Subgroups — C₁₃×#61915 #15748254

Order 3328.

1640 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3507	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3400	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3398	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3395	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3377	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3374	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3365	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3223	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3216	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#3210	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#3120	C₂	1	4	yes	maximal, complemented
13	C₁₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2985	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#564	—	2	2	no	—
17	C₁₃×#559	C₂²	1	2	yes	—
18	C₁₃×#557	—	2	1	no	—
19	C₁₃×#557	—	2	1	no	—
20	C₁₃×#557	C₂²	1	2	yes	—
21	C₁₃×#557	C₂²	1	2	yes	—
22	C₁₃×#557	C₂²	1	2	yes	—
23	C₁₃×#557	C₂²	1	2	yes	—
24	C₁₃×#557	C₂²	1	2	yes	—
25	C₁₃×#556	—	2	1	no	—
26	C₁₃×#556	C₂²	1	4	yes	—
27	C₁₃×#554	—	2	1	no	—
28	C₁₃×#552	—	2	2	no	—
29	C₁₃×#541	—	2	2	no	—
30	C₁₃×#541	—	2	2	no	—
31	C₁₃×#541	C₂²	1	4	yes	—
32	C₁₃×#539	—	2	2	no	—
33	C₁₃×#536	C₂²	1	2	yes	—
34	C₁₃×#533	C₂²	1	1	yes	characteristic
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	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#497	C₂²	1	2	yes	—
42	C₁₃×#497	C₂²	1	4	yes	—
43	C₁₃×#494	C₂²	1	1	yes	characteristic
44	C₁₃×#494	C₂²	1	4	yes	—
45	C₁₃×#492	C₂²	1	1	yes	characteristic
46	C₁₃×#491	C₂²	1	4	yes	—
47	C₁₃×#489	C₂²	1	2	yes	—
48	C₁₃×#488	C₂²	1	4	yes	—
49	C₁₃×#487	C₂²	1	1	yes	characteristic
50	C₁₃×#486	C₂²	1	1	yes	characteristic
51	C₁₃×#484	C₂²	1	2	yes	—
52	C₁₃×#483	C₂²	1	2	yes	—
53	C₁₃×#479	C₂²	1	4	yes	—
54	C₁₃×#478	C₂²	1	4	yes	—
55	C₁₃×#477	C₂²	1	2	yes	—
56	C₁₃×#475	C₂²	1	2	yes	—
57	C₁₃×#464	C₂²	1	4	yes	—
58	C₁₃×#464	C₂²	1	4	yes	—
59	C₁₃×#464	C₂²	1	4	yes	—
60	C₁₃×#462	C₂²	1	2	yes	—
61	C₁₃×#462	C₂²	1	2	yes	—
62	C₁₃×#462	C₂²	1	2	yes	—
63	C₁₃×#462	C₂²	1	4	yes	—
64	C₁₃×#462	C₂²	1	4	yes	—
65	C₁₃×#462	C₂²	1	4	yes	—
66	C₁₃×#461	C₂²	1	4	yes	—
67	C₁₃×#460	C₂²	1	2	yes	—
68	C₁₃×#452	C₂²	1	4	yes	—
69	C₁₃×#452	C₂²	1	4	yes	—
70	C₁₃×#451	C₂²	1	2	yes	—
71	C₁₃×#451	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×#441	C₂²	1	4	yes	—
76	C₁₃×#441	C₂²	1	4	yes	—
77	C₁₃×#440	C₂²	1	4	yes	—
78	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
79	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
80	C₄×C₁₃×Q₁₆	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	C₂³	1	2	yes	—
86	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
88	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
89	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
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×SD₁₆	C₂³	1	4	yes	—
94	C₁₃×C₄⋊Q₈	—	2	2	no	—
95	C₁₃×C₄⋊Q₈	—	2	2	no	—
96	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
97	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
98	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
