₂³	1	12	yes	—
74	C₂×C₁₃×#41	C₂³	1	8	yes	—
75	C₂²×Q₈×C₁₃	—	2	8	no	—
76	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
77	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
78	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
79	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
81	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
82	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
83	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
84	C₁₃×C₄⋊Q₈	C₂³	1	24	yes	—
85	C₁₃×C₄⋊Q₈	C₂³	1	24	yes	—
86	C₁₃×#127	C₂³	1	6	yes	—
87	C₁₃×#126	C₂³	1	8	yes	—
88	C₁₃×#126	C₂³	1	24	yes	—
89	C₁₃×#126	C₂³	1	24	yes	—
90	C₁₃×#126	C₂³	1	24	yes	—
91	C₁₃×#126	C₂³	1	48	yes	—
92	C₁₃×#125	C₂³	1	24	yes	—
93	C₁₃×#125	C₂³	1	24	yes	—
94	C₁₃×#125	C₂³	1	24	yes	—
95	C₁₃×#125	C₂³	1	24	yes	—
96	C₁₃×#125	C₂³	1	12	yes	—
97	C₁₃×#124	C₂³	1	8	yes	—
98	C₁₃×#124	C₂³	1	24	yes	—
99	C₁₃×#124	C₂³	1	24	yes	—
100	C₁₃×#124	C₂³	1	24	yes	—
101	C₁₃×#124	C₂³	1	12	yes	—
102	C₁₃×#123	C₂³	1	24	yes	—
103	C₁₃×#123	C₂³	1	8	yes	—
104	C₁₃×#123	C₂³	1	24	yes	—
105	C₁₃×#123	C₂³	1	24	yes	—
106	C₁₃×#123	C₂³	1	24	yes	—
107	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
108	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
109	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
110	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
111	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
112	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
113	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
114	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
115	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
116	C₁₃×#121	C₂³	1	12	yes	—
117	C₁₃×#121	C₂³	1	12	yes	—
118	C₁₃×#121	C₂³	1	8	yes	—
119	C₁₃×#121	C₂³	1	12	yes	—
120	C₁₃×#121	C₂³	1	24	yes	—
121	C₁₃×#121	C₂³	1	24	yes	—
122	C₁₃×#121	C₂³	1	4	yes	—
123	C₁₃×#120	C₂³	1	8	yes	—
124	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
125	C₄×Q₈×C₁₃	C₂³	1	24	yes	—
126	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
127	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
128	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
129	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
130	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
131	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
132	C₄×Q₈×C₁₃	C₂³	1	24	yes	—
133	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
134	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
135	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
136	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
137	C₄×Q₈×C₁₃	C₂³	1	24	yes	—
138	C₄×D₄×C₁₃	C₂³	1	8	yes	—
139	C₄×D₄×C₁₃	C₂³	1	12	yes	—
140	C₄×D₄×C₁₃	C₂³	1	24	yes	—
141	C₄×D₄×C₁₃	C₂³	1	12	yes	—
142	C₄×D₄×C₁₃	C₂³	1	24	yes	—
143	C₄×D₄×C₁₃	C₂³	1	24	yes	—
144	C₄×D₄×C₁₃	C₂³	1	24	yes	—
145	C₄×D₄×C₁₃	C₂³	1	12	yes	—
146	C₄×D₄×C₁₃	C₂³	1	12	yes	—
147	C₄×D₄×C₁₃	C₂³	1	24	yes	—
148	C₁₃×#117	C₂³	1	12	yes	—
149	C₁₃×#117	C₂³	1	12	yes	—
150	C₁₃×#117	C₂³	1	24	yes	—
151	C₁₃×#117	C₂³	1	12	yes	—
152	C₁₃×#117	C₂³	1	24	yes	—
153	C₁₃×#117	C₂³	1	24	yes	—
154	C₁₃×#117	C₂³	1	48	yes	—
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
160	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₁₃×C₂²⋊C₄	C₂³	1	3	yes	—
162	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
163	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
164	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
165	C₂×C₄²×C₁₃	C₂³	1	24	yes	—
166	#62850	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₁₃×#41	—	2	32	no	—
169	C₁₃×#41	—	2	48	no	—
170	C₂×Q₈×C₁₃	—	2	32	no	—
171	C₂×Q₈×C₁₃	—	2	32	no	—
172	C₂×Q₈×C₁₃	—	2	12	no	—
173	C₂×Q₈×C₁₃	#41	1	8	yes	—
174	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
175	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
