Subgroups — C₁₃×#60878 #15747217

Order 3328.

1666 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3242	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3231	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3231	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3230	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3229	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3160	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3139	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3097	C₂	1	4	yes	maximal
13	C₁₃×#3082	C₂	1	4	yes	maximal, complemented
14	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic
15	Q₈²×C₁₃	—	2	1	no	—
16	C₁₃×#557	—	2	1	no	—
17	C₁₃×#557	—	2	1	no	—
18	C₁₃×#557	—	2	1	no	—
19	C₁₃×#556	—	2	1	no	—
20	C₁₃×#556	—	2	1	no	—
21	C₁₃×#554	—	2	2	no	—
22	C₁₃×#554	—	2	1	no	—
23	C₁₃×#552	—	2	2	no	—
24	C₁₃×#552	—	2	2	no	—
25	D₄×Q₈×C₁₃	—	2	2	no	—
26	D₄×Q₈×C₁₃	—	2	1	no	—
27	C₁₃×#544	C₂²	1	2	yes	—
28	C₁₃×#544	C₂²	1	4	yes	—
29	C₁₃×#541	C₂²	1	4	yes	—
30	C₁₃×#536	C₂²	1	2	yes	—
31	C₁₃×#533	C₂²	1	2	yes	—
32	C₁₃×#533	C₂²	1	2	yes	—
33	C₁₃×#533	C₂²	1	1	yes	characteristic
34	C₁₃×#533	C₂²	1	1	yes	characteristic
35	C₁₃×#533	C₂²	1	2	yes	—
36	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
39	C₁₃×#520	C₂²	1	2	yes	—
40	C₁₃×#519	C₂²	1	2	yes	—
41	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
42	C₁₃×#501	C₂²	1	4	yes	—
43	C₁₃×#500	C₂²	1	1	yes	characteristic
44	C₁₃×#500	C₂²	1	1	yes	characteristic
45	C₁₃×#500	C₂²	1	2	yes	—
46	C₁₃×#499	C₂²	1	4	yes	—
47	C₁₃×#498	C₂²	1	1	yes	characteristic
48	C₁₃×#498	C₂²	1	1	yes	characteristic
49	C₁₃×#498	C₂²	1	2	yes	—
50	C₁₃×#491	C₂²	1	4	yes	—
51	C₁₃×#487	C₂²	1	2	yes	—
52	C₁₃×#487	C₂²	1	2	yes	—
53	C₁₃×#487	C₂²	1	4	yes	—
54	C₁₃×#487	C₂²	1	2	yes	—
55	C₁₃×#487	C₂²	1	2	yes	—
56	C₁₃×#485	C₂²	1	8	yes	—
57	C₁₃×#485	C₂²	1	8	yes	—
58	C₁₃×#484	C₂²	1	8	yes	—
59	C₁₃×#483	C₂²	1	8	yes	—
60	C₁₃×#479	C₂²	1	8	yes	—
61	C₁₃×#479	C₂²	1	8	yes	—
62	C₁₃×#477	C₂²	1	8	yes	—
63	C₁₃×#475	C₂²	1	8	yes	—
64	C₁₃×#433	C₂²	1	4	yes	—
65	C₁₃×#431	C₂²	1	2	yes	—
66	C₁₃×#431	C₂²	1	2	yes	—
67	C₁₃×#428	C₂²	1	4	yes	—
68	C₁₃×#427	C₂²	1	4	yes	—
69	C₁₃×#424	C₂²	1	2	yes	—
70	C₁₃×#419	C₂²	1	4	yes	—
71	C₂×C₁₃×#103	C₂²	1	4	yes	—
72	C₁₃×#408	C₂²	1	2	yes	—
73	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
74	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
76	C₂²×Q₈×C₁₃	—	2	1	no	—
77	C₂²×Q₈×C₁₃	—	2	2	no	—
78	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
79	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
80	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
81	C₁₃×C₄⋊Q₈	—	2	2	no	—
82	C₁₃×C₄⋊Q₈	—	2	2	no	—
83	C₁₃×C₄⋊Q₈	—	2	4	no	—
84	C₁₃×C₄⋊Q₈	—	2	2	no	—
85	C₁₃×C₄⋊Q₈	—	2	1	no	—
86	C₁₃×C₄⋊Q₈	—	2	2	no	—
87	C₁₃×C₄⋊Q₈	—	2	1	no	—
88	C₁₃×C₄⋊Q₈	—	2	1	no	—
89	C₁₃×C₄⋊Q₈	—	2	1	no	—
90	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
91	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
92	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
93	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
94	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
95	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
