Subgroups — C₁₃×#61335 #15747674

Order 3328.

1730 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3507	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3377	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3374	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3371	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3369	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3137	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3135	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#3084	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3044	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3037	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#2961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2947	C₂	1	2	yes	maximal, complemented
15	C₂×C₁₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#137	C₂²	1	2	yes	—
17	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
18	C₁₃×#559	C₂²	1	2	yes	—
19	Q₈²×C₁₃	—	2	1	no	—
20	Q₈²×C₁₃	C₂²	1	2	yes	—
21	C₁₃×#557	—	2	1	no	—
22	C₁₃×#557	—	2	2	no	—
23	C₁₃×#557	C₂²	1	2	yes	—
24	C₁₃×#557	C₂²	1	4	yes	—
25	C₁₃×#557	C₂²	1	2	yes	—
26	C₁₃×#556	—	2	1	no	—
27	C₁₃×#556	C₂²	1	4	yes	—
28	C₁₃×#554	—	2	1	no	—
29	C₁₃×#552	—	2	2	no	—
30	C₁₃×#544	—	2	2	no	—
31	C₁₃×#544	C₂²	1	2	yes	—
32	C₁₃×#539	—	2	2	no	—
33	C₁₃×#536	C₂²	1	2	yes	—
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×#529	—	2	2	no	—
39	C₁₃×#520	C₂²	1	2	yes	—
40	C₁₃×#519	C₂²	1	2	yes	—
41	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
43	C₁₃×#491	C₂²	1	2	yes	—
44	C₁₃×#491	C₂²	1	4	yes	—
45	C₁₃×#490	C₂²	1	2	yes	—
46	C₁₃×#489	C₂²	1	2	yes	—
47	C₁₃×#489	C₂²	1	4	yes	—
48	C₁₃×#489	C₂²	1	2	yes	—
49	C₁₃×#488	C₂²	1	4	yes	—
50	C₁₃×#487	C₂²	1	4	yes	—
51	C₁₃×#479	C₂²	1	4	yes	—
52	C₁₃×#479	C₂²	1	4	yes	—
53	C₁₃×#478	C₂²	1	4	yes	—
54	C₁₃×#477	C₂²	1	2	yes	—
55	C₁₃×#476	C₂²	1	4	yes	—
56	C₁₃×#475	C₂²	1	2	yes	—
57	C₁₃×#475	C₂²	1	4	yes	—
58	C₁₃×#464	C₂²	1	4	yes	—
59	C₁₃×#464	C₂²	1	4	yes	—
60	C₁₃×#464	C₂²	1	4	yes	—
61	C₁₃×#462	C₂²	1	2	yes	—
62	C₁₃×#462	C₂²	1	4	yes	—
63	C₁₃×#462	C₂²	1	4	yes	—
64	C₁₃×#460	C₂²	1	2	yes	—
65	C₁₃×#446	C₂²	1	4	yes	—
66	C₁₃×#446	C₂²	1	4	yes	—
67	C₁₃×#441	C₂²	1	4	yes	—
68	C₁₃×#441	C₂²	1	4	yes	—
69	C₁₃×#441	C₂²	1	4	yes	—
70	C₁₃×#440	C₂²	1	4	yes	—
71	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
72	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
73	C₁₃×#428	C₂²	1	2	yes	—
74	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
75	C₁₃×#424	C₂²	1	2	yes	—
76	C₁₃×#423	C₂²	1	1	yes	characteristic
77	C₁₃×#419	C₂²	1	2	yes	—
78	C₁₃×#417	C₂²	1	2	yes	—
79	C₁₃×#416	C₂²	1	2	yes	—
80	C₁₃×#416	C₂²	1	2	yes	—
81	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
82	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
83	C₁₃×#405	C₂²	1	2	yes	—
84	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
85	C₂×C₁₃×#41	C₂³	1	2	yes	—
86	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₁₃×#137	—	2	8	no	—
89	C₂×C₁₃×Q₁₆	—	2	4	no	—
90	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
91	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
92	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
93	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
94	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₁₃×C₄⋊Q₈	—	2	2	no	—
