Subgroups — C₁₃×#61851 #15748190

Order 3328.

1704 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3548	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3388	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3385	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3381	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3368	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3368	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3362	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3241	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3126	C₂	1	4	yes	maximal, complemented
13	C₁₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2985	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#562	—	2	2	no	—
17	Q₈²×C₁₃	—	2	1	no	—
18	Q₈²×C₁₃	C₂²	1	2	yes	—
19	C₁₃×#557	—	2	1	no	—
20	C₁₃×#557	—	2	2	no	—
21	C₁₃×#557	C₂²	1	2	yes	—
22	C₁₃×#557	C₂²	1	4	yes	—
23	C₁₃×#554	C₂²	1	2	yes	—
24	C₁₃×#554	C₂²	1	2	yes	—
25	C₁₃×#550	C₂²	1	2	yes	—
26	C₁₃×#550	C₂²	1	2	yes	—
27	C₁₃×#547	—	2	1	no	—
28	C₁₃×#547	—	2	1	no	—
29	C₁₃×#544	—	2	2	no	—
30	C₁₃×#544	C₂²	1	2	yes	—
31	C₁₃×#540	C₂²	1	4	yes	—
32	C₁₃×#537	—	2	2	no	—
33	C₁₃×#537	—	2	2	no	—
34	C₁₃×#533	—	2	2	no	—
35	C₁₃×#533	C₂²	1	1	yes	characteristic
36	C₁₃×#533	C₂²	1	1	yes	characteristic
37	C₁₃×#532	C₂²	1	1	yes	characteristic
38	C₁₃×#532	C₂²	1	1	yes	characteristic
39	C₁₃×#519	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#501	C₂²	1	4	yes	—
42	C₁₃×#501	C₂²	1	2	yes	—
43	C₁₃×#500	C₂²	1	1	yes	characteristic
44	C₁₃×#499	C₂²	1	4	yes	—
45	C₁₃×#498	C₂²	1	1	yes	characteristic
46	C₁₃×#490	C₂²	1	2	yes	—
47	C₁₃×#490	C₂²	1	4	yes	—
48	C₁₃×#486	C₂²	1	1	yes	characteristic
49	C₁₃×#486	C₂²	1	4	yes	—
50	C₁₃×#486	C₂²	1	1	yes	characteristic
51	C₁₃×#482	C₂²	1	4	yes	—
52	C₁₃×#482	C₂²	1	4	yes	—
53	C₁₃×#481	C₂²	1	2	yes	—
54	C₁₃×#480	C₂²	1	2	yes	—
55	C₁₃×#479	C₂²	1	4	yes	—
56	C₁₃×#479	C₂²	1	4	yes	—
57	C₁₃×#478	C₂²	1	4	yes	—
58	C₁₃×#478	C₂²	1	4	yes	—
59	C₁₃×#478	C₂²	1	4	yes	—
60	C₁₃×#477	C₂²	1	2	yes	—
61	C₁₃×#476	C₂²	1	2	yes	—
62	C₁₃×#476	C₂²	1	4	yes	—
63	C₁₃×#475	C₂²	1	2	yes	—
64	C₁₃×#474	C₂²	1	2	yes	—
65	C₁₃×#474	C₂²	1	4	yes	—
66	C₁₃×#460	C₂²	1	2	yes	—
67	C₁₃×#460	C₂²	1	2	yes	—
68	C₁₃×#460	C₂²	1	4	yes	—
69	C₁₃×#460	C₂²	1	4	yes	—
70	C₁₃×#448	C₂²	1	2	yes	—
71	C₁₃×#448	C₂²	1	2	yes	—
72	C₁₃×#446	C₂²	1	2	yes	—
73	C₁₃×#446	C₂²	1	4	yes	—
74	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
75	C₁₃×#440	C₂²	1	4	yes	—
76	C₁₃×#440	C₂²	1	4	yes	—
77	C₁₃×#440	C₂²	1	4	yes	—
78	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
79	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
80	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
81	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
82	C₁₃×#433	C₂²	1	4	yes	—
83	C₁₃×#432	C₂²	1	1	yes	characteristic
84	C₁₃×#431	C₂²	1	1	yes	characteristic
85	C₂×C₁₃×#41	—	2	2	no	—