96	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
98	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
99	C₁₃×#126	—	2	4	no	—
100	C₁₃×#126	—	2	4	no	—
101	C₁₃×#125	—	2	4	no	—
102	C₁₃×#125	—	2	4	no	—
103	C₁₃×#125	—	2	2	no	—
104	C₁₃×#125	—	2	4	no	—
105	C₁₃×#125	—	2	2	no	—
106	C₁₃×#125	—	2	2	no	—
107	C₁₃×#125	C₂³	1	4	yes	—
108	C₁₃×#125	C₂³	1	2	yes	—
109	C₁₃×#125	C₂³	1	2	yes	—
110	C₁₃×#124	—	2	2	no	—
111	C₁₃×#123	—	2	4	no	—
112	C₁₃×C₂²⋊Q₈	—	2	1	no	—
113	C₁₃×C₂²⋊Q₈	—	2	2	no	—
114	C₁₃×C₂²⋊Q₈	—	2	1	no	—
115	C₁₃×C₂²⋊Q₈	—	2	1	no	—
116	C₁₃×C₂²⋊Q₈	—	2	2	no	—
117	C₁₃×C₂²⋊Q₈	—	2	2	no	—
118	C₁₃×C₂²⋊Q₈	—	2	1	no	—
119	C₁₃×C₂²⋊Q₈	—	2	2	no	—
120	C₁₃×C₂²⋊Q₈	—	2	4	no	—
121	C₁₃×C₂²⋊Q₈	—	2	4	no	—
122	C₁₃×C₂²⋊Q₈	—	2	4	no	—
123	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
124	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
125	C₄×Q₈×C₁₃	—	2	2	no	—
126	C₄×Q₈×C₁₃	—	2	2	no	—
127	C₄×Q₈×C₁₃	—	2	2	no	—
128	C₄×Q₈×C₁₃	—	2	2	no	—
129	C₄×Q₈×C₁₃	—	2	1	no	—
130	C₄×Q₈×C₁₃	—	2	2	no	—
131	C₄×Q₈×C₁₃	—	2	2	no	—
132	C₄×Q₈×C₁₃	—	2	2	no	—
133	C₄×Q₈×C₁₃	—	2	1	no	—
134	C₄×Q₈×C₁₃	—	2	1	no	—
135	C₄×Q₈×C₁₃	—	2	1	no	—
136	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
137	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
138	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
139	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
140	C₄×D₄×C₁₃	—	2	4	no	—
141	C₄×D₄×C₁₃	—	2	2	no	—
142	C₄×D₄×C₁₃	D₄	1	2	yes	—
143	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
144	C₄×D₄×C₁₃	D₄	1	2	yes	—
145	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
146	C₁₃×#117	—	2	2	no	—
147	C₁₃×#117	—	2	2	no	—
148	C₁₃×#117	—	2	4	no	—
149	C₁₃×#117	C₂³	1	2	yes	—
150	C₁₃×#117	C₂³	1	2	yes	—
151	C₁₃×#117	C₂³	1	4	yes	—
152	C₁₃×#117	C₂³	1	1	yes	characteristic
153	C₁₃×#117	C₂³	1	2	yes	—
154	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
157	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
160	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
162	C₁₃×#107	C₂³	1	4	yes	—
163	C₁₃×#107	C₂³	1	4	yes	—
164	C₁₃×#107	C₂³	1	8	yes	—
165	C₁₃×#106	C₂³	1	4	yes	—
166	C₁₃×#106	C₂³	1	4	yes	—
167	C₁₃×#106	C₂³	1	8	yes	—
168	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
169	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
170	C₁₃×#103	C₂³	1	8	yes	—
171	C₁₃×#103	C₂³	1	8	yes	—
172	C₁₃×#103	C₂³	1	8	yes	—
173	C₁₃×#103	C₂³	1	8	yes	—
174	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
175	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
176	C₁₃×#97	C₂³	1	2	yes	—
177	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
178	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
179	C₄×C₈×C₁₃	C₂³	1	2	yes	—
180	C₄×C₈×C₁₃	C₂³	1	2	yes	—
181	#60878	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₁₃×#41	—	2	4	no	—
183	C₂×Q₈×C₁₃	—	2	1	no	—
184	C₂×Q₈×C₁₃	—	2	1	no	—
185	C₂×Q₈×C₁₃	—	2	1	no	—
186	C₂×Q₈×C₁₃	—	2	2	no	—
187	C₂×Q₈×C₁₃	—	2	2	no	—
188	C₂×Q₈×C₁₃	—	2	1	no	—
189	C₂×Q₈×C₁₃	—	2	4	no	—
190	C₂×Q₈×C₁₃	—	2	2	no	—
191	C₂×Q₈×C₁₃	—	2	8	no	—
192	C₂×Q₈×C₁₃	—	8	2	no	—
193	C₂×Q₈×C₁₃	—	8	4	no	—
194	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
196	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