97	C₁₃×C₄⋊Q₈	—	2	4	no	—
98	C₁₃×C₄⋊Q₈	—	2	2	no	—
99	C₁₃×C₄⋊Q₈	—	2	4	no	—
100	C₁₃×C₄⋊Q₈	—	2	2	no	—
101	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
102	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
103	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
104	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
106	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
107	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
108	C₁₃×#127	C₂³	1	1	yes	characteristic
109	C₁₃×#126	—	2	4	no	—
110	C₁₃×#126	—	2	4	no	—
111	C₁₃×#125	—	2	2	no	—
112	C₁₃×#125	—	2	4	no	—
113	C₁₃×#125	—	2	4	no	—
114	C₁₃×#125	—	2	4	no	—
115	C₁₃×#125	—	2	4	no	—
116	C₁₃×#125	—	2	2	no	—
117	C₁₃×#125	D₄	1	2	yes	—
118	C₁₃×#125	C₂³	1	4	yes	—
119	C₁₃×#125	C₂³	1	2	yes	—
120	C₁₃×#124	—	2	2	no	—
121	C₁₃×#124	C₂³	1	4	yes	—
122	C₁₃×#124	C₂³	1	2	yes	—
123	C₁₃×#123	—	2	4	no	—
124	C₁₃×#123	—	2	4	no	—
125	C₁₃×C₂²⋊Q₈	—	2	4	no	—
126	C₁₃×C₂²⋊Q₈	—	2	1	no	—
127	C₁₃×C₂²⋊Q₈	—	2	1	no	—
128	C₁₃×C₂²⋊Q₈	—	2	2	no	—
129	C₁₃×C₂²⋊Q₈	—	2	2	no	—
130	C₁₃×C₂²⋊Q₈	—	2	4	no	—
131	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
132	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
133	C₁₃×#121	—	2	1	no	—
134	C₁₃×#121	—	2	1	no	—
135	C₄×Q₈×C₁₃	—	2	2	no	—
136	C₄×Q₈×C₁₃	—	2	2	no	—
137	C₄×Q₈×C₁₃	—	2	2	no	—
138	C₄×Q₈×C₁₃	—	2	2	no	—
139	C₄×Q₈×C₁₃	—	2	4	no	—
140	C₄×Q₈×C₁₃	—	2	2	no	—
141	C₄×Q₈×C₁₃	—	2	1	no	—
142	C₄×Q₈×C₁₃	—	2	1	no	—
143	C₄×Q₈×C₁₃	—	2	1	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	C₂³	1	4	yes	—
148	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
149	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
150	C₄×Q₈×C₁₃	C₂³	1	2	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×Q₈×C₁₃	C₂³	1	2	yes	—
155	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
156	C₄×D₄×C₁₃	—	2	2	no	—
157	C₄×D₄×C₁₃	—	2	4	no	—
158	C₄×D₄×C₁₃	—	2	1	no	—
159	C₄×D₄×C₁₃	—	2	1	no	—
160	C₄×D₄×C₁₃	C₂³	1	4	yes	—
161	C₁₃×#117	—	2	2	no	—
162	C₁₃×#117	—	2	4	no	—
163	C₁₃×#117	—	2	4	no	—
164	C₁₃×#117	C₂³	1	2	yes	—
165	C₁₃×#117	C₂³	1	2	yes	—
166	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
167	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
169	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₁₃	—	2	1	no	—
172	C₂×C₄²×C₁₃	—	2	1	no	—
173	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
174	C₁₃×#107	C₂³	1	4	yes	—
175	C₁₃×#106	C₂³	1	4	yes	—
176	C₁₃×#106	C₂³	1	4	yes	—
177	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
178	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
179	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
180	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
181	C₁₃×#103	C₂³	1	4	yes	—
182	C₁₃×#103	C₂³	1	4	yes	—
183	C₁₃×#103	C₂³	1	2	yes	—
184	C₁₃×#103	C₂³	1	2	yes	—
185	C₁₃×#103	C₂³	1	2	yes	—
186	C₁₃×#103	C₂³	1	2	yes	—
187	C₁₃×#103	C₂³	1	4	yes	—
188	C₁₃×#103	C₂³	1	4	yes	—
189	C₁₃×#103	C₂³	1	4	yes	—
190	C₁₃×#102	C₂³	1	2	yes	—
191	C₁₃×#102	C₂³	1	2	yes	—
192	C₁₃×#102	C₂³	1	2	yes	—
193	C₁₃×#102	C₂³	1	2	yes	—
194	C₁₃×#102	C₂³	1	4	yes	—
195	C₁₃×#97	C₂³	1	2	yes	—
196	C₁₃×#97	C₂³	1	2	yes	—
197	C₁₃×#97	C₂³	1	4	yes	—
198	C₄×C₈×C₁₃	C₂³	1	4	yes	—
199	#61335	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₁₃×#41	—	2	4	no	—
