Subgroups — C₁₃×#61700 #15748039

Order 3328.

1842 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3341	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3340	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3305	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3303	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3227	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3188	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3091	C₂	1	4	yes	maximal, complemented
13	C₁₃×#2972	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#559	—	2	2	no	—
15	C₁₃×#556	C₂²	1	2	yes	complemented
16	C₁₃×#555	—	2	2	no	—
17	C₁₃×#555	—	2	2	no	—
18	C₁₃×#555	C₂²	1	4	yes	—
19	C₁₃×#555	C₂²	1	4	yes	—
20	C₁₃×#555	C₂²	1	2	yes	complemented
21	C₁₃×#553	—	2	2	no	—
22	C₁₃×#550	C₂²	1	2	yes	complemented
23	C₁₃×#547	C₂²	1	2	yes	complemented
24	C₁₃×#538	—	2	2	no	—
25	C₁₃×#535	—	2	1	no	—
26	C₁₃×#533	C₂²	1	1	yes	characteristic
27	C₁₃×#532	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#124	—	2	2	no	—
30	C₁₃×#525	C₂²	1	4	yes	—
31	C₂×C₁₃×#121	—	2	1	no	—
32	C₂×C₁₃×#121	C₂²	1	2	yes	—
33	C₁₃×#520	—	2	1	no	—
34	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#117	—	2	1	no	—
37	C₂×C₁₃×#117	C₂²	1	2	yes	—
38	C₁₃×#500	C₂²	1	2	yes	complemented
39	C₁₃×#498	C₂²	1	2	yes	complemented
40	C₁₃×#487	C₂²	1	2	yes	complemented
41	C₁₃×#486	C₂²	1	2	yes	complemented
42	C₁₃×#485	C₂²	1	8	yes	complemented
43	C₁₃×#484	C₂²	1	4	yes	—
44	C₁₃×#483	C₂²	1	2	yes	—
45	C₁₃×#482	C₂²	1	8	yes	complemented
46	C₁₃×#482	C₂²	1	8	yes	complemented
47	C₁₃×#481	C₂²	1	4	yes	—
48	C₁₃×#480	C₂²	1	2	yes	—
49	C₁₃×#477	C₂²	1	4	yes	complemented
50	C₁₃×#476	C₂²	1	4	yes	complemented
51	C₁₃×#476	C₂²	1	2	yes	complemented
52	C₁₃×#474	C₂²	1	2	yes	complemented
53	C₁₃×#466	C₂²	1	8	yes	complemented
54	C₁₃×#465	C₂²	1	8	yes	complemented
55	C₁₃×#461	C₂²	1	2	yes	complemented
56	C₁₃×#459	C₂²	1	2	yes	complemented
57	C₁₃×#450	C₂²	1	2	yes	—
58	C₁₃×#449	C₂²	1	8	yes	complemented
59	C₁₃×#447	C₂²	1	2	yes	—
60	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
61	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
62	C₈×D₄×C₁₃	C₂²	1	4	yes	complemented
63	C₈×D₄×C₁₃	C₂²	1	4	yes	complemented
64	C₁₃×#431	C₂²	1	1	yes	characteristic
65	C₁₃×#431	C₂²	1	1	yes	characteristic
66	C₁₃×#427	C₂²	1	8	yes	complemented
67	C₁₃×#416	C₂²	1	8	yes	complemented
68	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	—
69	C₂×C₁₃×#41	—	2	1	no	—
70	C₂×C₁₃×#41	C₂³	1	4	yes	—
71	C₂²×Q₈×C₁₃	—	2	1	no	—
72	C₂²×D₄×C₁₃	—	2	2	no	—
73	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
74	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	—	2	1	no	—
76	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
77	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
78	C₂×C₁₃×D₈	C₂³	1	4	yes	—
79	C₂²×C₈×C₁₃	C₂³	1	8	yes	—
80	C₁₃×C₄⋊Q₈	—	2	1	no	—
81	C₁₃×C₄⋊Q₈	—	2	1	no	—
