Subgroups — C₁₃×#32962 #15719301

Order 3328.

1422 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#518	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2628	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1864	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1862	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1854	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1798	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1786	C₂	1	2	yes	maximal
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
14	C₁₃×#518	—	2	4	no	—
15	C₁₃×#518	—	2	4	no	—
16	C₂×C₄×D₄×C₁₃	—	2	1	no	—
17	C₂×C₄×D₄×C₁₃	—	2	1	no	—
18	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
25	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
26	C₁₃×#476	—	2	4	no	—
27	C₁₃×#474	—	2	4	no	—
28	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
29	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
30	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₃×#102	C₂²	1	2	yes	—
33	C₂×C₁₃×#102	C₂²	1	2	yes	—
34	C₂×C₁₃×#102	C₂²	1	2	yes	—
35	C₂×C₁₃×#102	C₂²	1	2	yes	—
36	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
37	C₁₃×#400	—	2	1	no	—
38	C₁₃×#399	—	2	1	no	—
39	C₁₃×#395	—	2	1	no	—
40	C₁₃×#393	—	2	1	no	—
41	C₁₃×#389	C₂²	1	2	yes	complemented
42	C₁₃×#382	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#380	C₂²	1	2	yes	—
44	C₁₃×#340	C₂²	1	2	yes	complemented
45	C₁₃×#340	C₂²	1	2	yes	complemented
46	C₁₃×#336	C₂²	1	2	yes	complemented
47	C₂⁵×C₁₃	—	2	1	no	—
48	C₂²×Q₈×C₁₃	—	2	1	no	—
49	C₂²×D₄×C₁₃	—	2	2	no	—
50	C₂²×D₄×C₁₃	—	2	2	no	—
51	C₂²×D₄×C₁₃	—	2	2	no	—
52	C₂²×D₄×C₁₃	—	2	2	no	—
53	C₂²×D₄×C₁₃	—	2	1	no	—
54	C₂²×D₄×C₁₃	—	2	2	no	—
55	C₂²×D₄×C₁₃	Q₈	1	4	yes	complemented
56	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₃	—	2	1	no	—
59	C₂³×C₄×C₁₃	—	2	1	no	—
60	C₂³×C₄×C₁₃	—	2	1	no	—
61	C₂³×C₄×C₁₃	—	2	1	no	—
62	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
64	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
65	C₁₃×C₄⋊Q₈	—	2	2	no	—
66	C₁₃×C₄⋊Q₈	—	2	2	no	—
67	C₄×D₄×C₁₃	—	2	8	no	—
68	C₄×D₄×C₁₃	—	2	8	no	—
69	C₄×D₄×C₁₃	—	2	2	no	—
70	C₄×D₄×C₁₃	—	2	2	no	—
71	C₄×D₄×C₁₃	—	2	2	no	—
72	C₄×D₄×C₁₃	—	2	2	no	—
73	C₄×D₄×C₁₃	—	2	2	no	—
74	C₄×D₄×C₁₃	—	2	2	no	—
75	C₄×D₄×C₁₃	D₄	1	4	yes	—
76	C₄×D₄×C₁₃	D₄	1	4	yes	—
77	C₁₃×#117	—	2	2	no	—
78	C₁₃×#117	—	2	2	no	—
79	C₁₃×#117	—	2	2	no	—
80	C₁₃×#117	—	2	2	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
84	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
90	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
97	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
98	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	—	2	1	no	—
100	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₁₃×#107	—	2	4	no	—
103	C₁₃×#106	—	2	4	no	—
104	C₁₃×C₄⋊C₈	—	2	2	no	—
105	C₁₃×C₄⋊C₈	—	2	2	no	—
106	C₁₃×#102	—	2	4	no	—
107	C₁₃×#102	—	2	4	no	—
108	C₁₃×#102	—	2	4	no	—
109	C₁₃×#102	—	2	4	no	—
