Subgroups — C₁₃×#60948 #15747287

Order 3328.

1846 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3444	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3249	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3246	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3245	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3233	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3212	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3191	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3168	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3107	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3106	C₂	1	4	yes	maximal, complemented
11	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#533	C₂²	1	2	yes	—
13	C₁₃×#533	C₂²	1	2	yes	—
14	C₁₃×#533	C₂²	1	2	yes	—
15	C₁₃×#532	C₂²	1	2	yes	—
16	C₁₃×#532	C₂²	1	2	yes	—
17	C₁₃×#532	C₂²	1	2	yes	—
18	C₁₃×#529	—	2	2	no	—
19	C₁₃×#529	—	2	2	no	—
20	C₁₃×#529	—	2	2	no	—
21	C₁₃×#529	—	2	2	no	—
22	C₁₃×#529	C₂²	1	4	yes	—
23	C₁₃×#529	C₂²	1	4	yes	—
24	C₁₃×#525	—	2	2	no	—
25	C₁₃×#525	—	2	2	no	—
26	C₁₃×#525	C₂²	1	4	yes	—
27	C₄×C₁₃×#41	—	2	2	no	—
28	C₄×C₁₃×#41	—	2	2	no	—
29	C₄×C₁₃×#41	C₂²	1	4	yes	—
30	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#499	C₂²	1	4	yes	complemented
32	C₁₃×#495	C₂²	1	4	yes	complemented
33	C₁₃×#488	C₂²	1	8	yes	complemented
34	C₁₃×#485	C₂²	1	8	yes	—
35	C₁₃×#482	C₂²	1	8	yes	—
36	C₁₃×#477	C₂²	1	4	yes	complemented
37	C₁₃×#476	C₂²	1	4	yes	complemented
38	C₁₃×#475	C₂²	1	4	yes	complemented
39	C₁₃×#474	C₂²	1	4	yes	complemented
40	C₁₃×#467	C₂²	1	4	yes	—
41	C₁₃×#466	C₂²	1	4	yes	—
42	C₁₃×#465	C₂²	1	8	yes	—
43	C₁₃×#462	C₂²	1	4	yes	complemented
44	C₁₃×#461	C₂²	1	4	yes	complemented
45	C₁₃×#460	C₂²	1	4	yes	complemented
46	C₁₃×#459	C₂²	1	4	yes	complemented
47	C₁₃×#452	C₂²	1	8	yes	—
48	C₁₃×#449	C₂²	1	8	yes	—
49	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
50	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
51	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
52	C₁₃×#431	C₂²	1	4	yes	—
53	C₁₃×#431	C₂²	1	4	yes	—
54	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
57	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
58	C₂×C₁₃×#41	—	2	2	no	—
59	C₂×C₁₃×#41	—	2	2	no	—
60	C₂×C₁₃×#41	C₂³	1	4	yes	—
61	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
65	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
66	C₂×C₁₃×D₈	C₂³	1	4	yes	—
67	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
68	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
69	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
70	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
71	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
72	C₁₃×#127	C₂³	1	2	yes	—
73	C₁₃×#126	—	2	4	no	—
74	C₁₃×#126	—	2	4	no	—
75	C₁₃×#125	—	2	2	no	—
76	C₁₃×#125	—	2	2	no	—
77	C₁₃×#125	C₂³	1	4	yes	—
78	C₁₃×#124	—	2	2	no	—
79	C₁₃×#124	—	2	2	no	—
80	C₁₃×#124	C₂³	1	4	yes	—
81	C₁₃×#123	—	2	4	no	—
82	C₁₃×#123	—	2	4	no	—
83	C₁₃×#123	—	2	4	no	—
84	C₁₃×C₂²⋊Q₈	—	2	2	no	—
85	C₁₃×C₂²⋊Q₈	—	2	2	no	—
86	C₁₃×C₂²⋊Q₈	—	2	2	no	—
87	C₁₃×C₂²⋊Q₈	—	2	2	no	—
88	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
89	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
