Subgroups — C₁₃×#61321 #15747660

Order 3328.

2126 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	Q₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3368	C₂	1	6	yes	maximal, complemented
4	C₁₃×#3366	C₂	1	6	yes	maximal, complemented
5	C₁₃×#3362	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3358	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3138	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3077	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3038	C₂	1	3	yes	maximal, complemented
10	Q₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	3	yes	maximal, complemented
12	C₂²×C₁₃×#41	—	2	1	no	—
13	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	3	yes	—
14	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
15	C₁₃×#557	C₂²	1	3	yes	complemented
16	C₁₃×#554	—	2	3	no	—
17	C₁₃×#554	C₂²	1	3	yes	complemented
18	C₁₃×#550	—	2	1	no	—
19	C₁₃×#550	—	2	3	no	—
20	C₁₃×#550	C₂²	1	2	yes	—
21	C₁₃×#550	C₂²	1	6	yes	—
22	D₄×Q₈×C₁₃	—	2	1	no	—
23	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#533	—	2	3	no	—
25	C₁₃×#533	C₂²	1	3	yes	—
26	C₂×C₁₃×#127	C₂²	1	3	yes	—
27	C₂×C₁₃×#121	—	2	3	no	—
28	C₄×C₁₃×#41	C₂²	1	3	yes	—
29	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
30	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
32	C₁₃×#490	C₂²	1	12	yes	complemented
33	C₁₃×#486	C₂²	1	6	yes	complemented
34	C₁₃×#486	C₂²	1	6	yes	complemented
35	C₁₃×#478	C₂²	1	12	yes	complemented
36	C₁₃×#476	C₂²	1	6	yes	complemented
37	C₁₃×#474	C₂²	1	6	yes	complemented
38	C₁₃×#460	C₂²	1	6	yes	complemented
39	C₁₃×#460	C₂²	1	6	yes	complemented
40	C₁₃×#459	C₂²	1	6	yes	complemented
41	C₁₃×#459	C₂²	1	6	yes	complemented
42	C₁₃×#446	C₂²	1	6	yes	complemented
43	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
44	C₁₃×#442	C₂²	1	6	yes	complemented
45	C₁₃×#440	C₂²	1	6	yes	complemented
46	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	complemented
47	C₄×C₁₃×D₈	C₂²	1	6	yes	complemented
48	C₁₃×#428	C₂²	1	3	yes	—
49	C₁₃×#423	C₂²	1	3	yes	—
50	C₁₃×#418	C₂²	1	6	yes	—
51	C₁₃×#418	C₂²	1	3	yes	—
52	C₁₃×#417	C₂²	1	1	yes	characteristic
53	C₄×C₁₃×M₁₆	C₂²	1	3	yes	—
54	C₂×C₁₃×#41	—	2	6	no	—
55	C₂×C₁₃×#41	—	2	2	no	—
56	C₂×C₁₃×#41	—	4	8	no	—
57	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
58	C₂²×Q₈×C₁₃	—	2	1	no	—
59	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
60	C₂²×D₄×C₁₃	—	2	3	no	—
61	C₂²×D₄×C₁₃	—	2	3	no	—
62	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
63	C₂³×C₄×C₁₃	—	2	3	no	—
64	C₁₃×AGL(1,ℤ/8)	—	2	12	no	—
65	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
66	C₂×C₁₃×D₈	C₂³	1	6	yes	—
67	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×M₁₆	C₂³	1	3	yes	—
69	C₁₃×C₄⋊Q₈	—	2	3	no	—
70	C₁₃×C₄⋊Q₈	—	2	3	no	—
71	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
72	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
