Subgroups — C₁₃×#60877 #15747216

Order 3328.

1786 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3241	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3228	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3228	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3227	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3226	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×#3138	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3096	C₂	1	4	yes	maximal, complemented
13	C₁₃×#3081	C₂	1	4	yes	maximal, complemented
14	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#559	—	2	1	no	—
16	C₁₃×#559	—	2	1	no	—
17	Q₈²×C₁₃	—	2	1	no	—
18	C₁₃×#557	—	2	1	no	—
19	C₁₃×#554	—	2	2	no	—
20	C₁₃×#554	—	2	1	no	—
21	C₁₃×#550	—	2	1	no	—
22	C₁₃×#550	—	2	1	no	—
23	D₄×Q₈×C₁₃	—	2	2	no	—
24	D₄×Q₈×C₁₃	—	2	1	no	—
25	C₁₃×#546	—	2	2	no	—
26	C₁₃×#546	—	2	2	no	—
27	C₁₃×#544	C₂²	1	2	yes	—
28	C₁₃×#544	C₂²	1	4	yes	complemented
29	C₁₃×#540	C₂²	1	4	yes	—
30	C₁₃×#535	C₂²	1	2	yes	—
31	C₁₃×#533	C₂²	1	1	yes	characteristic
32	C₁₃×#533	C₂²	1	1	yes	characteristic
33	C₁₃×#533	C₂²	1	2	yes	complemented
34	C₁₃×#532	C₂²	1	2	yes	—
35	C₁₃×#532	C₂²	1	2	yes	—
36	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
38	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
39	C₁₃×#520	C₂²	1	2	yes	—
40	C₁₃×#518	C₂²	1	2	yes	—
41	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
42	C₁₃×#501	C₂²	1	4	yes	complemented
43	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#500	C₂²	1	2	yes	complemented
46	C₁₃×#499	C₂²	1	4	yes	complemented
47	C₁₃×#498	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#498	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#498	C₂²	1	2	yes	complemented
50	C₁₃×#490	C₂²	1	4	yes	—
51	C₁₃×#486	C₂²	1	2	yes	—
52	C₁₃×#486	C₂²	1	2	yes	—
53	C₁₃×#486	C₂²	1	4	yes	—
54	C₁₃×#486	C₂²	1	2	yes	—
55	C₁₃×#486	C₂²	1	2	yes	—
56	C₁₃×#482	C₂²	1	8	yes	complemented
57	C₁₃×#482	C₂²	1	8	yes	complemented
58	C₁₃×#481	C₂²	1	8	yes	complemented
59	C₁₃×#480	C₂²	1	8	yes	complemented
60	C₁₃×#478	C₂²	1	8	yes	complemented
61	C₁₃×#478	C₂²	1	8	yes	complemented
62	C₁₃×#476	C₂²	1	8	yes	complemented
63	C₁₃×#474	C₂²	1	8	yes	complemented
64	C₁₃×#433	C₂²	1	4	yes	complemented
65	C₁₃×#431	C₂²	1	2	yes	complemented
66	C₁₃×#431	C₂²	1	2	yes	complemented
67	C₁₃×#428	C₂²	1	4	yes	—
68	C₁₃×#427	C₂²	1	4	yes	—
69	C₁₃×#424	C₂²	1	2	yes	—
70	C₁₃×#418	C₂²	1	4	yes	—
71	C₂×C₁₃×#102	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	—	2	2	no	—
76	C₂×C₁₃×#41	—	2	2	no	—
77	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₁₃	—	2	1	no	—
79	C₂²×Q₈×C₁₃	—	2	2	no	—
80	C₂²×D₄×C₁₃	—	2	1	no	—
81	C₂²×D₄×C₁₃	—	2	1	no	—
82	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
83	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
84	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
85	C₁₃×C₄⋊Q₈	—	2	2	no	—
86	C₁₃×C₄⋊Q₈	—	2	4	no	—
87	C₁₃×C₄⋊Q₈	—	2	1	no	—
88	C₁₃×C₄⋊Q₈	—	2	1	no	—
89	C₁₃×C₄⋊Q₈	—	2	2	no	—