110	C₁₃×C₂²⋊C₈	—	2	4	no	—
111	C₁₃×#95	—	2	2	no	—
112	C₁₃×#95	—	2	1	no	—
113	C₁₃×#95	—	2	1	no	—
114	C₁₃×#95	—	2	2	no	—
115	#32962	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂⁴×C₁₃	—	2	4	no	—
117	C₂⁴×C₁₃	—	2	4	no	—
118	C₂⁴×C₁₃	—	2	1	no	—
119	C₂⁴×C₁₃	—	2	1	no	—
120	C₂⁴×C₁₃	—	2	4	no	—
121	C₂⁴×C₁₃	—	8	2	no	—
122	C₂⁴×C₁₃	—	8	2	no	—
123	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂×Q₈×C₁₃	—	4	2	no	—
125	C₂×Q₈×C₁₃	—	8	2	no	—
126	C₂×D₄×C₁₃	—	2	4	no	—
127	C₂×D₄×C₁₃	—	2	4	no	—
128	C₂×D₄×C₁₃	—	2	8	no	—
129	C₂×D₄×C₁₃	—	2	8	no	—
130	C₂×D₄×C₁₃	—	2	8	no	—
131	C₂×D₄×C₁₃	—	2	8	no	—
132	C₂×D₄×C₁₃	—	2	4	no	—
133	C₂×D₄×C₁₃	—	2	1	no	—
134	C₂×D₄×C₁₃	—	2	1	no	—
135	C₂×D₄×C₁₃	—	2	1	no	—
136	C₂×D₄×C₁₃	—	2	1	no	—
137	C₂×D₄×C₁₃	—	2	1	no	—
138	C₂×D₄×C₁₃	—	2	1	no	—
139	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
140	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
141	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
142	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
143	C₂×D₄×C₁₃	#41	1	2	yes	—
144	C₂×D₄×C₁₃	#41	1	2	yes	—
145	C₂²×C₄×C₁₃	—	2	1	no	—
146	C₂²×C₄×C₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂²×C₄×C₁₃	—	2	1	no	—
150	C₂²×C₄×C₁₃	—	2	1	no	—
151	C₂²×C₄×C₁₃	—	2	4	no	—
152	C₂²×C₄×C₁₃	—	2	4	no	—
153	C₂²×C₄×C₁₃	—	2	4	no	—
154	C₂²×C₄×C₁₃	—	2	4	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₃	—	8	2	no	—
158	C₂²×C₄×C₁₃	—	8	2	no	—
159	C₂²×C₄×C₁₃	—	8	2	no	—
160	C₂²×C₄×C₁₃	—	8	2	no	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
167	C₂²×C₄×C₁₃	#41	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
169	C₂×C₈×C₁₃	—	2	2	no	—
170	C₂×C₈×C₁₃	—	2	2	no	—
171	C₂×C₈×C₁₃	—	2	2	no	—
172	C₂×C₈×C₁₃	—	2	2	no	—
173	C₂×C₈×C₁₃	—	2	2	no	—
174	C₂×C₈×C₁₃	—	2	2	no	—
175	C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₁₃×C₄⋊C₄	—	2	2	no	—
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	2	no	—
180	C₁₃×C₄⋊C₄	—	2	2	no	—
181	C₁₃×C₄⋊C₄	—	2	2	no	—
182	C₁₃×C₄⋊C₄	—	2	2	no	—
183	C₁₃×C₄⋊C₄	—	4	2	no	—
184	C₁₃×C₄⋊C₄	—	8	2	no	—
185	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
186	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
187	C₁₃×C₂²⋊C₄	—	2	4	no	—
188	C₁₃×C₂²⋊C₄	—	2	4	no	—
189	C₁₃×C₂²⋊C₄	—	2	4	no	—
190	C₁₃×C₂²⋊C₄	—	2	2	no	—
191	C₁₃×C₂²⋊C₄	—	2	2	no	—
192	C₁₃×C₂²⋊C₄	—	2	4	no	—
193	C₁₃×C₂²⋊C₄	—	2	4	no	—
194	C₁₃×C₂²⋊C₄	—	8	2	no	—
195	C₄²×C₁₃	—	2	4	no	—
196	C₄²×C₁₃	—	2	1	no	—
197	C₄²×C₁₃	—	2	1	no	—
198	C₄²×C₁₃	C₂×D₄	1	2	yes	—
199	C₄²×C₁₃	C₂×D₄	1	2	yes	—
200	C₂×#518	C₂×C₁₃	1	1	yes	characteristic
201	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
202	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#2628	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#1864	C₂×C₁₃	1	2	yes	complemented
205	#1862	C₂×C₁₃	1	2	yes	complemented
206	#1854	C₂×C₁₃	1	2	yes	complemented
207	#1804	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#1804	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#1798	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#1786	C₂×C₁₃	1	2	yes	—
