Subgroups — C₁₃×#32963 #15719302

Order 3328.

1282 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#520	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#477	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×#1863	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1862	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1852	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1805	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×#1788	C₂	1	2	yes	maximal
12	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₁₃×#520	—	2	4	no	—
15	C₁₃×#520	—	2	4	no	—
16	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₃	—	2	1	no	—
19	C₂×C₄×D₄×C₁₃	—	2	1	no	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#117	—	2	1	no	—
23	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₁₃×#477	—	2	4	no	—
27	C₁₃×#474	—	2	4	no	—
28	C₂×C₁₃×#107	C₂²	1	2	yes	—
29	C₂×C₁₃×#107	C₂²	1	2	yes	—
30	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#103	C₂²	1	2	yes	—
33	C₂×C₁₃×#103	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	—
42	C₁₃×#382	C₂²	1	1	yes	characteristic
43	C₁₃×#380	C₂²	1	2	yes	—
44	C₁₃×#340	C₂²	1	2	yes	—
45	C₁₃×#340	C₂²	1	2	yes	—
46	C₁₃×#336	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	—	2	2	no	—
48	C₂×C₁₃×#41	—	2	2	no	—
49	C₂×C₁₃×#41	—	2	2	no	—
50	C₂×C₁₃×#41	—	2	2	no	—
51	C₂×C₁₃×#41	—	2	2	no	—
52	C₂×C₁₃×#41	Q₈	1	4	yes	complemented
53	C₂²×Q₈×C₁₃	—	2	1	no	—
54	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×D₄×C₁₃	—	2	1	no	—
56	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
63	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
64	C₁₃×C₄⋊Q₈	—	2	2	no	—
65	C₁₃×C₄⋊Q₈	—	2	2	no	—
66	C₄×Q₈×C₁₃	—	2	2	no	—
67	C₄×Q₈×C₁₃	—	2	2	no	—
68	C₄×Q₈×C₁₃	—	2	2	no	—
69	C₄×Q₈×C₁₃	D₄	1	4	yes	—
70	C₄×D₄×C₁₃	—	2	8	no	—
71	C₄×D₄×C₁₃	—	2	8	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	C₁₃×#117	—	2	8	no	—
77	C₁₃×#117	—	2	2	no	—
78	C₁₃×#117	—	2	2	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
87	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
88	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
96	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
97	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	—	2	1	no	—
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×#107	—	2	4	no	—
104	C₁₃×C₄⋊C₈	—	2	2	no	—
105	C₁₃×C₄⋊C₈	—	2	2	no	—
106	C₁₃×#103	—	2	4	no	—
107	C₁₃×#103	—	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	#32963	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂⁴×C₁₃	—	2	1	no	—
117	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₁₃×#41	—	2	8	no	—
119	C₁₃×#41	—	2	8	no	—
120	C₁₃×#41	—	2	8	no	—
121	C₁₃×#41	—	2	8	no	—
122	C₂×Q₈×C₁₃	—	2	1	no	—
123	C₂×Q₈×C₁₃	—	2	1	no	—
124	C₂×Q₈×C₁₃	—	2	1	no	—
125	C₂×Q₈×C₁₃	—	4	2	no	—
126	C₂×Q₈×C₁₃	—	8	2	no	—
127	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
128	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
129	C₂×Q₈×C₁₃	#41	1	2	yes	—
130	C₂×D₄×C₁₃	—	2	4	no	—
131	C₂×D₄×C₁₃	—	2	4	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	C₂×D₄	1	2	yes	—
137	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
138	C₂×D₄×C₁₃	#41	1	2	yes	—
139	C₂²×C₄×C₁₃	—	2	4	no	—
140	C₂²×C₄×C₁₃	—	2	4	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	2	4	no	—
143	C₂²×C₄×C₁₃	—	2	1	no	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
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	4	no	—
150	C₂²×C₄×C₁₃	—	2	4	no	—
151	C₂²×C₄×C₁₃	—	2	4	no	—
152	C₂²×C₄×C₁₃	—	2	2	no	—
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	—	8	2	no	—
155	C₂²×C₄×C₁₃	—	8	2	no	—
156	C₂²×C₄×C₁₃	—	8	2	no	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
163	C₂²×C₄×C₁₃	#41	1	2	yes	—