176	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
177	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
178	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
179	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
180	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
181	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
182	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
183	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
184	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₁₃	—	2	12	no	—
186	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
188	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
191	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
194	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
195	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
196	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
197	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
198	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
199	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
200	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
201	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
202	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
203	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
204	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
205	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
206	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
207	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
208	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
209	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
210	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
211	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
212	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
213	C₁₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
214	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
215	C₁₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
216	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
217	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
218	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
219	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
220	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
221	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
222	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
223	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
224	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
225	C₄²×C₁₃	C₂⁴	1	12	yes	—
226	C₄²×C₁₃	C₂⁴	1	8	yes	—
227	C₄²×C₁₃	C₂⁴	1	24	yes	—
228	C₄²×C₁₃	C₂⁴	1	24	yes	—
229	C₄²×C₁₃	C₂⁴	1	24	yes	—
230	C₄²×C₁₃	C₂⁴	1	6	yes	—
231	C₄²×C₁₃	C₂⁴	1	6	yes	—
232	#3524	C₂×C₁₃	1	8	yes	complemented
233	#3523	C₂×C₁₃	1	8	yes	complemented
234	#3518	C₂×C₁₃	1	8	yes	complemented
235	#3516	C₂×C₁₃	1	8	yes	complemented
236	#3507	C₂×C₁₃	1	6	yes	complemented
237	#3502	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#3497	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#3493	C₂×C₁₃	1	6	yes	complemented
240	#3486	C₂×C₁₃	1	2	yes	complemented
241	#3461	C₂×C₁₃	1	6	yes	complemented
242	#3455	C₂×C₁₃	1	6	yes	complemented
243	C₄×2₋¹⁺⁴	C₂×C₁₃	1	2	yes	complemented
244	C₂×#519	C₂×C₁₃	1	1	yes	characteristic, complemented
245	C₂³×C₁₃	—	2	2	no	—
246	C₂³×C₁₃	—	4	1	no	—
247	C₂³×C₁₃	—	4	1	no	—
248	C₂³×C₁₃	C₂⁵	1	2	yes	—
249	C₂³×C₁₃	C₂⁵	1	8	yes	—
250	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
251	Q₈×C₁₃	—	2	24	no	—
252	Q₈×C₁₃	—	2	24	no	—
253	Q₈×C₁₃	—	4	4	no	—
254	Q₈×C₁₃	—	4	12	no	—
255	Q₈×C₁₃	C₂×#41	1	16	yes	—
256	D₄×C₁₃	—	2	16	no	—
257	D₄×C₁₃	—	2	24	no	—
258	D₄×C₁₃	—	4	8	no	—
259	D₄×C₁₃	—	4	4	no	—
260	D₄×C₁₃	—	4	12	no	—
261	D₄×C₁₃	—	4	8	no	—