211	C₂³×C₁₃	—	2	16	no	—
212	C₂³×C₁₃	—	2	1	no	—
213	C₂³×C₁₃	—	2	2	no	—
214	C₂³×C₁₃	—	2	2	no	—
215	C₂³×C₁₃	—	2	2	no	—
216	C₂³×C₁₃	—	2	2	no	—
217	C₂³×C₁₃	—	2	1	no	—
218	C₂³×C₁₃	—	2	2	no	—
219	C₂³×C₁₃	—	2	2	no	—
220	C₂³×C₁₃	—	2	2	no	—
221	C₂³×C₁₃	—	2	2	no	—
222	C₂³×C₁₃	—	4	2	no	—
223	C₂³×C₁₃	—	4	2	no	—
224	C₂³×C₁₃	—	4	2	no	—
225	C₂³×C₁₃	—	4	2	no	—
226	C₂³×C₁₃	—	8	8	no	—
227	C₂³×C₁₃	—	8	8	no	—
228	C₂³×C₁₃	—	8	4	no	—
229	C₂³×C₁₃	—	8	4	no	—
230	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
231	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
232	Q₈×C₁₃	—	8	4	no	—
233	D₄×C₁₃	—	2	16	no	—
234	D₄×C₁₃	—	2	2	no	—
235	D₄×C₁₃	—	2	2	no	—
236	D₄×C₁₃	—	2	2	no	—
237	D₄×C₁₃	—	2	2	no	—
238	D₄×C₁₃	—	2	2	no	—
239	D₄×C₁₃	—	2	2	no	—
240	D₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
241	D₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	2	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	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	2	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	4	2	no	—
257	C₂×C₄×C₁₃	—	4	2	no	—
258	C₂×C₄×C₁₃	—	4	2	no	—
259	C₂×C₄×C₁₃	—	4	2	no	—
260	C₂×C₄×C₁₃	—	4	2	no	—
261	C₂×C₄×C₁₃	—	4	2	no	—
262	C₂×C₄×C₁₃	—	4	2	no	—
263	C₂×C₄×C₁₃	—	4	2	no	—
264	C₂×C₄×C₁₃	—	8	4	no	—
265	C₂×C₄×C₁₃	—	8	4	no	—
266	C₂×C₄×C₁₃	—	8	4	no	—
267	C₂×C₄×C₁₃	—	8	4	no	—
268	C₂×C₄×C₁₃	#120	1	2	yes	—
269	C₂×C₄×C₁₃	#120	1	2	yes	—
270	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
271	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
276	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
277	C₈×C₁₃	—	4	2	no	—
278	C₈×C₁₃	—	4	2	no	—
279	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
281	#518	—	2	4	no	—
282	#518	—	2	4	no	—
283	C₂×C₄×D₄	—	2	1	no	—
284	C₂×C₄×D₄	—	2	1	no	—
285	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
291	C₂²×C₂²⋊C₄	—	2	1	no	—
292	C₂²×C₂²⋊C₄	—	2	1	no	—
293	#476	—	2	4	no	—
294	#474	—	2	4	no	—
295	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
296	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
297	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
298	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
299	C₂×#102	C₂²×C₁₃	1	2	yes	—
300	C₂×#102	C₂²×C₁₃	1	2	yes	—
301	C₂×#102	C₂²×C₁₃	1	2	yes	—
302	C₂×#102	C₂²×C₁₃	1	2	yes	—
303	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
304	#400	—	2	1	no	—
305	#399	—	2	1	no	—
306	#395	—	2	1	no	—
307	#393	—	2	1	no	—
308	#389	C₂²×C₁₃	1	2	yes	complemented
309	#382	C₂²×C₁₃	1	1	yes	characteristic, complemented
310	#380	C₂²×C₁₃	1	2	yes	—
311	#340	C₂²×C₁₃	1	2	yes	complemented
312	#340	C₂²×C₁₃	1	2	yes	complemented
313	#336	C₂²×C₁₃	1	2	yes	complemented
314	C₂²×C₁₃	—	2	4	no	—
315	C₂²×C₁₃	—	2	2	no	—
316	C₂²×C₁₃	—	2	4	no	—
317	C₂²×C₁₃	—	2	4	no	—
318	C₂²×C₁₃	—	4	4	no	—
319	C₂²×C₁₃	—	4	4	no	—
320	C₂²×C₁₃	—	4	2	no	—
321	C₂²×C₁₃	—	4	4	no	—