197	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₁₃	—	2	2	no	—
199	C₂²×C₄×C₁₃	—	2	4	no	—
200	C₂²×C₄×C₁₃	—	2	2	no	—
201	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
203	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
207	C₁₃×M₁₆	—	2	4	no	—
208	C₂×C₈×C₁₃	—	2	4	no	—
209	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
210	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
211	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
212	C₁₃×C₄⋊C₄	—	2	2	no	—
213	C₁₃×C₄⋊C₄	—	2	1	no	—
214	C₁₃×C₄⋊C₄	—	2	2	no	—
215	C₁₃×C₄⋊C₄	—	2	2	no	—
216	C₁₃×C₄⋊C₄	—	2	4	no	—
217	C₁₃×C₄⋊C₄	—	2	2	no	—
218	C₁₃×C₄⋊C₄	—	2	2	no	—
219	C₁₃×C₄⋊C₄	—	2	2	no	—
220	C₁₃×C₄⋊C₄	—	2	4	no	—
221	C₁₃×C₄⋊C₄	—	2	2	no	—
222	C₁₃×C₄⋊C₄	—	2	1	no	—
223	C₁₃×C₄⋊C₄	—	2	1	no	—
224	C₁₃×C₄⋊C₄	—	2	4	no	—
225	C₁₃×C₄⋊C₄	—	2	4	no	—
226	C₁₃×C₄⋊C₄	—	2	1	no	—
227	C₁₃×C₄⋊C₄	—	2	4	no	—
228	C₁₃×C₄⋊C₄	—	2	2	no	—
229	C₁₃×C₄⋊C₄	—	2	4	no	—
230	C₁₃×C₄⋊C₄	—	2	2	no	—
231	C₁₃×C₄⋊C₄	—	2	2	no	—
232	C₁₃×C₄⋊C₄	—	2	2	no	—
233	C₁₃×C₄⋊C₄	—	2	4	no	—
234	C₁₃×C₄⋊C₄	—	2	4	no	—
235	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
236	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
237	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
238	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
239	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
240	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
241	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
242	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
243	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
244	C₁₃×C₂²⋊C₄	—	2	2	no	—
245	C₁₃×C₂²⋊C₄	—	2	4	no	—
246	C₁₃×C₂²⋊C₄	—	2	4	no	—
247	C₁₃×C₂²⋊C₄	—	2	4	no	—
248	C₁₃×C₂²⋊C₄	—	2	2	no	—
249	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
250	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
251	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
252	C₄²×C₁₃	—	2	4	no	—
253	C₄²×C₁₃	—	2	4	no	—
254	C₄²×C₁₃	—	2	4	no	—
255	C₄²×C₁₃	—	2	2	no	—
256	C₄²×C₁₃	—	2	2	no	—
257	C₄²×C₁₃	C₂×D₄	1	2	yes	—
258	C₄²×C₁₃	C₂×D₄	1	2	yes	—
259	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
260	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
261	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
262	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
263	C₄²×C₁₃	C₂⁴	1	2	yes	—
264	#3509	C₂×C₁₃	1	1	yes	characteristic
265	#3503	C₂×C₁₃	1	1	yes	characteristic
266	#3242	C₂×C₁₃	1	8	yes	complemented
267	#3231	C₂×C₁₃	1	2	yes	complemented
268	#3231	C₂×C₁₃	1	2	yes	complemented
269	#3230	C₂×C₁₃	1	2	yes	complemented
270	#3229	C₂×C₁₃	1	2	yes	complemented
271	#3165	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#3160	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#3139	C₂×C₁₃	1	1	yes	characteristic, complemented
274	C₂×#487	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#3097	C₂×C₁₃	1	4	yes	—
276	#3082	C₂×C₁₃	1	4	yes	complemented
277	#2922	C₂×C₁₃	1	1	yes	characteristic
278	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
279	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
280	Q₈×C₁₃	—	2	2	no	—
281	Q₈×C₁₃	—	2	8	no	—
282	Q₈×C₁₃	—	4	4	no	—
283	Q₈×C₁₃	—	4	2	no	—
284	Q₈×C₁₃	—	4	4	no	—
285	Q₈×C₁₃	—	4	2	no	—