90	C₁₃×#121	—	2	2	no	—
91	C₁₃×#121	—	2	2	no	—
92	C₁₃×#121	—	2	2	no	—
93	C₁₃×#121	—	2	2	no	—
94	C₁₃×#121	C₂³	1	4	yes	—
95	C₁₃×#121	C₂³	1	4	yes	—
96	C₁₃×#120	—	2	4	no	—
97	C₄×Q₈×C₁₃	—	2	2	no	—
98	C₄×Q₈×C₁₃	—	2	2	no	—
99	C₄×Q₈×C₁₃	—	2	2	no	—
100	C₄×Q₈×C₁₃	—	2	2	no	—
101	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
102	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
103	C₄×D₄×C₁₃	—	2	4	no	—
104	C₄×D₄×C₁₃	—	2	4	no	—
105	C₄×D₄×C₁₃	—	2	4	no	—
106	C₄×D₄×C₁₃	—	2	4	no	—
107	C₄×D₄×C₁₃	—	2	4	no	—
108	C₄×D₄×C₁₃	—	2	4	no	—
109	C₄×D₄×C₁₃	—	2	2	no	—
110	C₄×D₄×C₁₃	—	2	2	no	—
111	C₄×D₄×C₁₃	—	2	2	no	—
112	C₄×D₄×C₁₃	—	2	2	no	—
113	C₄×D₄×C₁₃	C₂³	1	4	yes	—
114	C₄×D₄×C₁₃	C₂³	1	4	yes	—
115	C₁₃×#117	—	2	2	no	—
116	C₁₃×#117	—	2	2	no	—
117	C₁₃×#117	—	2	4	no	—
118	C₁₃×#117	—	2	4	no	—
119	C₁₃×#117	—	2	4	no	—
120	C₁₃×#117	C₂³	1	4	yes	—
121	C₂×C₄²×C₁₃	—	2	4	no	—
122	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
123	C₂×C₄²×C₁₃	D₄	1	2	yes	—
124	C₂×C₄²×C₁₃	D₄	1	2	yes	—
125	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
126	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
129	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
130	C₁₃×#107	C₂³	1	4	yes	—
131	C₁₃×#107	C₂³	1	4	yes	—
132	C₁₃×#106	C₂³	1	8	yes	—
133	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
134	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
135	C₁₃×#103	C₂³	1	8	yes	—
136	C₁₃×#103	C₂³	1	8	yes	—
137	C₁₃×#102	C₂³	1	8	yes	—
138	C₁₃×#102	C₂³	1	8	yes	—
139	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
140	C₄×C₈×C₁₃	C₂³	1	4	yes	—
141	C₄×C₈×C₁₃	C₂³	1	4	yes	—
142	#60948	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
143	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₁₃×#41	—	4	4	no	—
145	C₁₃×#41	—	4	4	no	—
146	C₁₃×#41	—	4	8	no	—
147	C₁₃×#41	—	4	8	no	—
148	C₂×Q₈×C₁₃	—	2	2	no	—
149	C₂×Q₈×C₁₃	—	2	2	no	—
150	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
151	C₂×D₄×C₁₃	—	2	4	no	—
152	C₂×D₄×C₁₃	—	2	4	no	—
153	C₂×D₄×C₁₃	—	2	4	no	—
154	C₂×D₄×C₁₃	—	2	2	no	—
155	C₂×D₄×C₁₃	—	2	2	no	—
156	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₁₃	—	2	4	no	—
158	C₂²×C₄×C₁₃	—	2	4	no	—
159	C₂²×C₄×C₁₃	—	2	4	no	—
160	C₂²×C₄×C₁₃	—	2	4	no	—
161	C₂²×C₄×C₁₃	—	4	2	no	—
162	C₂²×C₄×C₁₃	—	4	1	no	—
163	C₂²×C₄×C₁₃	—	4	1	no	—
164	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₁₃×Q₁₆	—	4	4	no	—
177	C₁₃×SD₁₆	—	4	8	no	—
178	C₁₃×D₈	—	4	4	no	—
179	C₂×C₈×C₁₃	—	4	2	no	—
180	C₂×C₈×C₁₃	—	4	2	no	—
181	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
182	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
183	C₁₃×C₄⋊C₄	—	2	2	no	—
184	C₁₃×C₄⋊C₄	—	2	2	no	—
185	C₁₃×C₄⋊C₄	—	2	2	no	—
186	C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₁₃×C₄⋊C₄	—	2	4	no	—
188	C₁₃×C₄⋊C₄	—	2	4	no	—
189	C₁₃×C₄⋊C₄	—	2	4	no	—
190	C₁₃×C₄⋊C₄	—	2	4	no	—
191	C₁₃×C₄⋊C₄	—	2	4	no	—
192	C₁₃×C₄⋊C₄	—	2	4	no	—
193	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
194	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
195	C₁₃×C₂²⋊C₄	—	2	4	no	—
196	C₁₃×C₂²⋊C₄	—	2	4	no	—
197	C₁₃×C₂²⋊C₄	—	2	4	no	—
198	C₁₃×C₂²⋊C₄	—	2	4	no	—
199	C₁₃×C₂²⋊C₄	—	2	4	no	—
200	C₁₃×C₂²⋊C₄	—	2	4	no	—
201	C₁₃×C₂²⋊C₄	—	2	4	no	—
202	C₁₃×C₂²⋊C₄	—	2	4	no	—