82	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
85	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
87	C₁₃×#127	—	2	2	no	—
88	C₁₃×#127	C₂³	1	1	yes	characteristic
89	C₁₃×#126	—	2	4	no	—
90	C₁₃×#125	—	2	1	no	—
91	C₁₃×#124	—	2	2	no	—
92	C₁₃×#124	—	2	8	no	—
93	C₁₃×#124	—	2	8	no	—
94	C₁₃×#124	—	2	4	no	—
95	C₁₃×#124	—	2	1	no	—
96	C₁₃×#123	—	2	4	no	—
97	C₁₃×#123	—	2	4	no	—
98	C₁₃×C₂²⋊Q₈	—	2	1	no	—
99	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
100	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
101	C₁₃×#121	—	2	4	no	—
102	C₁₃×#121	—	2	4	no	—
103	C₁₃×#121	—	2	2	no	—
104	C₁₃×#121	—	2	2	no	—
105	C₁₃×#121	—	2	4	no	—
106	C₁₃×#121	—	2	1	no	—
107	C₁₃×#121	—	2	4	no	—
108	C₁₃×#121	C₂³	1	2	yes	—
109	C₁₃×#121	C₂³	1	8	yes	—
110	C₁₃×#121	C₂³	1	4	yes	—
111	C₁₃×#120	—	2	4	no	—
112	C₄×Q₈×C₁₃	—	2	2	no	—
113	C₄×Q₈×C₁₃	—	2	1	no	—
114	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
115	C₄×D₄×C₁₃	—	2	4	no	—
116	C₄×D₄×C₁₃	—	2	4	no	—
117	C₄×D₄×C₁₃	—	2	2	no	—
118	C₄×D₄×C₁₃	—	2	1	no	—
119	C₄×D₄×C₁₃	—	2	1	no	—
120	C₄×D₄×C₁₃	—	2	1	no	—
121	C₄×D₄×C₁₃	D₄	1	2	yes	—
122	C₄×D₄×C₁₃	D₄	1	2	yes	—
123	C₄×D₄×C₁₃	C₂³	1	2	yes	—
124	C₄×D₄×C₁₃	C₂³	1	2	yes	—
125	C₄×D₄×C₁₃	C₂³	1	2	yes	—
126	C₄×D₄×C₁₃	C₂³	1	2	yes	—
127	C₄×D₄×C₁₃	C₂³	1	2	yes	—
128	C₁₃×#117	—	2	4	no	—
129	C₁₃×#117	—	2	1	no	—
130	C₁₃×#117	—	2	4	no	—
131	C₁₃×#117	—	2	4	no	—
132	C₁₃×#117	—	2	2	no	—
133	C₁₃×#117	C₂³	1	8	yes	—
134	C₁₃×#117	C₂³	1	4	yes	—
135	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
138	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
141	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
142	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
143	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
144	C₂×C₄²×C₁₃	—	2	2	no	—
145	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
146	C₁₃×#107	C₂³	1	4	yes	—
147	C₁₃×#107	C₂³	1	8	yes	—
148	C₁₃×#106	C₂³	1	4	yes	—
149	C₁₃×#106	C₂³	1	8	yes	—
150	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
151	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
152	C₁₃×#103	C₂³	1	4	yes	—
153	C₁₃×#103	C₂³	1	8	yes	—
154	C₁₃×#102	C₂³	1	4	yes	—
155	C₁₃×#102	C₂³	1	8	yes	—
156	C₁₃×#102	C₂³	1	4	yes	—
157	C₁₃×#102	C₂³	1	4	yes	—
158	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
159	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
160	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
161	C₄×C₈×C₁₃	C₂³	1	2	yes	—
162	C₄×C₈×C₁₃	C₂³	1	2	yes	—
163	#61700	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂⁴×C₁₃	—	2	1	no	—
165	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
166	C₁₃×#41	—	4	8	no	—
167	C₁₃×#41	—	4	4	no	—
168	C₂×Q₈×C₁₃	—	2	1	no	—
169	C₂×Q₈×C₁₃	—	2	1	no	—
170	C₂×Q₈×C₁₃	—	2	2	no	—
171	C₂×Q₈×C₁₃	—	2	2	no	—
172	C₂×Q₈×C₁₃	—	8	2	no	—
173	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
174	C₂×D₄×C₁₃	—	2	2	no	—
175	C₂×D₄×C₁₃	—	2	4	no	—