86	C₂×C₁₃×#41	—	2	2	no	—
87	C₂×C₁₃×#41	—	2	1	no	—
88	C₂×C₁₃×#41	—	2	1	no	—
89	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
91	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
92	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
93	C₁₃×C₄⋊Q₈	—	2	2	no	—
94	C₁₃×C₄⋊Q₈	—	2	4	no	—
95	C₁₃×C₄⋊Q₈	—	2	2	no	—
96	C₁₃×C₄⋊Q₈	—	2	4	no	—
97	C₁₃×C₄⋊Q₈	—	2	2	no	—
98	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
99	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
100	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
101	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
102	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
103	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
104	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₁₃×#127	C₂³	1	1	yes	characteristic
106	C₁₃×#127	C₂³	1	4	yes	—
107	C₁₃×#127	C₂³	1	1	yes	characteristic
108	C₁₃×#125	—	2	4	no	—
109	C₁₃×#125	—	2	4	no	—
110	C₁₃×#125	—	2	4	no	—
111	C₁₃×#125	—	2	2	no	—
112	C₁₃×#125	D₄	1	2	yes	—
113	C₁₃×#125	C₂³	1	4	yes	—
114	C₁₃×#125	C₂³	1	2	yes	—
115	C₁₃×#125	C₂³	1	4	yes	—
116	C₁₃×#124	—	2	1	no	—
117	C₁₃×#124	—	2	1	no	—
118	C₁₃×#123	—	2	4	no	—
119	C₁₃×#123	—	2	4	no	—
120	C₁₃×C₂²⋊Q₈	—	2	2	no	—
121	C₁₃×C₂²⋊Q₈	—	2	2	no	—
122	C₁₃×C₂²⋊Q₈	—	2	1	no	—
123	C₁₃×C₂²⋊Q₈	—	2	1	no	—
124	C₁₃×C₂²⋊Q₈	—	2	4	no	—
125	C₁₃×C₂²⋊Q₈	—	2	4	no	—
126	C₁₃×C₂²⋊Q₈	—	2	4	no	—
127	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
128	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
129	C₁₃×#121	—	2	1	no	—
130	C₁₃×#121	—	2	1	no	—
131	C₁₃×#121	—	2	2	no	—
132	C₁₃×#121	—	2	2	no	—
133	C₁₃×#121	—	2	4	no	—
134	C₁₃×#121	—	2	4	no	—
135	C₁₃×#121	—	2	4	no	—
136	C₁₃×#121	—	2	4	no	—
137	C₁₃×#121	C₂³	1	2	yes	—
138	C₁₃×#121	C₂³	1	2	yes	—
139	C₄×Q₈×C₁₃	—	2	2	no	—
140	C₄×Q₈×C₁₃	—	2	2	no	—
141	C₄×Q₈×C₁₃	—	2	2	no	—
142	C₄×Q₈×C₁₃	—	2	4	no	—
143	C₄×Q₈×C₁₃	—	2	2	no	—
144	C₄×Q₈×C₁₃	—	2	1	no	—
145	C₄×Q₈×C₁₃	—	2	1	no	—
146	C₄×Q₈×C₁₃	—	2	1	no	—
147	C₄×Q₈×C₁₃	—	2	1	no	—
148	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
149	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
150	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
151	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
152	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
153	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
154	C₄×D₄×C₁₃	—	2	1	no	—
155	C₄×D₄×C₁₃	—	2	1	no	—
156	C₄×D₄×C₁₃	C₂³	1	2	yes	—
157	C₄×D₄×C₁₃	C₂³	1	4	yes	—
158	C₄×D₄×C₁₃	C₂³	1	4	yes	—
159	C₄×D₄×C₁₃	C₂³	1	2	yes	—
160	C₁₃×#117	—	2	4	no	—
161	C₁₃×#117	C₂³	1	2	yes	—
162	C₁₃×#117	C₂³	1	2	yes	—
163	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₁₃	—	2	1	no	—
168	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
169	C₁₃×#107	C₂³	1	4	yes	—
170	C₁₃×#107	C₂³	1	4	yes	—
171	C₁₃×#107	C₂³	1	4	yes	—
172	C₁₃×#106	C₂³	1	2	yes	—
173	C₁₃×#106	C₂³	1	2	yes	—
