Subgroups — C₁₃×#32964 #15719303

Order 3328.

1206 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#519	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2628	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1865	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1863	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1854	C₂	1	2	yes	maximal
8	C₁₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1798	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1787	C₂	1	2	yes	maximal
12	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₁₃×#519	—	2	4	no	—
15	C₁₃×#519	—	2	4	no	—
16	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
17	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
18	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#117	—	2	1	no	—
23	C₂×C₁₃×#117	—	2	1	no	—
24	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
26	C₁₃×#477	—	2	4	no	—
27	C₁₃×#475	—	2	4	no	—
28	C₂×C₁₃×#107	C₂²	1	2	yes	—
29	C₂×C₁₃×#106	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×#103	C₂²	1	2	yes	—
35	C₂×C₁₃×#103	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	C₂²×Q₈×C₁₃	—	2	2	no	—
48	C₂²×Q₈×C₁₃	—	2	2	no	—
49	C₂²×Q₈×C₁₃	—	2	2	no	—
50	C₂²×Q₈×C₁₃	—	2	2	no	—
51	C₂²×Q₈×C₁₃	—	2	1	no	—
52	C₂²×Q₈×C₁₃	—	2	1	no	—
53	C₂²×Q₈×C₁₃	—	2	2	no	—
54	C₂²×Q₈×C₁₃	Q₈	1	4	yes	complemented
55	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	—	2	1	no	—
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
61	C₁₃×C₄⋊Q₈	—	2	2	no	—
62	C₁₃×C₄⋊Q₈	—	2	2	no	—
63	C₄×Q₈×C₁₃	—	2	8	no	—
64	C₄×Q₈×C₁₃	—	2	8	no	—
65	C₄×Q₈×C₁₃	—	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	—	2	2	no	—
70	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×Q₈×C₁₃	D₄	1	4	yes	—
72	C₄×Q₈×C₁₃	D₄	1	4	yes	—
73	C₁₃×#117	—	2	8	no	—
74	C₁₃×#117	—	2	8	no	—
75	C₁₃×#117	—	2	2	no	—
76	C₁₃×#117	—	2	2	no	—
77	C₁₃×#117	—	2	2	no	—
78	C₁₃×#117	—	2	2	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
85	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
86	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
93	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
94	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₁₃	—	2	1	no	—
96	C₂×C₄²×C₁₃	—	2	1	no	—
97	C₂×C₄²×C₁₃	—	2	1	no	—
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×#106	—	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×#103	—	2	4	no	—
109	C₁₃×#103	—	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	#32964	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂×Q₈×C₁₃	—	2	4	no	—
118	C₂×Q₈×C₁₃	—	2	8	no	—
119	C₂×Q₈×C₁₃	—	2	8	no	—
120	C₂×Q₈×C₁₃	—	2	4	no	—
121	C₂×Q₈×C₁₃	—	2	8	no	—
122	C₂×Q₈×C₁₃	—	2	8	no	—
123	C₂×Q₈×C₁₃	—	2	4	no	—
124	C₂×Q₈×C₁₃	—	2	1	no	—
125	C₂×Q₈×C₁₃	—	2	1	no	—
126	C₂×Q₈×C₁₃	—	2	1	no	—
127	C₂×Q₈×C₁₃	—	2	1	no	—
128	C₂×Q₈×C₁₃	—	2	1	no	—
129	C₂×Q₈×C₁₃	—	2	1	no	—
130	C₂×Q₈×C₁₃	—	4	2	no	—
131	C₂×Q₈×C₁₃	—	8	2	no	—
132	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
133	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
134	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
135	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
136	C₂×Q₈×C₁₃	#41	1	2	yes	—
137	C₂×Q₈×C₁₃	#41	1	2	yes	—
138	C₂²×C₄×C₁₃	—	2	4	no	—
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	1	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	2	no	—
150	C₂²×C₄×C₁₃	—	2	2	no	—
151	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
