Subgroups — C₁₃×#61465 #15747804

Order 3328.

2156 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3483	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3391	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×C₁₃×SD₁₆	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×#3332	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3325	C₂	1	3	yes	maximal, complemented
10	C₁₃×#3274	C₂	1	3	yes	maximal, complemented
11	C₁₃×#3184	C₂	1	3	yes	maximal, complemented
12	C₁₃×#3115	C₂	1	3	yes	maximal, complemented
13	C₁₃×#3109	C₂	1	3	yes	maximal, complemented
14	C₁₃×#2971	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	3	yes	maximal, complemented
16	C₂²×C₁₃×#41	—	2	1	no	—
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	3	yes	—
18	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
19	C₁₃×#555	—	2	3	no	—
20	C₁₃×#555	C₂²	1	3	yes	complemented
21	C₁₃×#550	—	2	1	no	—
22	C₁₃×#550	C₂²	1	1	yes	characteristic
23	C₁₃×#550	C₂²	1	3	yes	complemented
24	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
25	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#548	—	2	1	no	—
27	C₁₃×#547	C₂²	1	3	yes	—
28	C₁₃×#546	—	2	3	no	—
29	D₄²×C₁₃	C₂²	1	3	yes	—
30	C₁₃×#532	—	2	3	no	—
31	C₁₃×#532	C₂²	1	3	yes	—
32	C₁₃×#532	C₂²	1	3	yes	complemented
33	C₁₃×#525	—	2	3	no	—
34	C₄×C₁₃×#41	—	2	1	no	—
35	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
36	C₄×C₁₃×#41	C₂²	1	3	yes	complemented
37	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
38	C₁₃×#498	C₂²	1	3	yes	complemented
39	C₁₃×#493	C₂²	1	3	yes	complemented
40	C₁₃×#486	C₂²	1	3	yes	complemented
41	C₁₃×#486	C₂²	1	3	yes	complemented
42	C₁₃×#482	C₂²	1	6	yes	complemented
43	C₁₃×#481	C₂²	1	6	yes	complemented
44	C₁₃×#476	C₂²	1	3	yes	—
45	C₁₃×#476	C₂²	1	3	yes	complemented
46	C₁₃×#475	C₂²	1	3	yes	complemented
47	C₁₃×#474	C₂²	1	3	yes	complemented
48	C₁₃×#469	C₂²	1	6	yes	complemented
49	C₁₃×#469	C₂²	1	6	yes	complemented
50	C₁₃×#460	C₂²	1	3	yes	complemented
51	C₁₃×#459	C₂²	1	3	yes	—
52	C₁₃×#459	C₂²	1	3	yes	complemented
53	C₁₃×#459	C₂²	1	3	yes	complemented
54	C₁₃×#449	C₂²	1	6	yes	complemented
55	C₁₃×#447	C₂²	1	6	yes	—
56	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
57	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#442	C₂²	1	3	yes	—
59	C₁₃×#442	C₂²	1	6	yes	complemented
60	C₁₃×#442	C₂²	1	3	yes	complemented
61	C₁₃×#440	C₂²	1	1	yes	characteristic
62	C₁₃×#440	C₂²	1	3	yes	complemented
63	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	—
64	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	complemented
65	C₄×C₁₃×D₈	C₂²	1	3	yes	—
66	C₄×C₁₃×D₈	C₂²	1	3	yes	complemented
67	C₁₃×#436	C₂²	1	3	yes	complemented
68	C₁₃×#436	C₂²	1	3	yes	complemented
69	C₁₃×#432	C₂²	1	3	yes	complemented
70	C₁₃×#428	C₂²	1	3	yes	complemented
71	C₁₃×#418	C₂²	1	3	yes	—
72	C₁₃×#417	C₂²	1	3	yes	complemented
73	C₄×C₁₃×M₁₆	C₂²	1	3	yes	complemented
74	C₂×C₁₃×#41	—	2	1	no	—
75	C₂×C₁₃×#41	—	2	1	no	—
76	C₂×C₁₃×#41	—	2	3	no	—
77	C₂×C₁₃×#41	—	2	3	no	—
78	C₂×C₁₃×#41	—	2	3	no	—
79	C₂×C₁₃×#41	—	4	8	no	—
80	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
81	C₂×C₁₃×#41	C₂³	1	3	yes	—
82	C₂²×Q₈×C₁₃	—	2	1	no	—
83	C₂²×D₄×C₁₃	—	2	3	no	—