174	C₁₃×#106	C₂³	1	4	yes	—
175	C₁₃×#106	C₂³	1	4	yes	—
176	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
177	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
178	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
179	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
180	C₁₃×#103	C₂³	1	2	yes	—
181	C₁₃×#103	C₂³	1	2	yes	—
182	C₁₃×#103	C₂³	1	4	yes	—
183	C₁₃×#102	C₂³	1	2	yes	—
184	C₁₃×#102	C₂³	1	4	yes	—
185	C₁₃×#102	C₂³	1	4	yes	—
186	C₁₃×#102	C₂³	1	2	yes	—
187	C₁₃×#102	C₂³	1	4	yes	—
188	C₁₃×#102	C₂³	1	4	yes	—
189	C₁₃×#102	C₂³	1	4	yes	—
190	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
192	C₁₃×#97	C₂³	1	2	yes	—
193	C₁₃×#97	C₂³	1	4	yes	—
194	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₁₃	C₂³	1	4	yes	—
197	#61851	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₁₃×#41	—	8	2	no	—
199	C₁₃×#41	—	8	2	no	—
200	C₁₃×#41	—	8	4	no	—
201	C₁₃×#41	—	8	4	no	—
202	C₂×Q₈×C₁₃	—	2	4	no	—
203	C₂×Q₈×C₁₃	—	2	1	no	—
204	C₂×Q₈×C₁₃	—	2	1	no	—
205	C₂×Q₈×C₁₃	—	2	1	no	—
206	C₂×Q₈×C₁₃	—	2	4	no	—
207	C₂×Q₈×C₁₃	—	2	1	no	—
208	C₂×Q₈×C₁₃	—	2	1	no	—
209	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
210	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
211	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
212	C₂×D₄×C₁₃	—	2	2	no	—
213	C₂×D₄×C₁₃	—	2	2	no	—
214	C₂×D₄×C₁₃	—	2	1	no	—
215	C₂×D₄×C₁₃	—	2	1	no	—
216	C₂×D₄×C₁₃	—	2	4	no	—
217	C₂×D₄×C₁₃	—	2	4	no	—
218	C₂×D₄×C₁₃	—	2	1	no	—
219	C₂×D₄×C₁₃	—	2	1	no	—
220	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
221	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃	—	2	1	no	—
223	C₂²×C₄×C₁₃	—	2	1	no	—
224	C₂²×C₄×C₁₃	—	2	2	no	—
225	C₂²×C₄×C₁₃	—	2	2	no	—
226	C₂²×C₄×C₁₃	—	2	4	no	—
227	C₂²×C₄×C₁₃	—	2	4	no	—
228	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₁₃×SD₁₆	—	2	4	no	—
232	C₁₃×SD₁₆	—	2	4	no	—
233	C₁₃×SD₁₆	—	2	8	no	—
234	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
235	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
236	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
237	C₁₃×C₄⋊C₄	—	2	1	no	—
238	C₁₃×C₄⋊C₄	—	2	1	no	—
239	C₁₃×C₄⋊C₄	—	2	2	no	—
240	C₁₃×C₄⋊C₄	—	2	2	no	—
241	C₁₃×C₄⋊C₄	—	2	4	no	—
242	C₁₃×C₄⋊C₄	—	2	4	no	—
243	C₁₃×C₄⋊C₄	—	2	1	no	—
244	C₁₃×C₄⋊C₄	—	2	4	no	—
245	C₁₃×C₄⋊C₄	—	2	4	no	—
246	C₁₃×C₄⋊C₄	—	2	2	no	—
247	C₁₃×C₄⋊C₄	—	2	1	no	—
248	C₁₃×C₄⋊C₄	—	2	1	no	—
249	C₁₃×C₄⋊C₄	—	2	4	no	—
250	C₁₃×C₄⋊C₄	—	2	4	no	—
251	C₁₃×C₄⋊C₄	—	2	2	no	—
252	C₁₃×C₄⋊C₄	—	2	4	no	—
253	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
254	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
255	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
256	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
257	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
258	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
259	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