90	C₁₃×C₄⋊Q₈	—	2	2	no	—
91	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
92	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
93	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
94	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
95	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
96	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
97	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
98	C₁₃×#127	—	2	2	no	—
99	C₁₃×#127	—	2	1	no	—
100	C₁₃×#127	—	2	1	no	—
101	C₁₃×#127	C₂³	1	2	yes	—
102	C₁₃×#127	C₂³	1	2	yes	—
103	C₁₃×#125	—	2	2	no	—
104	C₁₃×#125	—	2	4	no	—
105	C₁₃×#125	C₂³	1	4	yes	—
106	C₁₃×#125	C₂³	1	2	yes	—
107	C₁₃×#125	C₂³	1	2	yes	—
108	C₁₃×#124	—	2	2	no	—
109	C₁₃×#124	—	2	2	no	—
110	C₁₃×#124	—	2	2	no	—
111	C₁₃×#123	—	2	4	no	—
112	C₁₃×#123	—	2	4	no	—
113	C₁₃×C₂²⋊Q₈	—	2	1	no	—
114	C₁₃×C₂²⋊Q₈	—	2	1	no	—
115	C₁₃×C₂²⋊Q₈	—	2	1	no	—
116	C₁₃×C₂²⋊Q₈	—	2	1	no	—
117	C₁₃×C₂²⋊Q₈	—	2	2	no	—
118	C₁₃×C₂²⋊Q₈	—	2	2	no	—
119	C₁₃×C₂²⋊Q₈	—	2	4	no	—
120	C₁₃×C₂²⋊Q₈	—	2	4	no	—
121	C₁₃×C₂²⋊Q₈	—	2	4	no	—
122	C₁₃×#121	—	2	2	no	—
123	C₁₃×#121	—	2	2	no	—
124	C₁₃×#121	—	2	4	no	—
125	C₁₃×#121	—	2	4	no	—
126	C₁₃×#121	C₂³	1	4	yes	—
127	C₁₃×#121	C₂³	1	4	yes	—
128	C₁₃×#120	—	2	4	no	—
129	C₄×Q₈×C₁₃	—	2	2	no	—
130	C₄×Q₈×C₁₃	—	2	1	no	—
131	C₄×Q₈×C₁₃	—	2	1	no	—
132	C₄×Q₈×C₁₃	—	2	1	no	—
133	C₄×Q₈×C₁₃	—	2	1	no	—
134	C₄×Q₈×C₁₃	—	2	2	no	—
135	C₄×Q₈×C₁₃	—	2	2	no	—
136	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
137	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
138	C₄×D₄×C₁₃	—	2	4	no	—
139	C₄×D₄×C₁₃	—	2	2	no	—
140	C₄×D₄×C₁₃	—	2	2	no	—
141	C₄×D₄×C₁₃	—	2	2	no	—
142	C₄×D₄×C₁₃	—	2	2	no	—
143	C₄×D₄×C₁₃	—	2	2	no	—
144	C₄×D₄×C₁₃	D₄	1	2	yes	—
145	C₄×D₄×C₁₃	D₄	1	2	yes	—
146	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
147	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
148	C₄×D₄×C₁₃	C₂³	1	4	yes	—
149	C₄×D₄×C₁₃	C₂³	1	4	yes	—
150	C₁₃×#117	C₂³	1	2	yes	—
151	C₁₃×#117	C₂³	1	2	yes	—
152	C₁₃×#117	C₂³	1	4	yes	—
153	C₁₃×#117	C₂³	1	1	yes	characteristic
154	C₁₃×#117	C₂³	1	2	yes	—
155	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
159	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
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×#102	C₂³	1	8	yes	—
171	C₁₃×#102	C₂³	1	8	yes	—
172	C₁₃×#102	C₂³	1	8	yes	—
173	C₁₃×#102	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	#60877	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂⁴×C₁₃	—	2	2	no	—
183	C₁₃×#41	—	2	4	no	—
184	C₁₃×#41	—	8	4	no	—
185	C₁₃×#41	—	8	4	no	—
186	C₂×Q₈×C₁₃	—	2	1	no	—
187	C₂×Q₈×C₁₃	—	2	1	no	—
188	C₂×Q₈×C₁₃	—	2	1	no	—
189	C₂×Q₈×C₁₃	—	2	1	no	—
190	C₂×Q₈×C₁₃	—	2	2	no	—
191	C₂×Q₈×C₁₃	—	2	4	no	—
192	C₂×Q₈×C₁₃	—	2	2	no	—
193	C₂×Q₈×C₁₃	—	8	2	no	—
194	C₂×Q₈×C₁₃	—	8	4	no	—
195	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
196	C₂×D₄×C₁₃	—	2	4	no	—
197	C₂×D₄×C₁₃	—	2	4	no	—
198	C₂×D₄×C₁₃	—	2	2	no	—
199	C₂×D₄×C₁₃	—	2	2	no	—