322	C₂²×C₁₃	—	4	4	no	—
323	C₂²×C₁₃	—	4	2	no	—
324	C₂²×C₁₃	—	4	2	no	—
325	C₂²×C₁₃	—	4	1	no	—
326	C₂²×C₁₃	—	4	2	no	—
327	C₂²×C₁₃	—	4	2	no	—
328	C₂²×C₁₃	—	4	1	no	—
329	C₂²×C₁₃	—	8	16	no	—
330	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
331	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
332	C₂²×C₁₃	#525	1	1	yes	characteristic
333	C₂²×C₁₃	#576	1	2	yes	—
334	C₂²×C₁₃	#577	1	2	yes	—
335	C₄×C₁₃	—	2	2	no	—
336	C₄×C₁₃	—	2	2	no	—
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	4	1	no	—
339	C₄×C₁₃	—	4	2	no	—
340	C₄×C₁₃	—	4	1	no	—
341	C₄×C₁₃	—	4	2	no	—
342	C₄×C₁₃	—	8	2	no	—
343	C₄×C₁₃	—	8	2	no	—
344	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
345	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
346	C₄×C₁₃	#525	1	1	yes	characteristic
347	C₄×C₁₃	#525	1	1	yes	characteristic
348	C₂⁵	—	2	1	no	—
349	C₂²×Q₈	—	2	1	no	—
350	C₂²×D₄	—	2	2	no	—
351	C₂²×D₄	—	2	2	no	—
352	C₂²×D₄	—	2	2	no	—
353	C₂²×D₄	—	2	2	no	—
354	C₂²×D₄	—	2	1	no	—
355	C₂²×D₄	—	2	2	no	—
356	C₂²×D₄	Q₈×C₁₃	1	4	yes	complemented
357	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
358	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
359	C₂³×C₄	—	2	1	no	—
360	C₂³×C₄	—	2	1	no	—
361	C₂³×C₄	—	2	1	no	—
362	C₂³×C₄	—	2	1	no	—
363	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
365	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
366	C₄⋊Q₈	—	2	2	no	—
367	C₄⋊Q₈	—	2	2	no	—
368	C₄×D₄	—	2	8	no	—
369	C₄×D₄	—	2	8	no	—
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	—	2	2	no	—
372	C₄×D₄	—	2	2	no	—
373	C₄×D₄	—	2	2	no	—
374	C₄×D₄	—	2	2	no	—
375	C₄×D₄	—	2	2	no	—
376	C₄×D₄	D₄×C₁₃	1	4	yes	—
377	C₄×D₄	D₄×C₁₃	1	4	yes	—
378	#117	—	2	2	no	—
379	#117	—	2	2	no	—
380	#117	—	2	2	no	—
381	#117	—	2	2	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	2	no	—
384	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
385	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
387	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
388	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
390	C₂×C₂²⋊C₄	—	2	8	no	—
391	C₂×C₂²⋊C₄	—	2	8	no	—
392	C₂×C₂²⋊C₄	—	2	1	no	—
393	C₂×C₂²⋊C₄	—	2	1	no	—
394	C₂×C₂²⋊C₄	—	2	1	no	—
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₂²⋊C₄	—	2	1	no	—
397	C₂×C₂²⋊C₄	—	2	2	no	—
398	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
399	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
400	C₂×C₄²	—	2	1	no	—
401	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
402	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
403	#107	—	2	4	no	—
404	#106	—	2	4	no	—
405	C₄⋊C₈	—	2	2	no	—
406	C₄⋊C₈	—	2	2	no	—
407	#102	—	2	4	no	—
408	#102	—	2	4	no	—
409	#102	—	2	4	no	—
410	#102	—	2	4	no	—
411	C₂²⋊C₈	—	2	4	no	—
412	#95	—	2	2	no	—
413	#95	—	2	1	no	—
414	#95	—	2	1	no	—
415	#95	—	2	2	no	—
416	C₂×C₁₃	—	4	2	no	—
417	C₂×C₁₃	—	4	4	no	—
418	C₂×C₁₃	—	4	4	no	—
419	C₂×C₁₃	#2848	1	1	yes	characteristic
420	C₂×C₁₃	#3008	1	1	yes	characteristic