201	C₁₃×#41	—	2	4	no	—
202	C₂×Q₈×C₁₃	—	2	1	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	2	no	—
208	C₂×Q₈×C₁₃	—	2	2	no	—
209	C₂×Q₈×C₁₃	—	2	2	no	—
210	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
211	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
212	C₂×Q₈×C₁₃	#41	1	4	yes	—
213	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
214	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
215	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
216	C₂×D₄×C₁₃	—	2	2	no	—
217	C₂×D₄×C₁₃	—	2	1	no	—
218	C₂×D₄×C₁₃	—	2	1	no	—
219	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃	—	2	1	no	—
221	C₂²×C₄×C₁₃	—	2	1	no	—
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	4	no	—
226	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
229	C₁₃×Q₁₆	—	2	8	no	—
230	C₁₃×Q₁₆	—	2	8	no	—
231	C₁₃×SD₁₆	—	2	8	no	—
232	C₁₃×M₁₆	—	2	4	no	—
233	C₂×C₈×C₁₃	—	2	2	no	—
234	C₂×C₈×C₁₃	—	2	2	no	—
235	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
236	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
237	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
238	C₁₃×C₄⋊C₄	—	2	1	no	—
239	C₁₃×C₄⋊C₄	—	2	4	no	—
240	C₁₃×C₄⋊C₄	—	2	2	no	—
241	C₁₃×C₄⋊C₄	—	2	2	no	—
242	C₁₃×C₄⋊C₄	—	2	2	no	—
243	C₁₃×C₄⋊C₄	—	2	2	no	—
244	C₁₃×C₄⋊C₄	—	2	1	no	—
245	C₁₃×C₄⋊C₄	—	2	4	no	—
246	C₁₃×C₄⋊C₄	—	2	4	no	—
247	C₁₃×C₄⋊C₄	—	2	4	no	—
248	C₁₃×C₄⋊C₄	—	2	1	no	—
249	C₁₃×C₄⋊C₄	—	2	1	no	—
250	C₁₃×C₄⋊C₄	—	2	2	no	—
251	C₁₃×C₄⋊C₄	—	2	1	no	—
252	C₁₃×C₄⋊C₄	—	2	4	no	—
253	C₁₃×C₄⋊C₄	—	2	1	no	—
254	C₁₃×C₄⋊C₄	—	2	4	no	—
255	C₁₃×C₄⋊C₄	—	2	4	no	—
256	C₁₃×C₄⋊C₄	—	2	2	no	—
257	C₁₃×C₄⋊C₄	—	2	4	no	—
258	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
259	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
260	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
261	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
262	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
263	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
264	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
265	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
266	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
267	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
268	C₁₃×C₂²⋊C₄	—	2	2	no	—
269	C₁₃×C₂²⋊C₄	—	2	2	no	—
270	C₁₃×C₂²⋊C₄	—	2	4	no	—
271	C₁₃×C₂²⋊C₄	—	2	4	no	—
272	C₁₃×C₂²⋊C₄	—	2	2	no	—
273	C₁₃×C₂²⋊C₄	—	2	4	no	—
274	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
275	C₄²×C₁₃	—	2	2	no	—
276	C₄²×C₁₃	—	2	2	no	—
277	C₄²×C₁₃	—	2	2	no	—
278	C₄²×C₁₃	—	2	2	no	—
279	C₄²×C₁₃	—	2	4	no	—
280	C₄²×C₁₃	—	2	4	no	—
281	C₄²×C₁₃	—	2	4	no	—
282	C₄²×C₁₃	—	2	2	no	—
283	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
285	C₄²×C₁₃	C₂⁴	1	4	yes	—
286	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
287	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
288	#3507	C₂×C₁₃	1	1	yes	characteristic
289	#3502	C₂×C₁₃	1	1	yes	characteristic, complemented
290	#3377	C₂×C₁₃	1	4	yes	complemented
291	#3374	C₂×C₁₃	1	4	yes	complemented
292	#3371	C₂×C₁₃	1	4	yes	complemented
293	#3369	C₂×C₁₃	1	4	yes	complemented
294	#3137	C₂×C₁₃	1	2	yes	complemented
295	#3135	C₂×C₁₃	1	1	yes	characteristic
296	#3084	C₂×C₁₃	1	2	yes	complemented
297	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#3044	C₂×C₁₃	1	2	yes	complemented