203	C₁₃×C₂²⋊C₄	—	2	4	no	—
204	C₄²×C₁₃	—	2	4	no	—
205	C₄²×C₁₃	—	2	4	no	—
206	C₄²×C₁₃	—	2	4	no	—
207	C₄²×C₁₃	C₂×D₄	1	2	yes	—
208	C₄²×C₁₃	C₂×D₄	1	2	yes	—
209	C₄²×C₁₃	C₂×D₄	1	2	yes	—
210	C₄²×C₁₃	C₂×D₄	1	2	yes	—
211	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₁₃	C₂×D₄	1	2	yes	—
213	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
215	C₄²×C₁₃	C₂⁴	1	2	yes	—
216	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
217	#3444	C₂×C₁₃	1	2	yes	complemented
218	#3249	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#3246	C₂×C₁₃	1	2	yes	complemented
220	#3245	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#3233	C₂×C₁₃	1	4	yes	complemented
222	#3212	C₂×C₁₃	1	4	yes	complemented
223	#3191	C₂×C₁₃	1	4	yes	complemented
224	#3168	C₂×C₁₃	1	4	yes	complemented
225	#3107	C₂×C₁₃	1	4	yes	complemented
226	#3106	C₂×C₁₃	1	4	yes	complemented
227	C₂×#431	C₂×C₁₃	1	1	yes	characteristic, complemented
228	C₂³×C₁₃	—	2	2	no	—
229	C₂³×C₁₃	—	2	4	no	—
230	C₂³×C₁₃	—	4	1	no	—
231	C₂³×C₁₃	—	4	1	no	—
232	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
233	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
234	Q₈×C₁₃	—	2	4	no	—
235	Q₈×C₁₃	—	2	4	no	—
236	Q₈×C₁₃	—	4	4	no	—
237	Q₈×C₁₃	—	4	4	no	—
238	D₄×C₁₃	—	2	4	no	—
239	D₄×C₁₃	—	2	4	no	—
240	D₄×C₁₃	—	4	4	no	—
241	D₄×C₁₃	—	4	8	no	—
242	D₄×C₁₃	—	4	8	no	—
243	D₄×C₁₃	—	4	8	no	—
244	D₄×C₁₃	—	4	4	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	4	no	—
247	C₂×C₄×C₁₃	—	2	4	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	4	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	2	4	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	4	2	no	—
259	C₂×C₄×C₁₃	—	4	2	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	8	no	—
262	C₂×C₄×C₁₃	—	4	8	no	—
263	C₂×C₄×C₁₃	—	4	8	no	—
264	C₂×C₄×C₁₃	#135	1	4	yes	—
265	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
266	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
271	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
272	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
274	C₈×C₁₃	—	2	4	no	—
275	C₈×C₁₃	—	2	4	no	—
276	#533	C₂²×C₁₃	1	2	yes	—
277	#533	C₂²×C₁₃	1	2	yes	—
278	#533	C₂²×C₁₃	1	2	yes	—
279	#532	C₂²×C₁₃	1	2	yes	—
280	#532	C₂²×C₁₃	1	2	yes	—
281	#532	C₂²×C₁₃	1	2	yes	—
282	#529	—	2	2	no	—
283	#529	—	2	2	no	—
284	#529	—	2	2	no	—
285	#529	—	2	2	no	—
286	#529	C₂²×C₁₃	1	4	yes	—
287	#529	C₂²×C₁₃	1	4	yes	—
288	#525	—	2	2	no	—
289	#525	—	2	2	no	—
290	#525	C₂²×C₁₃	1	4	yes	—
291	C₄×#41	—	2	2	no	—
292	C₄×#41	—	2	2	no	—
293	C₄×#41	C₂²×C₁₃	1	4	yes	—
294	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
295	#499	C₂²×C₁₃	1	4	yes	complemented
296	#495	C₂²×C₁₃	1	4	yes	complemented
297	#488	C₂²×C₁₃	1	8	yes	complemented
298	#485	C₂²×C₁₃	1	8	yes	—
299	#482	C₂²×C₁₃	1	8	yes	—
300	#477	C₂²×C₁₃	1	4	yes	complemented
301	#476	C₂²×C₁₃	1	4	yes	complemented
302	#475	C₂²×C₁₃	1	4	yes	complemented
303	#474	C₂²×C₁₃	1	4	yes	complemented
304	#467	C₂²×C₁₃	1	4	yes	—
305	#466	C₂²×C₁₃	1	4	yes	—
306	#465	C₂²×C₁₃	1	8	yes	—
307	#462	C₂²×C₁₃	1	4	yes	complemented
308	#461	C₂²×C₁₃	1	4	yes	complemented
309	#460	C₂²×C₁₃	1	4	yes	complemented
310	#459	C₂²×C₁₃	1	4	yes	complemented
311	#452	C₂²×C₁₃	1	8	yes	—
