Subgroups — C₁₃×#62151 #15748490

Order 3328.

1986 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3518	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3362	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3354	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3353	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3325	C₂	1	3	yes	maximal, complemented
10	C₁₃×#3324	C₂	1	3	yes	maximal, complemented
11	C₁₃×#3251	C₂	1	3	yes	maximal, complemented
12	C₁₃×#3228	C₂	1	3	yes	maximal, complemented
13	C₁₃×#3105	C₂	1	3	yes	maximal, complemented
14	C₁₃×#3077	C₂	1	3	yes	maximal, complemented
15	C₁₃×#2991	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	—	2	1	no	—
17	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
18	C₁₃×#556	—	2	3	no	—
19	C₁₃×#556	C₂²	1	3	yes	complemented
20	C₁₃×#555	C₂²	1	3	yes	complemented
21	C₁₃×#550	C₂²	1	1	yes	characteristic
22	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#548	—	2	1	no	—
25	C₁₃×#548	—	2	1	no	—
26	C₁₃×#547	C₂²	1	3	yes	—
27	C₁₃×#546	—	2	3	no	—
28	D₄²×C₁₃	C₂²	1	3	yes	—
29	C₁₃×#542	—	2	3	no	—
30	C₁₃×#533	C₂²	1	3	yes	complemented
31	C₁₃×#532	C₂²	1	3	yes	—
32	C₁₃×#529	C₂²	1	3	yes	complemented
33	C₁₃×#525	—	2	3	no	—
34	C₁₃×#519	—	2	1	no	—
35	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
37	C₁₃×#500	C₂²	1	3	yes	complemented
38	C₁₃×#498	C₂²	1	3	yes	complemented
39	C₁₃×#486	C₂²	1	3	yes	complemented
40	C₁₃×#486	C₂²	1	3	yes	complemented
41	C₁₃×#484	C₂²	1	3	yes	complemented
42	C₁₃×#482	C₂²	1	6	yes	complemented
43	C₁₃×#482	C₂²	1	6	yes	complemented
44	C₁₃×#481	C₂²	1	3	yes	complemented
45	C₁₃×#478	C₂²	1	3	yes	—
46	C₁₃×#478	C₂²	1	6	yes	complemented
47	C₁₃×#478	C₂²	1	3	yes	complemented
48	C₁₃×#476	C₂²	1	3	yes	—
49	C₁₃×#476	C₂²	1	3	yes	complemented
50	C₁₃×#475	C₂²	1	3	yes	complemented
51	C₁₃×#474	C₂²	1	3	yes	—
52	C₁₃×#474	C₂²	1	3	yes	complemented
53	C₁₃×#474	C₂²	1	3	yes	complemented
54	C₁₃×#469	C₂²	1	6	yes	complemented
55	C₁₃×#468	C₂²	1	6	yes	complemented
56	C₁₃×#463	C₂²	1	1	yes	characteristic
57	C₁₃×#463	C₂²	1	3	yes	complemented
58	C₁₃×#460	C₂²	1	3	yes	complemented
59	C₁₃×#459	C₂²	1	3	yes	complemented
60	C₁₃×#450	C₂²	1	3	yes	—
61	C₁₃×#447	C₂²	1	3	yes	—
62	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
63	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
64	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	—
65	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	complemented
66	C₄×C₁₃×D₈	C₂²	1	3	yes	—
67	C₄×C₁₃×D₈	C₂²	1	3	yes	complemented
68	C₁₃×#436	C₂²	1	3	yes	complemented
69	C₁₃×#436	C₂²	1	3	yes	complemented
70	C₁₃×#431	C₂²	1	3	yes	complemented
71	C₁₃×#428	C₂²	1	6	yes	complemented
72	C₁₃×#423	C₂²	1	3	yes	complemented
73	C₁₃×#418	C₂²	1	6	yes	—
74	C₂×C₁₃×#41	—	2	1	no	—
75	C₂×C₁₃×#41	—	2	3	no	—
76	C₂×C₁₃×#41	—	2	3	no	—
77	C₂×C₁₃×#41	—	4	8	no	—
78	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
79	C₂²×Q₈×C₁₃	—	2	1	no	—
80	C₂²×Q₈×C₁₃	—	2	1	no	—
81	C₂²×D₄×C₁₃	—	2	3	no	—
82	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
83	C₂³×C₄×C₁₃	—	2	3	no	—
