Subgroups — C₁₃×#61286 #15747625

Order 3328.

1754 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3507	C₂	1	2	yes	maximal
2	C₁₃×#3356	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3352	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3342	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3338	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3336	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3160	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3097	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3078	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3059	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2931	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#2913	C₂	1	2	yes	maximal, complemented
14	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#131	C₂²	1	2	yes	—
16	C₁₃×#559	—	2	2	no	—
17	C₁₃×#557	—	2	2	no	—
18	C₁₃×#556	—	2	4	no	—
19	C₁₃×#556	C₂²	1	4	yes	—
20	C₁₃×#554	C₂²	1	4	yes	—
21	C₁₃×#552	C₂²	1	8	yes	—
22	C₁₃×#539	—	2	4	no	—
23	C₁₃×#536	C₂²	1	4	yes	—
24	C₁₃×#533	C₂²	1	2	yes	—
25	C₁₃×#532	C₂²	1	1	yes	characteristic
26	C₁₃×#529	—	2	4	no	—
27	C₁₃×#520	C₂²	1	4	yes	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
29	C₁₃×#500	C₂²	1	1	yes	characteristic
30	C₁₃×#500	C₂²	1	1	yes	characteristic
31	C₁₃×#499	C₂²	1	2	yes	—
32	C₁₃×#499	C₂²	1	2	yes	—
33	C₁₃×#498	C₂²	1	2	yes	—
34	C₁₃×#485	C₂²	1	8	yes	—
35	C₁₃×#485	C₂²	1	8	yes	—
36	C₁₃×#484	C₂²	1	8	yes	—
37	C₁₃×#483	C₂²	1	8	yes	—
38	C₁₃×#479	C₂²	1	8	yes	—
39	C₁₃×#477	C₂²	1	4	yes	—
40	C₁₃×#475	C₂²	1	4	yes	—
41	C₁₃×#470	C₂²	1	8	yes	—
42	C₁₃×#467	C₂²	1	4	yes	—
43	C₁₃×#467	C₂²	1	4	yes	—
44	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
45	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
46	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
47	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
48	C₁₃×#436	C₂²	1	2	yes	—
49	C₁₃×#436	C₂²	1	2	yes	—
50	C₈×D₄×C₁₃	C₂²	1	2	yes	—
51	C₈×D₄×C₁₃	C₂²	1	2	yes	—
52	C₁₃×#428	C₂²	1	4	yes	—
53	C₁₃×#428	C₂²	1	8	yes	—
54	C₁₃×#427	C₂²	1	2	yes	—
55	C₁₃×#427	C₂²	1	4	yes	—
56	C₁₃×#427	C₂²	1	2	yes	—
57	C₂×C₁₃×#107	C₂²	1	4	yes	—
58	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
59	C₁₃×#423	C₂²	1	1	yes	characteristic
60	C₁₃×#419	C₂²	1	4	yes	—
61	C₂×C₁₃×#103	C₂²	1	2	yes	—
62	C₁₃×#408	C₂²	1	2	yes	—
63	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
64	C₂×C₁₃×#41	C₂³	1	2	yes	—
65	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
66	C₂×C₁₃×Q₁₆	—	2	4	no	—
67	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
68	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
69	C₁₃×#131	—	2	8	no	—
70	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
71	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×C₄⋊Q₈	—	2	4	no	—
76	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
77	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
78	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
79	C₁₃×#127	D₄	1	1	yes	characteristic
80	C₁₃×#126	—	2	8	no	—
81	C₁₃×#126	—	2	8	no	—
82	C₁₃×#125	—	2	4	no	—
83	C₁₃×#125	—	2	8	no	—
84	C₁₃×#125	C₂³	1	4	yes	—
85	C₁₃×#124	—	2	4	no	—
86	C₁₃×#124	—	2	4	no	—
87	C₁₃×#124	D₄	1	2	yes	—
88	C₁₃×#123	—	2	8	no	—
89	C₁₃×#123	—	2	8	no	—
90	C₁₃×C₂²⋊Q₈	—	2	2	no	—
91	C₁₃×C₂²⋊Q₈	—	2	2	no	—
92	C₁₃×C₂²⋊Q₈	—	2	8	no	—
93	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
94	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
95	C₁₃×#121	D₄	1	2	yes	—
96	C₁₃×#121	D₄	1	2	yes	—
97	C₄×Q₈×C₁₃	—	2	4	no	—
98	C₄×Q₈×C₁₃	—	2	4	no	—
99	C₄×Q₈×C₁₃	—	2	2	no	—
100	C₄×Q₈×C₁₃	—	2	2	no	—
101	C₄×Q₈×C₁₃	—	2	2	no	—
102	C₄×Q₈×C₁₃	—	2	2	no	—
103	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
104	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