260	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
261	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
262	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
263	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
264	C₁₃×C₂²⋊C₄	—	2	2	no	—
265	C₁₃×C₂²⋊C₄	—	2	2	no	—
266	C₁₃×C₂²⋊C₄	—	2	2	no	—
267	C₁₃×C₂²⋊C₄	—	2	4	no	—
268	C₁₃×C₂²⋊C₄	—	2	4	no	—
269	C₁₃×C₂²⋊C₄	—	2	2	no	—
270	C₁₃×C₂²⋊C₄	—	2	2	no	—
271	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
272	C₄²×C₁₃	—	2	2	no	—
273	C₄²×C₁₃	—	2	2	no	—
274	C₄²×C₁₃	—	2	4	no	—
275	C₄²×C₁₃	—	2	4	no	—
276	C₄²×C₁₃	—	2	2	no	—
277	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
278	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
279	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
280	C₄²×C₁₃	C₂⁴	1	4	yes	—
281	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
282	#3548	C₂×C₁₃	1	1	yes	characteristic
283	#3502	C₂×C₁₃	1	1	yes	characteristic, complemented
284	#3388	C₂×C₁₃	1	4	yes	complemented
285	#3385	C₂×C₁₃	1	2	yes	complemented
286	#3381	C₂×C₁₃	1	2	yes	complemented
287	#3368	C₂×C₁₃	1	2	yes	complemented
288	#3368	C₂×C₁₃	1	4	yes	complemented
289	#3362	C₂×C₁₃	1	2	yes	complemented
290	#3241	C₂×C₁₃	1	4	yes	complemented
291	#3235	C₂×C₁₃	1	1	yes	characteristic, complemented
292	#3228	C₂×C₁₃	1	1	yes	characteristic, complemented
293	#3126	C₂×C₁₃	1	4	yes	complemented
294	#3112	C₂×C₁₃	1	1	yes	characteristic, complemented
295	#3103	C₂×C₁₃	1	1	yes	characteristic, complemented
296	#2985	C₂×C₁₃	1	1	yes	characteristic, complemented
297	C₂³×C₁₃	—	2	2	no	—
298	C₂³×C₁₃	—	2	2	no	—
299	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
300	Q₈×C₁₃	—	2	4	no	—
301	Q₈×C₁₃	—	2	4	no	—
302	Q₈×C₁₃	—	2	2	no	—
303	Q₈×C₁₃	—	4	2	no	—
304	Q₈×C₁₃	—	4	2	no	—
305	Q₈×C₁₃	—	8	1	no	—
306	Q₈×C₁₃	—	8	4	no	—
307	Q₈×C₁₃	—	8	1	no	—
308	Q₈×C₁₃	—	8	1	no	—
309	Q₈×C₁₃	2₋¹⁺⁴	1	4	yes	—
310	D₄×C₁₃	—	2	2	no	—
311	D₄×C₁₃	—	2	2	no	—
312	D₄×C₁₃	—	2	4	no	—
313	D₄×C₁₃	—	4	2	no	—
314	D₄×C₁₃	—	4	2	no	—
315	D₄×C₁₃	—	8	1	no	—
316	D₄×C₁₃	—	8	4	no	—
317	D₄×C₁₃	—	8	1	no	—
318	D₄×C₁₃	—	8	4	no	—
319	D₄×C₁₃	—	8	2	no	—
320	D₄×C₁₃	—	8	2	no	—
321	C₂×C₄×C₁₃	—	2	4	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	2	2	no	—
325	C₂×C₄×C₁₃	—	2	2	no	—
326	C₂×C₄×C₁₃	—	2	2	no	—
327	C₂×C₄×C₁₃	—	2	2	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	2	2	no	—
330	C₂×C₄×C₁₃	—	4	1	no	—
331	C₂×C₄×C₁₃	—	4	4	no	—
332	C₂×C₄×C₁₃	—	4	4	no	—
333	C₂×C₄×C₁₃	—	8	4	no	—
334	C₂×C₄×C₁₃	—	8	4	no	—
335	C₂×C₄×C₁₃	—	8	1	no	—
336	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
339	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
340	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
344	C₈×C₁₃	—	2	2	no	—
345	C₈×C₁₃	—	2	2	no	—
346	C₈×C₁₃	—	2	4	no	—
347	#562	—	2	2	no	—
348	Q₈²	—	2	1	no	—
349	Q₈²	C₂²×C₁₃	1	2	yes	—
350	#557	—	2	1	no	—
351	#557	—	2	2	no	—