200	C₂×D₄×C₁₃	—	2	2	no	—
201	C₂×D₄×C₁₃	—	2	2	no	—
202	C₂×D₄×C₁₃	—	2	2	no	—
203	C₂×D₄×C₁₃	—	2	8	no	—
204	C₂×D₄×C₁₃	—	8	2	no	—
205	C₂×D₄×C₁₃	—	8	2	no	—
206	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
207	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₁₃	—	2	4	no	—
210	C₂²×C₄×C₁₃	—	2	2	no	—
211	C₂²×C₄×C₁₃	—	2	4	no	—
212	C₂²×C₄×C₁₃	—	2	4	no	—
213	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
214	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
216	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
219	C₁₃×M₁₆	—	2	4	no	—
220	C₂×C₈×C₁₃	—	2	4	no	—
221	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
222	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
223	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
224	C₁₃×C₄⋊C₄	—	2	2	no	—
225	C₁₃×C₄⋊C₄	—	2	1	no	—
226	C₁₃×C₄⋊C₄	—	2	4	no	—
227	C₁₃×C₄⋊C₄	—	2	2	no	—
228	C₁₃×C₄⋊C₄	—	2	4	no	—
229	C₁₃×C₄⋊C₄	—	2	2	no	—
230	C₁₃×C₄⋊C₄	—	2	1	no	—
231	C₁₃×C₄⋊C₄	—	2	1	no	—
232	C₁₃×C₄⋊C₄	—	2	1	no	—
233	C₁₃×C₄⋊C₄	—	2	2	no	—
234	C₁₃×C₄⋊C₄	—	2	2	no	—
235	C₁₃×C₄⋊C₄	—	2	4	no	—
236	C₁₃×C₄⋊C₄	—	2	2	no	—
237	C₁₃×C₄⋊C₄	—	2	4	no	—
238	C₁₃×C₄⋊C₄	—	2	2	no	—
239	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
240	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
241	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
242	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
243	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
244	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
245	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
246	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
247	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
248	C₁₃×C₂²⋊C₄	—	2	2	no	—
249	C₁₃×C₂²⋊C₄	—	2	4	no	—
250	C₁₃×C₂²⋊C₄	—	2	2	no	—
251	C₁₃×C₂²⋊C₄	—	2	4	no	—
252	C₁₃×C₂²⋊C₄	—	2	4	no	—
253	C₁₃×C₂²⋊C₄	—	2	4	no	—
254	C₁₃×C₂²⋊C₄	—	2	4	no	—
255	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
256	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
257	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
258	C₄²×C₁₃	—	2	2	no	—
259	C₄²×C₁₃	—	2	4	no	—
260	C₄²×C₁₃	—	2	2	no	—
261	C₄²×C₁₃	C₂×D₄	1	2	yes	—
262	C₄²×C₁₃	C₂×D₄	1	2	yes	—
263	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
264	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
265	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
266	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
267	C₄²×C₁₃	C₂⁴	1	2	yes	—
268	#3508	C₂×C₁₃	1	1	yes	characteristic
269	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#3241	C₂×C₁₃	1	8	yes	complemented
271	#3228	C₂×C₁₃	1	2	yes	complemented
272	#3228	C₂×C₁₃	1	2	yes	complemented
273	#3227	C₂×C₁₃	1	2	yes	complemented
274	#3226	C₂×C₁₃	1	2	yes	complemented
275	#3165	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#3160	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#3138	C₂×C₁₃	1	1	yes	characteristic, complemented