299	#3037	C₂×C₁₃	1	1	yes	characteristic
300	#2961	C₂×C₁₃	1	1	yes	characteristic, complemented
301	#2947	C₂×C₁₃	1	2	yes	complemented
302	C₂×#441	C₂×C₁₃	1	1	yes	characteristic, complemented
303	C₂³×C₁₃	—	2	2	no	—
304	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
305	Q₈×C₁₃	—	2	4	no	—
306	Q₈×C₁₃	—	2	2	no	—
307	Q₈×C₁₃	—	2	2	no	—
308	Q₈×C₁₃	—	2	2	no	—
309	Q₈×C₁₃	—	2	2	no	—
310	Q₈×C₁₃	—	2	2	no	—
311	Q₈×C₁₃	—	4	2	no	—
312	Q₈×C₁₃	—	4	2	no	—
313	Q₈×C₁₃	—	4	2	no	—
314	Q₈×C₁₃	—	4	2	no	—
315	Q₈×C₁₃	—	8	1	no	—
316	Q₈×C₁₃	—	8	4	no	—
317	Q₈×C₁₃	C₂×#41	1	4	yes	—
318	D₄×C₁₃	—	2	2	no	—
319	D₄×C₁₃	—	2	2	no	—
320	D₄×C₁₃	—	4	2	no	—
321	D₄×C₁₃	—	4	4	no	—
322	D₄×C₁₃	—	8	1	no	—
323	C₂×C₄×C₁₃	—	2	4	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	—	2	2	no	—
331	C₂×C₄×C₁₃	—	4	1	no	—
332	C₂×C₄×C₁₃	—	4	1	no	—
333	C₂×C₄×C₁₃	—	4	2	no	—
334	C₂×C₄×C₁₃	—	4	4	no	—
335	C₂×C₄×C₁₃	—	8	4	no	—
336	C₂×C₄×C₁₃	—	8	1	no	—
337	C₂×C₄×C₁₃	—	8	1	no	—
338	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
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	4	yes	—
343	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
344	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
346	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
347	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
348	C₈×C₁₃	—	2	2	no	—
349	C₈×C₁₃	—	2	4	no	—
350	C₈×C₁₃	—	2	2	no	—
351	C₂×#137	C₂²×C₁₃	1	2	yes	—
352	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
353	#559	C₂²×C₁₃	1	2	yes	—
354	Q₈²	—	2	1	no	—
355	Q₈²	C₂²×C₁₃	1	2	yes	—
356	#557	—	2	1	no	—
357	#557	—	2	2	no	—
358	#557	C₂²×C₁₃	1	2	yes	—
359	#557	C₂²×C₁₃	1	4	yes	—
360	#557	C₂²×C₁₃	1	2	yes	—
361	#556	—	2	1	no	—
362	#556	C₂²×C₁₃	1	4	yes	—
363	#554	—	2	1	no	—
364	#552	—	2	2	no	—
365	#544	—	2	2	no	—
366	#544	C₂²×C₁₃	1	2	yes	—
367	#539	—	2	2	no	—
368	#536	C₂²×C₁₃	1	2	yes	—
369	#533	—	2	2	no	—
370	#533	C₂²×C₁₃	1	1	yes	characteristic
371	#533	C₂²×C₁₃	1	1	yes	characteristic
372	#532	C₂²×C₁₃	1	1	yes	characteristic
373	#529	—	2	2	no	—
374	#520	C₂²×C₁₃	1	2	yes	—
375	#519	C₂²×C₁₃	1	2	yes	—
376	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
377	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
378	#491	C₂²×C₁₃	1	2	yes	—
379	#491	C₂²×C₁₃	1	4	yes	—
380	#490	C₂²×C₁₃	1	2	yes	—
381	#489	C₂²×C₁₃	1	2	yes	—
382	#489	C₂²×C₁₃	1	4	yes	—
383	#489	C₂²×C₁₃	1	2	yes	—
384	#488	C₂²×C₁₃	1	4	yes	—
385	#487	C₂²×C₁₃	1	4	yes	—
386	#479	C₂²×C₁₃	1	4	yes	—
387	#479	C₂²×C₁₃	1	4	yes	—
388	#478	C₂²×C₁₃	1	4	yes	—
389	#477	C₂²×C₁₃	1	2	yes	—
390	#476	C₂²×C₁₃	1	4	yes	—
391	#475	C₂²×C₁₃	1	2	yes	—
392	#475	C₂²×C₁₃	1	4	yes	—
393	#464	C₂²×C₁₃	1	4	yes	—
394	#464	C₂²×C₁₃	1	4	yes	—
395	#464	C₂²×C₁₃	1	4	yes	—
396	#462	C₂²×C₁₃	1	4	yes	—
397	#462	C₂²×C₁₃	1	2	yes	—
398	#462	C₂²×C₁₃	1	4	yes	—
399	#460	C₂²×C₁₃	1	2	yes	—
400	#446	C₂²×C₁₃	1	4	yes	—
401	#446	C₂²×C₁₃	1	4	yes	—
402	#441	C₂²×C₁₃	1	4	yes	—
403	#441	C₂²×C₁₃	1	4	yes	—
404	#441	C₂²×C₁₃	1	4	yes	—
405	#440	C₂²×C₁₃	1	4	yes	—
406	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
407	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
408	#428	C₂²×C₁₃	1	2	yes	—
409	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
410	#424	C₂²×C₁₃	1	2	yes	—