176	C₂×D₄×C₁₃	—	2	4	no	—
177	C₂×D₄×C₁₃	—	2	8	no	—
178	C₂×D₄×C₁₃	—	2	4	no	—
179	C₂×D₄×C₁₃	—	2	1	no	—
180	C₂×D₄×C₁₃	—	2	1	no	—
181	C₂×D₄×C₁₃	—	2	1	no	—
182	C₂×D₄×C₁₃	—	4	2	no	—
183	C₂×D₄×C₁₃	—	8	4	no	—
184	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
185	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
186	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
187	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₁₃	—	2	1	no	—
189	C₂²×C₄×C₁₃	—	2	2	no	—
190	C₂²×C₄×C₁₃	—	2	2	no	—
191	C₂²×C₄×C₁₃	—	2	2	no	—
192	C₂²×C₄×C₁₃	—	2	2	no	—
193	C₂²×C₄×C₁₃	—	2	4	no	—
194	C₂²×C₄×C₁₃	—	4	4	no	—
195	C₂²×C₄×C₁₃	—	4	4	no	—
196	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
197	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
199	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
202	C₁₃×SD₁₆	—	4	4	no	—
203	C₁₃×D₈	—	4	4	no	—
204	C₂×C₈×C₁₃	—	4	8	no	—
205	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
206	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
207	C₁₃×C₄⋊C₄	—	2	1	no	—
208	C₁₃×C₄⋊C₄	—	2	2	no	—
209	C₁₃×C₄⋊C₄	—	2	2	no	—
210	C₁₃×C₄⋊C₄	—	2	4	no	—
211	C₁₃×C₄⋊C₄	—	2	1	no	—
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	1	no	—
216	C₁₃×C₄⋊C₄	—	2	1	no	—
217	C₁₃×C₄⋊C₄	—	2	2	no	—
218	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
219	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
220	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
221	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
222	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
223	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
224	C₁₃×C₂²⋊C₄	—	2	8	no	—
225	C₁₃×C₂²⋊C₄	—	2	2	no	—
226	C₁₃×C₂²⋊C₄	—	2	4	no	—
227	C₁₃×C₂²⋊C₄	—	2	4	no	—
228	C₁₃×C₂²⋊C₄	—	2	8	no	—
229	C₁₃×C₂²⋊C₄	—	2	2	no	—
230	C₁₃×C₂²⋊C₄	—	2	2	no	—
231	C₁₃×C₂²⋊C₄	—	2	4	no	—
232	C₁₃×C₂²⋊C₄	—	2	2	no	—
233	C₁₃×C₂²⋊C₄	—	2	2	no	—
234	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
235	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
236	C₄²×C₁₃	—	2	8	no	—
237	C₄²×C₁₃	—	2	4	no	—
238	C₄²×C₁₃	—	2	2	no	—
239	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
240	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
241	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
243	#3506	C₂×C₁₃	1	1	yes	characteristic, complemented
244	C₂×#555	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#3341	C₂×C₁₃	1	4	yes	complemented
246	#3340	C₂×C₁₃	1	4	yes	complemented
247	#3305	C₂×C₁₃	1	4	yes	complemented
248	#3303	C₂×C₁₃	1	4	yes	complemented
249	#3230	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#3227	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#3188	C₂×C₁₃	1	4	yes	complemented
252	#3101	C₂×C₁₃	1	1	yes	characteristic, complemented
253	#3100	C₂×C₁₃	1	1	yes	characteristic, complemented
254	#3091	C₂×C₁₃	1	4	yes	complemented
255	#2972	C₂×C₁₃	1	1	yes	characteristic, complemented