286	Q₈×C₁₃	—	4	2	no	—
287	Q₈×C₁₃	—	4	2	no	—
288	Q₈×C₁₃	—	8	4	no	—
289	Q₈×C₁₃	—	8	2	no	—
290	D₄×C₁₃	—	2	4	no	—
291	D₄×C₁₃	—	2	2	no	—
292	C₂×C₄×C₁₃	—	2	2	no	—
293	C₂×C₄×C₁₃	—	2	4	no	—
294	C₂×C₄×C₁₃	—	2	2	no	—
295	C₂×C₄×C₁₃	—	2	4	no	—
296	C₂×C₄×C₁₃	—	2	4	no	—
297	C₂×C₄×C₁₃	—	2	2	no	—
298	C₂×C₄×C₁₃	—	2	2	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	4	no	—
301	C₂×C₄×C₁₃	—	2	4	no	—
302	C₂×C₄×C₁₃	—	2	2	no	—
303	C₂×C₄×C₁₃	—	4	4	no	—
304	C₂×C₄×C₁₃	—	8	2	no	—
305	C₂×C₄×C₁₃	—	8	4	no	—
306	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
307	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
308	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
309	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
310	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
312	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
315	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
316	C₈×C₁₃	—	2	2	no	—
317	C₈×C₁₃	—	2	2	no	—
318	C₈×C₁₃	—	2	4	no	—
319	Q₈²	—	2	1	no	—
320	#557	—	2	1	no	—
321	#557	—	2	1	no	—
322	#557	—	2	1	no	—
323	#556	—	2	1	no	—
324	#556	—	2	1	no	—
325	#554	—	2	2	no	—
326	#554	—	2	1	no	—
327	#552	—	2	2	no	—
328	#552	—	2	2	no	—
329	D₄×Q₈	—	2	2	no	—
330	D₄×Q₈	—	2	1	no	—
331	#544	C₂²×C₁₃	1	2	yes	—
332	#544	C₂²×C₁₃	1	4	yes	—
333	#541	C₂²×C₁₃	1	4	yes	—
334	#536	C₂²×C₁₃	1	2	yes	—
335	#533	C₂²×C₁₃	1	2	yes	—
336	#533	C₂²×C₁₃	1	2	yes	—
337	#533	C₂²×C₁₃	1	1	yes	characteristic
338	#533	C₂²×C₁₃	1	1	yes	characteristic
339	#533	C₂²×C₁₃	1	2	yes	—
340	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
341	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
342	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
343	#520	C₂²×C₁₃	1	2	yes	—
344	#519	C₂²×C₁₃	1	2	yes	—
345	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
346	#501	C₂²×C₁₃	1	4	yes	—
347	#500	C₂²×C₁₃	1	1	yes	characteristic
348	#500	C₂²×C₁₃	1	1	yes	characteristic
349	#500	C₂²×C₁₃	1	2	yes	—
350	#499	C₂²×C₁₃	1	4	yes	—
351	#498	C₂²×C₁₃	1	1	yes	characteristic
352	#498	C₂²×C₁₃	1	1	yes	characteristic
353	#498	C₂²×C₁₃	1	2	yes	—
354	#491	C₂²×C₁₃	1	4	yes	—
355	#487	C₂²×C₁₃	1	2	yes	—
356	#487	C₂²×C₁₃	1	2	yes	—
357	#487	C₂²×C₁₃	1	4	yes	—
358	#487	C₂²×C₁₃	1	2	yes	—
359	#487	C₂²×C₁₃	1	2	yes	—
360	#485	C₂²×C₁₃	1	8	yes	—
361	#485	C₂²×C₁₃	1	8	yes	—
362	#484	C₂²×C₁₃	1	8	yes	—
363	#483	C₂²×C₁₃	1	8	yes	—
364	#479	C₂²×C₁₃	1	8	yes	—
365	#479	C₂²×C₁₃	1	8	yes	—
366	#477	C₂²×C₁₃	1	8	yes	—
367	#475	C₂²×C₁₃	1	8	yes	—
368	#433	C₂²×C₁₃	1	4	yes	—
369	#431	C₂²×C₁₃	1	2	yes	—
370	#431	C₂²×C₁₃	1	2	yes	—
371	#428	C₂²×C₁₃	1	4	yes	—
372	#427	C₂²×C₁₃	1	4	yes	—
373	#424	C₂²×C₁₃	1	2	yes	—
374	#419	C₂²×C₁₃	1	4	yes	—
375	C₂×#103	C₂²×C₁₃	1	4	yes	—
376	#408	C₂²×C₁₃	1	2	yes	—
377	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
378	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
379	C₂²×C₁₃	—	2	1	no	—
380	C₂²×C₁₃	—	2	1	no	—
381	C₂²×C₁₃	—	2	2	no	—
382	C₂²×C₁₃	—	2	2	no	—
383	C₂²×C₁₃	—	2	2	no	—
384	C₂²×C₁₃	#536	1	2	yes	—
385	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
386	C₄×C₁₃	—	2	2	no	—
387	C₄×C₁₃	—	2	2	no	—
388	C₄×C₁₃	—	2	1	no	—
389	C₄×C₁₃	—	2	2	no	—
390	C₄×C₁₃	—	2	1	no	—
391	C₄×C₁₃	—	4	4	no	—
392	C₄×C₁₃	—	4	4	no	—