411	#423	C₂²×C₁₃	1	1	yes	characteristic
412	#419	C₂²×C₁₃	1	2	yes	—
413	#417	C₂²×C₁₃	1	2	yes	—
414	#416	C₂²×C₁₃	1	2	yes	—
415	#416	C₂²×C₁₃	1	2	yes	—
416	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
418	#405	C₂²×C₁₃	1	2	yes	—
419	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
420	C₂²×C₁₃	—	2	1	no	—
421	C₂²×C₁₃	—	2	1	no	—
422	C₂²×C₁₃	—	4	2	no	—
423	C₂²×C₁₃	—	4	2	no	—
424	C₂²×C₁₃	—	4	2	no	—
425	C₂²×C₁₃	#548	1	2	yes	—
426	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
427	C₄×C₁₃	—	2	1	no	—
428	C₄×C₁₃	—	2	1	no	—
429	C₄×C₁₃	—	2	1	no	—
430	C₄×C₁₃	—	2	1	no	—
431	C₄×C₁₃	—	2	4	no	—
432	C₄×C₁₃	—	2	4	no	—
433	C₄×C₁₃	—	2	4	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	—	4	2	no	—
439	C₄×C₁₃	—	4	2	no	—
440	C₄×C₁₃	#548	1	2	yes	—
441	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
442	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
443	C₂×#41	C₂³×C₁₃	1	2	yes	—
444	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
445	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
446	#137	—	2	8	no	—
447	C₂×Q₁₆	—	2	4	no	—
448	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
449	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
450	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
451	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
452	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
453	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
454	C₄⋊Q₈	—	2	2	no	—
455	C₄⋊Q₈	—	2	4	no	—
456	C₄⋊Q₈	—	2	2	no	—
457	C₄⋊Q₈	—	2	4	no	—
458	C₄⋊Q₈	—	2	2	no	—
459	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
460	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
461	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
462	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
463	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
464	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
465	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
466	#127	C₂³×C₁₃	1	1	yes	characteristic
467	#126	—	2	4	no	—
468	#126	—	2	4	no	—
469	#125	—	2	2	no	—
470	#125	—	2	4	no	—
471	#125	—	2	4	no	—
472	#125	—	2	4	no	—
473	#125	—	2	4	no	—
474	#125	—	2	2	no	—
475	#125	D₄×C₁₃	1	2	yes	—
476	#125	C₂³×C₁₃	1	2	yes	—
477	#125	C₂³×C₁₃	1	4	yes	—
478	#124	—	2	2	no	—
479	#124	C₂³×C₁₃	1	2	yes	—
480	#124	C₂³×C₁₃	1	4	yes	—
481	#123	—	2	4	no	—
482	#123	—	2	4	no	—
483	C₂²⋊Q₈	—	2	4	no	—
484	C₂²⋊Q₈	—	2	1	no	—
485	C₂²⋊Q₈	—	2	1	no	—
486	C₂²⋊Q₈	—	2	2	no	—
487	C₂²⋊Q₈	—	2	2	no	—
488	C₂²⋊Q₈	—	2	4	no	—
489	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
490	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
491	#121	—	2	1	no	—
492	#121	—	2	1	no	—
493	C₄×Q₈	—	2	2	no	—
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	—	2	1	no	—
504	C₄×Q₈	—	2	1	no	—
505	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
506	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
507	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
508	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
509	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
510	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
511	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
512	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
513	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