256	C₂³×C₁₃	—	2	4	no	—
257	C₂³×C₁₃	—	2	2	no	—
258	C₂³×C₁₃	—	2	2	no	—
259	C₂³×C₁₃	—	4	2	no	—
260	C₂³×C₁₃	—	4	2	no	—
261	C₂³×C₁₃	—	4	2	no	—
262	C₂³×C₁₃	—	4	2	no	—
263	C₂³×C₁₃	—	4	2	no	—
264	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
265	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
266	Q₈×C₁₃	—	2	4	no	—
267	Q₈×C₁₃	—	4	2	no	—
268	Q₈×C₁₃	—	8	1	no	—
269	Q₈×C₁₃	—	8	2	no	—
270	Q₈×C₁₃	—	8	2	no	—
271	D₄×C₁₃	—	2	4	no	—
272	D₄×C₁₃	—	2	4	no	—
273	D₄×C₁₃	—	2	2	no	—
274	D₄×C₁₃	—	2	4	no	—
275	D₄×C₁₃	—	2	2	no	—
276	D₄×C₁₃	—	4	2	no	—
277	D₄×C₁₃	—	4	4	no	—
278	D₄×C₁₃	—	4	2	no	—
279	D₄×C₁₃	—	8	1	no	—
280	D₄×C₁₃	—	8	4	no	—
281	D₄×C₁₃	—	8	8	no	—
282	D₄×C₁₃	—	8	4	no	—
283	C₂×C₄×C₁₃	—	2	8	no	—
284	C₂×C₄×C₁₃	—	2	2	no	—
285	C₂×C₄×C₁₃	—	2	2	no	—
286	C₂×C₄×C₁₃	—	2	2	no	—
287	C₂×C₄×C₁₃	—	2	2	no	—
288	C₂×C₄×C₁₃	—	2	4	no	—
289	C₂×C₄×C₁₃	—	2	2	no	—
290	C₂×C₄×C₁₃	—	4	4	no	—
291	C₂×C₄×C₁₃	—	4	2	no	—
292	C₂×C₄×C₁₃	—	4	1	no	—
293	C₂×C₄×C₁₃	—	4	4	no	—
294	C₂×C₄×C₁₃	—	4	2	no	—
295	C₂×C₄×C₁₃	—	4	4	no	—
296	C₂×C₄×C₁₃	—	4	4	no	—
297	C₂×C₄×C₁₃	—	4	4	no	—
298	C₂×C₄×C₁₃	—	8	4	no	—
299	C₂×C₄×C₁₃	#135	1	4	yes	—
300	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
301	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
302	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
304	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
307	C₈×C₁₃	—	2	4	no	—
308	C₈×C₁₃	—	2	4	no	—
309	#559	—	2	2	no	—
310	#556	C₂²×C₁₃	1	2	yes	complemented
311	#555	—	2	2	no	—
312	#555	—	2	2	no	—
313	#555	C₂²×C₁₃	1	4	yes	—
314	#555	C₂²×C₁₃	1	4	yes	—
315	#555	C₂²×C₁₃	1	2	yes	complemented
316	#553	—	2	2	no	—
317	#550	C₂²×C₁₃	1	2	yes	complemented
318	#547	C₂²×C₁₃	1	2	yes	complemented
319	#538	—	2	2	no	—
320	#535	—	2	1	no	—
321	#533	C₂²×C₁₃	1	1	yes	characteristic
322	#532	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×#124	—	2	2	no	—
325	#525	C₂²×C₁₃	1	4	yes	—
326	C₂×#121	—	2	1	no	—
327	C₂×#121	C₂²×C₁₃	1	2	yes	—
328	#520	—	2	1	no	—
329	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×#117	—	2	1	no	—
332	C₂×#117	C₂²×C₁₃	1	2	yes	—
333	#500	C₂²×C₁₃	1	2	yes	complemented
334	#498	C₂²×C₁₃	1	2	yes	complemented
335	#487	C₂²×C₁₃	1	2	yes	complemented
336	#486	C₂²×C₁₃	1	2	yes	complemented
337	#485	C₂²×C₁₃	1	8	yes	complemented
338	#484	C₂²×C₁₃	1	4	yes	—
339	#483	C₂²×C₁₃	1	2	yes	—
340	#482	C₂²×C₁₃	1	8	yes	complemented
341	#482	C₂²×C₁₃	1	8	yes	complemented
342	#481	C₂²×C₁₃	1	4	yes	—
343	#480	C₂²×C₁₃	1	2	yes	—
344	#477	C₂²×C₁₃	1	4	yes	complemented
345	#476	C₂²×C₁₃	1	2	yes	complemented
346	#476	C₂²×C₁₃	1	4	yes	complemented
347	#474	C₂²×C₁₃	1	2	yes	complemented
348	#466	C₂²×C₁₃	1	8	yes	complemented
349	#465	C₂²×C₁₃	1	8	yes	complemented
350	#461	C₂²×C₁₃	1	2	yes	complemented
351	#459	C₂²×C₁₃	1	2	yes	complemented
352	#450	C₂²×C₁₃	1	2	yes	—
353	#449	C₂²×C₁₃	1	8	yes	complemented
354	#447	C₂²×C₁₃	1	2	yes	—