312	#449	C₂²×C₁₃	1	8	yes	—
313	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
314	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
315	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
316	#431	C₂²×C₁₃	1	4	yes	—
317	#431	C₂²×C₁₃	1	4	yes	—
318	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
321	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
322	C₂²×C₁₃	—	2	1	no	—
323	C₂²×C₁₃	—	2	1	no	—
324	C₂²×C₁₃	—	2	2	no	—
325	C₂²×C₁₃	—	2	2	no	—
326	C₂²×C₁₃	—	2	2	no	—
327	C₂²×C₁₃	—	4	4	no	—
328	C₂²×C₁₃	—	4	4	no	—
329	C₂²×C₁₃	—	4	4	no	—
330	C₂²×C₁₃	—	4	4	no	—
331	C₂²×C₁₃	C₂×#135	1	2	yes	—
332	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
333	C₄×C₁₃	—	2	2	no	—
334	C₄×C₁₃	—	2	1	no	—
335	C₄×C₁₃	—	2	1	no	—
336	C₄×C₁₃	—	2	1	no	—
337	C₄×C₁₃	—	2	1	no	—
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	—	4	4	no	—
340	C₄×C₁₃	—	4	4	no	—
341	C₄×C₁₃	—	4	4	no	—
342	C₄×C₁₃	C₂×#135	1	4	yes	—
343	C₄×C₁₃	#575	1	2	yes	—
344	C₄×C₁₃	#585	1	1	yes	characteristic
345	C₄×C₁₃	#585	1	1	yes	characteristic
346	C₂×#41	—	2	2	no	—
347	C₂×#41	—	2	2	no	—
348	C₂×#41	C₂³×C₁₃	1	4	yes	—
349	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
350	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
351	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
352	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
353	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
354	C₂×D₈	C₂³×C₁₃	1	4	yes	—
355	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
356	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
357	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
358	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
359	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
360	#127	C₂³×C₁₃	1	2	yes	—
361	#126	—	2	4	no	—
362	#126	—	2	4	no	—
363	#125	—	2	2	no	—
364	#125	—	2	2	no	—
365	#125	C₂³×C₁₃	1	4	yes	—
366	#124	—	2	2	no	—
367	#124	—	2	2	no	—
368	#124	C₂³×C₁₃	1	4	yes	—
369	#123	—	2	4	no	—
370	#123	—	2	4	no	—
371	#123	—	2	4	no	—
372	C₂²⋊Q₈	—	2	2	no	—
373	C₂²⋊Q₈	—	2	2	no	—
374	C₂²⋊Q₈	—	2	2	no	—
375	C₂²⋊Q₈	—	2	2	no	—
376	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
377	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
378	#121	—	2	2	no	—
379	#121	—	2	2	no	—
380	#121	—	2	2	no	—
381	#121	—	2	2	no	—
382	#121	C₂³×C₁₃	1	4	yes	—
383	#121	C₂³×C₁₃	1	4	yes	—
384	#120	—	2	4	no	—
385	C₄×Q₈	—	2	2	no	—
386	C₄×Q₈	—	2	2	no	—
387	C₄×Q₈	—	2	2	no	—
388	C₄×Q₈	—	2	2	no	—
389	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
390	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
391	C₄×D₄	—	2	4	no	—
392	C₄×D₄	—	2	4	no	—
393	C₄×D₄	—	2	4	no	—
394	C₄×D₄	—	2	4	no	—
395	C₄×D₄	—	2	4	no	—
396	C₄×D₄	—	2	4	no	—
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	—	2	2	no	—
400	C₄×D₄	—	2	2	no	—
401	C₄×D₄	C₂³×C₁₃	1	4	yes	—
402	C₄×D₄	C₂³×C₁₃	1	4	yes	—
403	#117	—	2	2	no	—
404	#117	—	2	2	no	—
405	#117	—	2	4	no	—
406	#117	—	2	4	no	—
407	#117	—	2	4	no	—
408	#117	C₂³×C₁₃	1	4	yes	—
409	C₂×C₄²	—	2	4	no	—
410	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
411	C₂×C₄²	D₄×C₁₃	1	2	yes	—
412	C₂×C₄²	D₄×C₁₃	1	2	yes	—
413	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
414	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