105	C₄×D₄×C₁₃	—	2	8	no	—
106	C₄×D₄×C₁₃	—	2	4	no	—
107	C₄×D₄×C₁₃	—	2	4	no	—
108	C₄×D₄×C₁₃	C₂³	1	2	yes	—
109	C₄×D₄×C₁₃	C₂³	1	2	yes	—
110	C₁₃×#117	—	2	8	no	—
111	C₁₃×#117	C₂³	1	4	yes	—
112	C₁₃×#117	C₂³	1	8	yes	—
113	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
116	C₂×C₄²×C₁₃	—	2	2	no	—
117	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
118	C₁₃×#107	C₂³	1	2	yes	—
119	C₁₃×#107	C₂³	1	2	yes	—
120	C₁₃×#107	C₂³	1	2	yes	—
121	C₁₃×#107	C₂³	1	8	yes	—
122	C₁₃×#107	C₂³	1	2	yes	—
123	C₁₃×#107	C₂³	1	2	yes	—
124	C₁₃×#107	C₂³	1	2	yes	—
125	C₁₃×#106	C₂³	1	4	yes	—
126	C₁₃×#106	C₂³	1	8	yes	—
127	C₁₃×#106	C₂³	1	4	yes	—
128	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
129	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
130	C₁₃×#103	C₂³	1	4	yes	—
131	C₁₃×#103	C₂³	1	4	yes	—
132	C₁₃×#103	C₂³	1	8	yes	—
133	C₁₃×#103	C₂³	1	8	yes	—
134	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
135	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
136	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
137	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
140	#61286	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₁₃×#41	—	2	4	no	—
142	C₁₃×#41	—	2	4	no	—
143	C₂×Q₈×C₁₃	—	2	2	no	—
144	C₂×Q₈×C₁₃	—	2	2	no	—
145	C₂×Q₈×C₁₃	—	2	2	no	—
146	C₂×Q₈×C₁₃	—	2	4	no	—
147	C₂×Q₈×C₁₃	—	2	4	no	—
148	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
149	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
150	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
151	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
152	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
153	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₁₃	—	2	2	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	—	2	8	no	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₁₃×Q₁₆	—	2	4	no	—
162	C₁₃×Q₁₆	—	2	4	no	—
163	C₁₃×M₁₆	—	2	4	no	—
164	C₁₃×M₁₆	—	2	8	no	—
165	C₂×C₈×C₁₃	—	2	2	no	—
166	C₂×C₈×C₁₃	—	2	8	no	—
167	C₂×C₈×C₁₃	#41	1	4	yes	—
168	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
169	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
171	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₁₃×C₄⋊C₄	—	2	4	no	—
174	C₁₃×C₄⋊C₄	—	2	4	no	—
175	C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₁₃×C₄⋊C₄	—	2	8	no	—
177	C₁₃×C₄⋊C₄	—	2	4	no	—
178	C₁₃×C₄⋊C₄	—	2	8	no	—
179	C₁₃×C₄⋊C₄	—	2	2	no	—
180	C₁₃×C₄⋊C₄	—	2	4	no	—
181	C₁₃×C₄⋊C₄	—	2	2	no	—
182	C₁₃×C₄⋊C₄	—	2	8	no	—
183	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
184	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
185	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
186	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
187	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
188	C₁₃×C₂²⋊C₄	—	2	8	no	—
189	C₁₃×C₂²⋊C₄	—	2	4	no	—
190	C₁₃×C₂²⋊C₄	—	2	8	no	—
191	C₁₃×C₂²⋊C₄	—	2	8	no	—
192	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
193	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
194	C₄²×C₁₃	—	2	4	no	—
195	C₄²×C₁₃	—	2	4	no	—
196	C₄²×C₁₃	—	2	8	no	—
197	C₄²×C₁₃	—	2	4	no	—
198	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
199	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
201	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
202	#3507	C₂×C₁₃	1	2	yes	—
203	#3356	C₂×C₁₃	1	4	yes	complemented
204	#3352	C₂×C₁₃	1	4	yes	complemented
205	#3342	C₂×C₁₃	1	2	yes	complemented
206	#3338	C₂×C₁₃	1	2	yes	complemented
207	#3336	C₂×C₁₃	1	4	yes	complemented
208	#3160	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#3097	C₂×C₁₃	1	4	yes	complemented
210	#3078	C₂×C₁₃	1	2	yes	complemented
211	#3059	C₂×C₁₃	1	2	yes	complemented
212	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#2931	C₂×C₁₃	1	1	yes	characteristic