355	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
356	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
357	C₈×D₄	C₂²×C₁₃	1	4	yes	complemented
358	C₈×D₄	C₂²×C₁₃	1	4	yes	complemented
359	#431	C₂²×C₁₃	1	1	yes	characteristic
360	#431	C₂²×C₁₃	1	1	yes	characteristic
361	#427	C₂²×C₁₃	1	8	yes	complemented
362	#416	C₂²×C₁₃	1	8	yes	complemented
363	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	—
364	C₂²×C₁₃	—	2	1	no	—
365	C₂²×C₁₃	—	2	1	no	—
366	C₂²×C₁₃	—	2	4	no	—
367	C₂²×C₁₃	—	2	4	no	—
368	C₂²×C₁₃	—	2	4	no	—
369	C₂²×C₁₃	—	4	2	no	—
370	C₂²×C₁₃	—	4	2	no	—
371	C₂²×C₁₃	—	4	2	no	—
372	C₂²×C₁₃	—	4	2	no	—
373	C₂²×C₁₃	—	4	2	no	—
374	C₂²×C₁₃	—	4	2	no	—
375	C₂²×C₁₃	—	8	4	no	—
376	C₂²×C₁₃	—	8	4	no	—
377	C₂²×C₁₃	C₂×#135	1	2	yes	—
378	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
379	C₄×C₁₃	—	2	1	no	—
380	C₄×C₁₃	—	2	1	no	—
381	C₄×C₁₃	—	2	1	no	—
382	C₄×C₁₃	—	2	4	no	—
383	C₄×C₁₃	—	4	4	no	—
384	C₄×C₁₃	—	4	2	no	—
385	C₄×C₁₃	—	4	2	no	—
386	C₄×C₁₃	—	4	2	no	—
387	C₄×C₁₃	—	4	2	no	—
388	C₄×C₁₃	C₂×#135	1	2	yes	—
389	C₄×C₁₃	C₂×#135	1	2	yes	—
390	C₄×C₁₃	#585	1	2	yes	—
391	C₂×#41	—	2	1	no	—
392	C₂×#41	C₂³×C₁₃	1	4	yes	—
393	C₂²×Q₈	—	2	1	no	—
394	C₂²×D₄	—	2	2	no	—
395	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
396	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
397	C₂³×C₄	—	2	1	no	—
398	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
399	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
400	C₂×D₈	C₂³×C₁₃	1	4	yes	—
401	C₂²×C₈	C₂³×C₁₃	1	8	yes	—
402	C₄⋊Q₈	—	2	1	no	—
403	C₄⋊Q₈	—	2	1	no	—
404	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
405	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
406	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
407	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
408	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
409	#127	—	2	2	no	—
410	#127	C₂³×C₁₃	1	1	yes	characteristic
411	#126	—	2	4	no	—
412	#125	—	2	1	no	—
413	#124	—	2	2	no	—
414	#124	—	2	8	no	—
415	#124	—	2	8	no	—
416	#124	—	2	4	no	—
417	#124	—	2	1	no	—
418	#123	—	2	4	no	—
419	#123	—	2	4	no	—
420	C₂²⋊Q₈	—	2	1	no	—
421	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
422	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
423	#121	—	2	4	no	—
424	#121	—	2	4	no	—
425	#121	—	2	2	no	—
426	#121	—	2	2	no	—
427	#121	—	2	4	no	—
428	#121	—	2	1	no	—
429	#121	—	2	4	no	—
430	#121	C₂³×C₁₃	1	8	yes	—
431	#121	C₂³×C₁₃	1	2	yes	—
432	#121	C₂³×C₁₃	1	4	yes	—
433	#120	—	2	4	no	—
434	C₄×Q₈	—	2	2	no	—
435	C₄×Q₈	—	2	1	no	—
436	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
437	C₄×D₄	—	2	4	no	—
438	C₄×D₄	—	2	4	no	—
439	C₄×D₄	—	2	2	no	—
440	C₄×D₄	—	2	1	no	—
441	C₄×D₄	—	2	1	no	—
442	C₄×D₄	—	2	1	no	—
443	C₄×D₄	D₄×C₁₃	1	2	yes	—
444	C₄×D₄	D₄×C₁₃	1	2	yes	—
445	C₄×D₄	C₂³×C₁₃	1	2	yes	—
446	C₄×D₄	C₂³×C₁₃	1	2	yes	—
447	C₄×D₄	C₂³×C₁₃	1	2	yes	—
448	C₄×D₄	C₂³×C₁₃	1	2	yes	—
449	C₄×D₄	C₂³×C₁₃	1	2	yes	—