99	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
100	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
101	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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×#126	—	2	4	no	—
107	C₁₃×#126	—	2	4	no	—
108	C₁₃×#126	—	2	4	no	—
109	C₁₃×#126	—	2	4	no	—
110	C₁₃×#125	—	2	2	no	—
111	C₁₃×#125	—	2	4	no	—
112	C₁₃×#125	—	2	2	no	—
113	C₁₃×#125	—	2	2	no	—
114	C₁₃×#125	—	2	4	no	—
115	C₁₃×#125	—	2	4	no	—
116	C₁₃×#125	—	2	4	no	—
117	C₁₃×#125	—	2	4	no	—
118	C₁₃×#125	—	2	4	no	—
119	C₁₃×#125	—	2	4	no	—
120	C₁₃×#125	—	2	1	no	—
121	C₁₃×#125	—	2	1	no	—
122	C₁₃×#125	D₄	1	2	yes	—
123	C₁₃×#125	C₂³	1	4	yes	—
124	C₁₃×#124	—	2	2	no	—
125	C₁₃×#124	C₂³	1	4	yes	—
126	C₁₃×#124	C₂³	1	2	yes	—
127	C₁₃×#123	—	2	4	no	—
128	C₁₃×#123	—	2	4	no	—
129	C₁₃×C₂²⋊Q₈	—	2	4	no	—
130	C₁₃×C₂²⋊Q₈	—	2	1	no	—
131	C₁₃×C₂²⋊Q₈	—	2	1	no	—
132	C₁₃×C₂²⋊Q₈	—	2	2	no	—
133	C₁₃×C₂²⋊Q₈	—	2	2	no	—
134	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
135	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
136	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
137	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
138	C₁₃×#121	—	2	1	no	—
139	C₁₃×#121	—	2	1	no	—
140	C₄×Q₈×C₁₃	—	2	2	no	—
141	C₄×Q₈×C₁₃	—	2	2	no	—
142	C₄×Q₈×C₁₃	—	2	2	no	—
143	C₄×Q₈×C₁₃	—	2	2	no	—
144	C₄×Q₈×C₁₃	—	2	2	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	—	2	1	no	—
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	4	yes	—
153	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
154	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
155	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
156	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
157	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
158	C₄×D₄×C₁₃	—	2	2	no	—
159	C₄×D₄×C₁₃	—	2	4	no	—
160	C₄×D₄×C₁₃	—	2	1	no	—
161	C₄×D₄×C₁₃	—	2	1	no	—
162	C₄×D₄×C₁₃	C₂³	1	4	yes	—
163	C₁₃×#117	—	2	1	no	—
164	C₁₃×#117	—	2	1	no	—
165	C₁₃×#117	—	2	2	no	—
166	C₁₃×#117	—	2	4	no	—
167	C₁₃×#117	C₂³	1	2	yes	—
168	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
170	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₁₃	—	2	1	no	—
172	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
173	C₁₃×#107	C₂³	1	2	yes	—
174	C₁₃×#107	C₂³	1	2	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	4	yes	—
182	C₁₃×#103	C₂³	1	2	yes	—
183	C₁₃×#103	C₂³	1	2	yes	—
184	C₁₃×#103	C₂³	1	2	yes	—
185	C₁₃×#103	C₂³	1	4	yes	—
186	C₁₃×#103	C₂³	1	4	yes	—
187	C₁₃×#103	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	#61915	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₁₃×#41	—	4	4	no	—
199	C₂×Q₈×C₁₃	—	2	1	no	—
200	C₂×Q₈×C₁₃	—	2	1	no	—
201	C₂×Q₈×C₁₃	—	2	1	no	—
202	C₂×Q₈×C₁₃	—	4	2	no	—
203	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
204	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
205	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
206	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
207	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
208	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