164	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₈×C₁₃	—	2	2	no	—
166	C₂×C₈×C₁₃	—	2	2	no	—
167	C₂×C₈×C₁₃	—	2	2	no	—
168	C₂×C₈×C₁₃	—	2	2	no	—
169	C₂×C₈×C₁₃	—	2	2	no	—
170	C₂×C₈×C₁₃	—	2	2	no	—
171	C₁₃×C₄⋊C₄	—	2	4	no	—
172	C₁₃×C₄⋊C₄	—	2	4	no	—
173	C₁₃×C₄⋊C₄	—	2	2	no	—
174	C₁₃×C₄⋊C₄	—	2	4	no	—
175	C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	—	2	2	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	—	4	2	no	—
183	C₁₃×C₄⋊C₄	—	8	2	no	—
184	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
185	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
186	C₁₃×C₂²⋊C₄	—	2	4	no	—
187	C₁₃×C₂²⋊C₄	—	2	4	no	—
188	C₁₃×C₂²⋊C₄	—	2	2	no	—
189	C₁₃×C₂²⋊C₄	—	2	2	no	—
190	C₁₃×C₂²⋊C₄	—	8	2	no	—
191	C₄²×C₁₃	—	2	4	no	—
192	C₄²×C₁₃	—	2	4	no	—
193	C₄²×C₁₃	—	2	1	no	—
194	C₄²×C₁₃	—	2	1	no	—
195	C₄²×C₁₃	C₂×D₄	1	2	yes	—
196	C₄²×C₁₃	C₂×D₄	1	2	yes	—
197	C₂×#520	C₂×C₁₃	1	1	yes	characteristic
198	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
199	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#2628	C₂×C₁₃	1	1	yes	characteristic, complemented
201	#1863	C₂×C₁₃	1	2	yes	complemented
202	#1862	C₂×C₁₃	1	2	yes	complemented
203	#1852	C₂×C₁₃	1	2	yes	complemented
204	#1805	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#1804	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#1798	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#1788	C₂×C₁₃	1	2	yes	—
208	C₂³×C₁₃	—	2	1	no	—
209	C₂³×C₁₃	—	2	2	no	—
210	C₂³×C₁₃	—	2	2	no	—
211	C₂³×C₁₃	—	2	1	no	—
212	C₂³×C₁₃	—	2	2	no	—
213	C₂³×C₁₃	—	2	2	no	—
214	C₂³×C₁₃	—	2	2	no	—
215	C₂³×C₁₃	—	4	2	no	—
216	C₂³×C₁₃	—	4	2	no	—
217	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
218	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
219	Q₈×C₁₃	—	2	2	no	—
220	Q₈×C₁₃	—	2	2	no	—
221	Q₈×C₁₃	—	2	2	no	—
222	Q₈×C₁₃	—	8	4	no	—
223	Q₈×C₁₃	C₂²⋊Q₈	1	4	yes	—
224	D₄×C₁₃	—	2	16	no	—
225	D₄×C₁₃	—	2	2	no	—
226	D₄×C₁₃	—	2	2	no	—
227	D₄×C₁₃	—	2	2	no	—
228	D₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
229	C₂×C₄×C₁₃	—	2	16	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	2	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	—	4	2	no	—
248	C₂×C₄×C₁₃	—	4	2	no	—
249	C₂×C₄×C₁₃	—	4	2	no	—
250	C₂×C₄×C₁₃	—	4	2	no	—
251	C₂×C₄×C₁₃	—	4	2	no	—
252	C₂×C₄×C₁₃	—	4	2	no	—
253	C₂×C₄×C₁₃	—	4	2	no	—
254	C₂×C₄×C₁₃	—	4	2	no	—
255	C₂×C₄×C₁₃	—	8	4	no	—
256	C₂×C₄×C₁₃	—	8	4	no	—
257	C₂×C₄×C₁₃	—	8	4	no	—
258	C₂×C₄×C₁₃	#120	1	2	yes	—
259	C₂×C₄×C₁₃	#120	1	2	yes	—
260	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
261	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
267	C₈×C₁₃	—	4	2	no	—
268	C₈×C₁₃	—	4	2	no	—
269	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
271	#520	—	2	4	no	—
272	#520	—	2	4	no	—
273	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
274	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×C₄×D₄	—	2	1	no	—
276	C₂×C₄×D₄	—	2	1	no	—
277	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×#117	—	2	1	no	—
280	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
281	C₂²×C₄⋊C₄	—	2	1	no	—
282	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
283	#477	—	2	4	no	—
284	#474	—	2	4	no	—
285	C₂×#107	C₂²×C₁₃	1	2	yes	—
286	C₂×#107	C₂²×C₁₃	1	2	yes	—
287	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×#103	C₂²×C₁₃	1	2	yes	—
290	C₂×#103	C₂²×C₁₃	1	2	yes	—
291	C₂×#102	C₂²×C₁₃	1	2	yes	—
292	C₂×#102	C₂²×C₁₃	1	2	yes	—
293	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
294	#400	—	2	1	no	—
295	#399	—	2	1	no	—
296	#395	—	2	1	no	—
297	#393	—	2	1	no	—
298	#389	C₂²×C₁₃	1	2	yes	—
299	#382	C₂²×C₁₃	1	1	yes	characteristic
300	#380	C₂²×C₁₃	1	2	yes	—
301	#340	C₂²×C₁₃	1	2	yes	—
302	#340	C₂²×C₁₃	1	2	yes	—
303	#336	C₂²×C₁₃	1	2	yes	—