84	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×SD₁₆	C₂³	1	3	yes	—
86	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×D₈	C₂³	1	3	yes	—
88	C₂×C₁₃×M₁₆	C₂³	1	6	yes	—
89	C₁₃×C₄⋊Q₈	—	2	3	no	—
90	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
91	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
92	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
93	C₁₃×#127	C₂³	1	3	yes	—
94	C₁₃×#126	—	2	6	no	—
95	C₁₃×#126	—	2	3	no	—
96	C₁₃×#125	C₂³	1	3	yes	—
97	C₁₃×#124	—	2	3	no	—
98	C₁₃×#124	—	2	6	no	—
99	C₁₃×#124	—	2	3	no	—
100	C₁₃×#124	C₂³	1	1	yes	characteristic
101	C₁₃×#123	—	2	3	no	—
102	C₁₃×#123	—	2	6	no	—
103	C₁₃×C₂²⋊Q₈	—	2	3	no	—
104	C₁₃×C₂²⋊Q₈	—	2	3	no	—
105	C₁₃×C₂²⋊Q₈	—	2	3	no	—
106	C₁₃×C₂²⋊Q₈	—	2	3	no	—
107	C₁₃×C₂²⋊Q₈	—	2	3	no	—
108	C₁₃×C₂²⋊Q₈	C₂³	1	3	yes	—
109	C₁₃×#121	—	2	3	no	—
110	C₁₃×#121	—	2	3	no	—
111	C₁₃×#121	—	2	3	no	—
112	C₁₃×#121	—	2	3	no	—
113	C₁₃×#121	C₂³	1	3	yes	—
114	C₁₃×#121	C₂³	1	6	yes	—
115	C₁₃×#120	—	2	6	no	—
116	C₄×Q₈×C₁₃	—	2	1	no	—
117	C₄×Q₈×C₁₃	—	2	3	no	—
118	C₄×Q₈×C₁₃	—	2	3	no	—
119	C₄×Q₈×C₁₃	—	2	3	no	—
120	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
121	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
122	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
123	C₄×D₄×C₁₃	—	2	3	no	—
124	C₄×D₄×C₁₃	—	2	3	no	—
125	C₄×D₄×C₁₃	—	2	3	no	—
126	C₄×D₄×C₁₃	—	2	3	no	—
127	C₄×D₄×C₁₃	D₄	1	3	yes	—
128	C₄×D₄×C₁₃	C₂³	1	3	yes	—
129	C₄×D₄×C₁₃	C₂³	1	3	yes	—
130	C₄×D₄×C₁₃	C₂³	1	3	yes	—
131	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
132	C₄×D₄×C₁₃	C₂³	1	3	yes	—
133	C₄×D₄×C₁₃	C₂³	1	3	yes	—
134	C₁₃×#117	—	2	3	no	—
135	C₁₃×#117	—	2	3	no	—
136	C₁₃×#117	D₄	1	3	yes	—
137	C₁₃×#117	C₂³	1	6	yes	—
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
139	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
140	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
141	C₁₃×#107	C₂³	1	3	yes	—
142	C₁₃×#107	C₂³	1	6	yes	—
143	C₁₃×#107	C₂³	1	3	yes	—
144	C₁₃×#106	C₂³	1	3	yes	—
145	C₁₃×#106	C₂³	1	6	yes	—
146	C₁₃×#106	C₂³	1	3	yes	—
147	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
148	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
149	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
150	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
151	C₁₃×#103	C₂³	1	3	yes	—
152	C₁₃×#103	C₂³	1	1	yes	characteristic
153	C₁₃×#102	C₂³	1	3	yes	—
154	C₁₃×#102	C₂³	1	3	yes	—
155	C₁₃×#102	C₂³	1	6	yes	—
156	C₁₃×#102	C₂³	1	6	yes	—
157	C₁₃×#102	C₂³	1	3	yes	—
158	C₁₃×#102	C₂³	1	1	yes	characteristic
159	C₁₃×#102	C₂³	1	3	yes	—
160	C₁₃×#102	C₂³	1	3	yes	—
161	C₁₃×C₂²⋊C₈	C₂³	1	3	yes	—
162	C₁₃×C₂²⋊C₈	C₂³	1	3	yes	—
163	C₄×C₈×C₁₃	C₂³	1	3	yes	—
164	C₄×C₈×C₁₃	C₂³	1	3	yes	—
165	#62151	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂⁴×C₁₃	—	2	3	no	—
167	C₁₃×#41	—	2	4	no	—
168	C₁₃×#41	—	4	12	no	—
169	C₁₃×#41	—	4	12	no	—
170	C₁₃×#41	—	4	4	no	—
171	C₂×Q₈×C₁₃	—	2	3	no	—
172	C₂×Q₈×C₁₃	—	2	3	no	—
173	C₂×Q₈×C₁₃	—	2	3	no	—
174	C₂×Q₈×C₁₃	—	4	4	no	—
175	C₂×Q₈×C₁₃	—	4	4	no	—
176	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂×D₄×C₁₃	—	2	6	no	—
179	C₂×D₄×C₁₃	—	2	6	no	—