73	C₁₃×#127	—	2	3	no	—
74	C₁₃×#127	—	2	3	no	—
75	C₁₃×#127	C₂³	1	6	yes	—
76	C₁₃×#127	C₂³	1	6	yes	—
77	C₁₃×#125	—	2	6	no	—
78	C₁₃×#125	C₂³	1	6	yes	—
79	C₁₃×C₂²⋊Q₈	—	2	3	no	—
80	C₁₃×C₂²⋊Q₈	—	2	3	no	—
81	C₁₃×C₂²⋊Q₈	—	2	3	no	—
82	C₁₃×C₂²⋊Q₈	—	2	3	no	—
83	C₁₃×C₂²⋊Q₈	—	2	6	no	—
84	C₁₃×#121	—	2	6	no	—
85	C₁₃×#121	—	2	12	no	—
86	C₁₃×#121	—	2	6	no	—
87	C₄×Q₈×C₁₃	—	2	1	no	—
88	C₄×Q₈×C₁₃	—	2	3	no	—
89	C₄×Q₈×C₁₃	—	2	3	no	—
90	C₄×Q₈×C₁₃	—	2	3	no	—
91	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
92	C₄×Q₈×C₁₃	D₄	1	3	yes	—
93	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
94	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
95	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
97	C₄×D₄×C₁₃	—	2	3	no	—
98	C₄×D₄×C₁₃	—	2	3	no	—
99	C₄×D₄×C₁₃	—	2	3	no	—
100	C₄×D₄×C₁₃	—	2	3	no	—
101	C₄×D₄×C₁₃	C₂³	1	3	yes	—
102	C₄×D₄×C₁₃	C₂³	1	6	yes	—
103	C₄×D₄×C₁₃	C₂³	1	6	yes	—
104	C₄×D₄×C₁₃	C₂³	1	3	yes	—
105	C₁₃×#117	—	2	3	no	—
106	C₁₃×#117	C₂³	1	3	yes	—
107	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
108	C₂×C₁₃×C₄⋊C₄	D₄	1	3	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
111	C₂×C₄²×C₁₃	—	2	3	no	—
112	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
113	C₁₃×#107	C₂³	1	6	yes	—
114	C₁₃×#106	C₂³	1	6	yes	—
115	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
116	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
117	C₁₃×#103	C₂³	1	2	yes	—
118	C₁₃×#102	C₂³	1	2	yes	—
119	C₁₃×#102	C₂³	1	6	yes	—
120	C₁₃×#102	C₂³	1	6	yes	—
121	C₁₃×#102	C₂³	1	12	yes	—
122	C₁₃×#102	C₂³	1	12	yes	—
123	C₁₃×#97	C₂³	1	6	yes	—
124	C₄×C₈×C₁₃	C₂³	1	6	yes	—
125	#61321	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂⁴×C₁₃	—	2	3	no	—
127	C₁₃×#41	—	2	2	no	—
128	C₁₃×#41	—	4	24	no	—
129	C₁₃×#41	—	4	8	no	—
130	C₁₃×#41	#41	1	4	yes	complemented
131	C₂×Q₈×C₁₃	—	2	4	no	—
132	C₂×Q₈×C₁₃	—	2	3	no	—
133	C₂×Q₈×C₁₃	—	2	3	no	—
134	C₂×Q₈×C₁₃	—	4	4	no	—
135	C₂×Q₈×C₁₃	C₂×D₄	1	3	yes	—
136	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₂×D₄×C₁₃	—	2	1	no	—
139	C₂×D₄×C₁₃	—	2	3	no	—
140	C₂×D₄×C₁₃	—	2	6	no	—
141	C₂×D₄×C₁₃	—	2	6	no	—
142	C₂×D₄×C₁₃	—	2	6	no	—
143	C₂×D₄×C₁₃	—	2	6	no	—
144	C₂×D₄×C₁₃	—	2	6	no	—
145	C₂×D₄×C₁₃	—	2	6	no	—
146	C₂×D₄×C₁₃	—	4	12	no	—
147	C₂×D₄×C₁₃	—	8	6	no	—
148	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
149	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	—	2	1	no	—
151	C₂²×C₄×C₁₃	—	2	1	no	—
152	C₂²×C₄×C₁₃	—	2	3	no	—
153	C₂²×C₄×C₁₃	—	2	6	no	—
154	C₂²×C₄×C₁₃	—	2	6	no	—
155	C₂²×C₄×C₁₃	—	2	3	no	—
156	C₂²×C₄×C₁₃	—	4	12	no	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₁₃×SD₁₆	—	2	12	no	—
161	C₁₃×D₈	—	2	12	no	—
162	C₁₃×M₁₆	—	2	6	no	—
163	C₁₃×M₁₆	—	2	2	no	—
164	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
165	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
166	C₁₃×C₄⋊C₄	—	2	6	no	—