278	C₂×#486	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#3096	C₂×C₁₃	1	4	yes	complemented
280	#3081	C₂×C₁₃	1	4	yes	complemented
281	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
282	C₂³×C₁₃	—	2	4	no	—
283	C₂³×C₁₃	—	4	4	no	—
284	C₂³×C₁₃	—	8	2	no	—
285	C₂³×C₁₃	—	8	2	no	—
286	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
287	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
288	Q₈×C₁₃	—	2	2	no	—
289	Q₈×C₁₃	—	4	2	no	—
290	Q₈×C₁₃	—	4	4	no	—
291	Q₈×C₁₃	—	4	2	no	—
292	Q₈×C₁₃	—	4	2	no	—
293	Q₈×C₁₃	—	4	2	no	—
294	Q₈×C₁₃	—	8	4	no	—
295	Q₈×C₁₃	—	8	2	no	—
296	D₄×C₁₃	—	2	4	no	—
297	D₄×C₁₃	—	2	2	no	—
298	D₄×C₁₃	—	2	8	no	—
299	D₄×C₁₃	—	4	4	no	—
300	D₄×C₁₃	—	4	4	no	—
301	D₄×C₁₃	—	4	4	no	—
302	D₄×C₁₃	—	8	2	no	—
303	D₄×C₁₃	—	8	2	no	—
304	D₄×C₁₃	—	8	4	no	—
305	D₄×C₁₃	—	8	4	no	—
306	C₂×C₄×C₁₃	—	2	2	no	—
307	C₂×C₄×C₁₃	—	2	4	no	—
308	C₂×C₄×C₁₃	—	2	2	no	—
309	C₂×C₄×C₁₃	—	2	4	no	—
310	C₂×C₄×C₁₃	—	2	4	no	—
311	C₂×C₄×C₁₃	—	2	2	no	—
312	C₂×C₄×C₁₃	—	2	2	no	—
313	C₂×C₄×C₁₃	—	2	2	no	—
314	C₂×C₄×C₁₃	—	2	4	no	—
315	C₂×C₄×C₁₃	—	2	2	no	—
316	C₂×C₄×C₁₃	—	8	4	no	—
317	C₂×C₄×C₁₃	—	8	4	no	—
318	C₂×C₄×C₁₃	—	8	2	no	—
319	C₂×C₄×C₁₃	—	8	4	no	—
320	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
321	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
329	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
330	C₈×C₁₃	—	2	2	no	—
331	C₈×C₁₃	—	2	2	no	—
332	C₈×C₁₃	—	2	4	no	—
333	#559	—	2	1	no	—
334	#559	—	2	1	no	—
335	Q₈²	—	2	1	no	—
336	#557	—	2	1	no	—
337	#554	—	2	2	no	—
338	#554	—	2	1	no	—
339	#550	—	2	1	no	—
340	#550	—	2	1	no	—
341	D₄×Q₈	—	2	2	no	—
342	D₄×Q₈	—	2	1	no	—
343	#546	—	2	2	no	—
344	#546	—	2	2	no	—
345	#544	C₂²×C₁₃	1	2	yes	—
346	#544	C₂²×C₁₃	1	4	yes	complemented
347	#540	C₂²×C₁₃	1	4	yes	—
348	#535	C₂²×C₁₃	1	2	yes	—
349	#533	C₂²×C₁₃	1	1	yes	characteristic
350	#533	C₂²×C₁₃	1	1	yes	characteristic
351	#533	C₂²×C₁₃	1	2	yes	complemented
352	#532	C₂²×C₁₃	1	2	yes	—
353	#532	C₂²×C₁₃	1	2	yes	—
354	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
355	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
356	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
357	#520	C₂²×C₁₃	1	2	yes	—
358	#518	C₂²×C₁₃	1	2	yes	—
359	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
360	#501	C₂²×C₁₃	1	4	yes	complemented
361	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
362	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
363	#500	C₂²×C₁₃	1	2	yes	complemented
364	#499	C₂²×C₁₃	1	4	yes	complemented
365	#498	C₂²×C₁₃	1	1	yes	characteristic, complemented
366	#498	C₂²×C₁₃	1	1	yes	characteristic, complemented
367	#498	C₂²×C₁₃	1	2	yes	complemented
368	#490	C₂²×C₁₃	1	4	yes	—
369	#486	C₂²×C₁₃	1	2	yes	—
370	#486	C₂²×C₁₃	1	2	yes	—
371	#486	C₂²×C₁₃	1	4	yes	—
372	#486	C₂²×C₁₃	1	2	yes	—
373	#486	C₂²×C₁₃	1	2	yes	—
374	#482	C₂²×C₁₃	1	8	yes	complemented
375	#482	C₂²×C₁₃	1	8	yes	complemented
376	#481	C₂²×C₁₃	1	8	yes	complemented
377	#480	C₂²×C₁₃	1	8	yes	complemented
378	#478	C₂²×C₁₃	1	8	yes	complemented