393	C₄×C₁₃	—	4	2	no	—
394	C₄×C₁₃	—	4	2	no	—
395	C₄×C₁₃	—	4	2	no	—
396	C₄×C₁₃	—	4	2	no	—
397	C₄×C₁₃	#536	1	2	yes	—
398	C₄×C₁₃	#577	1	2	yes	—
399	C₄×C₁₃	#578	1	2	yes	—
400	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
401	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
402	C₂²×Q₈	—	2	1	no	—
403	C₂²×Q₈	—	2	2	no	—
404	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
405	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
406	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
407	C₄⋊Q₈	—	2	2	no	—
408	C₄⋊Q₈	—	2	2	no	—
409	C₄⋊Q₈	—	2	4	no	—
410	C₄⋊Q₈	—	2	2	no	—
411	C₄⋊Q₈	—	2	1	no	—
412	C₄⋊Q₈	—	2	2	no	—
413	C₄⋊Q₈	—	2	1	no	—
414	C₄⋊Q₈	—	2	1	no	—
415	C₄⋊Q₈	—	2	1	no	—
416	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
417	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
418	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
419	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
420	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
421	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
422	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
423	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
424	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
425	#126	—	2	4	no	—
426	#126	—	2	4	no	—
427	#125	—	2	4	no	—
428	#125	—	2	4	no	—
429	#125	—	2	2	no	—
430	#125	—	2	4	no	—
431	#125	—	2	2	no	—
432	#125	—	2	2	no	—
433	#125	C₂³×C₁₃	1	2	yes	—
434	#125	C₂³×C₁₃	1	4	yes	—
435	#125	C₂³×C₁₃	1	2	yes	—
436	#124	—	2	2	no	—
437	#123	—	2	4	no	—
438	C₂²⋊Q₈	—	2	1	no	—
439	C₂²⋊Q₈	—	2	2	no	—
440	C₂²⋊Q₈	—	2	1	no	—
441	C₂²⋊Q₈	—	2	1	no	—
442	C₂²⋊Q₈	—	2	2	no	—
443	C₂²⋊Q₈	—	2	2	no	—
444	C₂²⋊Q₈	—	2	1	no	—
445	C₂²⋊Q₈	—	2	2	no	—
446	C₂²⋊Q₈	—	2	4	no	—
447	C₂²⋊Q₈	—	2	4	no	—
448	C₂²⋊Q₈	—	2	4	no	—
449	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
450	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
451	C₄×Q₈	—	2	2	no	—
452	C₄×Q₈	—	2	2	no	—
453	C₄×Q₈	—	2	2	no	—
454	C₄×Q₈	—	2	2	no	—
455	C₄×Q₈	—	2	1	no	—
456	C₄×Q₈	—	2	2	no	—
457	C₄×Q₈	—	2	2	no	—
458	C₄×Q₈	—	2	2	no	—
459	C₄×Q₈	—	2	1	no	—
460	C₄×Q₈	—	2	1	no	—
461	C₄×Q₈	—	2	1	no	—
462	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
463	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
464	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
465	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
466	C₄×D₄	—	2	4	no	—
467	C₄×D₄	—	2	2	no	—
468	C₄×D₄	D₄×C₁₃	1	2	yes	—
469	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
470	C₄×D₄	D₄×C₁₃	1	2	yes	—
471	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
472	#117	—	2	2	no	—
473	#117	—	2	2	no	—
474	#117	—	2	4	no	—
475	#117	C₂³×C₁₃	1	2	yes	—
476	#117	C₂³×C₁₃	1	2	yes	—
477	#117	C₂³×C₁₃	1	4	yes	—
478	#117	C₂³×C₁₃	1	1	yes	characteristic
479	#117	C₂³×C₁₃	1	2	yes	—
480	C₂×C₄⋊C₄	—	2	1	no	—
481	C₂×C₄⋊C₄	—	2	1	no	—
482	C₂×C₄⋊C₄	—	2	1	no	—
483	C₂×C₄⋊C₄	—	2	2	no	—
484	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
486	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
487	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
488	#107	C₂³×C₁₃	1	4	yes	—
489	#107	C₂³×C₁₃	1	4	yes	—
490	#107	C₂³×C₁₃	1	8	yes	—
491	#106	C₂³×C₁₃	1	4	yes	—
492	#106	C₂³×C₁₃	1	4	yes	—