180	C₂×D₄×C₁₃	—	2	3	no	—
181	C₂×D₄×C₁₃	—	2	3	no	—
182	C₂×D₄×C₁₃	—	2	3	no	—
183	C₂×D₄×C₁₃	—	2	3	no	—
184	C₂×D₄×C₁₃	—	4	3	no	—
185	C₂×D₄×C₁₃	—	4	12	no	—
186	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
187	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
188	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
189	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	—	2	3	no	—
191	C₂²×C₄×C₁₃	—	2	3	no	—
192	C₂²×C₄×C₁₃	—	2	1	no	—
193	C₂²×C₄×C₁₃	—	2	3	no	—
194	C₂²×C₄×C₁₃	—	2	3	no	—
195	C₂²×C₄×C₁₃	—	2	3	no	—
196	C₂²×C₄×C₁₃	—	4	12	no	—
197	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
198	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
199	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
200	C₁₃×SD₁₆	—	2	2	no	—
201	C₁₃×SD₁₆	—	4	3	no	—
202	C₁₃×D₈	—	2	2	no	—
203	C₁₃×D₈	—	4	3	no	—
204	C₁₃×M₁₆	—	4	6	no	—
205	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
206	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
207	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
208	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
209	C₁₃×C₄⋊C₄	—	2	3	no	—
210	C₁₃×C₄⋊C₄	—	2	3	no	—
211	C₁₃×C₄⋊C₄	—	2	3	no	—
212	C₁₃×C₄⋊C₄	—	2	3	no	—
213	C₁₃×C₄⋊C₄	—	2	3	no	—
214	C₁₃×C₄⋊C₄	—	2	3	no	—
215	C₁₃×C₄⋊C₄	—	2	3	no	—
216	C₁₃×C₄⋊C₄	—	2	3	no	—
217	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
218	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
219	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
220	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
221	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
222	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
223	C₁₃×C₂²⋊C₄	—	2	6	no	—
224	C₁₃×C₂²⋊C₄	—	2	3	no	—
225	C₁₃×C₂²⋊C₄	—	2	1	no	—
226	C₁₃×C₂²⋊C₄	—	2	3	no	—
227	C₁₃×C₂²⋊C₄	—	2	3	no	—
228	C₁₃×C₂²⋊C₄	—	2	3	no	—
229	C₁₃×C₂²⋊C₄	—	2	3	no	—
230	C₁₃×C₂²⋊C₄	—	2	1	no	—
231	C₁₃×C₂²⋊C₄	—	2	1	no	—
232	C₁₃×C₂²⋊C₄	—	2	6	no	—
233	C₁₃×C₂²⋊C₄	—	2	3	no	—
234	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
235	C₄²×C₁₃	—	2	6	no	—
236	C₄²×C₁₃	—	2	3	no	—
237	C₄²×C₁₃	C₂×D₄	1	3	yes	—
238	C₄²×C₁₃	C₂×D₄	1	3	yes	—
239	C₄²×C₁₃	C₂⁴	1	3	yes	—
240	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
241	#3518	C₂×C₁₃	1	1	yes	characteristic, complemented
242	D₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
243	Q₈×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
244	Q₈×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#3362	C₂×C₁₃	1	1	yes	characteristic, complemented
246	#3358	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#3354	C₂×C₁₃	1	3	yes	complemented
248	#3353	C₂×C₁₃	1	3	yes	complemented
249	#3325	C₂×C₁₃	1	3	yes	complemented
250	#3324	C₂×C₁₃	1	3	yes	complemented
251	#3251	C₂×C₁₃	1	3	yes	complemented
252	#3228	C₂×C₁₃	1	3	yes	complemented
253	#3105	C₂×C₁₃	1	3	yes	complemented
254	#3077	C₂×C₁₃	1	3	yes	complemented
255	#2991	C₂×C₁₃	1	1	yes	characteristic, complemented
256	C₂³×C₁₃	—	2	1	no	—
257	C₂³×C₁₃	—	2	1	no	—
258	C₂³×C₁₃	—	2	3	no	—
259	C₂³×C₁₃	—	4	6	no	—
260	C₂³×C₁₃	—	4	6	no	—
261	C₂³×C₁₃	—	8	3	no	—