214	#2913	C₂×C₁₃	1	2	yes	complemented
215	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
216	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
217	Q₈×C₁₃	—	2	4	no	—
218	Q₈×C₁₃	—	2	4	no	—
219	Q₈×C₁₃	—	2	4	no	—
220	Q₈×C₁₃	—	4	4	no	—
221	Q₈×C₁₃	—	4	4	no	—
222	Q₈×C₁₃	—	8	2	no	—
223	D₄×C₁₃	—	2	8	no	—
224	D₄×C₁₃	—	2	4	no	—
225	D₄×C₁₃	—	2	4	no	—
226	D₄×C₁₃	—	4	2	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	2	4	no	—
230	C₂×C₄×C₁₃	—	2	4	no	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	4	no	—
233	C₂×C₄×C₁₃	—	2	4	no	—
234	C₂×C₄×C₁₃	—	4	1	no	—
235	C₂×C₄×C₁₃	—	4	4	no	—
236	C₂×C₄×C₁₃	—	8	2	no	—
237	C₂×C₄×C₁₃	—	8	8	no	—
238	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
240	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
245	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
246	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
247	C₈×C₁₃	—	2	4	no	—
248	C₈×C₁₃	—	2	1	no	—
249	C₈×C₁₃	—	2	1	no	—
250	C₈×C₁₃	C₂×#41	1	2	yes	—
251	C₈×C₁₃	C₂×#41	1	2	yes	—
252	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
253	C₂×#131	C₂²×C₁₃	1	2	yes	—
254	#559	—	2	2	no	—
255	#557	—	2	2	no	—
256	#556	—	2	4	no	—
257	#556	C₂²×C₁₃	1	4	yes	—
258	#554	C₂²×C₁₃	1	4	yes	—
259	#552	C₂²×C₁₃	1	8	yes	—
260	#539	—	2	4	no	—
261	#536	C₂²×C₁₃	1	4	yes	—
262	#533	C₂²×C₁₃	1	2	yes	—
263	#532	C₂²×C₁₃	1	1	yes	characteristic
264	#529	—	2	4	no	—
265	#520	C₂²×C₁₃	1	4	yes	—
266	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
267	#500	C₂²×C₁₃	1	1	yes	characteristic
268	#500	C₂²×C₁₃	1	1	yes	characteristic
269	#499	C₂²×C₁₃	1	2	yes	—
270	#499	C₂²×C₁₃	1	2	yes	—
271	#498	C₂²×C₁₃	1	2	yes	—
272	#485	C₂²×C₁₃	1	8	yes	—
273	#485	C₂²×C₁₃	1	8	yes	—
274	#484	C₂²×C₁₃	1	8	yes	—
275	#483	C₂²×C₁₃	1	8	yes	—
276	#479	C₂²×C₁₃	1	8	yes	—
277	#477	C₂²×C₁₃	1	4	yes	—
278	#475	C₂²×C₁₃	1	4	yes	—
279	#470	C₂²×C₁₃	1	8	yes	—
280	#467	C₂²×C₁₃	1	4	yes	—
281	#467	C₂²×C₁₃	1	4	yes	—
282	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
283	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
284	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
285	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
286	#436	C₂²×C₁₃	1	2	yes	—
287	#436	C₂²×C₁₃	1	2	yes	—
288	C₈×D₄	C₂²×C₁₃	1	2	yes	—
289	C₈×D₄	C₂²×C₁₃	1	2	yes	—
290	#428	C₂²×C₁₃	1	4	yes	—
291	#428	C₂²×C₁₃	1	8	yes	—
292	#427	C₂²×C₁₃	1	4	yes	—
293	#427	C₂²×C₁₃	1	2	yes	—
294	#427	C₂²×C₁₃	1	2	yes	—
295	C₂×#107	C₂²×C₁₃	1	4	yes	—
296	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
297	#423	C₂²×C₁₃	1	1	yes	characteristic
298	#419	C₂²×C₁₃	1	4	yes	—
299	C₂×#103	C₂²×C₁₃	1	2	yes	—
300	#408	C₂²×C₁₃	1	2	yes	—
301	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
302	C₂²×C₁₃	—	2	1	no	—
303	C₂²×C₁₃	—	2	1	no	—
304	C₂²×C₁₃	—	2	4	no	—
305	C₂²×C₁₃	—	2	4	no	—
306	C₂²×C₁₃	—	2	4	no	—
307	C₂²×C₁₃	#547	1	2	yes	—
308	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
309	C₄×C₁₃	—	2	1	no	—
310	C₄×C₁₃	—	2	1	no	—
311	C₄×C₁₃	—	2	4	no	—
312	C₄×C₁₃	—	2	1	no	—
313	C₄×C₁₃	—	4	4	no	—
314	C₄×C₁₃	—	4	4	no	—
315	C₄×C₁₃	—	4	4	no	—
316	C₄×C₁₃	—	4	4	no	—
317	C₄×C₁₃	#547	1	2	yes	—
318	C₄×C₁₃	#578	1	2	yes	—
319	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
320	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
321	C₂×#41	C₂³×C₁₃	1	2	yes	—
322	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
323	C₂×Q₁₆	—	2	4	no	—
324	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
325	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
326	#131	—	2	8	no	—
327	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
328	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
329	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