84	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
85	C₂³×C₄×C₁₃	—	2	3	no	—
86	C₁₃×AGL(1,ℤ/8)	—	2	12	no	—
87	C₂×C₁₃×SD₁₆	C₂³	1	3	yes	—
88	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×D₈	C₂³	1	3	yes	—
90	C₂×C₁₃×D₈	C₂³	1	3	yes	—
91	C₂×C₁₃×D₈	C₂³	1	6	yes	—
92	C₂×C₁₃×M₁₆	C₂³	1	3	yes	—
93	C₂×C₁₃×M₁₆	C₂³	1	3	yes	—
94	C₁₃×C₄⋊Q₈	—	2	3	no	—
95	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
96	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
97	C₁₃×#127	—	2	3	no	—
98	C₁₃×#127	C₂³	1	3	yes	—
99	C₁₃×#127	C₂³	1	3	yes	—
100	C₁₃×#124	—	2	6	no	—
101	C₁₃×#124	—	2	3	no	—
102	C₁₃×#124	—	2	3	no	—
103	C₁₃×#123	—	2	6	no	—
104	C₁₃×C₂²⋊Q₈	—	2	3	no	—
105	C₁₃×C₂²⋊Q₈	—	2	3	no	—
106	C₁₃×#121	—	2	3	no	—
107	C₁₃×#121	—	2	3	no	—
108	C₁₃×#121	—	2	3	no	—
109	C₁₃×#121	—	2	3	no	—
110	C₁₃×#121	—	2	3	no	—
111	C₁₃×#121	—	2	3	no	—
112	C₁₃×#121	—	2	6	no	—
113	C₁₃×#121	C₂³	1	6	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	D₄	1	1	yes	characteristic
118	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
119	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
120	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
121	C₄×D₄×C₁₃	—	2	3	no	—
122	C₄×D₄×C₁₃	—	2	3	no	—
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	—	2	3	no	—
128	C₄×D₄×C₁₃	D₄	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	3	yes	—
132	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
133	C₄×D₄×C₁₃	C₂³	1	3	yes	—
134	C₄×D₄×C₁₃	C₂³	1	3	yes	—
135	C₄×D₄×C₁₃	C₂³	1	3	yes	—
136	C₁₃×#117	—	2	3	no	—
137	C₁₃×#117	—	2	3	no	—
138	C₁₃×#117	D₄	1	3	yes	—
139	C₁₃×#117	C₂³	1	3	yes	—
140	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
141	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
142	C₂×C₄²×C₁₃	—	2	3	no	—
143	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
144	C₁₃×#107	C₂³	1	1	yes	characteristic
145	C₁₃×#107	C₂³	1	3	yes	—
146	C₁₃×#106	C₂³	1	3	yes	—
147	C₁₃×#106	C₂³	1	3	yes	—
148	C₁₃×#106	C₂³	1	6	yes	—
149	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
150	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
151	C₁₃×#103	C₂³	1	1	yes	characteristic
152	C₁₃×#103	C₂³	1	3	yes	—
153	C₁₃×#102	C₂³	1	3	yes	—
154	C₁₃×#102	C₂³	1	3	yes	—
155	C₁₃×#102	C₂³	1	1	yes	characteristic
156	C₁₃×#102	C₂³	1	3	yes	—
157	C₁₃×#102	C₂³	1	3	yes	—
158	C₁₃×#102	C₂³	1	3	yes	—
159	C₁₃×#102	C₂³	1	6	yes	—
160	C₁₃×#102	C₂³	1	6	yes	—
161	C₁₃×C₂²⋊C₈	C₂³	1	6	yes	—
162	C₁₃×#97	C₂³	1	1	yes	characteristic
163	C₁₃×#97	C₂³	1	3	yes	—
164	C₄×C₈×C₁₃	C₂³	1	3	yes	—
165	C₄×C₈×C₁₃	C₂³	1	3	yes	—
166	#61465	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂⁴×C₁₃	—	2	3	no	—
168	C₁₃×#41	—	2	4	no	—
169	C₁₃×#41	—	2	6	no	—
170	C₁₃×#41	—	4	3	no	—
171	C₁₃×#41	—	4	12	no	—
172	C₁₃×#41	—	4	12	no	—
173	C₁₃×#41	—	4	4	no	—
174	C₁₃×#41	—	4	4	no	—
175	C₁₃×#41	—	8	6	no	—
176	C₂×Q₈×C₁₃	—	2	3	no	—
177	C₂×Q₈×C₁₃	—	2	3	no	—
178	C₂×Q₈×C₁₃	—	4	4	no	—
179	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
181	C₂×D₄×C₁₃	—	2	6	no	—
182	C₂×D₄×C₁₃	—	2	3	no	—
183	C₂×D₄×C₁₃	—	2	6	no	—
184	C₂×D₄×C₁₃	—	2	6	no	—
185	C₂×D₄×C₁₃	—	2	3	no	—
186	C₂×D₄×C₁₃	—	2	3	no	—
187	C₂×D₄×C₁₃	—	2	3	no	—
188	C₂×D₄×C₁₃	—	2	3	no	—
189	C₂×D₄×C₁₃	—	2	3	no	—