167	C₁₃×C₄⋊C₄	—	2	3	no	—
168	C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₁₃×C₄⋊C₄	—	2	3	no	—
170	C₁₃×C₄⋊C₄	—	2	3	no	—
171	C₁₃×C₄⋊C₄	—	2	3	no	—
172	C₁₃×C₄⋊C₄	—	2	6	no	—
173	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
174	C₁₃×C₄⋊C₄	C₂×D₄	1	6	yes	—
175	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
176	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
177	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
178	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
179	C₁₃×C₂²⋊C₄	—	2	3	no	—
180	C₁₃×C₂²⋊C₄	—	2	6	no	—
181	C₁₃×C₂²⋊C₄	—	2	6	no	—
182	C₁₃×C₂²⋊C₄	—	2	3	no	—
183	C₁₃×C₂²⋊C₄	—	2	3	no	—
184	C₄²×C₁₃	—	2	3	no	—
185	C₄²×C₁₃	—	2	3	no	—
186	C₄²×C₁₃	—	2	3	no	—
187	C₄²×C₁₃	C₂×D₄	1	3	yes	—
188	C₄²×C₁₃	C₂×D₄	1	3	yes	—
189	C₄²×C₁₃	C₂⁴	1	3	yes	—
190	C₄²×C₁₃	C₂⁴	1	3	yes	—
191	Q₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
192	C₂×#550	C₂×C₁₃	1	1	yes	characteristic, complemented
193	#3368	C₂×C₁₃	1	6	yes	complemented
194	#3366	C₂×C₁₃	1	6	yes	complemented
195	#3362	C₂×C₁₃	1	2	yes	complemented
196	#3358	C₂×C₁₃	1	2	yes	complemented
197	#3138	C₂×C₁₃	1	3	yes	complemented
198	#3077	C₂×C₁₃	1	3	yes	complemented
199	#3038	C₂×C₁₃	1	3	yes	complemented
200	Q₈×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
201	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	3	yes	complemented
202	C₂³×C₁₃	—	2	1	no	—
203	C₂³×C₁₃	—	2	6	no	—
204	C₂³×C₁₃	—	4	6	no	—
205	C₂³×C₁₃	—	4	6	no	—
206	C₂³×C₁₃	—	4	6	no	—
207	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	Q₈×C₁₃	—	2	6	no	—
209	Q₈×C₁₃	—	2	1	no	—
210	Q₈×C₁₃	—	4	6	no	—
211	Q₈×C₁₃	—	8	3	no	—
212	Q₈×C₁₃	AGL(1,ℤ/8)	1	4	yes	complemented
213	Q₈×C₁₃	C₂×#41	1	2	yes	complemented
214	D₄×C₁₃	—	2	4	no	—
215	D₄×C₁₃	—	2	6	no	—
216	D₄×C₁₃	—	2	1	no	—
217	D₄×C₁₃	—	2	6	no	—
218	D₄×C₁₃	—	4	12	no	—
219	D₄×C₁₃	—	4	6	no	—
220	D₄×C₁₃	—	4	12	no	—
221	D₄×C₁₃	—	8	6	no	—
222	D₄×C₁₃	—	8	6	no	—
223	D₄×C₁₃	C₂×#41	1	2	yes	complemented
224	C₂×C₄×C₁₃	—	2	1	no	—
225	C₂×C₄×C₁₃	—	2	4	no	—
226	C₂×C₄×C₁₃	—	2	6	no	—
227	C₂×C₄×C₁₃	—	2	3	no	—
228	C₂×C₄×C₁₃	—	2	3	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	4	3	no	—
231	C₂×C₄×C₁₃	—	4	12	no	—
232	C₂×C₄×C₁₃	—	4	2	no	—
233	C₂×C₄×C₁₃	—	4	12	no	—
234	C₂×C₄×C₁₃	—	4	6	no	—
235	C₂×C₄×C₁₃	—	8	3	no	—
236	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
237	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
238	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
239	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
241	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
242	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
243	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
244	C₈×C₁₃	—	2	6	no	—
245	C₈×C₁₃	—	2	2	no	—
246	C₂²×#41	—	2	1	no	—
247	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	3	yes	—