493	#106	C₂³×C₁₃	1	8	yes	—
494	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
495	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
496	#103	C₂³×C₁₃	1	8	yes	—
497	#103	C₂³×C₁₃	1	8	yes	—
498	#103	C₂³×C₁₃	1	8	yes	—
499	#103	C₂³×C₁₃	1	8	yes	—
500	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
501	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
502	#97	C₂³×C₁₃	1	2	yes	—
503	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
504	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
505	C₄×C₈	C₂³×C₁₃	1	2	yes	—
506	C₄×C₈	C₂³×C₁₃	1	2	yes	—
507	C₂×C₁₃	—	2	2	no	—
508	C₂×C₁₃	—	4	2	no	—
509	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
510	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
511	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
512	#41	—	2	4	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	2	1	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	2	no	—
517	C₂×Q₈	—	2	2	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	—	2	4	no	—
520	C₂×Q₈	—	2	2	no	—
521	C₂×Q₈	—	2	8	no	—
522	C₂×Q₈	—	8	2	no	—
523	C₂×Q₈	—	8	4	no	—
524	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
525	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
526	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
527	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	4	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
532	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
533	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
534	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
535	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
536	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
537	M₁₆	—	2	4	no	—
538	C₂×C₈	—	2	4	no	—
539	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
540	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
541	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	2	no	—
545	C₄⋊C₄	—	2	2	no	—
546	C₄⋊C₄	—	2	4	no	—
547	C₄⋊C₄	—	2	2	no	—
548	C₄⋊C₄	—	2	2	no	—
549	C₄⋊C₄	—	2	2	no	—
550	C₄⋊C₄	—	2	4	no	—
551	C₄⋊C₄	—	2	2	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	4	no	—
555	C₄⋊C₄	—	2	4	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	4	no	—
558	C₄⋊C₄	—	2	2	no	—
559	C₄⋊C₄	—	2	4	no	—
560	C₄⋊C₄	—	2	2	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
566	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
567	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
568	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
569	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
570	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
571	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
572	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
573	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
574	C₂²⋊C₄	—	2	2	no	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	2	no	—
579	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
580	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
581	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
582	C₄²	—	2	4	no	—
583	C₄²	—	2	4	no	—
584	C₄²	—	2	4	no	—
585	C₄²	—	2	2	no	—
586	C₄²	—	2	2	no	—
587	C₄²	C₂×D₄×C₁₃	1	2	yes	—