304	C₂²×C₁₃	—	2	4	no	—
305	C₂²×C₁₃	—	2	2	no	—
306	C₂²×C₁₃	—	2	4	no	—
307	C₂²×C₁₃	—	4	4	no	—
308	C₂²×C₁₃	—	4	2	no	—
309	C₂²×C₁₃	—	4	4	no	—
310	C₂²×C₁₃	—	4	1	no	—
311	C₂²×C₁₃	—	4	2	no	—
312	C₂²×C₁₃	—	4	1	no	—
313	C₂²×C₁₃	—	4	2	no	—
314	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
315	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
316	C₂²×C₁₃	#525	1	1	yes	characteristic
317	C₂²×C₁₃	#576	1	2	yes	—
318	C₂²×C₁₃	#578	1	2	yes	—
319	C₄×C₁₃	—	2	2	no	—
320	C₄×C₁₃	—	2	4	no	—
321	C₄×C₁₃	—	2	2	no	—
322	C₄×C₁₃	—	2	2	no	—
323	C₄×C₁₃	—	4	1	no	—
324	C₄×C₁₃	—	4	2	no	—
325	C₄×C₁₃	—	4	2	no	—
326	C₄×C₁₃	—	4	1	no	—
327	C₄×C₁₃	—	8	2	no	—
328	C₄×C₁₃	—	8	2	no	—
329	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
330	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
331	C₄×C₁₃	#525	1	1	yes	characteristic
332	C₄×C₁₃	#525	1	1	yes	characteristic
333	C₂×#41	—	2	2	no	—
334	C₂×#41	—	2	2	no	—
335	C₂×#41	—	2	2	no	—
336	C₂×#41	—	2	2	no	—
337	C₂×#41	—	2	2	no	—
338	C₂×#41	Q₈×C₁₃	1	4	yes	complemented
339	C₂²×Q₈	—	2	1	no	—
340	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
341	C₂²×D₄	—	2	1	no	—
342	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
343	C₂³×C₄	—	2	1	no	—
344	C₂³×C₄	—	2	1	no	—
345	C₂³×C₄	—	2	1	no	—
346	C₂³×C₄	—	2	1	no	—
347	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
348	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
349	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
350	C₄⋊Q₈	—	2	2	no	—
351	C₄⋊Q₈	—	2	2	no	—
352	C₄×Q₈	—	2	2	no	—
353	C₄×Q₈	—	2	2	no	—
354	C₄×Q₈	—	2	2	no	—
355	C₄×Q₈	D₄×C₁₃	1	4	yes	—
356	C₄×D₄	—	2	8	no	—
357	C₄×D₄	—	2	8	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	2	2	no	—
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	D₄×C₁₃	1	4	yes	—
362	#117	—	2	8	no	—
363	#117	—	2	2	no	—
364	#117	—	2	2	no	—
365	C₂×C₄⋊C₄	—	2	8	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	2	no	—
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	—	2	2	no	—
373	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
374	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
379	C₂×C₂²⋊C₄	—	2	1	no	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	2	no	—
382	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
383	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	—	2	1	no	—
386	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
387	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
388	#107	—	2	4	no	—
389	#107	—	2	4	no	—
390	C₄⋊C₈	—	2	2	no	—
391	C₄⋊C₈	—	2	2	no	—
392	#103	—	2	4	no	—
393	#103	—	2	4	no	—
394	#102	—	2	4	no	—
395	#102	—	2	4	no	—
396	C₂²⋊C₈	—	2	4	no	—
397	#95	—	2	2	no	—
398	#95	—	2	1	no	—
399	#95	—	2	1	no	—
400	#95	—	2	2	no	—
401	C₂×C₁₃	—	4	2	no	—
402	C₂×C₁₃	—	4	4	no	—
403	C₂×C₁₃	#2848	1	1	yes	characteristic
404	C₂×C₁₃	#3008	1	1	yes	characteristic
405	C₂×C₁₃	#3011	1	1	yes	characteristic
406	C₂×C₁₃	#3083	1	2	yes	—
407	C₂×C₁₃	#3124	1	2	yes	—
408	C₂⁴	—	2	1	no	—
409	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
410	#41	—	2	8	no	—
411	#41	—	2	8	no	—
412	#41	—	2	8	no	—
413	#41	—	2	8	no	—
414	C₂×Q₈	—	2	1	no	—
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	4	2	no	—
418	C₂×Q₈	—	8	2	no	—
419	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
420	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
421	C₂×Q₈	C₁₃×#41	1	2	yes	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
429	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
430	C₂×D₄	C₁₃×#41	1	2	yes	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	8	2	no	—
447	C₂²×C₄	—	8	2	no	—
448	C₂²×C₄	—	8	2	no	—
449	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
454	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