415	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
416	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
417	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
418	#107	C₂³×C₁₃	1	4	yes	—
419	#107	C₂³×C₁₃	1	4	yes	—
420	#106	C₂³×C₁₃	1	8	yes	—
421	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
422	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
423	#103	C₂³×C₁₃	1	8	yes	—
424	#103	C₂³×C₁₃	1	8	yes	—
425	#102	C₂³×C₁₃	1	8	yes	—
426	#102	C₂³×C₁₃	1	8	yes	—
427	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
428	C₄×C₈	C₂³×C₁₃	1	4	yes	—
429	C₄×C₈	C₂³×C₁₃	1	4	yes	—
430	C₂×C₁₃	—	2	2	no	—
431	C₂×C₁₃	—	4	2	no	—
432	C₂×C₁₃	—	8	4	no	—
433	C₂×C₁₃	#3449	1	1	yes	characteristic
434	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
435	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
436	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
437	#41	—	4	4	no	—
438	#41	—	4	4	no	—
439	#41	—	4	8	no	—
440	#41	—	4	8	no	—
441	C₂×Q₈	—	2	2	no	—
442	C₂×Q₈	—	2	2	no	—
443	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	—	2	4	no	—
446	C₂×D₄	—	2	4	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	4	2	no	—
455	C₂²×C₄	—	4	1	no	—
456	C₂²×C₄	—	4	1	no	—
457	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
458	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
460	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
461	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
462	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
464	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
466	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
467	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
468	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
469	Q₁₆	—	4	4	no	—
470	SD₁₆	—	4	8	no	—
471	D₈	—	4	4	no	—
472	C₂×C₈	—	4	2	no	—
473	C₂×C₈	—	4	2	no	—
474	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
475	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	4	no	—
481	C₄⋊C₄	—	2	4	no	—
482	C₄⋊C₄	—	2	4	no	—
483	C₄⋊C₄	—	2	4	no	—
484	C₄⋊C₄	—	2	4	no	—
485	C₄⋊C₄	—	2	4	no	—
486	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
487	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
488	C₂²⋊C₄	—	2	4	no	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	4	no	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	—	2	4	no	—
495	C₂²⋊C₄	—	2	4	no	—
496	C₂²⋊C₄	—	2	4	no	—
497	C₄²	—	2	4	no	—
498	C₄²	—	2	4	no	—
499	C₄²	—	2	4	no	—
500	C₄²	C₂×D₄×C₁₃	1	2	yes	—
501	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
502	C₄²	C₂×D₄×C₁₃	1	2	yes	—
503	C₄²	C₂×D₄×C₁₃	1	2	yes	—
504	C₄²	C₂×D₄×C₁₃	1	2	yes	—
505	C₄²	C₂×D₄×C₁₃	1	2	yes	—
506	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
507	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
508	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
509	C₄²	C₂⁴×C₁₃	1	2	yes	—
510	C₁₃	#60948	1	1	yes	characteristic, direct product factor, Sylow
511	C₂³	—	2	2	no	—
512	C₂³	—	2	4	no	—
513	C₂³	—	4	1	no	—
514	C₂³	—	4	1	no	—
515	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
516	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
517	Q₈	—	2	4	no	—
518	Q₈	—	2	4	no	—
519	Q₈	—	4	4	no	—