514	C₄×D₄	—	2	2	no	—
515	C₄×D₄	—	2	4	no	—
516	C₄×D₄	—	2	1	no	—
517	C₄×D₄	—	2	1	no	—
518	C₄×D₄	C₂³×C₁₃	1	4	yes	—
519	#117	—	2	2	no	—
520	#117	—	2	4	no	—
521	#117	—	2	4	no	—
522	#117	C₂³×C₁₃	1	2	yes	—
523	#117	C₂³×C₁₃	1	2	yes	—
524	C₂×C₄⋊C₄	—	2	1	no	—
525	C₂×C₄⋊C₄	—	2	1	no	—
526	C₂×C₄⋊C₄	—	2	2	no	—
527	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
529	C₂×C₄²	—	2	1	no	—
530	C₂×C₄²	—	2	1	no	—
531	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
532	#107	C₂³×C₁₃	1	4	yes	—
533	#106	C₂³×C₁₃	1	4	yes	—
534	#106	C₂³×C₁₃	1	4	yes	—
535	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
536	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
537	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
538	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
539	#103	C₂³×C₁₃	1	4	yes	—
540	#103	C₂³×C₁₃	1	4	yes	—
541	#103	C₂³×C₁₃	1	2	yes	—
542	#103	C₂³×C₁₃	1	2	yes	—
543	#103	C₂³×C₁₃	1	2	yes	—
544	#103	C₂³×C₁₃	1	2	yes	—
545	#103	C₂³×C₁₃	1	4	yes	—
546	#103	C₂³×C₁₃	1	4	yes	—
547	#103	C₂³×C₁₃	1	4	yes	—
548	#102	C₂³×C₁₃	1	2	yes	—
549	#102	C₂³×C₁₃	1	2	yes	—
550	#102	C₂³×C₁₃	1	2	yes	—
551	#102	C₂³×C₁₃	1	2	yes	—
552	#102	C₂³×C₁₃	1	4	yes	—
553	#97	C₂³×C₁₃	1	2	yes	—
554	#97	C₂³×C₁₃	1	2	yes	—
555	#97	C₂³×C₁₃	1	4	yes	—
556	C₄×C₈	C₂³×C₁₃	1	4	yes	—
557	C₂×C₁₃	—	2	2	no	—
558	C₂×C₁₃	—	8	2	no	—
559	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
560	C₂×C₁₃	#3586	1	1	yes	characteristic
561	C₂×C₁₃	#3586	1	1	yes	characteristic
562	#41	—	2	4	no	—
563	#41	—	2	4	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	1	no	—
567	C₂×Q₈	—	2	1	no	—
568	C₂×Q₈	—	2	4	no	—
569	C₂×Q₈	—	2	2	no	—
570	C₂×Q₈	—	2	2	no	—
571	C₂×Q₈	—	2	2	no	—
572	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
573	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
574	C₂×Q₈	C₁₃×#41	1	4	yes	—
575	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
576	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
577	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	2	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	Q₁₆	—	2	8	no	—
592	Q₁₆	—	2	8	no	—
593	SD₁₆	—	2	8	no	—
594	M₁₆	—	2	4	no	—
595	C₂×C₈	—	2	2	no	—
596	C₂×C₈	—	2	2	no	—
597	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
598	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
599	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	2	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	2	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
621	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
622	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
623	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
624	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
625	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
626	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
627	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
628	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
629	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
637	C₄²	—	2	2	no	—
638	C₄²	—	2	2	no	—
639	C₄²	—	2	2	no	—
640	C₄²	—	2	2	no	—
641	C₄²	—	2	4	no	—
642	C₄²	—	2	4	no	—
643	C₄²	—	2	4	no	—
644	C₄²	—	2	2	no	—
645	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