379	#478	C₂²×C₁₃	1	8	yes	complemented
380	#476	C₂²×C₁₃	1	8	yes	complemented
381	#474	C₂²×C₁₃	1	8	yes	complemented
382	#433	C₂²×C₁₃	1	4	yes	complemented
383	#431	C₂²×C₁₃	1	2	yes	complemented
384	#431	C₂²×C₁₃	1	2	yes	complemented
385	#428	C₂²×C₁₃	1	4	yes	—
386	#427	C₂²×C₁₃	1	4	yes	—
387	#424	C₂²×C₁₃	1	2	yes	—
388	#418	C₂²×C₁₃	1	4	yes	—
389	C₂×#102	C₂²×C₁₃	1	4	yes	—
390	#408	C₂²×C₁₃	1	2	yes	—
391	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
393	C₂²×C₁₃	—	2	1	no	—
394	C₂²×C₁₃	—	2	1	no	—
395	C₂²×C₁₃	—	2	2	no	—
396	C₂²×C₁₃	—	2	2	no	—
397	C₂²×C₁₃	—	2	2	no	—
398	C₂²×C₁₃	—	4	4	no	—
399	C₂²×C₁₃	—	4	4	no	—
400	C₂²×C₁₃	—	4	4	no	—
401	C₂²×C₁₃	—	16	4	no	—
402	C₂²×C₁₃	#536	1	2	yes	—
403	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
404	C₄×C₁₃	—	2	2	no	—
405	C₄×C₁₃	—	2	2	no	—
406	C₄×C₁₃	—	2	1	no	—
407	C₄×C₁₃	—	2	2	no	—
408	C₄×C₁₃	—	2	1	no	—
409	C₄×C₁₃	—	4	2	no	—
410	C₄×C₁₃	—	4	4	no	—
411	C₄×C₁₃	—	4	2	no	—
412	C₄×C₁₃	—	4	2	no	—
413	C₄×C₁₃	—	4	2	no	—
414	C₄×C₁₃	#536	1	2	yes	—
415	C₄×C₁₃	#576	1	2	yes	—
416	C₄×C₁₃	#577	1	2	yes	—
417	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
418	C₂×#41	—	2	2	no	—
419	C₂×#41	—	2	2	no	—
420	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
421	C₂²×Q₈	—	2	1	no	—
422	C₂²×Q₈	—	2	2	no	—
423	C₂²×D₄	—	2	1	no	—
424	C₂²×D₄	—	2	1	no	—
425	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
426	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
427	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
428	C₄⋊Q₈	—	2	2	no	—
429	C₄⋊Q₈	—	2	4	no	—
430	C₄⋊Q₈	—	2	1	no	—
431	C₄⋊Q₈	—	2	1	no	—
432	C₄⋊Q₈	—	2	2	no	—
433	C₄⋊Q₈	—	2	2	no	—
434	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
435	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
436	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
437	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
438	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
439	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
440	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
441	#127	—	2	2	no	—
442	#127	—	2	1	no	—
443	#127	—	2	1	no	—
444	#127	C₂³×C₁₃	1	2	yes	—
445	#127	C₂³×C₁₃	1	2	yes	—
446	#125	—	2	2	no	—
447	#125	—	2	4	no	—
448	#125	C₂³×C₁₃	1	2	yes	—
449	#125	C₂³×C₁₃	1	2	yes	—
450	#125	C₂³×C₁₃	1	4	yes	—
451	#124	—	2	2	no	—
452	#124	—	2	2	no	—
453	#124	—	2	2	no	—
454	#123	—	2	4	no	—
455	#123	—	2	4	no	—
456	C₂²⋊Q₈	—	2	1	no	—
457	C₂²⋊Q₈	—	2	1	no	—
458	C₂²⋊Q₈	—	2	1	no	—
459	C₂²⋊Q₈	—	2	1	no	—
460	C₂²⋊Q₈	—	2	2	no	—
461	C₂²⋊Q₈	—	2	2	no	—
462	C₂²⋊Q₈	—	2	4	no	—
463	C₂²⋊Q₈	—	2	4	no	—
464	C₂²⋊Q₈	—	2	4	no	—
465	#121	—	2	2	no	—
466	#121	—	2	2	no	—
467	#121	—	2	4	no	—
468	#121	—	2	4	no	—
469	#121	C₂³×C₁₃	1	4	yes	—
470	#121	C₂³×C₁₃	1	4	yes	—
471	#120	—	2	4	no	—
472	C₄×Q₈	—	2	2	no	—
473	C₄×Q₈	—	2	1	no	—
474	C₄×Q₈	—	2	1	no	—
475	C₄×Q₈	—	2	1	no	—
476	C₄×Q₈	—	2	1	no	—
477	C₄×Q₈	—	2	2	no	—
478	C₄×Q₈	—	2	2	no	—
479	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