330	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
331	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
332	C₄⋊Q₈	—	2	4	no	—
333	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
334	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
335	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
336	#127	D₄×C₁₃	1	1	yes	characteristic
337	#126	—	2	8	no	—
338	#126	—	2	8	no	—
339	#125	—	2	4	no	—
340	#125	—	2	8	no	—
341	#125	C₂³×C₁₃	1	4	yes	—
342	#124	—	2	4	no	—
343	#124	—	2	4	no	—
344	#124	D₄×C₁₃	1	2	yes	—
345	#123	—	2	8	no	—
346	#123	—	2	8	no	—
347	C₂²⋊Q₈	—	2	2	no	—
348	C₂²⋊Q₈	—	2	2	no	—
349	C₂²⋊Q₈	—	2	8	no	—
350	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
351	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
352	#121	D₄×C₁₃	1	2	yes	—
353	#121	D₄×C₁₃	1	2	yes	—
354	C₄×Q₈	—	2	4	no	—
355	C₄×Q₈	—	2	4	no	—
356	C₄×Q₈	—	2	2	no	—
357	C₄×Q₈	—	2	2	no	—
358	C₄×Q₈	—	2	2	no	—
359	C₄×Q₈	—	2	2	no	—
360	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
361	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
362	C₄×D₄	—	2	8	no	—
363	C₄×D₄	—	2	4	no	—
364	C₄×D₄	—	2	4	no	—
365	C₄×D₄	C₂³×C₁₃	1	2	yes	—
366	C₄×D₄	C₂³×C₁₃	1	2	yes	—
367	#117	—	2	8	no	—
368	#117	C₂³×C₁₃	1	4	yes	—
369	#117	C₂³×C₁₃	1	8	yes	—
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
372	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
373	C₂×C₄²	—	2	2	no	—
374	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
375	#107	C₂³×C₁₃	1	2	yes	—
376	#107	C₂³×C₁₃	1	2	yes	—
377	#107	C₂³×C₁₃	1	2	yes	—
378	#107	C₂³×C₁₃	1	8	yes	—
379	#107	C₂³×C₁₃	1	2	yes	—
380	#107	C₂³×C₁₃	1	2	yes	—
381	#107	C₂³×C₁₃	1	2	yes	—
382	#106	C₂³×C₁₃	1	4	yes	—
383	#106	C₂³×C₁₃	1	8	yes	—
384	#106	C₂³×C₁₃	1	4	yes	—
385	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
386	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
387	#103	C₂³×C₁₃	1	4	yes	—
388	#103	C₂³×C₁₃	1	4	yes	—
389	#103	C₂³×C₁₃	1	8	yes	—
390	#103	C₂³×C₁₃	1	8	yes	—
391	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
392	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
393	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
394	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
395	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
396	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
397	C₂×C₁₃	—	2	2	no	—
398	C₂×C₁₃	—	4	4	no	—
399	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
400	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
401	C₂×C₁₃	#3584	1	1	yes	characteristic
402	#41	—	2	4	no	—
403	#41	—	2	4	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	4	no	—
408	C₂×Q₈	—	2	4	no	—
409	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
410	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
411	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
412	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
413	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
414	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	8	no	—
418	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
420	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
421	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
422	Q₁₆	—	2	4	no	—
423	Q₁₆	—	2	4	no	—
424	M₁₆	—	2	4	no	—
425	M₁₆	—	2	8	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	8	no	—
428	C₂×C₈	C₁₃×#41	1	4	yes	—
429	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
430	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
431	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
432	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
433	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	2	4	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	8	no	—
438	C₄⋊C₄	—	2	4	no	—