352	#557	C₂²×C₁₃	1	2	yes	—
353	#557	C₂²×C₁₃	1	4	yes	—
354	#554	C₂²×C₁₃	1	2	yes	—
355	#554	C₂²×C₁₃	1	2	yes	—
356	#550	C₂²×C₁₃	1	2	yes	—
357	#550	C₂²×C₁₃	1	2	yes	—
358	#547	—	2	1	no	—
359	#547	—	2	1	no	—
360	#544	—	2	2	no	—
361	#544	C₂²×C₁₃	1	2	yes	—
362	#540	C₂²×C₁₃	1	4	yes	—
363	#537	—	2	2	no	—
364	#537	—	2	2	no	—
365	#533	—	2	2	no	—
366	#533	C₂²×C₁₃	1	1	yes	characteristic
367	#533	C₂²×C₁₃	1	1	yes	characteristic
368	#532	C₂²×C₁₃	1	1	yes	characteristic
369	#532	C₂²×C₁₃	1	1	yes	characteristic
370	#519	C₂²×C₁₃	1	2	yes	—
371	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
372	#501	C₂²×C₁₃	1	4	yes	—
373	#501	C₂²×C₁₃	1	2	yes	—
374	#500	C₂²×C₁₃	1	1	yes	characteristic
375	#499	C₂²×C₁₃	1	4	yes	—
376	#498	C₂²×C₁₃	1	1	yes	characteristic
377	#490	C₂²×C₁₃	1	2	yes	—
378	#490	C₂²×C₁₃	1	4	yes	—
379	#486	C₂²×C₁₃	1	1	yes	characteristic
380	#486	C₂²×C₁₃	1	4	yes	—
381	#486	C₂²×C₁₃	1	1	yes	characteristic
382	#482	C₂²×C₁₃	1	4	yes	—
383	#482	C₂²×C₁₃	1	4	yes	—
384	#481	C₂²×C₁₃	1	2	yes	—
385	#480	C₂²×C₁₃	1	2	yes	—
386	#479	C₂²×C₁₃	1	4	yes	—
387	#479	C₂²×C₁₃	1	4	yes	—
388	#478	C₂²×C₁₃	1	4	yes	—
389	#478	C₂²×C₁₃	1	4	yes	—
390	#478	C₂²×C₁₃	1	4	yes	—
391	#477	C₂²×C₁₃	1	2	yes	—
392	#476	C₂²×C₁₃	1	2	yes	—
393	#476	C₂²×C₁₃	1	4	yes	—
394	#475	C₂²×C₁₃	1	2	yes	—
395	#474	C₂²×C₁₃	1	2	yes	—
396	#474	C₂²×C₁₃	1	4	yes	—
397	#460	C₂²×C₁₃	1	2	yes	—
398	#460	C₂²×C₁₃	1	2	yes	—
399	#460	C₂²×C₁₃	1	4	yes	—
400	#460	C₂²×C₁₃	1	4	yes	—
401	#448	C₂²×C₁₃	1	2	yes	—
402	#448	C₂²×C₁₃	1	2	yes	—
403	#446	C₂²×C₁₃	1	2	yes	—
404	#446	C₂²×C₁₃	1	4	yes	—
405	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
406	#440	C₂²×C₁₃	1	4	yes	—
407	#440	C₂²×C₁₃	1	4	yes	—
408	#440	C₂²×C₁₃	1	4	yes	—
409	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
410	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
411	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
412	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
413	#433	C₂²×C₁₃	1	4	yes	—
414	#432	C₂²×C₁₃	1	1	yes	characteristic
415	#431	C₂²×C₁₃	1	1	yes	characteristic
416	C₂²×C₁₃	—	2	1	no	—
417	C₂²×C₁₃	—	2	1	no	—
418	C₂²×C₁₃	—	2	1	no	—
419	C₂²×C₁₃	—	4	2	no	—
420	C₂²×C₁₃	—	4	2	no	—
421	C₂²×C₁₃	—	4	2	no	—
422	C₂²×C₁₃	—	4	2	no	—
423	C₂²×C₁₃	—	4	2	no	—
424	C₂²×C₁₃	—	4	2	no	—
425	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
426	C₄×C₁₃	—	2	1	no	—
427	C₄×C₁₃	—	2	1	no	—
428	C₄×C₁₃	—	2	4	no	—
429	C₄×C₁₃	—	2	4	no	—
430	C₄×C₁₃	—	2	1	no	—
431	C₄×C₁₃	—	2	1	no	—
432	C₄×C₁₃	—	2	4	no	—
433	C₄×C₁₃	—	4	2	no	—
434	C₄×C₁₃	—	4	2	no	—
435	C₄×C₁₃	—	4	2	no	—
436	C₄×C₁₃	—	4	2	no	—
437	C₄×C₁₃	—	4	2	no	—
438	C₄×C₁₃	#577	1	2	yes	—
439	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
440	C₂×#41	—	2	2	no	—
441	C₂×#41	—	2	2	no	—
442	C₂×#41	—	2	1	no	—
443	C₂×#41	—	2	1	no	—
444	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