262	C₂×C₄×C₁₃	—	2	6	no	—
263	C₂×C₄×C₁₃	—	2	24	no	—
264	C₂×C₄×C₁₃	—	2	48	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	3	no	—
267	C₂×C₄×C₁₃	—	4	24	no	—
268	C₂×C₄×C₁₃	—	4	8	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	4	3	no	—
271	C₂×C₄×C₁₃	C₂×#41	1	12	yes	—
272	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
273	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
274	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
276	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
277	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
278	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
279	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
280	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
281	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
282	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
283	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
284	#559	C₂²×C₁₃	1	12	yes	complemented
285	Q₈²	C₂²×C₁₃	1	4	yes	complemented
286	#557	C₂²×C₁₃	1	4	yes	complemented
287	#557	C₂²×C₁₃	1	8	yes	complemented
288	#557	C₂²×C₁₃	1	12	yes	complemented
289	#556	C₂²×C₁₃	1	24	yes	—
290	#556	C₂²×C₁₃	1	24	yes	complemented
291	#556	C₂²×C₁₃	1	12	yes	complemented
292	#555	C₂²×C₁₃	1	24	yes	—
293	#554	C₂²×C₁₃	1	12	yes	complemented
294	#553	C₂²×C₁₃	1	24	yes	—
295	#552	C₂²×C₁₃	1	24	yes	—
296	#552	C₂²×C₁₃	1	24	yes	complemented
297	#550	C₂²×C₁₃	1	4	yes	complemented
298	D₄×Q₈	C₂²×C₁₃	1	8	yes	—
299	D₄×Q₈	C₂²×C₁₃	1	8	yes	—
300	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
301	#548	C₂²×C₁₃	1	8	yes	—
302	#548	C₂²×C₁₃	1	8	yes	—
303	#548	C₂²×C₁₃	1	8	yes	complemented
304	#544	C₂²×C₁₃	1	6	yes	—
305	#542	C₂²×C₁₃	1	12	yes	—
306	#542	C₂²×C₁₃	1	12	yes	—
307	#542	C₂²×C₁₃	1	24	yes	complemented
308	#541	C₂²×C₁₃	1	12	yes	—
309	#541	C₂²×C₁₃	1	24	yes	complemented
310	#540	C₂²×C₁₃	1	12	yes	—
311	#539	C₂²×C₁₃	1	12	yes	—
312	#539	C₂²×C₁₃	1	12	yes	—
313	#538	C₂²×C₁₃	1	4	yes	—
314	#538	C₂²×C₁₃	1	12	yes	—
315	#537	C₂²×C₁₃	1	6	yes	—
316	#536	C₂²×C₁₃	1	12	yes	—
317	#533	C₂²×C₁₃	1	6	yes	—
318	#533	C₂²×C₁₃	1	24	yes	complemented
319	#532	C₂²×C₁₃	1	6	yes	—
320	#529	C₂²×C₁₃	1	24	yes	—
321	#529	C₂²×C₁₃	1	24	yes	—
322	#529	C₂²×C₁₃	1	24	yes	—
323	#529	C₂²×C₁₃	1	24	yes	complemented
324	#525	C₂²×C₁₃	1	12	yes	—
325	#520	C₂²×C₁₃	1	12	yes	—
326	#520	C₂²×C₁₃	1	8	yes	complemented
327	#519	C₂²×C₁₃	1	8	yes	—
328	#519	C₂²×C₁₃	1	8	yes	—
329	#519	C₂²×C₁₃	1	2	yes	—
330	#519	C₂²×C₁₃	1	8	yes	complemented
331	C₄×#41	C₂²×C₁₃	1	12	yes	—
332	C₄×#41	C₂²×C₁₃	1	8	yes	complemented
333	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×C₄×Q₈	C₂²×C₁₃	1	3	yes	—
335	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×C₄×Q₈	C₂²×C₁₃	1	3	yes	—
337	C₂×C₄×Q₈	C₂²×C₁₃	1	8	yes	complemented
338	C₂×#117	C₂²×C₁₃	1	3	yes	—
339	C₂×#117	C₂²×C₁₃	1	3	yes	—
340	C₂²×C₁₃	—	2	1	no	—
341	C₂²×C₁₃	—	2	1	no	—
342	C₂²×C₁₃	—	2	2	no	—
343	C₂²×C₁₃	—	2	8	no	—
344	C₂²×C₁₃	—	2	8	no	—
345	C₂²×C₁₃	—	2	8	no	—
346	C₂²×C₁₃	—	2	2	no	—
347	C₂²×C₁₃	—	2	2	no	—
348	C₂²×C₁₃	—	4	4	no	—
349	C₂²×C₁₃	C₂²×#41	1	2	yes	—
350	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
351	C₄×C₁₃	—	2	8	no	—
352	C₄×C₁₃	—	2	6	no	—
353	C₄×C₁₃	—	2	6	no	—
354	C₄×C₁₃	—	2	2	no	—
355	C₄×C₁₃	—	2	8	no	—
356	C₄×C₁₃	—	2	1	no	—
357	C₄×C₁₃	—	2	6	no	—
358	C₄×C₁₃	—	2	8	no	—
359	C₄×C₁₃	—	2	1	no	—
360	C₄×C₁₃	C₂²×#41	1	12	yes	—
361	2₋¹⁺⁴	—	2	16	no	—
362	C₂×#41	C₂³×C₁₃	1	12	yes	—
363	C₂×#41	C₂³×C₁₃	1	8	yes	—
364	C₂²×Q₈	—	2	8	no	—
365	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
366	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
367	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
368	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
369	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