209	C₂×D₄×C₁₃	—	2	2	no	—
210	C₂×D₄×C₁₃	—	2	1	no	—
211	C₂×D₄×C₁₃	—	2	1	no	—
212	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₃	—	2	1	no	—
214	C₂²×C₄×C₁₃	—	2	1	no	—
215	C₂²×C₄×C₁₃	—	2	2	no	—
216	C₂²×C₄×C₁₃	—	2	4	no	—
217	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
220	C₁₃×Q₁₆	—	4	2	no	—
221	C₁₃×Q₁₆	—	4	4	no	—
222	C₁₃×Q₁₆	—	4	4	no	—
223	C₁₃×Q₁₆	—	4	2	no	—
224	C₁₃×Q₁₆	—	4	4	no	—
225	C₁₃×SD₁₆	—	4	4	no	—
226	C₁₃×SD₁₆	—	4	4	no	—
227	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
228	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
229	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
230	C₁₃×C₄⋊C₄	—	2	1	no	—
231	C₁₃×C₄⋊C₄	—	2	4	no	—
232	C₁₃×C₄⋊C₄	—	2	2	no	—
233	C₁₃×C₄⋊C₄	—	2	2	no	—
234	C₁₃×C₄⋊C₄	—	2	4	no	—
235	C₁₃×C₄⋊C₄	—	2	1	no	—
236	C₁₃×C₄⋊C₄	—	2	1	no	—
237	C₁₃×C₄⋊C₄	—	2	1	no	—
238	C₁₃×C₄⋊C₄	—	2	1	no	—
239	C₁₃×C₄⋊C₄	—	2	1	no	—
240	C₁₃×C₄⋊C₄	—	2	1	no	—
241	C₁₃×C₄⋊C₄	—	2	1	no	—
242	C₁₃×C₄⋊C₄	—	2	1	no	—
243	C₁₃×C₄⋊C₄	—	2	4	no	—
244	C₁₃×C₄⋊C₄	—	2	2	no	—
245	C₁₃×C₄⋊C₄	—	2	2	no	—
246	C₁₃×C₄⋊C₄	—	2	4	no	—
247	C₁₃×C₄⋊C₄	—	2	4	no	—
248	C₁₃×C₄⋊C₄	—	2	4	no	—
249	C₁₃×C₄⋊C₄	—	2	4	no	—
250	C₁₃×C₄⋊C₄	—	2	2	no	—
251	C₁₃×C₄⋊C₄	—	2	2	no	—
252	C₁₃×C₄⋊C₄	—	2	4	no	—
253	C₁₃×C₄⋊C₄	—	2	4	no	—
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	4	yes	—
257	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
258	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
259	C₁₃×C₄⋊C₄	C₂×D₄	1	4	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×C₂²⋊C₄	—	2	2	no	—
264	C₁₃×C₂²⋊C₄	—	2	2	no	—
265	C₁₃×C₂²⋊C₄	—	2	2	no	—
266	C₁₃×C₂²⋊C₄	—	2	4	no	—
267	C₁₃×C₂²⋊C₄	—	2	4	no	—
268	C₁₃×C₂²⋊C₄	—	2	2	no	—
269	C₁₃×C₂²⋊C₄	—	2	4	no	—
270	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
271	C₄²×C₁₃	—	2	2	no	—
272	C₄²×C₁₃	—	2	2	no	—
273	C₄²×C₁₃	—	2	4	no	—
274	C₄²×C₁₃	—	2	2	no	—
275	C₄²×C₁₃	—	2	2	no	—
276	C₄²×C₁₃	—	2	4	no	—
277	C₄²×C₁₃	—	2	4	no	—
278	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
279	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
281	C₄²×C₁₃	C₂⁴	1	4	yes	—
282	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
283	#3556	C₂×C₁₃	1	1	yes	characteristic, complemented
284	#3507	C₂×C₁₃	1	1	yes	characteristic
285	#3400	C₂×C₁₃	1	2	yes	complemented
286	#3398	C₂×C₁₃	1	4	yes	complemented
287	#3395	C₂×C₁₃	1	2	yes	complemented
288	#3377	C₂×C₁₃	1	4	yes	complemented
289	#3374	C₂×C₁₃	1	2	yes	complemented
290	#3365	C₂×C₁₃	1	2	yes	complemented
291	#3223	C₂×C₁₃	1	4	yes	complemented
292	#3216	C₂×C₁₃	1	1	yes	characteristic
293	#3210	C₂×C₁₃	1	1	yes	characteristic
294	#3120	C₂×C₁₃	1	4	yes	complemented
295	#3113	C₂×C₁₃	1	1	yes	characteristic, complemented
296	#3104	C₂×C₁₃	1	1	yes	characteristic, complemented
297	#2985	C₂×C₁₃	1	1	yes	characteristic, complemented
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	2	no	—
302	Q₈×C₁₃	—	2	4	no	—
303	Q₈×C₁₃	—	2	2	no	—
304	Q₈×C₁₃	—	2	2	no	—
305	Q₈×C₁₃	—	2	2	no	—
306	Q₈×C₁₃	—	2	4	no	—
307	Q₈×C₁₃	—	4	2	no	—
308	Q₈×C₁₃	—	4	2	no	—
309	Q₈×C₁₃	—	4	2	no	—
310	Q₈×C₁₃	—	4	2	no	—
311	D₄×C₁₃	—	2	4	no	—
312	D₄×C₁₃	—	4	4	no	—