646	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
647	C₄²	C₂⁴×C₁₃	1	4	yes	—
648	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
649	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
650	C₁₃	#61335	1	1	yes	characteristic, direct product factor, Sylow
651	C₂³	—	2	2	no	—
652	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
653	Q₈	—	2	4	no	—
654	Q₈	—	2	2	no	—
655	Q₈	—	2	2	no	—
656	Q₈	—	2	2	no	—
657	Q₈	—	2	2	no	—
658	Q₈	—	2	2	no	—
659	Q₈	—	4	2	no	—
660	Q₈	—	4	2	no	—
661	Q₈	—	4	2	no	—
662	Q₈	—	4	2	no	—
663	Q₈	—	8	1	no	—
664	Q₈	—	8	4	no	—
665	Q₈	C₂×C₁₃×#41	1	4	yes	—
666	D₄	—	2	2	no	—
667	D₄	—	2	2	no	—
668	D₄	—	4	2	no	—
669	D₄	—	4	4	no	—
670	D₄	—	8	1	no	—
671	C₂×C₄	—	2	4	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	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	2	no	—
682	C₂×C₄	—	4	4	no	—
683	C₂×C₄	—	8	4	no	—
684	C₂×C₄	—	8	1	no	—
685	C₂×C₄	—	8	1	no	—
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	C₂²×D₄×C₁₃	1	1	yes	characteristic
690	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
691	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
692	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
693	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
694	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
695	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
696	C₈	—	2	2	no	—
697	C₈	—	2	4	no	—
698	C₈	—	2	2	no	—
699	C₂²	—	2	1	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	C₁₃×#548	1	2	yes	—
705	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
706	C₄	—	2	1	no	—
707	C₄	—	2	1	no	—
708	C₄	—	2	1	no	—
709	C₄	—	2	1	no	—
710	C₄	—	2	4	no	—
711	C₄	—	2	4	no	—
712	C₄	—	2	4	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	2	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	2	no	—
719	C₄	C₁₃×#548	1	2	yes	—
720	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
721	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
722	C₂	—	2	2	no	—
723	C₂	—	8	2	no	—
724	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
725	C₂	C₁₃×#3586	1	1	yes	characteristic
726	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#532	C₂²
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×#3377	C₂	semidirect
4. C₁₃×#3374	C₂	semidirect
5. C₁₃×#3371	C₂	semidirect
6. C₁₃×#3369	C₂	semidirect
7. C₁₃×#3137	C₂	semidirect
9. C₁₃×#3084	C₂	semidirect
10. C₁₃×#3078	C₂	semidirect
11. C₁₃×#3044	C₂	semidirect
13. C₁₃×#2961	C₂	semidirect
14. C₁₃×#2947	C₂	semidirect
15. C₂×C₁₃×#441	C₂	semidirect
199. #61335	C₁₃	direct (N × H)
289. #3502	C₂×C₁₃	semidirect
290. #3377	C₂×C₁₃	semidirect
291. #3374	C₂×C₁₃	semidirect
292. #3371	C₂×C₁₃	semidirect
293. #3369	C₂×C₁₃	semidirect
294. #3137	C₂×C₁₃	semidirect
296. #3084	C₂×C₁₃	semidirect
297. #3078	C₂×C₁₃	semidirect
298. #3044	C₂×C₁₃	semidirect
300. #2961	C₂×C₁₃	semidirect
301. #2947	C₂×C₁₃	semidirect
302. C₂×#441	C₂×C₁₃	semidirect
650. C₁₃	#61335	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×#3507	2
C₁₃×#3502	2
C₁₃×#3377	2
C₁₃×#3374	2
C₁₃×#3371	2
C₁₃×#3369	2
C₁₃×#3137	2
C₁₃×#3135	2
C₁₃×#3084	2
C₁₃×#3078	2
C₁₃×#3044	2
C₁₃×#3037	2
C₁₃×#2961	2
C₁₃×#2947	2
C₂×C₁₃×#441	2
#61335	13

Subgroups — C13×#61335 #15747674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61335 #15747674