445	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
446	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
447	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
448	C₄⋊Q₈	—	2	2	no	—
449	C₄⋊Q₈	—	2	4	no	—
450	C₄⋊Q₈	—	2	2	no	—
451	C₄⋊Q₈	—	2	4	no	—
452	C₄⋊Q₈	—	2	2	no	—
453	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
454	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
455	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
456	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
457	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
458	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
459	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
460	#127	C₂³×C₁₃	1	1	yes	characteristic
461	#127	C₂³×C₁₃	1	1	yes	characteristic
462	#127	C₂³×C₁₃	1	4	yes	—
463	#125	—	2	4	no	—
464	#125	—	2	4	no	—
465	#125	—	2	4	no	—
466	#125	—	2	2	no	—
467	#125	D₄×C₁₃	1	2	yes	—
468	#125	C₂³×C₁₃	1	2	yes	—
469	#125	C₂³×C₁₃	1	4	yes	—
470	#125	C₂³×C₁₃	1	4	yes	—
471	#124	—	2	1	no	—
472	#124	—	2	1	no	—
473	#123	—	2	4	no	—
474	#123	—	2	4	no	—
475	C₂²⋊Q₈	—	2	2	no	—
476	C₂²⋊Q₈	—	2	2	no	—
477	C₂²⋊Q₈	—	2	1	no	—
478	C₂²⋊Q₈	—	2	1	no	—
479	C₂²⋊Q₈	—	2	4	no	—
480	C₂²⋊Q₈	—	2	4	no	—
481	C₂²⋊Q₈	—	2	4	no	—
482	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
483	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
484	#121	—	2	1	no	—
485	#121	—	2	1	no	—
486	#121	—	2	2	no	—
487	#121	—	2	2	no	—
488	#121	—	2	4	no	—
489	#121	—	2	4	no	—
490	#121	—	2	4	no	—
491	#121	—	2	4	no	—
492	#121	C₂³×C₁₃	1	2	yes	—
493	#121	C₂³×C₁₃	1	2	yes	—
494	C₄×Q₈	—	2	2	no	—
495	C₄×Q₈	—	2	2	no	—
496	C₄×Q₈	—	2	2	no	—
497	C₄×Q₈	—	2	4	no	—
498	C₄×Q₈	—	2	2	no	—
499	C₄×Q₈	—	2	1	no	—
500	C₄×Q₈	—	2	1	no	—
501	C₄×Q₈	—	2	1	no	—
502	C₄×Q₈	—	2	1	no	—
503	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
504	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
505	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
506	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
507	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
508	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
509	C₄×D₄	—	2	1	no	—
510	C₄×D₄	—	2	1	no	—
511	C₄×D₄	C₂³×C₁₃	1	2	yes	—
512	C₄×D₄	C₂³×C₁₃	1	2	yes	—
513	C₄×D₄	C₂³×C₁₃	1	4	yes	—
514	C₄×D₄	C₂³×C₁₃	1	4	yes	—
515	#117	—	2	4	no	—
516	#117	C₂³×C₁₃	1	2	yes	—
517	#117	C₂³×C₁₃	1	2	yes	—
518	C₂×C₄⋊C₄	—	2	1	no	—
519	C₂×C₄⋊C₄	—	2	2	no	—
520	C₂×C₄⋊C₄	—	2	2	no	—
521	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
522	C₂×C₄²	—	2	1	no	—
523	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
524	#107	C₂³×C₁₃	1	4	yes	—
525	#107	C₂³×C₁₃	1	4	yes	—
526	#107	C₂³×C₁₃	1	4	yes	—
527	#106	C₂³×C₁₃	1	2	yes	—
528	#106	C₂³×C₁₃	1	2	yes	—
529	#106	C₂³×C₁₃	1	4	yes	—
530	#106	C₂³×C₁₃	1	4	yes	—
531	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
532	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