480	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
481	C₄×D₄	—	2	4	no	—
482	C₄×D₄	—	2	2	no	—
483	C₄×D₄	—	2	2	no	—
484	C₄×D₄	—	2	2	no	—
485	C₄×D₄	—	2	2	no	—
486	C₄×D₄	—	2	2	no	—
487	C₄×D₄	D₄×C₁₃	1	2	yes	—
488	C₄×D₄	D₄×C₁₃	1	2	yes	—
489	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
490	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
491	C₄×D₄	C₂³×C₁₃	1	4	yes	—
492	C₄×D₄	C₂³×C₁₃	1	4	yes	—
493	#117	C₂³×C₁₃	1	2	yes	—
494	#117	C₂³×C₁₃	1	2	yes	—
495	#117	C₂³×C₁₃	1	4	yes	—
496	#117	C₂³×C₁₃	1	1	yes	characteristic
497	#117	C₂³×C₁₃	1	2	yes	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	2	2	no	—
500	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
502	C₂×C₂²⋊C₄	—	2	4	no	—
503	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
504	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
505	#107	C₂³×C₁₃	1	4	yes	—
506	#107	C₂³×C₁₃	1	4	yes	—
507	#107	C₂³×C₁₃	1	8	yes	—
508	#106	C₂³×C₁₃	1	4	yes	—
509	#106	C₂³×C₁₃	1	4	yes	—
510	#106	C₂³×C₁₃	1	8	yes	—
511	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
512	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
513	#102	C₂³×C₁₃	1	8	yes	—
514	#102	C₂³×C₁₃	1	8	yes	—
515	#102	C₂³×C₁₃	1	8	yes	—
516	#102	C₂³×C₁₃	1	8	yes	—
517	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
518	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
519	#97	C₂³×C₁₃	1	2	yes	—
520	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
521	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
522	C₄×C₈	C₂³×C₁₃	1	2	yes	—
523	C₄×C₈	C₂³×C₁₃	1	2	yes	—
524	C₂×C₁₃	—	2	2	no	—
525	C₂×C₁₃	—	4	2	no	—
526	C₂×C₁₃	—	8	4	no	—
527	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
528	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
529	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
530	C₂⁴	—	2	2	no	—
531	#41	—	2	4	no	—
532	#41	—	8	4	no	—
533	#41	—	8	4	no	—
534	C₂×Q₈	—	2	1	no	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	2	2	no	—
539	C₂×Q₈	—	2	4	no	—
540	C₂×Q₈	—	2	2	no	—
541	C₂×Q₈	—	8	2	no	—
542	C₂×Q₈	—	8	4	no	—
543	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	2	4	no	—
546	C₂×D₄	—	2	2	no	—
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	8	no	—
552	C₂×D₄	—	8	2	no	—
553	C₂×D₄	—	8	2	no	—
554	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
555	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
556	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	2	4	no	—
561	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
562	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
564	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
565	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
567	M₁₆	—	2	4	no	—
568	C₂×C₈	—	2	4	no	—
569	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
570	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
571	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	2	no	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	2	no	—