190	C₂×D₄×C₁₃	—	4	3	no	—
191	C₂×D₄×C₁₃	—	4	12	no	—
192	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
193	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
194	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
195	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₁₃	—	2	3	no	—
197	C₂²×C₄×C₁₃	—	2	3	no	—
198	C₂²×C₄×C₁₃	—	2	3	no	—
199	C₂²×C₄×C₁₃	—	2	3	no	—
200	C₂²×C₄×C₁₃	—	2	1	no	—
201	C₂²×C₄×C₁₃	—	2	3	no	—
202	C₂²×C₄×C₁₃	—	2	3	no	—
203	C₂²×C₄×C₁₃	—	2	3	no	—
204	C₂²×C₄×C₁₃	—	4	12	no	—
205	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
206	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
207	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
208	C₁₃×SD₁₆	—	2	6	no	—
209	C₁₃×SD₁₆	#41	1	4	yes	complemented
210	C₁₃×D₈	—	2	6	no	—
211	C₁₃×D₈	—	2	6	no	—
212	C₁₃×D₈	—	4	6	no	—
213	C₁₃×M₁₆	—	2	6	no	—
214	C₁₃×M₁₆	—	4	3	no	—
215	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
216	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
217	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
218	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
219	C₁₃×C₄⋊C₄	—	2	3	no	—
220	C₁₃×C₄⋊C₄	—	2	1	no	—
221	C₁₃×C₄⋊C₄	—	2	3	no	—
222	C₁₃×C₄⋊C₄	—	2	3	no	—
223	C₁₃×C₄⋊C₄	—	2	3	no	—
224	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
225	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
226	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
227	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
228	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
229	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
230	C₁₃×C₂²⋊C₄	—	2	3	no	—
231	C₁₃×C₂²⋊C₄	—	2	1	no	—
232	C₁₃×C₂²⋊C₄	—	2	3	no	—
233	C₁₃×C₂²⋊C₄	—	2	3	no	—
234	C₁₃×C₂²⋊C₄	—	2	3	no	—
235	C₁₃×C₂²⋊C₄	—	2	6	no	—
236	C₁₃×C₂²⋊C₄	—	2	3	no	—
237	C₁₃×C₂²⋊C₄	—	2	3	no	—
238	C₁₃×C₂²⋊C₄	—	2	6	no	—
239	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
240	C₄²×C₁₃	—	2	1	no	—
241	C₄²×C₁₃	—	2	3	no	—
242	C₄²×C₁₃	—	2	3	no	—
243	C₄²×C₁₃	C₂×D₄	1	3	yes	—
244	C₄²×C₁₃	C₂×D₄	1	3	yes	—
245	C₄²×C₁₃	C₂⁴	1	3	yes	—
246	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
247	#3483	C₂×C₁₃	1	1	yes	characteristic, complemented
248	D₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#3391	C₂×C₁₃	1	1	yes	characteristic, complemented
250	Q₈×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#3362	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#3358	C₂×C₁₃	1	1	yes	characteristic, complemented
253	#3354	C₂×C₁₃	1	3	yes	complemented
254	#3332	C₂×C₁₃	1	3	yes	complemented
255	#3325	C₂×C₁₃	1	3	yes	complemented
256	#3274	C₂×C₁₃	1	3	yes	complemented
257	#3184	C₂×C₁₃	1	3	yes	complemented
258	#3115	C₂×C₁₃	1	3	yes	complemented
259	#3109	C₂×C₁₃	1	3	yes	complemented
260	#2971	C₂×C₁₃	1	1	yes	characteristic, complemented
261	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	3	yes	complemented
262	C₂³×C₁₃	—	2	1	no	—
263	C₂³×C₁₃	—	2	3	no	—
264	C₂³×C₁₃	—	2	3	no	—
265	C₂³×C₁₃	—	4	6	no	—
266	C₂³×C₁₃	—	4	6	no	—
267	C₂³×C₁₃	—	8	3	no	—
268	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
269	Q₈×C₁₃	—	2	1	no	—
270	Q₈×C₁₃	—	4	6	no	—
271	Q₈×C₁₃	—	8	3	no	—
272	Q₈×C₁₃	AGL(1,ℤ/8)	1	4	yes	complemented