262	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
263	Q₈×C₁₃	—	2	1	no	—
264	Q₈×C₁₃	—	2	1	no	—
265	Q₈×C₁₃	—	4	6	no	—
266	Q₈×C₁₃	—	4	6	no	—
267	Q₈×C₁₃	—	8	3	no	—
268	Q₈×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
269	D₄×C₁₃	—	2	6	no	—
270	D₄×C₁₃	—	2	1	no	—
271	D₄×C₁₃	—	2	3	no	—
272	D₄×C₁₃	—	2	1	no	—
273	D₄×C₁₃	—	2	1	no	—
274	D₄×C₁₃	—	2	3	no	—
275	D₄×C₁₃	—	4	6	no	—
276	D₄×C₁₃	—	4	12	no	—
277	D₄×C₁₃	—	4	6	no	—
278	D₄×C₁₃	—	8	3	no	—
279	D₄×C₁₃	—	8	3	no	—
280	D₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
281	C₂×C₄×C₁₃	—	2	6	no	—
282	C₂×C₄×C₁₃	—	2	3	no	—
283	C₂×C₄×C₁₃	—	2	3	no	—
284	C₂×C₄×C₁₃	—	2	1	no	—
285	C₂×C₄×C₁₃	—	2	3	no	—
286	C₂×C₄×C₁₃	—	2	3	no	—
287	C₂×C₄×C₁₃	—	2	1	no	—
288	C₂×C₄×C₁₃	—	2	3	no	—
289	C₂×C₄×C₁₃	—	4	3	no	—
290	C₂×C₄×C₁₃	—	4	2	no	—
291	C₂×C₄×C₁₃	—	4	6	no	—
292	C₂×C₄×C₁₃	—	4	6	no	—
293	C₂×C₄×C₁₃	—	4	6	no	—
294	C₂×C₄×C₁₃	—	4	6	no	—
295	C₂×C₄×C₁₃	—	4	6	no	—
296	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
297	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
298	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
300	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
301	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
302	C₈×C₁₃	—	2	1	no	—
303	C₈×C₁₃	—	2	1	no	—
304	C₈×C₁₃	—	2	3	no	—
305	C₈×C₁₃	—	2	3	no	—
306	C₂²×#41	—	2	1	no	—
307	Q₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
308	#556	—	2	3	no	—
309	#556	C₂²×C₁₃	1	3	yes	complemented
310	#555	C₂²×C₁₃	1	3	yes	complemented
311	#550	C₂²×C₁₃	1	1	yes	characteristic
312	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
313	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
314	#548	—	2	1	no	—
315	#548	—	2	1	no	—
316	#547	C₂²×C₁₃	1	3	yes	—
317	#546	—	2	3	no	—
318	D₄²	C₂²×C₁₃	1	3	yes	—
319	#542	—	2	3	no	—
320	#533	C₂²×C₁₃	1	3	yes	complemented
321	#532	C₂²×C₁₃	1	3	yes	—
322	#529	C₂²×C₁₃	1	3	yes	complemented
323	#525	—	2	3	no	—
324	#519	—	2	1	no	—
325	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
327	#500	C₂²×C₁₃	1	3	yes	complemented
328	#498	C₂²×C₁₃	1	3	yes	complemented
329	#486	C₂²×C₁₃	1	3	yes	complemented
330	#486	C₂²×C₁₃	1	3	yes	complemented
331	#484	C₂²×C₁₃	1	3	yes	complemented
332	#482	C₂²×C₁₃	1	6	yes	complemented
333	#482	C₂²×C₁₃	1	6	yes	complemented
334	#481	C₂²×C₁₃	1	3	yes	complemented
335	#478	C₂²×C₁₃	1	3	yes	—
336	#478	C₂²×C₁₃	1	6	yes	complemented
337	#478	C₂²×C₁₃	1	3	yes	complemented
338	#476	C₂²×C₁₃	1	3	yes	—
339	#476	C₂²×C₁₃	1	3	yes	complemented
340	#475	C₂²×C₁₃	1	3	yes	complemented
341	#474	C₂²×C₁₃	1	3	yes	—
342	#474	C₂²×C₁₃	1	3	yes	complemented
343	#474	C₂²×C₁₃	1	3	yes	complemented
344	#469	C₂²×C₁₃	1	6	yes	complemented
345	#468	C₂²×C₁₃	1	6	yes	complemented
346	#463	C₂²×C₁₃	1	1	yes	characteristic
347	#463	C₂²×C₁₃	1	3	yes	complemented
348	#460	C₂²×C₁₃	1	3	yes	complemented
349	#459	C₂²×C₁₃	1	3	yes	complemented
350	#450	C₂²×C₁₃	1	3	yes	—
351	#447	C₂²×C₁₃	1	3	yes	—
352	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
353	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
354	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	—