450	#117	—	2	4	no	—
451	#117	—	2	1	no	—
452	#117	—	2	4	no	—
453	#117	—	2	4	no	—
454	#117	—	2	2	no	—
455	#117	C₂³×C₁₃	1	8	yes	—
456	#117	C₂³×C₁₃	1	4	yes	—
457	C₂×C₄⋊C₄	—	2	1	no	—
458	C₂×C₄⋊C₄	—	2	2	no	—
459	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
462	C₂×C₂²⋊C₄	—	2	2	no	—
463	C₂×C₂²⋊C₄	—	2	2	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
466	C₂×C₄²	—	2	2	no	—
467	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
468	#107	C₂³×C₁₃	1	4	yes	—
469	#107	C₂³×C₁₃	1	8	yes	—
470	#106	C₂³×C₁₃	1	4	yes	—
471	#106	C₂³×C₁₃	1	8	yes	—
472	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
473	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
474	#103	C₂³×C₁₃	1	4	yes	—
475	#103	C₂³×C₁₃	1	8	yes	—
476	#102	C₂³×C₁₃	1	4	yes	—
477	#102	C₂³×C₁₃	1	8	yes	—
478	#102	C₂³×C₁₃	1	4	yes	—
479	#102	C₂³×C₁₃	1	4	yes	—
480	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
481	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
482	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
483	C₄×C₈	C₂³×C₁₃	1	2	yes	—
484	C₄×C₈	C₂³×C₁₃	1	2	yes	—
485	C₂×C₁₃	—	2	2	no	—
486	C₂×C₁₃	—	4	4	no	—
487	C₂×C₁₃	—	8	2	no	—
488	C₂×C₁₃	—	8	2	no	—
489	C₂×C₁₃	#3485	1	1	yes	characteristic
490	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
491	C₂×C₁₃	#3585	1	1	yes	characteristic
492	C₂⁴	—	2	1	no	—
493	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
494	#41	—	4	8	no	—
495	#41	—	4	4	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	2	no	—
499	C₂×Q₈	—	2	2	no	—
500	C₂×Q₈	—	8	2	no	—
501	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
502	C₂×D₄	—	2	2	no	—
503	C₂×D₄	—	2	4	no	—
504	C₂×D₄	—	2	4	no	—
505	C₂×D₄	—	2	8	no	—
506	C₂×D₄	—	2	4	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	4	2	no	—
511	C₂×D₄	—	8	4	no	—
512	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
513	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
514	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
515	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	2	no	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	—	4	4	no	—
523	C₂²×C₄	—	4	4	no	—
524	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
525	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
526	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
527	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
528	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
529	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
530	SD₁₆	—	4	4	no	—
531	D₈	—	4	4	no	—
532	C₂×C₈	—	4	8	no	—
533	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
534	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	2	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	2	no	—
546	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
547	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
548	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