248	Q₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
249	#557	C₂²×C₁₃	1	3	yes	complemented
250	#554	—	2	3	no	—
251	#554	C₂²×C₁₃	1	3	yes	complemented
252	#550	—	2	1	no	—
253	#550	—	2	3	no	—
254	#550	C₂²×C₁₃	1	2	yes	—
255	#550	C₂²×C₁₃	1	6	yes	—
256	D₄×Q₈	—	2	1	no	—
257	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
258	#533	—	2	3	no	—
259	#533	C₂²×C₁₃	1	3	yes	—
260	C₂×#127	C₂²×C₁₃	1	3	yes	—
261	C₂×#121	—	2	3	no	—
262	C₄×#41	C₂²×C₁₃	1	3	yes	—
263	C₂×C₄×Q₈	—	2	1	no	—
264	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
266	#490	C₂²×C₁₃	1	12	yes	complemented
267	#486	C₂²×C₁₃	1	6	yes	complemented
268	#486	C₂²×C₁₃	1	6	yes	complemented
269	#478	C₂²×C₁₃	1	12	yes	complemented
270	#476	C₂²×C₁₃	1	6	yes	complemented
271	#474	C₂²×C₁₃	1	6	yes	complemented
272	#460	C₂²×C₁₃	1	6	yes	complemented
273	#460	C₂²×C₁₃	1	6	yes	complemented
274	#459	C₂²×C₁₃	1	6	yes	complemented
275	#459	C₂²×C₁₃	1	6	yes	complemented
276	#446	C₂²×C₁₃	1	6	yes	complemented
277	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
278	#442	C₂²×C₁₃	1	6	yes	complemented
279	#440	C₂²×C₁₃	1	6	yes	complemented
280	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	complemented
281	C₄×D₈	C₂²×C₁₃	1	6	yes	complemented
282	#428	C₂²×C₁₃	1	3	yes	—
283	#423	C₂²×C₁₃	1	3	yes	—
284	#418	C₂²×C₁₃	1	6	yes	—
285	#418	C₂²×C₁₃	1	3	yes	—
286	#417	C₂²×C₁₃	1	1	yes	characteristic
287	C₄×M₁₆	C₂²×C₁₃	1	3	yes	—
288	C₂²×C₁₃	—	2	1	no	—
289	C₂²×C₁₃	—	2	1	no	—
290	C₂²×C₁₃	—	2	2	no	—
291	C₂²×C₁₃	—	4	1	no	—
292	C₂²×C₁₃	—	4	1	no	—
293	C₂²×C₁₃	—	4	6	no	—
294	C₂²×C₁₃	—	4	6	no	—
295	C₂²×C₁₃	—	4	6	no	—
296	C₂²×C₁₃	—	8	12	no	—
297	C₂²×C₁₃	#548	1	2	yes	—
298	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
299	C₄×C₁₃	—	2	3	no	—
300	C₄×C₁₃	—	2	3	no	—
301	C₄×C₁₃	—	2	2	no	—
302	C₄×C₁₃	—	2	3	no	—
303	C₄×C₁₃	—	4	3	no	—
304	C₄×C₁₃	—	4	2	no	—
305	C₄×C₁₃	—	4	3	no	—
306	C₄×C₁₃	#548	1	2	yes	—
307	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	6	yes	—
308	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
309	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
310	C₂×#41	—	2	6	no	—
311	C₂×#41	—	2	2	no	—
312	C₂×#41	—	4	8	no	—
313	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
314	C₂²×Q₈	—	2	1	no	—
315	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
316	C₂²×D₄	—	2	3	no	—
317	C₂²×D₄	—	2	3	no	—
318	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
319	C₂³×C₄	—	2	3	no	—
320	AGL(1,ℤ/8)	—	2	12	no	—
321	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
322	C₂×D₈	C₂³×C₁₃	1	6	yes	—
323	C₂×M₁₆	C₂³×C₁₃	1	3	yes	—
324	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
325	C₄⋊Q₈	—	2	3	no	—
326	C₄⋊Q₈	—	2	3	no	—
327	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
328	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
329	#127	—	2	3	no	—
330	#127	—	2	3	no	—