533	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
534	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
535	#103	C₂³×C₁₃	1	2	yes	—
536	#103	C₂³×C₁₃	1	2	yes	—
537	#103	C₂³×C₁₃	1	4	yes	—
538	#102	C₂³×C₁₃	1	2	yes	—
539	#102	C₂³×C₁₃	1	4	yes	—
540	#102	C₂³×C₁₃	1	4	yes	—
541	#102	C₂³×C₁₃	1	2	yes	—
542	#102	C₂³×C₁₃	1	4	yes	—
543	#102	C₂³×C₁₃	1	4	yes	—
544	#102	C₂³×C₁₃	1	4	yes	—
545	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
546	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
547	#97	C₂³×C₁₃	1	2	yes	—
548	#97	C₂³×C₁₃	1	4	yes	—
549	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
550	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
551	C₄×C₈	C₂³×C₁₃	1	4	yes	—
552	C₂×C₁₃	—	4	1	no	—
553	C₂×C₁₃	—	8	2	no	—
554	C₂×C₁₃	—	8	2	no	—
555	C₂×C₁₃	#3486	1	1	yes	characteristic
556	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
557	C₂×C₁₃	#3585	1	1	yes	characteristic
558	#41	—	8	2	no	—
559	#41	—	8	2	no	—
560	#41	—	8	4	no	—
561	#41	—	8	4	no	—
562	C₂×Q₈	—	2	4	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	4	no	—
567	C₂×Q₈	—	2	1	no	—
568	C₂×Q₈	—	2	1	no	—
569	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
570	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
571	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
581	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
590	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
591	SD₁₆	—	2	4	no	—
592	SD₁₆	—	2	4	no	—
593	SD₁₆	—	2	8	no	—
594	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
595	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
596	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
614	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
615	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
616	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
617	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
618	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
619	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
620	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
621	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
622	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
623	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
624	C₂²⋊C₄	—	2	2	no	—
625	C₂²⋊C₄	—	2	2	no	—
626	C₂²⋊C₄	—	2	2	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
632	C₄²	—	2	2	no	—
633	C₄²	—	2	2	no	—
634	C₄²	—	2	4	no	—
635	C₄²	—	2	4	no	—
636	C₄²	—	2	2	no	—
637	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
638	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
639	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
640	C₄²	C₂⁴×C₁₃	1	4	yes	—
641	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
642	C₁₃	#61851	1	1	yes	characteristic, direct product factor, Sylow
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