157	C₂²×C₄×C₁₃	#41	1	2	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
159	C₂×C₈×C₁₃	—	2	2	no	—
160	C₂×C₈×C₁₃	—	2	2	no	—
161	C₂×C₈×C₁₃	—	2	2	no	—
162	C₂×C₈×C₁₃	—	2	2	no	—
163	C₂×C₈×C₁₃	—	2	2	no	—
164	C₂×C₈×C₁₃	—	2	2	no	—
165	C₁₃×C₄⋊C₄	—	2	4	no	—
166	C₁₃×C₄⋊C₄	—	2	4	no	—
167	C₁₃×C₄⋊C₄	—	2	4	no	—
168	C₁₃×C₄⋊C₄	—	2	4	no	—
169	C₁₃×C₄⋊C₄	—	2	2	no	—
170	C₁₃×C₄⋊C₄	—	2	2	no	—
171	C₁₃×C₄⋊C₄	—	2	1	no	—
172	C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₁₃×C₄⋊C₄	—	2	2	no	—
174	C₁₃×C₄⋊C₄	—	2	2	no	—
175	C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₁₃×C₄⋊C₄	—	2	2	no	—
177	C₁₃×C₄⋊C₄	—	4	2	no	—
178	C₁₃×C₄⋊C₄	—	8	2	no	—
179	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
180	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
181	C₁₃×C₂²⋊C₄	—	2	4	no	—
182	C₁₃×C₂²⋊C₄	—	2	2	no	—
183	C₁₃×C₂²⋊C₄	—	2	2	no	—
184	C₁₃×C₂²⋊C₄	—	8	2	no	—
185	C₄²×C₁₃	—	2	4	no	—
186	C₄²×C₁₃	—	2	4	no	—
187	C₄²×C₁₃	—	2	4	no	—
188	C₄²×C₁₃	—	2	4	no	—
189	C₄²×C₁₃	—	2	4	no	—
190	C₄²×C₁₃	—	2	1	no	—
191	C₄²×C₁₃	—	2	1	no	—
192	C₄²×C₁₃	C₂×D₄	1	2	yes	—
193	C₄²×C₁₃	C₂×D₄	1	2	yes	—
194	C₂×#519	C₂×C₁₃	1	1	yes	characteristic
195	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
196	C₂×#475	C₂×C₁₃	1	1	yes	characteristic, complemented
197	#2628	C₂×C₁₃	1	1	yes	characteristic
198	#1865	C₂×C₁₃	1	2	yes	complemented
199	#1863	C₂×C₁₃	1	2	yes	complemented
200	#1854	C₂×C₁₃	1	2	yes	—
201	#1805	C₂×C₁₃	1	1	yes	characteristic, complemented
202	#1805	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#1798	C₂×C₁₃	1	1	yes	characteristic
204	#1787	C₂×C₁₃	1	2	yes	—
205	C₂³×C₁₃	—	2	1	no	—
206	C₂³×C₁₃	—	2	1	no	—
207	C₂³×C₁₃	—	2	2	no	—
208	C₂³×C₁₃	—	2	2	no	—
209	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
210	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
211	Q₈×C₁₃	—	2	16	no	—
212	Q₈×C₁₃	—	2	2	no	—
213	Q₈×C₁₃	—	2	2	no	—
214	Q₈×C₁₃	—	2	2	no	—
215	Q₈×C₁₃	—	2	2	no	—
216	Q₈×C₁₃	—	2	2	no	—
217	Q₈×C₁₃	—	2	2	no	—
218	Q₈×C₁₃	—	8	4	no	—
219	Q₈×C₁₃	C₂²⋊Q₈	1	4	yes	—
220	Q₈×C₁₃	C₂²⋊Q₈	1	4	yes	—
221	C₂×C₄×C₁₃	—	2	16	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	2	1	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	2	1	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	1	no	—
237	C₂×C₄×C₁₃	—	2	1	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	2	no	—
242	C₂×C₄×C₁₃	—	4	2	no	—
243	C₂×C₄×C₁₃	—	4	2	no	—
244	C₂×C₄×C₁₃	—	4	2	no	—
245	C₂×C₄×C₁₃	—	4	2	no	—
246	C₂×C₄×C₁₃	—	4	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	#120	1	2	yes	—
251	C₂×C₄×C₁₃	#120	1	2	yes	—
252	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
253	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
259	C₈×C₁₃	—	4	2	no	—
260	C₈×C₁₃	—	4	2	no	—
261	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
263	#519	—	2	4	no	—
264	#519	—	2	4	no	—
265	C₂×C₄×Q₈	—	2	1	no	—
266	C₂×C₄×Q₈	—	2	1	no	—
267	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
269	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×#117	—	2	1	no	—
272	C₂×#117	—	2	1	no	—
273	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
274	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
275	#477	—	2	4	no	—
276	#475	—	2	4	no	—
277	C₂×#107	C₂²×C₁₃	1	2	yes	—
278	C₂×#106	C₂²×C₁₃	1	2	yes	—
279	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
281	C₂×#103	C₂²×C₁₃	1	2	yes	—
282	C₂×#103	C₂²×C₁₃	1	2	yes	—
283	C₂×#103	C₂²×C₁₃	1	2	yes	—
284	C₂×#103	C₂²×C₁₃	1	2	yes	—
285	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