331	#127	C₂³×C₁₃	1	6	yes	—
332	#127	C₂³×C₁₃	1	6	yes	—
333	#125	—	2	6	no	—
334	#125	C₂³×C₁₃	1	6	yes	—
335	C₂²⋊Q₈	—	2	3	no	—
336	C₂²⋊Q₈	—	2	3	no	—
337	C₂²⋊Q₈	—	2	3	no	—
338	C₂²⋊Q₈	—	2	3	no	—
339	C₂²⋊Q₈	—	2	6	no	—
340	#121	—	2	6	no	—
341	#121	—	2	12	no	—
342	#121	—	2	6	no	—
343	C₄×Q₈	—	2	1	no	—
344	C₄×Q₈	—	2	3	no	—
345	C₄×Q₈	—	2	3	no	—
346	C₄×Q₈	—	2	3	no	—
347	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
348	C₄×Q₈	D₄×C₁₃	1	3	yes	—
349	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
350	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
351	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
352	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
353	C₄×D₄	—	2	3	no	—
354	C₄×D₄	—	2	3	no	—
355	C₄×D₄	—	2	3	no	—
356	C₄×D₄	—	2	3	no	—
357	C₄×D₄	C₂³×C₁₃	1	6	yes	—
358	C₄×D₄	C₂³×C₁₃	1	6	yes	—
359	C₄×D₄	C₂³×C₁₃	1	3	yes	—
360	C₄×D₄	C₂³×C₁₃	1	3	yes	—
361	#117	—	2	3	no	—
362	#117	C₂³×C₁₃	1	3	yes	—
363	C₂×C₄⋊C₄	—	2	3	no	—
364	C₂×C₄⋊C₄	D₄×C₁₃	1	3	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
366	C₂×C₂²⋊C₄	—	2	3	no	—
367	C₂×C₄²	—	2	3	no	—
368	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
369	#107	C₂³×C₁₃	1	6	yes	—
370	#106	C₂³×C₁₃	1	6	yes	—
371	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
372	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
373	#103	C₂³×C₁₃	1	2	yes	—
374	#102	C₂³×C₁₃	1	2	yes	—
375	#102	C₂³×C₁₃	1	6	yes	—
376	#102	C₂³×C₁₃	1	6	yes	—
377	#102	C₂³×C₁₃	1	12	yes	—
378	#102	C₂³×C₁₃	1	12	yes	—
379	#97	C₂³×C₁₃	1	6	yes	—
380	C₄×C₈	C₂³×C₁₃	1	6	yes	—
381	C₂×C₁₃	—	2	2	no	—
382	C₂×C₁₃	—	4	2	no	—
383	C₂×C₁₃	—	8	6	no	—
384	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
385	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
386	C₂×C₁₃	#3585	1	1	yes	characteristic
387	C₂⁴	—	2	3	no	—
388	#41	—	2	2	no	—
389	#41	—	4	24	no	—
390	#41	—	4	8	no	—
391	#41	C₁₃×#41	1	4	yes	complemented
392	C₂×Q₈	—	2	4	no	—
393	C₂×Q₈	—	2	3	no	—
394	C₂×Q₈	—	2	3	no	—
395	C₂×Q₈	—	4	4	no	—
396	C₂×Q₈	C₂×D₄×C₁₃	1	3	yes	—
397	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
398	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	—	2	3	no	—
401	C₂×D₄	—	2	6	no	—
402	C₂×D₄	—	2	6	no	—
403	C₂×D₄	—	2	6	no	—
404	C₂×D₄	—	2	6	no	—
405	C₂×D₄	—	2	6	no	—
406	C₂×D₄	—	2	6	no	—
407	C₂×D₄	—	4	12	no	—
408	C₂×D₄	—	8	6	no	—
409	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
410	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	3	no	—
414	C₂²×C₄	—	2	6	no	—
415	C₂²×C₄	—	2	6	no	—
416	C₂²×C₄	—	2	3	no	—
417	C₂²×C₄	—	4	12	no	—
418	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
419	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
420	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
421	SD₁₆	—	2	12	no	—
422	D₈	—	2	12	no	—
423	M₁₆	—	2	6	no	—
424	M₁₆	—	2	2	no	—
425	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