313	D₄×C₁₃	—	4	2	no	—
314	D₄×C₁₃	—	8	1	no	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	2	2	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	2	no	—
323	C₂×C₄×C₁₃	—	2	2	no	—
324	C₂×C₄×C₁₃	—	4	1	no	—
325	C₂×C₄×C₁₃	—	4	4	no	—
326	C₂×C₄×C₁₃	—	4	2	no	—
327	C₂×C₄×C₁₃	—	8	4	no	—
328	C₂×C₄×C₁₃	—	8	1	no	—
329	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
332	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
333	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
337	C₈×C₁₃	—	2	2	no	—
338	C₈×C₁₃	—	2	4	no	—
339	C₈×C₁₃	—	2	2	no	—
340	#564	—	2	2	no	—
341	#559	C₂²×C₁₃	1	2	yes	—
342	#557	—	2	1	no	—
343	#557	—	2	1	no	—
344	#557	C₂²×C₁₃	1	2	yes	—
345	#557	C₂²×C₁₃	1	2	yes	—
346	#557	C₂²×C₁₃	1	2	yes	—
347	#557	C₂²×C₁₃	1	2	yes	—
348	#557	C₂²×C₁₃	1	2	yes	—
349	#556	—	2	1	no	—
350	#556	C₂²×C₁₃	1	4	yes	—
351	#554	—	2	1	no	—
352	#552	—	2	2	no	—
353	#541	—	2	2	no	—
354	#541	—	2	2	no	—
355	#541	C₂²×C₁₃	1	4	yes	—
356	#539	—	2	2	no	—
357	#536	C₂²×C₁₃	1	2	yes	—
358	#533	C₂²×C₁₃	1	1	yes	characteristic
359	#533	C₂²×C₁₃	1	1	yes	characteristic
360	#533	C₂²×C₁₃	1	1	yes	characteristic
361	#532	C₂²×C₁₃	1	1	yes	characteristic
362	#529	—	2	2	no	—
363	#520	C₂²×C₁₃	1	2	yes	—
364	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
365	#497	C₂²×C₁₃	1	2	yes	—
366	#497	C₂²×C₁₃	1	4	yes	—
367	#494	C₂²×C₁₃	1	1	yes	characteristic
368	#494	C₂²×C₁₃	1	4	yes	—
369	#492	C₂²×C₁₃	1	1	yes	characteristic
370	#491	C₂²×C₁₃	1	4	yes	—
371	#489	C₂²×C₁₃	1	2	yes	—
372	#488	C₂²×C₁₃	1	4	yes	—
373	#487	C₂²×C₁₃	1	1	yes	characteristic
374	#486	C₂²×C₁₃	1	1	yes	characteristic
375	#484	C₂²×C₁₃	1	2	yes	—
376	#483	C₂²×C₁₃	1	2	yes	—
377	#479	C₂²×C₁₃	1	4	yes	—
378	#478	C₂²×C₁₃	1	4	yes	—
379	#477	C₂²×C₁₃	1	2	yes	—
380	#475	C₂²×C₁₃	1	2	yes	—
381	#464	C₂²×C₁₃	1	4	yes	—
382	#464	C₂²×C₁₃	1	4	yes	—
383	#464	C₂²×C₁₃	1	4	yes	—
384	#462	C₂²×C₁₃	1	2	yes	—
385	#462	C₂²×C₁₃	1	2	yes	—
386	#462	C₂²×C₁₃	1	2	yes	—
387	#462	C₂²×C₁₃	1	4	yes	—
388	#462	C₂²×C₁₃	1	4	yes	—
389	#462	C₂²×C₁₃	1	4	yes	—
390	#461	C₂²×C₁₃	1	4	yes	—
391	#460	C₂²×C₁₃	1	2	yes	—
392	#452	C₂²×C₁₃	1	4	yes	—
393	#452	C₂²×C₁₃	1	4	yes	—
394	#451	C₂²×C₁₃	1	2	yes	—
395	#451	C₂²×C₁₃	1	2	yes	—
396	#446	C₂²×C₁₃	1	2	yes	—
397	#446	C₂²×C₁₃	1	4	yes	—
398	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
399	#441	C₂²×C₁₃	1	4	yes	—
400	#441	C₂²×C₁₃	1	4	yes	—
401	#440	C₂²×C₁₃	1	4	yes	—
402	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
403	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
404	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
405	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
406	#433	C₂²×C₁₃	1	4	yes	—
407	#432	C₂²×C₁₃	1	1	yes	characteristic
408	#431	C₂²×C₁₃	1	1	yes	characteristic
409	C₂²×C₁₃	—	2	1	no	—
410	C₂²×C₁₃	—	2	1	no	—
411	C₂²×C₁₃	—	2	1	no	—
412	C₂²×C₁₃	—	4	2	no	—
413	C₂²×C₁₃	—	4	2	no	—
414	C₂²×C₁₃	—	4	2	no	—
415	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
416	C₄×C₁₃	—	2	1	no	—
417	C₄×C₁₃	—	2	1	no	—
418	C₄×C₁₃	—	2	4	no	—
419	C₄×C₁₃	—	2	1	no	—
420	C₄×C₁₃	—	2	1	no	—
421	C₄×C₁₃	—	2	4	no	—
422	C₄×C₁₃	—	4	2	no	—
423	C₄×C₁₃	—	4	2	no	—