587	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
588	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
589	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
590	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
591	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
592	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
593	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
594	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
595	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
596	C₂²⋊C₄	—	2	2	no	—
597	C₂²⋊C₄	—	2	4	no	—
598	C₂²⋊C₄	—	2	2	no	—
599	C₂²⋊C₄	—	2	4	no	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
604	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
605	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
606	C₄²	—	2	2	no	—
607	C₄²	—	2	4	no	—
608	C₄²	—	2	2	no	—
609	C₄²	C₂×D₄×C₁₃	1	2	yes	—
610	C₄²	C₂×D₄×C₁₃	1	2	yes	—
611	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
612	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
613	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
614	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
615	C₄²	C₂⁴×C₁₃	1	2	yes	—
616	C₁₃	#60877	1	1	yes	characteristic, direct product factor, Sylow
617	C₂³	—	2	4	no	—
618	C₂³	—	4	4	no	—
619	C₂³	—	8	2	no	—
620	C₂³	—	8	2	no	—
621	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
622	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
623	Q₈	—	2	2	no	—
624	Q₈	—	4	2	no	—
625	Q₈	—	4	4	no	—
626	Q₈	—	4	2	no	—
627	Q₈	—	4	2	no	—
628	Q₈	—	4	2	no	—
629	Q₈	—	8	4	no	—
630	Q₈	—	8	2	no	—
631	D₄	—	2	4	no	—
632	D₄	—	2	2	no	—
633	D₄	—	2	8	no	—
634	D₄	—	4	4	no	—
635	D₄	—	4	4	no	—
636	D₄	—	4	4	no	—
637	D₄	—	8	2	no	—
638	D₄	—	8	2	no	—
639	D₄	—	8	4	no	—
640	D₄	—	8	4	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	8	4	no	—
652	C₂×C₄	—	8	4	no	—
653	C₂×C₄	—	8	2	no	—
654	C₂×C₄	—	8	4	no	—
655	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
656	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
657	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
658	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
659	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
660	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
661	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
662	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
663	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
664	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
665	C₈	—	2	2	no	—
666	C₈	—	2	2	no	—
667	C₈	—	2	4	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	4	4	no	—
674	C₂²	—	4	4	no	—
675	C₂²	—	4	4	no	—
676	C₂²	—	16	4	no	—
677	C₂²	C₁₃×#536	1	2	yes	—
678	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
679	C₄	—	2	2	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	2	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	4	no	—