439	C₄⋊C₄	—	2	8	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	8	no	—
444	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
445	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
446	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
447	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
448	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
449	C₂²⋊C₄	—	2	8	no	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	8	no	—
452	C₂²⋊C₄	—	2	8	no	—
453	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
454	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
455	C₄²	—	2	4	no	—
456	C₄²	—	2	4	no	—
457	C₄²	—	2	8	no	—
458	C₄²	—	2	4	no	—
459	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
460	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
461	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
462	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
463	C₁₃	#61286	1	1	yes	characteristic, direct product factor, Sylow
464	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
465	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
466	Q₈	—	2	4	no	—
467	Q₈	—	2	4	no	—
468	Q₈	—	2	4	no	—
469	Q₈	—	4	4	no	—
470	Q₈	—	4	4	no	—
471	Q₈	—	8	2	no	—
472	D₄	—	2	8	no	—
473	D₄	—	2	4	no	—
474	D₄	—	2	4	no	—
475	D₄	—	4	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	8	2	no	—
486	C₂×C₄	—	8	8	no	—
487	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
488	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
489	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
490	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
491	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
492	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
493	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
494	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
495	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
496	C₈	—	2	4	no	—
497	C₈	—	2	1	no	—
498	C₈	—	2	1	no	—
499	C₈	C₂×C₁₃×#41	1	2	yes	—
500	C₈	C₂×C₁₃×#41	1	2	yes	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	2	4	no	—
505	C₂²	—	2	4	no	—
506	C₂²	C₁₃×#547	1	2	yes	—
507	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	2	1	no	—
511	C₄	—	2	4	no	—
512	C₄	—	4	4	no	—
513	C₄	—	4	4	no	—
514	C₄	—	4	4	no	—
515	C₄	—	4	4	no	—
516	C₄	C₁₃×#547	1	2	yes	—
517	C₄	C₁₃×#578	1	2	yes	—
518	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
519	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
520	C₂	—	2	2	no	—
521	C₂	—	4	4	no	—
522	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
523	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
524	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3356	C₂	semidirect
3. C₁₃×#3352	C₂	semidirect
4. C₁₃×#3342	C₂	semidirect
5. C₁₃×#3338	C₂	semidirect
6. C₁₃×#3336	C₂	semidirect
7. C₁₃×#3160	C₂	semidirect
8. C₁₃×#3097	C₂	semidirect
9. C₁₃×#3078	C₂	semidirect
10. C₁₃×#3059	C₂	semidirect
11. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
13. C₁₃×#2913	C₂	semidirect
140. #61286	C₁₃	direct (N × H)
203. #3356	C₂×C₁₃	semidirect
204. #3352	C₂×C₁₃	semidirect
205. #3342	C₂×C₁₃	semidirect
206. #3338	C₂×C₁₃	semidirect
207. #3336	C₂×C₁₃	semidirect
208. #3160	C₂×C₁₃	semidirect
209. #3097	C₂×C₁₃	semidirect
210. #3078	C₂×C₁₃	semidirect
211. #3059	C₂×C₁₃	semidirect
212. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
214. #2913	C₂×C₁₃	semidirect
463. C₁₃	#61286	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×#3507	2
C₁₃×#3356	2
C₁₃×#3352	2
C₁₃×#3342	2
C₁₃×#3338	2
C₁₃×#3336	2
C₁₃×#3160	2
C₁₃×#3097	2
C₁₃×#3078	2
C₁₃×#3059	2
C₂×C₄×C₁₃×Q₁₆	2
C₁₃×#2931	2
C₁₃×#2913	2
#61286	13

Subgroups — C13×#61286 #15747625

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61286 #15747625