273	Q₈×C₁₃	C₂×#41	1	2	yes	complemented
274	D₄×C₁₃	—	2	6	no	—
275	D₄×C₁₃	—	2	3	no	—
276	D₄×C₁₃	—	2	3	no	—
277	D₄×C₁₃	—	2	1	no	—
278	D₄×C₁₃	—	2	3	no	—
279	D₄×C₁₃	—	2	3	no	—
280	D₄×C₁₃	—	4	6	no	—
281	D₄×C₁₃	—	4	6	no	—
282	D₄×C₁₃	—	4	12	no	—
283	D₄×C₁₃	—	4	6	no	—
284	D₄×C₁₃	—	4	6	no	—
285	D₄×C₁₃	—	8	3	no	—
286	D₄×C₁₃	—	8	3	no	—
287	D₄×C₁₃	—	8	6	no	—
288	D₄×C₁₃	C₂×#41	1	2	yes	—
289	C₂×C₄×C₁₃	—	2	1	no	—
290	C₂×C₄×C₁₃	—	2	6	no	—
291	C₂×C₄×C₁₃	—	2	3	no	—
292	C₂×C₄×C₁₃	—	2	3	no	—
293	C₂×C₄×C₁₃	—	2	1	no	—
294	C₂×C₄×C₁₃	—	2	3	no	—
295	C₂×C₄×C₁₃	—	2	1	no	—
296	C₂×C₄×C₁₃	—	2	3	no	—
297	C₂×C₄×C₁₃	—	4	3	no	—
298	C₂×C₄×C₁₃	—	4	6	no	—
299	C₂×C₄×C₁₃	—	4	2	no	—
300	C₂×C₄×C₁₃	—	4	6	no	—
301	C₂×C₄×C₁₃	—	4	6	no	—
302	C₂×C₄×C₁₃	—	4	6	no	—
303	C₂×C₄×C₁₃	—	4	6	no	—
304	C₂×C₄×C₁₃	—	4	6	no	—
305	C₂×C₄×C₁₃	—	4	6	no	—
306	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
308	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
309	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
310	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
311	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
312	C₈×C₁₃	—	2	3	no	—
313	C₈×C₁₃	—	2	1	no	—
314	C₈×C₁₃	—	2	3	no	—
315	C₈×C₁₃	C₂×#41	1	2	yes	complemented
316	C₂²×#41	—	2	1	no	—
317	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	3	yes	—
318	Q₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
319	#555	—	2	3	no	—
320	#555	C₂²×C₁₃	1	3	yes	complemented
321	#550	—	2	1	no	—
322	#550	C₂²×C₁₃	1	1	yes	characteristic
323	#550	C₂²×C₁₃	1	3	yes	complemented
324	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
325	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
326	#548	—	2	1	no	—
327	#547	C₂²×C₁₃	1	3	yes	—
328	#546	—	2	3	no	—
329	D₄²	C₂²×C₁₃	1	3	yes	—
330	#532	—	2	3	no	—
331	#532	C₂²×C₁₃	1	3	yes	—
332	#532	C₂²×C₁₃	1	3	yes	complemented
333	#525	—	2	3	no	—
334	C₄×#41	—	2	1	no	—
335	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
336	C₄×#41	C₂²×C₁₃	1	3	yes	complemented
337	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
338	#498	C₂²×C₁₃	1	3	yes	complemented
339	#493	C₂²×C₁₃	1	3	yes	complemented
340	#486	C₂²×C₁₃	1	3	yes	complemented
341	#486	C₂²×C₁₃	1	3	yes	complemented
342	#482	C₂²×C₁₃	1	6	yes	complemented
343	#481	C₂²×C₁₃	1	6	yes	complemented
344	#476	C₂²×C₁₃	1	3	yes	—
345	#476	C₂²×C₁₃	1	3	yes	complemented
346	#475	C₂²×C₁₃	1	3	yes	complemented
347	#474	C₂²×C₁₃	1	3	yes	complemented
348	#469	C₂²×C₁₃	1	6	yes	complemented
349	#469	C₂²×C₁₃	1	6	yes	complemented
350	#460	C₂²×C₁₃	1	3	yes	complemented
351	#459	C₂²×C₁₃	1	3	yes	—
352	#459	C₂²×C₁₃	1	3	yes	complemented
353	#459	C₂²×C₁₃	1	3	yes	complemented
354	#449	C₂²×C₁₃	1	6	yes	complemented
355	#447	C₂²×C₁₃	1	6	yes	—
356	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
357	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
358	#442	C₂²×C₁₃	1	3	yes	—
359	#442	C₂²×C₁₃	1	6	yes	complemented
360	#442	C₂²×C₁₃	1	3	yes	complemented
361	#440	C₂²×C₁₃	1	1	yes	characteristic
362	#440	C₂²×C₁₃	1	3	yes	complemented
363	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	—
364	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	complemented
365	C₄×D₈	C₂²×C₁₃	1	3	yes	—