370	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
371	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
372	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
373	C₄⋊Q₈	C₂³×C₁₃	1	24	yes	—
374	C₄⋊Q₈	C₂³×C₁₃	1	24	yes	—
375	#127	C₂³×C₁₃	1	6	yes	—
376	#126	C₂³×C₁₃	1	8	yes	—
377	#126	C₂³×C₁₃	1	24	yes	—
378	#126	C₂³×C₁₃	1	24	yes	—
379	#126	C₂³×C₁₃	1	24	yes	—
380	#126	C₂³×C₁₃	1	48	yes	—
381	#125	C₂³×C₁₃	1	24	yes	—
382	#125	C₂³×C₁₃	1	24	yes	—
383	#125	C₂³×C₁₃	1	24	yes	—
384	#125	C₂³×C₁₃	1	24	yes	—
385	#125	C₂³×C₁₃	1	12	yes	—
386	#124	C₂³×C₁₃	1	8	yes	—
387	#124	C₂³×C₁₃	1	24	yes	—
388	#124	C₂³×C₁₃	1	24	yes	—
389	#124	C₂³×C₁₃	1	24	yes	—
390	#124	C₂³×C₁₃	1	12	yes	—
391	#123	C₂³×C₁₃	1	24	yes	—
392	#123	C₂³×C₁₃	1	8	yes	—
393	#123	C₂³×C₁₃	1	24	yes	—
394	#123	C₂³×C₁₃	1	24	yes	—
395	#123	C₂³×C₁₃	1	24	yes	—
396	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
397	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
398	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
399	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
400	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
401	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
402	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
403	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
404	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
405	#121	C₂³×C₁₃	1	12	yes	—
406	#121	C₂³×C₁₃	1	12	yes	—
407	#121	C₂³×C₁₃	1	8	yes	—
408	#121	C₂³×C₁₃	1	12	yes	—
409	#121	C₂³×C₁₃	1	24	yes	—
410	#121	C₂³×C₁₃	1	24	yes	—
411	#121	C₂³×C₁₃	1	4	yes	—
412	#120	C₂³×C₁₃	1	8	yes	—
413	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
414	C₄×Q₈	C₂³×C₁₃	1	24	yes	—
415	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
416	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
417	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
418	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
419	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
420	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
421	C₄×Q₈	C₂³×C₁₃	1	24	yes	—
422	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
423	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
424	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
425	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
426	C₄×Q₈	C₂³×C₁₃	1	24	yes	—
427	C₄×D₄	C₂³×C₁₃	1	8	yes	—
428	C₄×D₄	C₂³×C₁₃	1	12	yes	—
429	C₄×D₄	C₂³×C₁₃	1	24	yes	—
430	C₄×D₄	C₂³×C₁₃	1	12	yes	—
431	C₄×D₄	C₂³×C₁₃	1	24	yes	—
432	C₄×D₄	C₂³×C₁₃	1	24	yes	—
433	C₄×D₄	C₂³×C₁₃	1	24	yes	—
434	C₄×D₄	C₂³×C₁₃	1	12	yes	—
435	C₄×D₄	C₂³×C₁₃	1	12	yes	—
436	C₄×D₄	C₂³×C₁₃	1	24	yes	—
437	#117	C₂³×C₁₃	1	12	yes	—
438	#117	C₂³×C₁₃	1	12	yes	—
439	#117	C₂³×C₁₃	1	24	yes	—
440	#117	C₂³×C₁₃	1	12	yes	—
441	#117	C₂³×C₁₃	1	24	yes	—
442	#117	C₂³×C₁₃	1	24	yes	—
443	#117	C₂³×C₁₃	1	48	yes	—
444	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
445	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
446	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
447	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
448	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
450	C₂×C₂²⋊C₄	C₂³×C₁₃	1	3	yes	—
451	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
452	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
453	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
454	C₂×C₄²	C₂³×C₁₃	1	24	yes	—
455	C₂×C₁₃	—	2	2	no	—
456	C₂×C₁₃	—	4	8	no	—
457	C₂×C₁₃	—	4	2	no	—
458	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
459	C₂×C₁₃	2₋¹⁺⁶	1	1	yes	characteristic
460	C₂×C₁₃	2₋¹⁺⁶	1	1	yes	characteristic
461	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
462	#41	—	2	32	no	—
463	#41	—	2	48	no	—
464	C₂×Q₈	—	2	32	no	—
465	C₂×Q₈	—	2	32	no	—
466	C₂×Q₈	—	2	12	no	—
467	C₂×Q₈	C₁₃×#41	1	8	yes	—