421	C₂×C₁₃	#3009	1	1	yes	characteristic
422	C₂×C₁₃	#3081	1	2	yes	—
423	C₂×C₁₃	#3118	1	2	yes	—
424	C₂⁴	—	2	4	no	—
425	C₂⁴	—	2	4	no	—
426	C₂⁴	—	2	1	no	—
427	C₂⁴	—	2	1	no	—
428	C₂⁴	—	2	4	no	—
429	C₂⁴	—	8	2	no	—
430	C₂⁴	—	8	2	no	—
431	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
432	C₂×Q₈	—	4	2	no	—
433	C₂×Q₈	—	8	2	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	2	8	no	—
437	C₂×D₄	—	2	8	no	—
438	C₂×D₄	—	2	8	no	—
439	C₂×D₄	—	2	8	no	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
448	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
449	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
450	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
451	C₂×D₄	C₁₃×#41	1	2	yes	—
452	C₂×D₄	C₁₃×#41	1	2	yes	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	8	2	no	—
466	C₂²×C₄	—	8	2	no	—
467	C₂²×C₄	—	8	2	no	—
468	C₂²×C₄	—	8	2	no	—
469	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
473	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
474	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
475	C₂²×C₄	C₁₃×#41	1	2	yes	—
476	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	4	2	no	—
492	C₄⋊C₄	—	8	2	no	—
493	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
494	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
495	C₂²⋊C₄	—	2	4	no	—
496	C₂²⋊C₄	—	2	4	no	—
497	C₂²⋊C₄	—	2	4	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	4	no	—
501	C₂²⋊C₄	—	2	4	no	—
502	C₂²⋊C₄	—	8	2	no	—
503	C₄²	—	2	4	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	C₂×D₄×C₁₃	1	2	yes	—
507	C₄²	C₂×D₄×C₁₃	1	2	yes	—
508	C₁₃	#32962	1	1	yes	characteristic, direct product factor, Sylow
509	C₂³	—	2	16	no	—
510	C₂³	—	2	1	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	2	2	no	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	2	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	2	no	—
519	C₂³	—	2	2	no	—
520	C₂³	—	4	2	no	—
521	C₂³	—	4	2	no	—
522	C₂³	—	4	2	no	—
523	C₂³	—	4	2	no	—
524	C₂³	—	8	8	no	—
525	C₂³	—	8	4	no	—
526	C₂³	—	8	4	no	—
527	C₂³	—	8	8	no	—
528	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
529	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
530	Q₈	—	8	4	no	—
531	D₄	—	2	16	no	—
532	D₄	—	2	2	no	—
533	D₄	—	2	2	no	—
534	D₄	—	2	2	no	—
535	D₄	—	2	2	no	—
536	D₄	—	2	2	no	—
537	D₄	—	2	2	no	—
538	D₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
539	D₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	8	4	no	—
563	C₂×C₄	—	8	4	no	—
564	C₂×C₄	—	8	4	no	—
565	C₂×C₄	—	8	4	no	—
566	C₂×C₄	C₁₃×#120	1	2	yes	—
567	C₂×C₄	C₁₃×#120	1	2	yes	—
568	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
569	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
570	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
571	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
572	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
573	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