424	C₄×C₁₃	—	4	2	no	—
425	C₄×C₁₃	—	4	2	no	—
426	C₄×C₁₃	—	4	2	no	—
427	C₄×C₁₃	—	4	2	no	—
428	C₄×C₁₃	—	4	2	no	—
429	C₄×C₁₃	#578	1	2	yes	—
430	C₄×C₁₃	#585	1	2	yes	—
431	C₂×#41	C₂³×C₁₃	1	2	yes	—
432	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
433	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
434	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
435	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
436	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
437	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
438	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
439	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
440	C₄⋊Q₈	—	2	2	no	—
441	C₄⋊Q₈	—	2	2	no	—
442	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
443	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
444	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
445	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
446	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
447	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
448	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
449	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
450	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
451	#127	C₂³×C₁₃	1	1	yes	characteristic
452	#126	—	2	4	no	—
453	#126	—	2	4	no	—
454	#126	—	2	4	no	—
455	#126	—	2	4	no	—
456	#125	—	2	2	no	—
457	#125	—	2	4	no	—
458	#125	—	2	2	no	—
459	#125	—	2	2	no	—
460	#125	—	2	4	no	—
461	#125	—	2	4	no	—
462	#125	—	2	4	no	—
463	#125	—	2	4	no	—
464	#125	—	2	4	no	—
465	#125	—	2	4	no	—
466	#125	—	2	1	no	—
467	#125	—	2	1	no	—
468	#125	D₄×C₁₃	1	2	yes	—
469	#125	C₂³×C₁₃	1	4	yes	—
470	#124	—	2	2	no	—
471	#124	C₂³×C₁₃	1	2	yes	—
472	#124	C₂³×C₁₃	1	4	yes	—
473	#123	—	2	4	no	—
474	#123	—	2	4	no	—
475	C₂²⋊Q₈	—	2	4	no	—
476	C₂²⋊Q₈	—	2	1	no	—
477	C₂²⋊Q₈	—	2	1	no	—
478	C₂²⋊Q₈	—	2	2	no	—
479	C₂²⋊Q₈	—	2	2	no	—
480	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
481	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
482	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
483	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
484	#121	—	2	1	no	—
485	#121	—	2	1	no	—
486	C₄×Q₈	—	2	2	no	—
487	C₄×Q₈	—	2	2	no	—
488	C₄×Q₈	—	2	2	no	—
489	C₄×Q₈	—	2	2	no	—
490	C₄×Q₈	—	2	2	no	—
491	C₄×Q₈	—	2	1	no	—
492	C₄×Q₈	—	2	1	no	—
493	C₄×Q₈	—	2	1	no	—
494	C₄×Q₈	—	2	1	no	—
495	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
496	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
497	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
498	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
499	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
500	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
501	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
502	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
503	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
504	C₄×D₄	—	2	2	no	—
505	C₄×D₄	—	2	4	no	—
506	C₄×D₄	—	2	1	no	—
507	C₄×D₄	—	2	1	no	—
508	C₄×D₄	C₂³×C₁₃	1	4	yes	—
509	#117	—	2	1	no	—
510	#117	—	2	1	no	—
511	#117	—	2	2	no	—