426	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
427	C₄⋊C₄	—	2	6	no	—
428	C₄⋊C₄	—	2	3	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	3	no	—
431	C₄⋊C₄	—	2	3	no	—
432	C₄⋊C₄	—	2	3	no	—
433	C₄⋊C₄	—	2	6	no	—
434	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
435	C₄⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
436	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
437	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
438	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
439	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
440	C₂²⋊C₄	—	2	3	no	—
441	C₂²⋊C₄	—	2	6	no	—
442	C₂²⋊C₄	—	2	6	no	—
443	C₂²⋊C₄	—	2	3	no	—
444	C₂²⋊C₄	—	2	3	no	—
445	C₄²	—	2	3	no	—
446	C₄²	—	2	3	no	—
447	C₄²	—	2	3	no	—
448	C₄²	C₂×D₄×C₁₃	1	3	yes	—
449	C₄²	C₂×D₄×C₁₃	1	3	yes	—
450	C₄²	C₂⁴×C₁₃	1	3	yes	—
451	C₄²	C₂⁴×C₁₃	1	3	yes	—
452	C₁₃	#61321	1	1	yes	characteristic, direct product factor, Sylow
453	C₂³	—	2	1	no	—
454	C₂³	—	2	6	no	—
455	C₂³	—	4	6	no	—
456	C₂³	—	4	6	no	—
457	C₂³	—	4	6	no	—
458	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
459	Q₈	—	2	6	no	—
460	Q₈	—	2	1	no	—
461	Q₈	—	4	6	no	—
462	Q₈	—	8	3	no	—
463	Q₈	C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
464	Q₈	C₂×C₁₃×#41	1	2	yes	complemented
465	D₄	—	2	4	no	—
466	D₄	—	2	6	no	—
467	D₄	—	2	1	no	—
468	D₄	—	2	6	no	—
469	D₄	—	4	12	no	—
470	D₄	—	4	6	no	—
471	D₄	—	4	12	no	—
472	D₄	—	8	6	no	—
473	D₄	—	8	6	no	—
474	D₄	C₂×C₁₃×#41	1	2	yes	complemented
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	6	no	—
478	C₂×C₄	—	2	3	no	—
479	C₂×C₄	—	2	3	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	4	3	no	—
482	C₂×C₄	—	4	12	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	12	no	—
485	C₂×C₄	—	4	6	no	—
486	C₂×C₄	—	8	3	no	—
487	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
488	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
489	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
490	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
491	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
492	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
493	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
494	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
495	C₈	—	2	6	no	—
496	C₈	—	2	2	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	4	1	no	—
502	C₂²	—	4	6	no	—
503	C₂²	—	4	6	no	—
504	C₂²	—	4	6	no	—
505	C₂²	—	8	12	no	—
506	C₂²	C₁₃×#548	1	2	yes	—
507	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
508	C₄	—	2	3	no	—
509	C₄	—	2	3	no	—
510	C₄	—	2	3	no	—
511	C₄	—	2	2	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	3	no	—
514	C₄	—	4	3	no	—
515	C₄	C₁₃×#548	1	2	yes	—
516	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	6	yes	—
517	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