574	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
575	C₈	—	4	2	no	—
576	C₈	—	4	2	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	4	no	—
580	C₂²	—	2	4	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	4	no	—
588	C₂²	—	4	4	no	—
589	C₂²	—	4	2	no	—
590	C₂²	—	4	4	no	—
591	C₂²	—	4	4	no	—
592	C₂²	—	8	16	no	—
593	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
594	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
595	C₂²	C₁₃×#525	1	1	yes	characteristic
596	C₂²	C₁₃×#576	1	2	yes	—
597	C₂²	C₁₃×#577	1	2	yes	—
598	C₄	—	2	2	no	—
599	C₄	—	2	2	no	—
600	C₄	—	2	2	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	2	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	2	no	—
605	C₄	—	8	2	no	—
606	C₄	—	8	2	no	—
607	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
608	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
609	C₄	C₁₃×#525	1	1	yes	characteristic
610	C₄	C₁₃×#525	1	1	yes	characteristic
611	C₂	—	4	2	no	—
612	C₂	—	4	4	no	—
613	C₂	—	4	4	no	—
614	C₂	C₁₃×#2848	1	1	yes	characteristic
615	C₂	C₁₃×#3008	1	1	yes	characteristic
616	C₂	C₁₃×#3009	1	1	yes	characteristic
617	C₂	C₁₃×#3081	1	2	yes	—
618	C₂	C₁₃×#3118	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#476	C₂	semidirect
3. C₂×C₁₃×#474	C₂	semidirect
4. C₁₃×#2628	C₂	semidirect
5. C₁₃×#1864	C₂	semidirect
6. C₁₃×#1862	C₂	semidirect
7. C₁₃×#1854	C₂	semidirect
8. C₁₃×#1804	C₂	semidirect
9. C₁₃×#1804	C₂	semidirect
10. C₁₃×#1798	C₂	semidirect
13. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
28. C₂×C₁₃×#107	C₂²	semidirect
29. C₂×C₁₃×#106	C₂²	semidirect
30. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
31. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
41. C₁₃×#389	C₂²	semidirect
42. C₁₃×#382	C₂²	semidirect
44. C₁₃×#340	C₂²	semidirect
45. C₁₃×#340	C₂²	semidirect
46. C₁₃×#336	C₂²	semidirect
55. C₂²×D₄×C₁₃	Q₈	semidirect
115. #32962	C₁₃	direct (N × H)
201. C₂×#476	C₂×C₁₃	semidirect
202. C₂×#474	C₂×C₁₃	semidirect
203. #2628	C₂×C₁₃	semidirect
204. #1864	C₂×C₁₃	semidirect
205. #1862	C₂×C₁₃	semidirect
206. #1854	C₂×C₁₃	semidirect
207. #1804	C₂×C₁₃	semidirect
208. #1804	C₂×C₁₃	semidirect
209. #1798	C₂×C₁₃	semidirect
280. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
295. C₂×#107	C₂²×C₁₃	semidirect
296. C₂×#106	C₂²×C₁₃	semidirect
297. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
298. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
308. #389	C₂²×C₁₃	semidirect
309. #382	C₂²×C₁₃	semidirect
311. #340	C₂²×C₁₃	semidirect
312. #340	C₂²×C₁₃	semidirect
313. #336	C₂²×C₁₃	semidirect
356. C₂²×D₄	Q₈×C₁₃	semidirect
508. C₁₃	#32962	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#518	2
C₂×C₁₃×#476	2
C₂×C₁₃×#474	2
C₁₃×#2628	2
C₁₃×#1864	2
C₁₃×#1862	2
C₁₃×#1854	2
C₁₃×#1804	2
C₁₃×#1798	2
C₁₃×#1786	2
#32962	13

Subgroups — C13×#32962 #15719301

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32962 #15719301