686	C₄	—	4	2	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	2	no	—
689	C₄	C₁₃×#536	1	2	yes	—
690	C₄	C₁₃×#576	1	2	yes	—
691	C₄	C₁₃×#577	1	2	yes	—
692	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
693	C₂	—	2	2	no	—
694	C₂	—	4	2	no	—
695	C₂	—	8	4	no	—
696	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
697	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
698	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3508	C₂
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
2. C₁₃×#3503	C₂	semidirect
3. C₁₃×#3241	C₂	semidirect
4. C₁₃×#3228	C₂	semidirect
5. C₁₃×#3228	C₂	semidirect
6. C₁₃×#3227	C₂	semidirect
7. C₁₃×#3226	C₂	semidirect
8. C₁₃×#3165	C₂	semidirect
9. C₁₃×#3160	C₂	semidirect
10. C₁₃×#3138	C₂	semidirect
11. C₂×C₁₃×#486	C₂	semidirect
12. C₁₃×#3096	C₂	semidirect
13. C₁₃×#3081	C₂	semidirect
14. C₁₃×#2922	C₂	semidirect
28. C₁₃×#544	C₂²	semidirect
33. C₁₃×#533	C₂²	semidirect
37. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
42. C₁₃×#501	C₂²	semidirect
43. C₁₃×#500	C₂²	semidirect
44. C₁₃×#500	C₂²	semidirect
45. C₁₃×#500	C₂²	semidirect
46. C₁₃×#499	C₂²	semidirect
47. C₁₃×#498	C₂²	semidirect
48. C₁₃×#498	C₂²	semidirect
49. C₁₃×#498	C₂²	semidirect
56. C₁₃×#482	C₂²	semidirect
57. C₁₃×#482	C₂²	semidirect
58. C₁₃×#481	C₂²	semidirect
59. C₁₃×#480	C₂²	semidirect
60. C₁₃×#478	C₂²	semidirect
61. C₁₃×#478	C₂²	semidirect
62. C₁₃×#476	C₂²	semidirect
63. C₁₃×#474	C₂²	semidirect
64. C₁₃×#433	C₂²	semidirect
65. C₁₃×#431	C₂²	semidirect
66. C₁₃×#431	C₂²	semidirect
181. #60877	C₁₃	direct (N × H)
269. #3503	C₂×C₁₃	semidirect
270. #3241	C₂×C₁₃	semidirect
271. #3228	C₂×C₁₃	semidirect
272. #3228	C₂×C₁₃	semidirect
273. #3227	C₂×C₁₃	semidirect
274. #3226	C₂×C₁₃	semidirect
275. #3165	C₂×C₁₃	semidirect
276. #3160	C₂×C₁₃	semidirect
277. #3138	C₂×C₁₃	semidirect
278. C₂×#486	C₂×C₁₃	semidirect
279. #3096	C₂×C₁₃	semidirect
280. #3081	C₂×C₁₃	semidirect
281. #2922	C₂×C₁₃	semidirect
346. #544	C₂²×C₁₃	semidirect
351. #533	C₂²×C₁₃	semidirect
355. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
360. #501	C₂²×C₁₃	semidirect
361. #500	C₂²×C₁₃	semidirect
362. #500	C₂²×C₁₃	semidirect
363. #500	C₂²×C₁₃	semidirect
364. #499	C₂²×C₁₃	semidirect
365. #498	C₂²×C₁₃	semidirect
366. #498	C₂²×C₁₃	semidirect
367. #498	C₂²×C₁₃	semidirect
374. #482	C₂²×C₁₃	semidirect
375. #482	C₂²×C₁₃	semidirect
376. #481	C₂²×C₁₃	semidirect
377. #480	C₂²×C₁₃	semidirect
378. #478	C₂²×C₁₃	semidirect
379. #478	C₂²×C₁₃	semidirect
380. #476	C₂²×C₁₃	semidirect
381. #474	C₂²×C₁₃	semidirect
382. #433	C₂²×C₁₃	semidirect
383. #431	C₂²×C₁₃	semidirect
384. #431	C₂²×C₁₃	semidirect
616. C₁₃	#60877	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×#3508	2
C₁₃×#3503	2
C₁₃×#3241	2
C₁₃×#3228	2
C₁₃×#3227	2
C₁₃×#3226	2
C₁₃×#3165	2
C₁₃×#3160	2
C₁₃×#3138	2
C₂×C₁₃×#486	2
C₁₃×#3096	2
C₁₃×#3081	2
C₁₃×#2922	2
#60877	13

Subgroups — C13×#60877 #15747216

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60877 #15747216