366	C₄×D₈	C₂²×C₁₃	1	3	yes	complemented
367	#436	C₂²×C₁₃	1	3	yes	complemented
368	#436	C₂²×C₁₃	1	3	yes	complemented
369	#432	C₂²×C₁₃	1	3	yes	complemented
370	#428	C₂²×C₁₃	1	3	yes	complemented
371	#418	C₂²×C₁₃	1	3	yes	—
372	#417	C₂²×C₁₃	1	3	yes	complemented
373	C₄×M₁₆	C₂²×C₁₃	1	3	yes	complemented
374	C₂²×C₁₃	—	2	3	no	—
375	C₂²×C₁₃	—	2	3	no	—
376	C₂²×C₁₃	—	2	2	no	—
377	C₂²×C₁₃	—	2	3	no	—
378	C₂²×C₁₃	—	4	1	no	—
379	C₂²×C₁₃	—	4	1	no	—
380	C₂²×C₁₃	—	4	3	no	—
381	C₂²×C₁₃	—	4	3	no	—
382	C₂²×C₁₃	—	4	3	no	—
383	C₂²×C₁₃	—	4	3	no	—
384	C₂²×C₁₃	—	4	3	no	—
385	C₂²×C₁₃	—	4	3	no	—
386	C₂²×C₁₃	—	8	12	no	—
387	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
388	C₄×C₁₃	—	2	1	no	—
389	C₄×C₁₃	—	2	3	no	—
390	C₄×C₁₃	—	2	3	no	—
391	C₄×C₁₃	—	2	2	no	—
392	C₄×C₁₃	—	2	1	no	—
393	C₄×C₁₃	—	4	3	no	—
394	C₄×C₁₃	—	4	1	no	—
395	C₄×C₁₃	—	4	1	no	—
396	C₄×C₁₃	—	4	3	no	—
397	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	6	yes	—
398	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
399	C₄×C₁₃	#585	1	1	yes	characteristic
400	C₂×#41	—	2	1	no	—
401	C₂×#41	—	2	1	no	—
402	C₂×#41	—	2	3	no	—
403	C₂×#41	—	2	3	no	—
404	C₂×#41	—	2	3	no	—
405	C₂×#41	—	4	8	no	—
406	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
407	C₂×#41	C₂³×C₁₃	1	3	yes	—
408	C₂²×Q₈	—	2	1	no	—
409	C₂²×D₄	—	2	3	no	—
410	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
411	C₂³×C₄	—	2	3	no	—
412	AGL(1,ℤ/8)	—	2	12	no	—
413	C₂×SD₁₆	C₂³×C₁₃	1	3	yes	—
414	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
415	C₂×D₈	C₂³×C₁₃	1	3	yes	—
416	C₂×D₈	C₂³×C₁₃	1	3	yes	—
417	C₂×D₈	C₂³×C₁₃	1	6	yes	—
418	C₂×M₁₆	C₂³×C₁₃	1	3	yes	—
419	C₂×M₁₆	C₂³×C₁₃	1	3	yes	—
420	C₄⋊Q₈	—	2	3	no	—
421	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
422	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
423	#127	—	2	3	no	—
424	#127	C₂³×C₁₃	1	3	yes	—
425	#127	C₂³×C₁₃	1	3	yes	—
426	#124	—	2	6	no	—
427	#124	—	2	3	no	—
428	#124	—	2	3	no	—
429	#123	—	2	6	no	—
430	C₂²⋊Q₈	—	2	3	no	—
431	C₂²⋊Q₈	—	2	3	no	—
432	#121	—	2	3	no	—
433	#121	—	2	3	no	—
434	#121	—	2	3	no	—
435	#121	—	2	3	no	—
436	#121	—	2	3	no	—
437	#121	—	2	3	no	—
438	#121	—	2	6	no	—
439	#121	C₂³×C₁₃	1	6	yes	—
440	#121	C₂³×C₁₃	1	6	yes	—
441	#120	—	2	6	no	—
442	C₄×Q₈	—	2	1	no	—
443	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
444	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
445	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
446	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
447	C₄×D₄	—	2	3	no	—
448	C₄×D₄	—	2	3	no	—
449	C₄×D₄	—	2	3	no	—
450	C₄×D₄	—	2	3	no	—
451	C₄×D₄	—	2	3	no	—
452	C₄×D₄	—	2	3	no	—
453	C₄×D₄	—	2	3	no	—
454	C₄×D₄	D₄×C₁₃	1	3	yes	—
455	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
456	C₄×D₄	C₂³×C₁₃	1	3	yes	—
457	C₄×D₄	C₂³×C₁₃	1	3	yes	—
458	C₄×D₄	C₂³×C₁₃	1	3	yes	—
459	C₄×D₄	C₂³×C₁₃	1	3	yes	—
460	C₄×D₄	C₂³×C₁₃	1	3	yes	—
461	C₄×D₄	C₂³×C₁₃	1	3	yes	—
462	#117	—	2	3	no	—
463	#117	—	2	3	no	—
464	#117	D₄×C₁₃	1	3	yes	—
465	#117	C₂³×C₁₃	1	3	yes	—
466	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
467	C₂×C₂²⋊C₄	—	2	3	no	—
468	C₂×C₄²	—	2	3	no	—
469	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
470	#107	C₂³×C₁₃	1	1	yes	characteristic