512	#117	—	2	4	no	—
513	#117	C₂³×C₁₃	1	2	yes	—
514	C₂×C₄⋊C₄	—	2	1	no	—
515	C₂×C₄⋊C₄	—	2	2	no	—
516	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
517	C₂×C₄²	—	2	1	no	—
518	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
519	#107	C₂³×C₁₃	1	2	yes	—
520	#107	C₂³×C₁₃	1	2	yes	—
521	#106	C₂³×C₁₃	1	4	yes	—
522	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
523	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
524	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
525	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
526	#103	C₂³×C₁₃	1	2	yes	—
527	#103	C₂³×C₁₃	1	4	yes	—
528	#103	C₂³×C₁₃	1	2	yes	—
529	#103	C₂³×C₁₃	1	2	yes	—
530	#103	C₂³×C₁₃	1	2	yes	—
531	#103	C₂³×C₁₃	1	4	yes	—
532	#103	C₂³×C₁₃	1	4	yes	—
533	#103	C₂³×C₁₃	1	4	yes	—
534	#102	C₂³×C₁₃	1	4	yes	—
535	#102	C₂³×C₁₃	1	4	yes	—
536	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
537	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
538	#97	C₂³×C₁₃	1	2	yes	—
539	#97	C₂³×C₁₃	1	4	yes	—
540	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
541	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
542	C₄×C₈	C₂³×C₁₃	1	4	yes	—
543	C₂×C₁₃	—	4	1	no	—
544	C₂×C₁₃	—	8	2	no	—
545	C₂×C₁₃	#3487	1	1	yes	characteristic
546	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
547	C₂×C₁₃	#3586	1	1	yes	characteristic
548	#41	—	4	4	no	—
549	C₂×Q₈	—	2	1	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	4	2	no	—
553	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
554	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
555	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
556	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
557	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
558	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	4	no	—
567	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
568	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
569	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
570	Q₁₆	—	4	2	no	—
571	Q₁₆	—	4	4	no	—
572	Q₁₆	—	4	4	no	—
573	Q₁₆	—	4	2	no	—
574	Q₁₆	—	4	4	no	—
575	SD₁₆	—	4	4	no	—
576	SD₁₆	—	4	4	no	—
577	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
578	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
579	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	2	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
605	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
606	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
607	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
608	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
609	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
610	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
611	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
612	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	2	2	no	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	2	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
621	C₄²	—	2	2	no	—
622	C₄²	—	2	2	no	—
623	C₄²	—	2	4	no	—
624	C₄²	—	2	2	no	—
625	C₄²	—	2	2	no	—
626	C₄²	—	2	4	no	—
627	C₄²	—	2	4	no	—