549	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
550	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
551	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
552	C₂²⋊C₄	—	2	8	no	—
553	C₂²⋊C₄	—	2	2	no	—
554	C₂²⋊C₄	—	2	4	no	—
555	C₂²⋊C₄	—	2	4	no	—
556	C₂²⋊C₄	—	2	8	no	—
557	C₂²⋊C₄	—	2	2	no	—
558	C₂²⋊C₄	—	2	2	no	—
559	C₂²⋊C₄	—	2	4	no	—
560	C₂²⋊C₄	—	2	2	no	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
563	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
564	C₄²	—	2	8	no	—
565	C₄²	—	2	4	no	—
566	C₄²	—	2	2	no	—
567	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
568	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
569	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
570	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
571	C₁₃	#61700	1	1	yes	characteristic, direct product factor, Sylow
572	C₂³	—	2	4	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	2	no	—
575	C₂³	—	4	2	no	—
576	C₂³	—	4	2	no	—
577	C₂³	—	4	2	no	—
578	C₂³	—	4	2	no	—
579	C₂³	—	4	2	no	—
580	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
581	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
582	Q₈	—	2	4	no	—
583	Q₈	—	4	2	no	—
584	Q₈	—	8	2	no	—
585	Q₈	—	8	2	no	—
586	Q₈	—	8	1	no	—
587	D₄	—	2	4	no	—
588	D₄	—	2	4	no	—
589	D₄	—	2	2	no	—
590	D₄	—	2	4	no	—
591	D₄	—	2	2	no	—
592	D₄	—	4	2	no	—
593	D₄	—	4	4	no	—
594	D₄	—	4	2	no	—
595	D₄	—	8	1	no	—
596	D₄	—	8	8	no	—
597	D₄	—	8	4	no	—
598	D₄	—	8	4	no	—
599	C₂×C₄	—	2	8	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	4	4	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	4	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	4	no	—
612	C₂×C₄	—	4	4	no	—
613	C₂×C₄	—	4	4	no	—
614	C₂×C₄	—	8	4	no	—
615	C₂×C₄	C₁₃×#135	1	4	yes	—
616	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
617	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
618	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
619	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
620	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
621	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
622	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
623	C₈	—	2	4	no	—
624	C₈	—	2	4	no	—
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	4	no	—
628	C₂²	—	2	4	no	—
629	C₂²	—	2	4	no	—
630	C₂²	—	4	2	no	—
631	C₂²	—	4	2	no	—
632	C₂²	—	4	2	no	—
633	C₂²	—	4	2	no	—
634	C₂²	—	4	2	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	8	4	no	—
637	C₂²	—	8	4	no	—
638	C₂²	C₂×C₁₃×#135	1	2	yes	—
639	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
640	C₄	—	2	1	no	—
641	C₄	—	2	1	no	—
642	C₄	—	2	1	no	—
643	C₄	—	2	4	no	—
644	C₄	—	4	2	no	—
645	C₄	—	4	2	no	—
646	C₄	—	4	4	no	—
647	C₄	—	4	2	no	—
648	C₄	—	4	2	no	—
649	C₄	C₂×C₁₃×#135	1	2	yes	—
650	C₄	C₂×C₁₃×#135	1	2	yes	—
651	C₄	C₁₃×#585	1	2	yes	—
652	C₂	—	2	2	no	—
653	C₂	—	4	4	no	—
654	C₂	—	8	2	no	—