468	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
469	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
470	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
471	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
472	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
473	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
474	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
475	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
476	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
477	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
478	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
479	C₂²×C₄	—	2	12	no	—
480	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
481	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
482	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
483	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
484	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
485	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
486	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
487	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
488	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
489	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
490	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
491	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
492	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
493	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
494	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
495	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
496	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
497	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
498	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
499	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
500	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
501	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
502	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
503	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
504	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
505	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
506	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
507	C₂²⋊C₄	C₂⁴×C₁₃	1	2	yes	—
508	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
509	C₂²⋊C₄	C₂⁴×C₁₃	1	2	yes	—
510	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
511	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
512	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
513	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
514	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
515	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
516	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
517	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
518	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
519	C₄²	C₂⁴×C₁₃	1	12	yes	—
520	C₄²	C₂⁴×C₁₃	1	8	yes	—
521	C₄²	C₂⁴×C₁₃	1	24	yes	—
522	C₄²	C₂⁴×C₁₃	1	24	yes	—
523	C₄²	C₂⁴×C₁₃	1	24	yes	—
524	C₄²	C₂⁴×C₁₃	1	6	yes	—
525	C₄²	C₂⁴×C₁₃	1	6	yes	—
526	C₁₃	#62850	1	1	yes	characteristic, direct product factor, Sylow
527	C₂³	—	2	2	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	4	1	no	—
530	C₂³	C₂⁵×C₁₃	1	2	yes	—
531	C₂³	C₂⁵×C₁₃	1	8	yes	—
532	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
533	Q₈	—	2	24	no	—
534	Q₈	—	2	24	no	—
535	Q₈	—	4	4	no	—
536	Q₈	—	4	12	no	—
537	Q₈	C₂×C₁₃×#41	1	16	yes	—
538	D₄	—	2	16	no	—
539	D₄	—	2	24	no	—
540	D₄	—	4	8	no	—
541	D₄	—	4	4	no	—
542	D₄	—	4	12	no	—
543	D₄	—	4	8	no	—
544	C₂×C₄	—	2	6	no	—
545	C₂×C₄	—	2	24	no	—
546	C₂×C₄	—	2	48	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	3	no	—
549	C₂×C₄	—	4	24	no	—
550	C₂×C₄	—	4	8	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	3	no	—