518	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
519	C₂	—	2	2	no	—
520	C₂	—	4	2	no	—
521	C₂	—	8	6	no	—
522	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
523	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
524	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. Q₈×C₁₃×#41	C₂	semidirect
2. C₂×C₁₃×#550	C₂	semidirect
3. C₁₃×#3368	C₂	semidirect
4. C₁₃×#3366	C₂	semidirect
5. C₁₃×#3362	C₂	semidirect
6. C₁₃×#3358	C₂	semidirect
7. C₁₃×#3138	C₂	semidirect
8. C₁₃×#3077	C₂	semidirect
9. C₁₃×#3038	C₂	semidirect
10. Q₈×C₁₃×M₁₆	C₂	semidirect
11. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
14. Q₈²×C₁₃	C₂²	semidirect
15. C₁₃×#557	C₂²	semidirect
17. C₁₃×#554	C₂²	semidirect
23. D₄×Q₈×C₁₃	C₂²	semidirect
32. C₁₃×#490	C₂²	semidirect
33. C₁₃×#486	C₂²	semidirect
34. C₁₃×#486	C₂²	semidirect
35. C₁₃×#478	C₂²	semidirect
36. C₁₃×#476	C₂²	semidirect
37. C₁₃×#474	C₂²	semidirect
38. C₁₃×#460	C₂²	semidirect
39. C₁₃×#460	C₂²	semidirect
40. C₁₃×#459	C₂²	semidirect
41. C₁₃×#459	C₂²	semidirect
42. C₁₃×#446	C₂²	semidirect
43. C₈×Q₈×C₁₃	C₂²	semidirect
44. C₁₃×#442	C₂²	semidirect
45. C₁₃×#440	C₂²	semidirect
46. C₄×C₁₃×SD₁₆	C₂²	semidirect
47. C₄×C₁₃×D₈	C₂²	semidirect
125. #61321	C₁₃	direct (N × H)
130. C₁₃×#41	#41	semidirect
191. Q₈×#41	C₂×C₁₃	semidirect
192. C₂×#550	C₂×C₁₃	semidirect
193. #3368	C₂×C₁₃	semidirect
194. #3366	C₂×C₁₃	semidirect
195. #3362	C₂×C₁₃	semidirect
196. #3358	C₂×C₁₃	semidirect
197. #3138	C₂×C₁₃	semidirect
198. #3077	C₂×C₁₃	semidirect
199. #3038	C₂×C₁₃	semidirect
200. Q₈×M₁₆	C₂×C₁₃	semidirect
201. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
212. Q₈×C₁₃	AGL(1,ℤ/8)	semidirect
213. Q₈×C₁₃	C₂×#41	semidirect
223. D₄×C₁₃	C₂×#41	semidirect
248. Q₈²	C₂²×C₁₃	semidirect
249. #557	C₂²×C₁₃	semidirect
251. #554	C₂²×C₁₃	semidirect
257. D₄×Q₈	C₂²×C₁₃	semidirect
266. #490	C₂²×C₁₃	semidirect
267. #486	C₂²×C₁₃	semidirect
268. #486	C₂²×C₁₃	semidirect
269. #478	C₂²×C₁₃	semidirect
270. #476	C₂²×C₁₃	semidirect
271. #474	C₂²×C₁₃	semidirect
272. #460	C₂²×C₁₃	semidirect
273. #460	C₂²×C₁₃	semidirect
274. #459	C₂²×C₁₃	semidirect
275. #459	C₂²×C₁₃	semidirect
276. #446	C₂²×C₁₃	semidirect
277. C₈×Q₈	C₂²×C₁₃	semidirect
278. #442	C₂²×C₁₃	semidirect
279. #440	C₂²×C₁₃	semidirect
280. C₄×SD₁₆	C₂²×C₁₃	semidirect
281. C₄×D₈	C₂²×C₁₃	semidirect
391. #41	C₁₃×#41	semidirect
452. C₁₃	#61321	direct (N × H)
463. Q₈	C₁₃×AGL(1,ℤ/8)	semidirect
464. Q₈	C₂×C₁₃×#41	semidirect
474. D₄	C₂×C₁₃×#41	semidirect

Maximal subgroups

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

subgroup	index
Q₈×C₁₃×#41	2
C₂×C₁₃×#550	2
C₁₃×#3368	2
C₁₃×#3366	2
C₁₃×#3362	2
C₁₃×#3358	2
C₁₃×#3138	2
C₁₃×#3077	2
C₁₃×#3038	2
Q₈×C₁₃×M₁₆	2
C₄×C₁₃×AGL(1,ℤ/8)	2
#61321	13

Subgroups — C13×#61321 #15747660

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61321 #15747660