355	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	complemented
356	C₄×D₈	C₂²×C₁₃	1	3	yes	—
357	C₄×D₈	C₂²×C₁₃	1	3	yes	complemented
358	#436	C₂²×C₁₃	1	3	yes	complemented
359	#436	C₂²×C₁₃	1	3	yes	complemented
360	#431	C₂²×C₁₃	1	3	yes	complemented
361	#428	C₂²×C₁₃	1	6	yes	complemented
362	#423	C₂²×C₁₃	1	3	yes	complemented
363	#418	C₂²×C₁₃	1	6	yes	—
364	C₂²×C₁₃	—	2	3	no	—
365	C₂²×C₁₃	—	2	3	no	—
366	C₂²×C₁₃	—	2	2	no	—
367	C₂²×C₁₃	—	2	3	no	—
368	C₂²×C₁₃	—	4	1	no	—
369	C₂²×C₁₃	—	4	1	no	—
370	C₂²×C₁₃	—	4	1	no	—
371	C₂²×C₁₃	—	4	3	no	—
372	C₂²×C₁₃	—	4	3	no	—
373	C₂²×C₁₃	—	4	1	no	—
374	C₂²×C₁₃	—	4	1	no	—
375	C₂²×C₁₃	—	4	3	no	—
376	C₂²×C₁₃	—	8	12	no	—
377	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
378	C₄×C₁₃	—	2	1	no	—
379	C₄×C₁₃	—	2	3	no	—
380	C₄×C₁₃	—	2	3	no	—
381	C₄×C₁₃	—	2	1	no	—
382	C₄×C₁₃	—	4	3	no	—
383	C₄×C₁₃	—	4	1	no	—
384	C₄×C₁₃	—	4	1	no	—
385	C₄×C₁₃	—	4	3	no	—
386	C₄×C₁₃	—	4	3	no	—
387	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	6	yes	—
388	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
389	C₄×C₁₃	#585	1	1	yes	characteristic
390	C₂×#41	—	2	1	no	—
391	C₂×#41	—	2	3	no	—
392	C₂×#41	—	2	3	no	—
393	C₂×#41	—	4	8	no	—
394	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
395	C₂²×Q₈	—	2	1	no	—
396	C₂²×Q₈	—	2	1	no	—
397	C₂²×D₄	—	2	3	no	—
398	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
399	C₂³×C₄	—	2	3	no	—
400	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
401	C₂×SD₁₆	C₂³×C₁₃	1	3	yes	—
402	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
403	C₂×D₈	C₂³×C₁₃	1	3	yes	—
404	C₂×M₁₆	C₂³×C₁₃	1	6	yes	—
405	C₄⋊Q₈	—	2	3	no	—
406	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
407	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
408	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
409	#127	C₂³×C₁₃	1	3	yes	—
410	#126	—	2	6	no	—
411	#126	—	2	3	no	—
412	#125	C₂³×C₁₃	1	3	yes	—
413	#124	—	2	3	no	—
414	#124	—	2	6	no	—
415	#124	—	2	3	no	—
416	#124	C₂³×C₁₃	1	1	yes	characteristic
417	#123	—	2	3	no	—
418	#123	—	2	6	no	—
419	C₂²⋊Q₈	—	2	3	no	—
420	C₂²⋊Q₈	—	2	3	no	—
421	C₂²⋊Q₈	—	2	3	no	—
422	C₂²⋊Q₈	—	2	3	no	—
423	C₂²⋊Q₈	—	2	3	no	—
424	C₂²⋊Q₈	C₂³×C₁₃	1	3	yes	—
425	#121	—	2	3	no	—
426	#121	—	2	3	no	—
427	#121	—	2	3	no	—
428	#121	—	2	3	no	—
429	#121	C₂³×C₁₃	1	3	yes	—
430	#121	C₂³×C₁₃	1	6	yes	—
431	#120	—	2	6	no	—
432	C₄×Q₈	—	2	1	no	—
433	C₄×Q₈	—	2	3	no	—
434	C₄×Q₈	—	2	3	no	—
435	C₄×Q₈	—	2	3	no	—
436	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
437	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
438	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
439	C₄×D₄	—	2	3	no	—
440	C₄×D₄	—	2	3	no	—
441	C₄×D₄	—	2	3	no	—
442	C₄×D₄	—	2	3	no	—
443	C₄×D₄	D₄×C₁₃	1	3	yes	—
444	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
445	C₄×D₄	C₂³×C₁₃	1	3	yes	—
446	C₄×D₄	C₂³×C₁₃	1	3	yes	—
447	C₄×D₄	C₂³×C₁₃	1	3	yes	—
448	C₄×D₄	C₂³×C₁₃	1	3	yes	—
449	C₄×D₄	C₂³×C₁₃	1	3	yes	—
450	#117	—	2	3	no	—
451	#117	—	2	3	no	—
452	#117	D₄×C₁₃	1	3	yes	—
453	#117	C₂³×C₁₃	1	6	yes	—
454	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