628	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
629	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
630	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
631	C₄²	C₂⁴×C₁₃	1	4	yes	—
632	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
633	C₁₃	#61915	1	1	yes	characteristic, direct product factor, Sylow
634	C₂³	—	2	2	no	—
635	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
636	Q₈	—	2	4	no	—
637	Q₈	—	2	2	no	—
638	Q₈	—	2	4	no	—
639	Q₈	—	2	2	no	—
640	Q₈	—	2	2	no	—
641	Q₈	—	2	2	no	—
642	Q₈	—	2	4	no	—
643	Q₈	—	4	2	no	—
644	Q₈	—	4	2	no	—
645	Q₈	—	4	2	no	—
646	Q₈	—	4	2	no	—
647	D₄	—	2	4	no	—
648	D₄	—	4	4	no	—
649	D₄	—	4	2	no	—
650	D₄	—	8	1	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	4	no	—
662	C₂×C₄	—	4	2	no	—
663	C₂×C₄	—	8	4	no	—
664	C₂×C₄	—	8	1	no	—
665	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
666	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
667	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
668	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
669	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
670	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
671	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
672	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
673	C₈	—	2	2	no	—
674	C₈	—	2	4	no	—
675	C₈	—	2	2	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	2	1	no	—
678	C₂²	—	2	1	no	—
679	C₂²	—	4	2	no	—
680	C₂²	—	4	2	no	—
681	C₂²	—	4	2	no	—
682	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
683	C₄	—	2	1	no	—
684	C₄	—	2	4	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	4	no	—
688	C₄	—	2	1	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	2	no	—
693	C₄	—	4	2	no	—
694	C₄	—	4	2	no	—
695	C₄	—	4	2	no	—
696	C₄	C₁₃×#578	1	2	yes	—
697	C₄	C₁₃×#585	1	2	yes	—
698	C₂	—	4	1	no	—
699	C₂	—	8	2	no	—
700	C₂	C₁₃×#3487	1	1	yes	characteristic
701	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
702	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
1. C₁₃×#3556	C₂	semidirect
3. C₁₃×#3400	C₂	semidirect
4. C₁₃×#3398	C₂	semidirect
5. C₁₃×#3395	C₂	semidirect
6. C₁₃×#3377	C₂	semidirect
7. C₁₃×#3374	C₂	semidirect
8. C₁₃×#3365	C₂	semidirect
9. C₁₃×#3223	C₂	semidirect
12. C₁₃×#3120	C₂	semidirect
13. C₁₃×#3113	C₂	semidirect
14. C₁₃×#3104	C₂	semidirect
15. C₁₃×#2985	C₂	semidirect
197. #61915	C₁₃	direct (N × H)
283. #3556	C₂×C₁₃	semidirect
285. #3400	C₂×C₁₃	semidirect
286. #3398	C₂×C₁₃	semidirect
287. #3395	C₂×C₁₃	semidirect
288. #3377	C₂×C₁₃	semidirect
289. #3374	C₂×C₁₃	semidirect
290. #3365	C₂×C₁₃	semidirect
291. #3223	C₂×C₁₃	semidirect
294. #3120	C₂×C₁₃	semidirect
295. #3113	C₂×C₁₃	semidirect
296. #3104	C₂×C₁₃	semidirect
297. #2985	C₂×C₁₃	semidirect
633. C₁₃	#61915	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×#3556	2
C₁₃×#3507	2
C₁₃×#3400	2
C₁₃×#3398	2
C₁₃×#3395	2
C₁₃×#3377	2
C₁₃×#3374	2
C₁₃×#3365	2
C₁₃×#3223	2
C₁₃×#3216	2
C₁₃×#3210	2
C₁₃×#3120	2
C₁₃×#3113	2
C₁₃×#3104	2
C₁₃×#2985	2
#61915	13

Subgroups — C13×#61915 #15748254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61915 #15748254