455	C₂²×C₄	C₁₃×#41	1	2	yes	—
456	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	2	2	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	4	2	no	—
475	C₄⋊C₄	—	8	2	no	—
476	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
477	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	2	2	no	—
482	C₂²⋊C₄	—	8	2	no	—
483	C₄²	—	2	4	no	—
484	C₄²	—	2	4	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	C₂×D₄×C₁₃	1	2	yes	—
488	C₄²	C₂×D₄×C₁₃	1	2	yes	—
489	C₁₃	#32963	1	1	yes	characteristic, direct product factor, Sylow
490	C₂³	—	2	1	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	1	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	4	2	no	—
498	C₂³	—	4	2	no	—
499	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
500	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
501	Q₈	—	2	2	no	—
502	Q₈	—	2	2	no	—
503	Q₈	—	2	2	no	—
504	Q₈	—	8	4	no	—
505	Q₈	C₁₃×C₂²⋊Q₈	1	4	yes	—
506	D₄	—	2	16	no	—
507	D₄	—	2	2	no	—
508	D₄	—	2	2	no	—
509	D₄	—	2	2	no	—
510	D₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
511	C₂×C₄	—	2	16	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	8	4	no	—
538	C₂×C₄	—	8	4	no	—
539	C₂×C₄	—	8	4	no	—
540	C₂×C₄	C₁₃×#120	1	2	yes	—
541	C₂×C₄	C₁₃×#120	1	2	yes	—
542	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
543	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
544	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
545	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
546	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
547	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
548	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
549	C₈	—	4	2	no	—
550	C₈	—	4	2	no	—
551	C₂²	—	2	4	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	4	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	4	no	—
561	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
562	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
563	C₂²	C₁₃×#525	1	1	yes	characteristic
564	C₂²	C₁₃×#576	1	2	yes	—
565	C₂²	C₁₃×#578	1	2	yes	—
566	C₄	—	2	2	no	—
567	C₄	—	2	2	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	4	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	2	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	1	no	—
574	C₄	—	8	2	no	—
575	C₄	—	8	2	no	—
576	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
577	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
578	C₄	C₁₃×#525	1	1	yes	characteristic
579	C₄	C₁₃×#525	1	1	yes	characteristic
580	C₂	—	4	2	no	—
581	C₂	—	4	4	no	—
582	C₂	C₁₃×#2848	1	1	yes	characteristic
583	C₂	C₁₃×#3008	1	1	yes	characteristic
584	C₂	C₁₃×#3011	1	1	yes	characteristic
585	C₂	C₁₃×#3083	1	2	yes	—
586	C₂	C₁₃×#3124	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	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×#477	C₂	semidirect
3. C₂×C₁₃×#474	C₂	semidirect
4. C₁₃×#2628	C₂	semidirect
5. C₁₃×#1863	C₂	semidirect
6. C₁₃×#1862	C₂	semidirect
7. C₁₃×#1852	C₂	semidirect
8. C₁₃×#1805	C₂	semidirect
9. C₁₃×#1804	C₂	semidirect
10. C₁₃×#1798	C₂	semidirect
52. C₂×C₁₃×#41	Q₈	semidirect
115. #32963	C₁₃	direct (N × H)
198. C₂×#477	C₂×C₁₃	semidirect
199. C₂×#474	C₂×C₁₃	semidirect
200. #2628	C₂×C₁₃	semidirect
201. #1863	C₂×C₁₃	semidirect
202. #1862	C₂×C₁₃	semidirect
203. #1852	C₂×C₁₃	semidirect
204. #1805	C₂×C₁₃	semidirect
205. #1804	C₂×C₁₃	semidirect
206. #1798	C₂×C₁₃	semidirect
338. C₂×#41	Q₈×C₁₃	semidirect
489. C₁₃	#32963	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×#520	2
C₂×C₁₃×#477	2
C₂×C₁₃×#474	2
C₁₃×#2628	2
C₁₃×#1863	2
C₁₃×#1862	2
C₁₃×#1852	2
C₁₃×#1805	2
C₁₃×#1804	2
C₁₃×#1798	2
C₁₃×#1788	2
#32963	13

Subgroups — C13×#32963 #15719302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32963 #15719302