471	#107	C₂³×C₁₃	1	3	yes	—
472	#106	C₂³×C₁₃	1	3	yes	—
473	#106	C₂³×C₁₃	1	3	yes	—
474	#106	C₂³×C₁₃	1	6	yes	—
475	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
476	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
477	#103	C₂³×C₁₃	1	1	yes	characteristic
478	#103	C₂³×C₁₃	1	3	yes	—
479	#102	C₂³×C₁₃	1	3	yes	—
480	#102	C₂³×C₁₃	1	3	yes	—
481	#102	C₂³×C₁₃	1	1	yes	characteristic
482	#102	C₂³×C₁₃	1	3	yes	—
483	#102	C₂³×C₁₃	1	3	yes	—
484	#102	C₂³×C₁₃	1	3	yes	—
485	#102	C₂³×C₁₃	1	6	yes	—
486	#102	C₂³×C₁₃	1	6	yes	—
487	C₂²⋊C₈	C₂³×C₁₃	1	6	yes	—
488	#97	C₂³×C₁₃	1	1	yes	characteristic
489	#97	C₂³×C₁₃	1	3	yes	—
490	C₄×C₈	C₂³×C₁₃	1	3	yes	—
491	C₄×C₈	C₂³×C₁₃	1	3	yes	—
492	C₂×C₁₃	—	4	3	no	—
493	C₂×C₁₃	—	4	2	no	—
494	C₂×C₁₃	—	8	3	no	—
495	C₂×C₁₃	—	8	3	no	—
496	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
497	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
498	C₂×C₁₃	#3585	1	1	yes	characteristic
499	C₂⁴	—	2	3	no	—
500	#41	—	2	4	no	—
501	#41	—	2	6	no	—
502	#41	—	4	3	no	—
503	#41	—	4	12	no	—
504	#41	—	4	12	no	—
505	#41	—	4	4	no	—
506	#41	—	4	4	no	—
507	#41	—	8	6	no	—
508	C₂×Q₈	—	2	3	no	—
509	C₂×Q₈	—	2	3	no	—
510	C₂×Q₈	—	4	4	no	—
511	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
512	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
513	C₂×D₄	—	2	6	no	—
514	C₂×D₄	—	2	3	no	—
515	C₂×D₄	—	2	6	no	—
516	C₂×D₄	—	2	6	no	—
517	C₂×D₄	—	2	3	no	—
518	C₂×D₄	—	2	3	no	—
519	C₂×D₄	—	2	3	no	—
520	C₂×D₄	—	2	3	no	—
521	C₂×D₄	—	2	3	no	—
522	C₂×D₄	—	4	3	no	—
523	C₂×D₄	—	4	12	no	—
524	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
525	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
526	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
527	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
528	C₂²×C₄	—	2	3	no	—
529	C₂²×C₄	—	2	3	no	—
530	C₂²×C₄	—	2	3	no	—
531	C₂²×C₄	—	2	3	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	3	no	—
534	C₂²×C₄	—	2	3	no	—
535	C₂²×C₄	—	2	3	no	—
536	C₂²×C₄	—	4	12	no	—
537	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
538	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
539	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
540	SD₁₆	—	2	6	no	—
541	SD₁₆	C₁₃×#41	1	4	yes	complemented
542	D₈	—	2	6	no	—
543	D₈	—	2	6	no	—
544	D₈	—	4	6	no	—
545	M₁₆	—	2	6	no	—
546	M₁₆	—	4	3	no	—
547	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
548	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
549	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
550	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
551	C₄⋊C₄	—	2	3	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	3	no	—
554	C₄⋊C₄	—	2	3	no	—
555	C₄⋊C₄	—	2	3	no	—
556	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
557	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
558	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
559	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
560	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
561	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
562	C₂²⋊C₄	—	2	3	no	—
563	C₂²⋊C₄	—	2	1	no	—
564	C₂²⋊C₄	—	2	3	no	—
565	C₂²⋊C₄	—	2	3	no	—
566	C₂²⋊C₄	—	2	3	no	—
567	C₂²⋊C₄	—	2	6	no	—
568	C₂²⋊C₄	—	2	3	no	—