455	C₂×C₂²⋊C₄	—	2	3	no	—
456	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
457	#107	C₂³×C₁₃	1	3	yes	—
458	#107	C₂³×C₁₃	1	6	yes	—
459	#107	C₂³×C₁₃	1	3	yes	—
460	#106	C₂³×C₁₃	1	3	yes	—
461	#106	C₂³×C₁₃	1	6	yes	—
462	#106	C₂³×C₁₃	1	3	yes	—
463	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
464	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
465	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
466	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
467	#103	C₂³×C₁₃	1	3	yes	—
468	#103	C₂³×C₁₃	1	1	yes	characteristic
469	#102	C₂³×C₁₃	1	3	yes	—
470	#102	C₂³×C₁₃	1	3	yes	—
471	#102	C₂³×C₁₃	1	6	yes	—
472	#102	C₂³×C₁₃	1	6	yes	—
473	#102	C₂³×C₁₃	1	3	yes	—
474	#102	C₂³×C₁₃	1	1	yes	characteristic
475	#102	C₂³×C₁₃	1	3	yes	—
476	#102	C₂³×C₁₃	1	3	yes	—
477	C₂²⋊C₈	C₂³×C₁₃	1	3	yes	—
478	C₂²⋊C₈	C₂³×C₁₃	1	3	yes	—
479	C₄×C₈	C₂³×C₁₃	1	3	yes	—
480	C₄×C₈	C₂³×C₁₃	1	3	yes	—
481	C₂×C₁₃	—	4	3	no	—
482	C₂×C₁₃	—	4	2	no	—
483	C₂×C₁₃	—	8	1	no	—
484	C₂×C₁₃	—	8	3	no	—
485	C₂×C₁₃	#3489	1	1	yes	characteristic
486	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
487	C₂×C₁₃	#3584	1	1	yes	characteristic
488	C₂⁴	—	2	3	no	—
489	#41	—	2	4	no	—
490	#41	—	4	12	no	—
491	#41	—	4	12	no	—
492	#41	—	4	4	no	—
493	C₂×Q₈	—	2	3	no	—
494	C₂×Q₈	—	2	3	no	—
495	C₂×Q₈	—	2	3	no	—
496	C₂×Q₈	—	4	4	no	—
497	C₂×Q₈	—	4	4	no	—
498	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
499	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
500	C₂×D₄	—	2	6	no	—
501	C₂×D₄	—	2	6	no	—
502	C₂×D₄	—	2	3	no	—
503	C₂×D₄	—	2	3	no	—
504	C₂×D₄	—	2	3	no	—
505	C₂×D₄	—	2	3	no	—
506	C₂×D₄	—	4	3	no	—
507	C₂×D₄	—	4	12	no	—
508	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
509	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
510	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
511	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
512	C₂²×C₄	—	2	3	no	—
513	C₂²×C₄	—	2	3	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	3	no	—
516	C₂²×C₄	—	2	3	no	—
517	C₂²×C₄	—	2	3	no	—
518	C₂²×C₄	—	4	12	no	—
519	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
520	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
521	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
522	SD₁₆	—	2	2	no	—
523	SD₁₆	—	4	3	no	—
524	D₈	—	2	2	no	—
525	D₈	—	4	3	no	—
526	M₁₆	—	4	6	no	—
527	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
528	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
529	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
530	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
531	C₄⋊C₄	—	2	3	no	—
532	C₄⋊C₄	—	2	3	no	—
533	C₄⋊C₄	—	2	3	no	—
534	C₄⋊C₄	—	2	3	no	—
535	C₄⋊C₄	—	2	3	no	—
536	C₄⋊C₄	—	2	3	no	—
537	C₄⋊C₄	—	2	3	no	—
538	C₄⋊C₄	—	2	3	no	—
539	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
540	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
541	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
542	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
543	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
544	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