655	C₂	—	8	2	no	—
656	C₂	C₁₃×#3485	1	1	yes	characteristic
657	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
658	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×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3506	C₂	semidirect
2. C₂×C₁₃×#555	C₂	semidirect
3. C₁₃×#3341	C₂	semidirect
4. C₁₃×#3340	C₂	semidirect
5. C₁₃×#3305	C₂	semidirect
6. C₁₃×#3303	C₂	semidirect
7. C₁₃×#3230	C₂	semidirect
8. C₁₃×#3227	C₂	semidirect
9. C₁₃×#3188	C₂	semidirect
10. C₁₃×#3101	C₂	semidirect
11. C₁₃×#3100	C₂	semidirect
12. C₁₃×#3091	C₂	semidirect
13. C₁₃×#2972	C₂	semidirect
15. C₁₃×#556	C₂²	semidirect
20. C₁₃×#555	C₂²	semidirect
22. C₁₃×#550	C₂²	semidirect
23. C₁₃×#547	C₂²	semidirect
38. C₁₃×#500	C₂²	semidirect
39. C₁₃×#498	C₂²	semidirect
40. C₁₃×#487	C₂²	semidirect
41. C₁₃×#486	C₂²	semidirect
42. C₁₃×#485	C₂²	semidirect
45. C₁₃×#482	C₂²	semidirect
46. C₁₃×#482	C₂²	semidirect
49. C₁₃×#477	C₂²	semidirect
50. C₁₃×#476	C₂²	semidirect
51. C₁₃×#476	C₂²	semidirect
52. C₁₃×#474	C₂²	semidirect
53. C₁₃×#466	C₂²	semidirect
54. C₁₃×#465	C₂²	semidirect
55. C₁₃×#461	C₂²	semidirect
56. C₁₃×#459	C₂²	semidirect
58. C₁₃×#449	C₂²	semidirect
60. C₄×C₁₃×SD₁₆	C₂²	semidirect
61. C₄×C₁₃×D₈	C₂²	semidirect
62. C₈×D₄×C₁₃	C₂²	semidirect
63. C₈×D₄×C₁₃	C₂²	semidirect
66. C₁₃×#427	C₂²	semidirect
67. C₁₃×#416	C₂²	semidirect
163. #61700	C₁₃	direct (N × H)
243. #3506	C₂×C₁₃	semidirect
244. C₂×#555	C₂×C₁₃	semidirect
245. #3341	C₂×C₁₃	semidirect
246. #3340	C₂×C₁₃	semidirect
247. #3305	C₂×C₁₃	semidirect
248. #3303	C₂×C₁₃	semidirect
249. #3230	C₂×C₁₃	semidirect
250. #3227	C₂×C₁₃	semidirect
251. #3188	C₂×C₁₃	semidirect
252. #3101	C₂×C₁₃	semidirect
253. #3100	C₂×C₁₃	semidirect
254. #3091	C₂×C₁₃	semidirect
255. #2972	C₂×C₁₃	semidirect
310. #556	C₂²×C₁₃	semidirect
315. #555	C₂²×C₁₃	semidirect
317. #550	C₂²×C₁₃	semidirect
318. #547	C₂²×C₁₃	semidirect
333. #500	C₂²×C₁₃	semidirect
334. #498	C₂²×C₁₃	semidirect
335. #487	C₂²×C₁₃	semidirect
336. #486	C₂²×C₁₃	semidirect
337. #485	C₂²×C₁₃	semidirect
340. #482	C₂²×C₁₃	semidirect
341. #482	C₂²×C₁₃	semidirect
344. #477	C₂²×C₁₃	semidirect
345. #476	C₂²×C₁₃	semidirect
346. #476	C₂²×C₁₃	semidirect
347. #474	C₂²×C₁₃	semidirect
348. #466	C₂²×C₁₃	semidirect
349. #465	C₂²×C₁₃	semidirect
350. #461	C₂²×C₁₃	semidirect
351. #459	C₂²×C₁₃	semidirect
353. #449	C₂²×C₁₃	semidirect
355. C₄×SD₁₆	C₂²×C₁₃	semidirect
356. C₄×D₈	C₂²×C₁₃	semidirect
357. C₈×D₄	C₂²×C₁₃	semidirect
358. C₈×D₄	C₂²×C₁₃	semidirect
361. #427	C₂²×C₁₃	semidirect
362. #416	C₂²×C₁₃	semidirect
571. C₁₃	#61700	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×#3506	2
C₂×C₁₃×#555	2
C₁₃×#3341	2
C₁₃×#3340	2
C₁₃×#3305	2
C₁₃×#3303	2
C₁₃×#3230	2
C₁₃×#3227	2
C₁₃×#3188	2
C₁₃×#3101	2
C₁₃×#3100	2
C₁₃×#3091	2
C₁₃×#2972	2
#61700	13

Subgroups — C13×#61700 #15748039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61700 #15748039