553	C₂×C₄	C₂×C₁₃×#41	1	12	yes	—
554	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
555	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
556	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
557	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
558	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
559	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
560	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
561	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
562	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
563	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
564	C₂²	—	2	1	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	2	8	no	—
568	C₂²	—	2	8	no	—
569	C₂²	—	2	8	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	4	4	no	—
573	C₂²	C₂²×C₁₃×#41	1	2	yes	—
574	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
575	C₄	—	2	8	no	—
576	C₄	—	2	6	no	—
577	C₄	—	2	6	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	8	no	—
580	C₄	—	2	1	no	—
581	C₄	—	2	6	no	—
582	C₄	—	2	8	no	—
583	C₄	—	2	1	no	—
584	C₄	C₂²×C₁₃×#41	1	12	yes	—
585	C₂	—	2	2	no	—
586	C₂	—	4	2	no	—
587	C₂	—	4	8	no	—
588	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
589	C₂	C₁₃×2₋¹⁺⁶	1	1	yes	characteristic
590	C₂	C₁₃×2₋¹⁺⁶	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
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×#3524	C₂	semidirect
2. C₁₃×#3523	C₂	semidirect
3. C₁₃×#3518	C₂	semidirect
4. C₁₃×#3516	C₂	semidirect
5. C₁₃×#3507	C₂	semidirect
6. C₁₃×#3502	C₂	semidirect
7. C₁₃×#3497	C₂	semidirect
8. C₁₃×#3493	C₂	semidirect
9. C₁₃×#3486	C₂	semidirect
10. C₁₃×#3461	C₂	semidirect
11. C₁₃×#3455	C₂	semidirect
12. C₄×C₁₃×2₋¹⁺⁴	C₂	semidirect
13. C₂×C₁₃×#519	C₂	semidirect
16. C₁₃×#559	C₂²	semidirect
17. Q₈²×C₁₃	C₂²	semidirect
18. C₁₃×#557	C₂²	semidirect
19. C₁₃×#557	C₂²	semidirect
20. C₁₃×#557	C₂²	semidirect
22. C₁₃×#556	C₂²	semidirect
23. C₁₃×#556	C₂²	semidirect
25. C₁₃×#554	C₂²	semidirect
28. C₁₃×#552	C₂²	semidirect
29. C₁₃×#550	C₂²	semidirect
32. D₄×Q₈×C₁₃	C₂²	semidirect
35. C₁₃×#548	C₂²	semidirect
39. C₁₃×#542	C₂²	semidirect
41. C₁₃×#541	C₂²	semidirect
50. C₁₃×#533	C₂²	semidirect
55. C₁₃×#529	C₂²	semidirect
58. C₁₃×#520	C₂²	semidirect
62. C₁₃×#519	C₂²	semidirect
64. C₄×C₁₃×#41	C₂²	semidirect
69. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
166. #62850	C₁₃	direct (N × H)
232. #3524	C₂×C₁₃	semidirect
233. #3523	C₂×C₁₃	semidirect
234. #3518	C₂×C₁₃	semidirect
235. #3516	C₂×C₁₃	semidirect
236. #3507	C₂×C₁₃	semidirect
237. #3502	C₂×C₁₃	semidirect
238. #3497	C₂×C₁₃	semidirect
239. #3493	C₂×C₁₃	semidirect
240. #3486	C₂×C₁₃	semidirect
241. #3461	C₂×C₁₃	semidirect
242. #3455	C₂×C₁₃	semidirect
243. C₄×2₋¹⁺⁴	C₂×C₁₃	semidirect
244. C₂×#519	C₂×C₁₃	semidirect
284. #559	C₂²×C₁₃	semidirect
285. Q₈²	C₂²×C₁₃	semidirect
286. #557	C₂²×C₁₃	semidirect
287. #557	C₂²×C₁₃	semidirect
288. #557	C₂²×C₁₃	semidirect
290. #556	C₂²×C₁₃	semidirect
291. #556	C₂²×C₁₃	semidirect
293. #554	C₂²×C₁₃	semidirect
296. #552	C₂²×C₁₃	semidirect
297. #550	C₂²×C₁₃	semidirect
300. D₄×Q₈	C₂²×C₁₃	semidirect
303. #548	C₂²×C₁₃	semidirect
307. #542	C₂²×C₁₃	semidirect
309. #541	C₂²×C₁₃	semidirect
318. #533	C₂²×C₁₃	semidirect
323. #529	C₂²×C₁₃	semidirect
326. #520	C₂²×C₁₃	semidirect
330. #519	C₂²×C₁₃	semidirect
332. C₄×#41	C₂²×C₁₃	semidirect
337. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
526. C₁₃	#62850	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×#3524	2
C₁₃×#3523	2
C₁₃×#3518	2
C₁₃×#3516	2
C₁₃×#3507	2
C₁₃×#3502	2
C₁₃×#3497	2
C₁₃×#3493	2
C₁₃×#3486	2
C₁₃×#3461	2
C₁₃×#3455	2
C₄×C₁₃×2₋¹⁺⁴	2
C₂×C₁₃×#519	2
#62850	13

Subgroups — C13×#62850 #15749189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62850 #15749189