588	C₄²	C₂×D₄×C₁₃	1	2	yes	—
589	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
590	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
591	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
592	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
593	C₄²	C₂⁴×C₁₃	1	2	yes	—
594	C₁₃	#60878	1	1	yes	characteristic, direct product factor, Sylow
595	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
596	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
597	Q₈	—	2	2	no	—
598	Q₈	—	2	8	no	—
599	Q₈	—	4	4	no	—
600	Q₈	—	4	4	no	—
601	Q₈	—	4	2	no	—
602	Q₈	—	4	2	no	—
603	Q₈	—	4	2	no	—
604	Q₈	—	4	2	no	—
605	Q₈	—	8	4	no	—
606	Q₈	—	8	2	no	—
607	D₄	—	2	4	no	—
608	D₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	4	4	no	—
621	C₂×C₄	—	8	2	no	—
622	C₂×C₄	—	8	4	no	—
623	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
624	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
625	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
626	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
627	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
628	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
629	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
630	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
631	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
632	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
633	C₈	—	2	2	no	—
634	C₈	—	2	2	no	—
635	C₈	—	2	4	no	—
636	C₂²	—	2	1	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	2	no	—
641	C₂²	C₁₃×#536	1	2	yes	—
642	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
643	C₄	—	2	2	no	—
644	C₄	—	2	1	no	—
645	C₄	—	2	2	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	2	no	—
648	C₄	—	4	4	no	—
649	C₄	—	4	2	no	—
650	C₄	—	4	2	no	—
651	C₄	—	4	2	no	—
652	C₄	—	4	2	no	—
653	C₄	—	4	4	no	—
654	C₄	C₁₃×#536	1	2	yes	—
655	C₄	C₁₃×#577	1	2	yes	—
656	C₄	C₁₃×#578	1	2	yes	—
657	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
658	C₂	—	2	2	no	—
659	C₂	—	4	2	no	—
660	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
661	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
662	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#41	C₂³
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
3. C₁₃×#3242	C₂	semidirect
4. C₁₃×#3231	C₂	semidirect
5. C₁₃×#3231	C₂	semidirect
6. C₁₃×#3230	C₂	semidirect
7. C₁₃×#3229	C₂	semidirect
8. C₁₃×#3165	C₂	semidirect
9. C₁₃×#3160	C₂	semidirect
10. C₁₃×#3139	C₂	semidirect
11. C₂×C₁₃×#487	C₂	semidirect
13. C₁₃×#3082	C₂	semidirect
181. #60878	C₁₃	direct (N × H)
266. #3242	C₂×C₁₃	semidirect
267. #3231	C₂×C₁₃	semidirect
268. #3231	C₂×C₁₃	semidirect
269. #3230	C₂×C₁₃	semidirect
270. #3229	C₂×C₁₃	semidirect
271. #3165	C₂×C₁₃	semidirect
272. #3160	C₂×C₁₃	semidirect
273. #3139	C₂×C₁₃	semidirect
274. C₂×#487	C₂×C₁₃	semidirect
276. #3082	C₂×C₁₃	semidirect
594. C₁₃	#60878	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×#3509	2
C₁₃×#3503	2
C₁₃×#3242	2
C₁₃×#3231	2
C₁₃×#3230	2
C₁₃×#3229	2
C₁₃×#3165	2
C₁₃×#3160	2
C₁₃×#3139	2
C₂×C₁₃×#487	2
C₁₃×#3097	2
C₁₃×#3082	2
C₁₃×#2922	2
#60878	13

Subgroups — C13×#60878 #15747217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60878 #15747217