545	C₂²⋊C₄	—	2	6	no	—
546	C₂²⋊C₄	—	2	3	no	—
547	C₂²⋊C₄	—	2	1	no	—
548	C₂²⋊C₄	—	2	3	no	—
549	C₂²⋊C₄	—	2	3	no	—
550	C₂²⋊C₄	—	2	3	no	—
551	C₂²⋊C₄	—	2	3	no	—
552	C₂²⋊C₄	—	2	1	no	—
553	C₂²⋊C₄	—	2	1	no	—
554	C₂²⋊C₄	—	2	6	no	—
555	C₂²⋊C₄	—	2	3	no	—
556	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
557	C₄²	—	2	6	no	—
558	C₄²	—	2	3	no	—
559	C₄²	C₂×D₄×C₁₃	1	3	yes	—
560	C₄²	C₂×D₄×C₁₃	1	3	yes	—
561	C₄²	C₂⁴×C₁₃	1	3	yes	—
562	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
563	C₁₃	#62151	1	1	yes	characteristic, direct product factor, Sylow
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	3	no	—
567	C₂³	—	4	6	no	—
568	C₂³	—	4	6	no	—
569	C₂³	—	8	3	no	—
570	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
571	Q₈	—	2	1	no	—
572	Q₈	—	2	1	no	—
573	Q₈	—	4	6	no	—
574	Q₈	—	4	6	no	—
575	Q₈	—	8	3	no	—
576	Q₈	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
577	D₄	—	2	6	no	—
578	D₄	—	2	1	no	—
579	D₄	—	2	3	no	—
580	D₄	—	2	1	no	—
581	D₄	—	2	1	no	—
582	D₄	—	2	3	no	—
583	D₄	—	4	6	no	—
584	D₄	—	4	12	no	—
585	D₄	—	4	6	no	—
586	D₄	—	8	3	no	—
587	D₄	—	8	3	no	—
588	D₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
589	C₂×C₄	—	2	6	no	—
590	C₂×C₄	—	2	3	no	—
591	C₂×C₄	—	2	3	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	3	no	—
594	C₂×C₄	—	2	3	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	3	no	—
597	C₂×C₄	—	4	3	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	6	no	—
600	C₂×C₄	—	4	6	no	—
601	C₂×C₄	—	4	6	no	—
602	C₂×C₄	—	4	6	no	—
603	C₂×C₄	—	4	6	no	—
604	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
605	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
606	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
607	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
608	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
609	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
610	C₈	—	2	1	no	—
611	C₈	—	2	1	no	—
612	C₈	—	2	3	no	—
613	C₈	—	2	3	no	—
614	C₂²	—	2	3	no	—
615	C₂²	—	2	3	no	—
616	C₂²	—	2	3	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	3	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	3	no	—
624	C₂²	—	4	3	no	—
625	C₂²	—	4	1	no	—
626	C₂²	—	8	12	no	—
627	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
628	C₄	—	2	1	no	—
629	C₄	—	2	1	no	—
630	C₄	—	2	3	no	—
631	C₄	—	2	3	no	—
632	C₄	—	4	1	no	—
633	C₄	—	4	3	no	—
634	C₄	—	4	3	no	—
635	C₄	—	4	3	no	—
636	C₄	—	4	1	no	—
637	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	6	yes	—
638	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
639	C₄	C₁₃×#585	1	1	yes	characteristic
640	C₂	—	4	3	no	—
641	C₂	—	4	2	no	—
642	C₂	—	8	3	no	—
643	C₂	—	8	1	no	—
644	C₂	C₁₃×#3489	1	1	yes	characteristic
645	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
646	C₂	C₁₃×#3584	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 ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3518	C₂	semidirect
2. D₄×C₁₃×#41	C₂	semidirect
3. Q₈×C₁₃×SD₁₆	C₂	semidirect
4. Q₈×C₁₃×D₈	C₂	semidirect
5. C₁₃×#3362	C₂	semidirect
6. C₁₃×#3358	C₂	semidirect
7. C₁₃×#3354	C₂	semidirect