646	Q₈	—	2	4	no	—
647	Q₈	—	2	4	no	—
648	Q₈	—	2	2	no	—
649	Q₈	—	4	2	no	—
650	Q₈	—	4	2	no	—
651	Q₈	—	8	1	no	—
652	Q₈	—	8	1	no	—
653	Q₈	—	8	1	no	—
654	Q₈	—	8	4	no	—
655	Q₈	C₁₃×2₋¹⁺⁴	1	4	yes	—
656	D₄	—	2	2	no	—
657	D₄	—	2	2	no	—
658	D₄	—	2	4	no	—
659	D₄	—	4	2	no	—
660	D₄	—	4	2	no	—
661	D₄	—	8	1	no	—
662	D₄	—	8	4	no	—
663	D₄	—	8	1	no	—
664	D₄	—	8	4	no	—
665	D₄	—	8	2	no	—
666	D₄	—	8	2	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	4	no	—
678	C₂×C₄	—	4	4	no	—
679	C₂×C₄	—	8	4	no	—
680	C₂×C₄	—	8	4	no	—
681	C₂×C₄	—	8	1	no	—
682	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
683	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
684	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
685	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
686	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
687	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
688	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
689	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
690	C₈	—	2	2	no	—
691	C₈	—	2	2	no	—
692	C₈	—	2	4	no	—
693	C₂²	—	2	1	no	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
703	C₄	—	2	1	no	—
704	C₄	—	2	4	no	—
705	C₄	—	2	1	no	—
706	C₄	—	2	1	no	—
707	C₄	—	2	4	no	—
708	C₄	—	2	4	no	—
709	C₄	—	2	1	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	C₁₃×#577	1	2	yes	—
716	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
717	C₂	—	4	1	no	—
718	C₂	—	8	2	no	—
719	C₂	—	8	2	no	—
720	C₂	C₁₃×#3486	1	1	yes	characteristic
721	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
722	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3548	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3502	C₂	semidirect
3. C₁₃×#3388	C₂	semidirect
4. C₁₃×#3385	C₂	semidirect
5. C₁₃×#3381	C₂	semidirect
6. C₁₃×#3368	C₂	semidirect
7. C₁₃×#3368	C₂	semidirect
8. C₁₃×#3362	C₂	semidirect
9. C₁₃×#3241	C₂	semidirect
10. C₁₃×#3235	C₂	semidirect
11. C₁₃×#3228	C₂	semidirect
12. C₁₃×#3126	C₂	semidirect
13. C₁₃×#3112	C₂	semidirect
14. C₁₃×#3103	C₂	semidirect
15. C₁₃×#2985	C₂	semidirect
197. #61851	C₁₃	direct (N × H)
283. #3502	C₂×C₁₃	semidirect
284. #3388	C₂×C₁₃	semidirect
285. #3385	C₂×C₁₃	semidirect
286. #3381	C₂×C₁₃	semidirect
287. #3368	C₂×C₁₃	semidirect
288. #3368	C₂×C₁₃	semidirect
289. #3362	C₂×C₁₃	semidirect
290. #3241	C₂×C₁₃	semidirect
291. #3235	C₂×C₁₃	semidirect
292. #3228	C₂×C₁₃	semidirect
293. #3126	C₂×C₁₃	semidirect
294. #3112	C₂×C₁₃	semidirect
295. #3103	C₂×C₁₃	semidirect
296. #2985	C₂×C₁₃	semidirect
642. C₁₃	#61851	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×#3548	2
C₁₃×#3502	2
C₁₃×#3388	2
C₁₃×#3385	2
C₁₃×#3381	2
C₁₃×#3368	2
C₁₃×#3362	2
C₁₃×#3241	2
C₁₃×#3235	2
C₁₃×#3228	2
C₁₃×#3126	2
C₁₃×#3112	2
C₁₃×#3103	2
C₁₃×#2985	2
#61851	13

Subgroups — C13×#61851 #15748190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61851 #15748190