520	Q₈	—	4	4	no	—
521	D₄	—	2	4	no	—
522	D₄	—	2	4	no	—
523	D₄	—	4	4	no	—
524	D₄	—	4	8	no	—
525	D₄	—	4	8	no	—
526	D₄	—	4	8	no	—
527	D₄	—	4	4	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	8	no	—
545	C₂×C₄	—	4	8	no	—
546	C₂×C₄	—	4	8	no	—
547	C₂×C₄	C₁₃×#135	1	4	yes	—
548	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
549	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
550	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
551	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
553	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
554	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
555	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
556	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
557	C₈	—	2	4	no	—
558	C₈	—	2	4	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	4	4	no	—
566	C₂²	—	4	4	no	—
567	C₂²	—	4	4	no	—
568	C₂²	C₂×C₁₃×#135	1	2	yes	—
569	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	1	no	—
576	C₄	—	4	4	no	—
577	C₄	—	4	4	no	—
578	C₄	—	4	4	no	—
579	C₄	C₂×C₁₃×#135	1	4	yes	—
580	C₄	C₁₃×#575	1	2	yes	—
581	C₄	C₁₃×#585	1	1	yes	characteristic
582	C₄	C₁₃×#585	1	1	yes	characteristic
583	C₂	—	2	2	no	—
584	C₂	—	4	2	no	—
585	C₂	—	8	4	no	—
586	C₂	C₁₃×#3449	1	1	yes	characteristic
587	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
588	C₂	C₂×C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3444	C₂	semidirect
2. C₁₃×#3249	C₂	semidirect
3. C₁₃×#3246	C₂	semidirect
4. C₁₃×#3245	C₂	semidirect
5. C₁₃×#3233	C₂	semidirect
6. C₁₃×#3212	C₂	semidirect
7. C₁₃×#3191	C₂	semidirect
8. C₁₃×#3168	C₂	semidirect
9. C₁₃×#3107	C₂	semidirect
10. C₁₃×#3106	C₂	semidirect
11. C₂×C₁₃×#431	C₂	semidirect
31. C₁₃×#499	C₂²	semidirect
32. C₁₃×#495	C₂²	semidirect
33. C₁₃×#488	C₂²	semidirect
36. C₁₃×#477	C₂²	semidirect
37. C₁₃×#476	C₂²	semidirect
38. C₁₃×#475	C₂²	semidirect
39. C₁₃×#474	C₂²	semidirect
43. C₁₃×#462	C₂²	semidirect
44. C₁₃×#461	C₂²	semidirect
45. C₁₃×#460	C₂²	semidirect
46. C₁₃×#459	C₂²	semidirect
49. C₄×C₁₃×Q₁₆	C₂²	semidirect
50. C₄×C₁₃×SD₁₆	C₂²	semidirect
51. C₄×C₁₃×D₈	C₂²	semidirect
142. #60948	C₁₃	direct (N × H)
217. #3444	C₂×C₁₃	semidirect
218. #3249	C₂×C₁₃	semidirect
219. #3246	C₂×C₁₃	semidirect
220. #3245	C₂×C₁₃	semidirect
221. #3233	C₂×C₁₃	semidirect
222. #3212	C₂×C₁₃	semidirect
223. #3191	C₂×C₁₃	semidirect
224. #3168	C₂×C₁₃	semidirect
225. #3107	C₂×C₁₃	semidirect
226. #3106	C₂×C₁₃	semidirect
227. C₂×#431	C₂×C₁₃	semidirect
295. #499	C₂²×C₁₃	semidirect
296. #495	C₂²×C₁₃	semidirect
297. #488	C₂²×C₁₃	semidirect
300. #477	C₂²×C₁₃	semidirect
301. #476	C₂²×C₁₃	semidirect
302. #475	C₂²×C₁₃	semidirect
303. #474	C₂²×C₁₃	semidirect
307. #462	C₂²×C₁₃	semidirect
308. #461	C₂²×C₁₃	semidirect
309. #460	C₂²×C₁₃	semidirect
310. #459	C₂²×C₁₃	semidirect
313. C₄×Q₁₆	C₂²×C₁₃	semidirect
314. C₄×SD₁₆	C₂²×C₁₃	semidirect
315. C₄×D₈	C₂²×C₁₃	semidirect
510. C₁₃	#60948	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×#3444	2
C₁₃×#3249	2
C₁₃×#3246	2
C₁₃×#3245	2
C₁₃×#3233	2
C₁₃×#3212	2
C₁₃×#3191	2
C₁₃×#3168	2
C₁₃×#3107	2
C₁₃×#3106	2
C₂×C₁₃×#431	2
#60948	13

Subgroups — C13×#60948 #15747287

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60948 #15747287