8. C₁₃×#3353	C₂	semidirect
9. C₁₃×#3325	C₂	semidirect
10. C₁₃×#3324	C₂	semidirect
11. C₁₃×#3251	C₂	semidirect
12. C₁₃×#3228	C₂	semidirect
13. C₁₃×#3105	C₂	semidirect
14. C₁₃×#3077	C₂	semidirect
15. C₁₃×#2991	C₂	semidirect
17. Q₈²×C₁₃	C₂²	semidirect
19. C₁₃×#556	C₂²	semidirect
20. C₁₃×#555	C₂²	semidirect
23. D₄×Q₈×C₁₃	C₂²	semidirect
30. C₁₃×#533	C₂²	semidirect
32. C₁₃×#529	C₂²	semidirect
37. C₁₃×#500	C₂²	semidirect
38. C₁₃×#498	C₂²	semidirect
39. C₁₃×#486	C₂²	semidirect
40. C₁₃×#486	C₂²	semidirect
41. C₁₃×#484	C₂²	semidirect
42. C₁₃×#482	C₂²	semidirect
43. C₁₃×#482	C₂²	semidirect
44. C₁₃×#481	C₂²	semidirect
46. C₁₃×#478	C₂²	semidirect
47. C₁₃×#478	C₂²	semidirect
49. C₁₃×#476	C₂²	semidirect
50. C₁₃×#475	C₂²	semidirect
52. C₁₃×#474	C₂²	semidirect
53. C₁₃×#474	C₂²	semidirect
54. C₁₃×#469	C₂²	semidirect
55. C₁₃×#468	C₂²	semidirect
57. C₁₃×#463	C₂²	semidirect
58. C₁₃×#460	C₂²	semidirect
59. C₁₃×#459	C₂²	semidirect
62. C₈×Q₈×C₁₃	C₂²	semidirect
63. C₈×Q₈×C₁₃	C₂²	semidirect
65. C₄×C₁₃×SD₁₆	C₂²	semidirect
67. C₄×C₁₃×D₈	C₂²	semidirect
68. C₁₃×#436	C₂²	semidirect
69. C₁₃×#436	C₂²	semidirect
70. C₁₃×#431	C₂²	semidirect
71. C₁₃×#428	C₂²	semidirect
72. C₁₃×#423	C₂²	semidirect
165. #62151	C₁₃	direct (N × H)
241. #3518	C₂×C₁₃	semidirect
242. D₄×#41	C₂×C₁₃	semidirect
243. Q₈×SD₁₆	C₂×C₁₃	semidirect
244. Q₈×D₈	C₂×C₁₃	semidirect
245. #3362	C₂×C₁₃	semidirect
246. #3358	C₂×C₁₃	semidirect
247. #3354	C₂×C₁₃	semidirect
248. #3353	C₂×C₁₃	semidirect
249. #3325	C₂×C₁₃	semidirect
250. #3324	C₂×C₁₃	semidirect
251. #3251	C₂×C₁₃	semidirect
252. #3228	C₂×C₁₃	semidirect
253. #3105	C₂×C₁₃	semidirect
254. #3077	C₂×C₁₃	semidirect
255. #2991	C₂×C₁₃	semidirect
307. Q₈²	C₂²×C₁₃	semidirect
309. #556	C₂²×C₁₃	semidirect
310. #555	C₂²×C₁₃	semidirect
313. D₄×Q₈	C₂²×C₁₃	semidirect
320. #533	C₂²×C₁₃	semidirect
322. #529	C₂²×C₁₃	semidirect
327. #500	C₂²×C₁₃	semidirect
328. #498	C₂²×C₁₃	semidirect
329. #486	C₂²×C₁₃	semidirect
330. #486	C₂²×C₁₃	semidirect
331. #484	C₂²×C₁₃	semidirect
332. #482	C₂²×C₁₃	semidirect
333. #482	C₂²×C₁₃	semidirect
334. #481	C₂²×C₁₃	semidirect
336. #478	C₂²×C₁₃	semidirect
337. #478	C₂²×C₁₃	semidirect
339. #476	C₂²×C₁₃	semidirect
340. #475	C₂²×C₁₃	semidirect
342. #474	C₂²×C₁₃	semidirect
343. #474	C₂²×C₁₃	semidirect
344. #469	C₂²×C₁₃	semidirect
345. #468	C₂²×C₁₃	semidirect
347. #463	C₂²×C₁₃	semidirect
348. #460	C₂²×C₁₃	semidirect
349. #459	C₂²×C₁₃	semidirect
352. C₈×Q₈	C₂²×C₁₃	semidirect
353. C₈×Q₈	C₂²×C₁₃	semidirect
355. C₄×SD₁₆	C₂²×C₁₃	semidirect
357. C₄×D₈	C₂²×C₁₃	semidirect
358. #436	C₂²×C₁₃	semidirect
359. #436	C₂²×C₁₃	semidirect
360. #431	C₂²×C₁₃	semidirect
361. #428	C₂²×C₁₃	semidirect
362. #423	C₂²×C₁₃	semidirect
563. C₁₃	#62151	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×#3518	2
D₄×C₁₃×#41	2
Q₈×C₁₃×SD₁₆	2
Q₈×C₁₃×D₈	2
C₁₃×#3362	2
C₁₃×#3358	2
C₁₃×#3354	2
C₁₃×#3353	2
C₁₃×#3325	2
C₁₃×#3324	2
C₁₃×#3251	2
C₁₃×#3228	2
C₁₃×#3105	2
C₁₃×#3077	2
C₁₃×#2991	2
#62151	13

Subgroups — C13×#62151 #15748490

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62151 #15748490