569	C₂²⋊C₄	—	2	3	no	—
570	C₂²⋊C₄	—	2	6	no	—
571	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
572	C₄²	—	2	1	no	—
573	C₄²	—	2	3	no	—
574	C₄²	—	2	3	no	—
575	C₄²	C₂×D₄×C₁₃	1	3	yes	—
576	C₄²	C₂×D₄×C₁₃	1	3	yes	—
577	C₄²	C₂⁴×C₁₃	1	3	yes	—
578	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
579	C₁₃	#61465	1	1	yes	characteristic, direct product factor, Sylow
580	C₂³	—	2	1	no	—
581	C₂³	—	2	3	no	—
582	C₂³	—	2	3	no	—
583	C₂³	—	4	6	no	—
584	C₂³	—	4	6	no	—
585	C₂³	—	8	3	no	—
586	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
587	Q₈	—	2	1	no	—
588	Q₈	—	4	6	no	—
589	Q₈	—	8	3	no	—
590	Q₈	C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
591	Q₈	C₂×C₁₃×#41	1	2	yes	complemented
592	D₄	—	2	6	no	—
593	D₄	—	2	3	no	—
594	D₄	—	2	3	no	—
595	D₄	—	2	1	no	—
596	D₄	—	2	3	no	—
597	D₄	—	2	3	no	—
598	D₄	—	4	6	no	—
599	D₄	—	4	6	no	—
600	D₄	—	4	12	no	—
601	D₄	—	4	6	no	—
602	D₄	—	4	6	no	—
603	D₄	—	8	3	no	—
604	D₄	—	8	3	no	—
605	D₄	—	8	6	no	—
606	D₄	C₂×C₁₃×#41	1	2	yes	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	6	no	—
609	C₂×C₄	—	2	3	no	—
610	C₂×C₄	—	2	3	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	3	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	3	no	—
615	C₂×C₄	—	4	3	no	—
616	C₂×C₄	—	4	6	no	—
617	C₂×C₄	—	4	2	no	—
618	C₂×C₄	—	4	6	no	—
619	C₂×C₄	—	4	6	no	—
620	C₂×C₄	—	4	6	no	—
621	C₂×C₄	—	4	6	no	—
622	C₂×C₄	—	4	6	no	—
623	C₂×C₄	—	4	6	no	—
624	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
625	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
626	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
627	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
628	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
629	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
630	C₈	—	2	3	no	—
631	C₈	—	2	1	no	—
632	C₈	—	2	3	no	—
633	C₈	C₂×C₁₃×#41	1	2	yes	complemented
634	C₂²	—	2	3	no	—
635	C₂²	—	2	3	no	—
636	C₂²	—	2	3	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	1	no	—
640	C₂²	—	4	3	no	—
641	C₂²	—	4	3	no	—
642	C₂²	—	4	3	no	—
643	C₂²	—	4	3	no	—
644	C₂²	—	4	3	no	—
645	C₂²	—	4	3	no	—
646	C₂²	—	8	12	no	—
647	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	3	no	—
651	C₄	—	2	3	no	—
652	C₄	—	2	2	no	—
653	C₄	—	4	1	no	—
654	C₄	—	4	1	no	—
655	C₄	—	4	3	no	—
656	C₄	—	4	3	no	—
657	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	6	yes	—
658	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
659	C₄	C₁₃×#585	1	1	yes	characteristic
660	C₂	—	4	3	no	—
661	C₂	—	4	2	no	—
662	C₂	—	8	3	no	—
663	C₂	—	8	3	no	—
664	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
665	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
666	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 ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3483	C₂	semidirect
2. D₄×C₁₃×#41	C₂	semidirect
3. C₁₃×#3391	C₂	semidirect
4. Q₈×C₁₃×SD₁₆	C₂	semidirect
5. C₁₃×#3362	C₂	semidirect
6. C₁₃×#3358	C₂	semidirect
7. C₁₃×#3354	C₂	semidirect
8. C₁₃×#3332	C₂	semidirect
9. C₁₃×#3325	C₂	semidirect
10. C₁₃×#3274	C₂	semidirect
11. C₁₃×#3184	C₂	semidirect
12. C₁₃×#3115	C₂	semidirect
13. C₁₃×#3109	C₂	semidirect
14. C₁₃×#2971	C₂	semidirect
15. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
18. Q₈²×C₁₃	C₂²	semidirect
20. C₁₃×#555	C₂²	semidirect
23. C₁₃×#550	C₂²	semidirect
24. C₁₃×#550	C₂²	semidirect
32. C₁₃×#532	C₂²	semidirect
36. C₄×C₁₃×#41	C₂²	semidirect
38. C₁₃×#498	C₂²	semidirect
39. C₁₃×#493	C₂²	semidirect
40. C₁₃×#486	C₂²	semidirect
41. C₁₃×#486	C₂²	semidirect
42. C₁₃×#482	C₂²	semidirect
43. C₁₃×#481	C₂²	semidirect
45. C₁₃×#476	C₂²	semidirect
46. C₁₃×#475	C₂²	semidirect
47. C₁₃×#474	C₂²	semidirect
48. C₁₃×#469	C₂²	semidirect
49. C₁₃×#469	C₂²	semidirect
50. C₁₃×#460	C₂²	semidirect
52. C₁₃×#459	C₂²	semidirect
53. C₁₃×#459	C₂²	semidirect
54. C₁₃×#449	C₂²	semidirect
56. C₈×Q₈×C₁₃	C₂²	semidirect
57. C₈×Q₈×C₁₃	C₂²	semidirect
59. C₁₃×#442	C₂²	semidirect
60. C₁₃×#442	C₂²	semidirect
62. C₁₃×#440	C₂²	semidirect
64. C₄×C₁₃×SD₁₆	C₂²	semidirect
66. C₄×C₁₃×D₈	C₂²	semidirect
67. C₁₃×#436	C₂²	semidirect
68. C₁₃×#436	C₂²	semidirect
69. C₁₃×#432	C₂²	semidirect
70. C₁₃×#428	C₂²	semidirect
72. C₁₃×#417	C₂²	semidirect
73. C₄×C₁₃×M₁₆	C₂²	semidirect
166. #61465	C₁₃	direct (N × H)
209. C₁₃×SD₁₆	#41	semidirect
247. #3483	C₂×C₁₃	semidirect
248. D₄×#41	C₂×C₁₃	semidirect
249. #3391	C₂×C₁₃	semidirect
250. Q₈×SD₁₆	C₂×C₁₃	semidirect
251. #3362	C₂×C₁₃	semidirect
252. #3358	C₂×C₁₃	semidirect
253. #3354	C₂×C₁₃	semidirect
254. #3332	C₂×C₁₃	semidirect
255. #3325	C₂×C₁₃	semidirect
256. #3274	C₂×C₁₃	semidirect
257. #3184	C₂×C₁₃	semidirect
258. #3115	C₂×C₁₃	semidirect
259. #3109	C₂×C₁₃	semidirect
260. #2971	C₂×C₁₃	semidirect
261. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
272. Q₈×C₁₃	AGL(1,ℤ/8)	semidirect
273. Q₈×C₁₃	C₂×#41	semidirect
315. C₈×C₁₃	C₂×#41	semidirect
318. Q₈²	C₂²×C₁₃	semidirect
320. #555	C₂²×C₁₃	semidirect
323. #550	C₂²×C₁₃	semidirect
324. #550	C₂²×C₁₃	semidirect
332. #532	C₂²×C₁₃	semidirect
336. C₄×#41	C₂²×C₁₃	semidirect
338. #498	C₂²×C₁₃	semidirect
339. #493	C₂²×C₁₃	semidirect
340. #486	C₂²×C₁₃	semidirect
341. #486	C₂²×C₁₃	semidirect
342. #482	C₂²×C₁₃	semidirect
343. #481	C₂²×C₁₃	semidirect
345. #476	C₂²×C₁₃	semidirect
346. #475	C₂²×C₁₃	semidirect
347. #474	C₂²×C₁₃	semidirect
348. #469	C₂²×C₁₃	semidirect
349. #469	C₂²×C₁₃	semidirect
350. #460	C₂²×C₁₃	semidirect
352. #459	C₂²×C₁₃	semidirect
353. #459	C₂²×C₁₃	semidirect
354. #449	C₂²×C₁₃	semidirect
356. C₈×Q₈	C₂²×C₁₃	semidirect
357. C₈×Q₈	C₂²×C₁₃	semidirect
359. #442	C₂²×C₁₃	semidirect
360. #442	C₂²×C₁₃	semidirect
362. #440	C₂²×C₁₃	semidirect
364. C₄×SD₁₆	C₂²×C₁₃	semidirect
366. C₄×D₈	C₂²×C₁₃	semidirect
367. #436	C₂²×C₁₃	semidirect
368. #436	C₂²×C₁₃	semidirect
369. #432	C₂²×C₁₃	semidirect
370. #428	C₂²×C₁₃	semidirect
372. #417	C₂²×C₁₃	semidirect
373. C₄×M₁₆	C₂²×C₁₃	semidirect
541. SD₁₆	C₁₃×#41	semidirect
579. C₁₃	#61465	direct (N × H)
590. Q₈	C₁₃×AGL(1,ℤ/8)	semidirect
591. Q₈	C₂×C₁₃×#41	semidirect
633. C₈	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
C₁₃×#3483	2
D₄×C₁₃×#41	2
C₁₃×#3391	2
Q₈×C₁₃×SD₁₆	2
C₁₃×#3362	2
C₁₃×#3358	2
C₁₃×#3354	2
C₁₃×#3332	2
C₁₃×#3325	2
C₁₃×#3274	2
C₁₃×#3184	2
C₁₃×#3115	2
C₁₃×#3109	2
C₁₃×#2971	2
C₄×C₁₃×AGL(1,ℤ/8)	2
#61465	13

Subgroups — C13×#61465 #15747804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61465 #15747804