286	#400	—	2	1	no	—
287	#399	—	2	1	no	—
288	#395	—	2	1	no	—
289	#393	—	2	1	no	—
290	#389	C₂²×C₁₃	1	2	yes	—
291	#382	C₂²×C₁₃	1	1	yes	characteristic
292	#380	C₂²×C₁₃	1	2	yes	—
293	#340	C₂²×C₁₃	1	2	yes	—
294	#340	C₂²×C₁₃	1	2	yes	—
295	#336	C₂²×C₁₃	1	2	yes	—
296	C₂²×C₁₃	—	2	4	no	—
297	C₂²×C₁₃	—	2	2	no	—
298	C₂²×C₁₃	—	4	2	no	—
299	C₂²×C₁₃	—	4	1	no	—
300	C₂²×C₁₃	—	4	1	no	—
301	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
302	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
303	C₂²×C₁₃	#525	1	1	yes	characteristic
304	C₂²×C₁₃	#577	1	2	yes	—
305	C₂²×C₁₃	#578	1	2	yes	—
306	C₄×C₁₃	—	2	4	no	—
307	C₄×C₁₃	—	2	4	no	—
308	C₄×C₁₃	—	2	2	no	—
309	C₄×C₁₃	—	2	2	no	—
310	C₄×C₁₃	—	2	2	no	—
311	C₄×C₁₃	—	4	1	no	—
312	C₄×C₁₃	—	4	2	no	—
313	C₄×C₁₃	—	4	1	no	—
314	C₄×C₁₃	—	4	2	no	—
315	C₄×C₁₃	—	8	2	no	—
316	C₄×C₁₃	—	8	2	no	—
317	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
318	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
319	C₄×C₁₃	#525	1	1	yes	characteristic
320	C₄×C₁₃	#525	1	1	yes	characteristic
321	C₂²×Q₈	—	2	2	no	—
322	C₂²×Q₈	—	2	2	no	—
323	C₂²×Q₈	—	2	2	no	—
324	C₂²×Q₈	—	2	2	no	—
325	C₂²×Q₈	—	2	1	no	—
326	C₂²×Q₈	—	2	1	no	—
327	C₂²×Q₈	—	2	2	no	—
328	C₂²×Q₈	Q₈×C₁₃	1	4	yes	complemented
329	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
330	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
331	C₂³×C₄	—	2	1	no	—
332	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
333	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
334	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
335	C₄⋊Q₈	—	2	2	no	—
336	C₄⋊Q₈	—	2	2	no	—
337	C₄×Q₈	—	2	8	no	—
338	C₄×Q₈	—	2	8	no	—
339	C₄×Q₈	—	2	2	no	—
340	C₄×Q₈	—	2	2	no	—
341	C₄×Q₈	—	2	2	no	—
342	C₄×Q₈	—	2	2	no	—
343	C₄×Q₈	—	2	2	no	—
344	C₄×Q₈	—	2	2	no	—
345	C₄×Q₈	D₄×C₁₃	1	4	yes	—
346	C₄×Q₈	D₄×C₁₃	1	4	yes	—
347	#117	—	2	8	no	—
348	#117	—	2	8	no	—
349	#117	—	2	2	no	—
350	#117	—	2	2	no	—
351	#117	—	2	2	no	—
352	#117	—	2	2	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	2	no	—
359	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
360	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
368	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	—	2	1	no	—
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	—	2	1	no	—
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
375	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
376	#107	—	2	4	no	—
377	#106	—	2	4	no	—
378	C₄⋊C₈	—	2	2	no	—
379	C₄⋊C₈	—	2	2	no	—
380	#103	—	2	4	no	—
381	#103	—	2	4	no	—
382	#103	—	2	4	no	—
383	#103	—	2	4	no	—
384	C₂²⋊C₈	—	2	4	no	—
385	#95	—	2	2	no	—
386	#95	—	2	1	no	—
387	#95	—	2	1	no	—
388	#95	—	2	2	no	—
389	C₂×C₁₃	—	4	2	no	—
390	C₂×C₁₃	#2848	1	1	yes	characteristic
391	C₂×C₁₃	#3010	1	1	yes	characteristic
392	C₂×C₁₃	#3011	1	1	yes	characteristic
393	C₂×C₁₃	#3082	1	2	yes	—
394	C₂×C₁₃	#3121	1	2	yes	—
395	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
396	C₂×Q₈	—	2	4	no	—
397	C₂×Q₈	—	2	8	no	—
398	C₂×Q₈	—	2	8	no	—
399	C₂×Q₈	—	2	4	no	—
400	C₂×Q₈	—	2	8	no	—
401	C₂×Q₈	—	2	8	no	—
402	C₂×Q₈	—	2	4	no	—
403	C₂×Q₈	—	2	1	no	—
404	C₂×Q₈	—	2	1	no	—
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	—	4	2	no	—
410	C₂×Q₈	—	8	2	no	—
411	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
412	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
413	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
414	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
415	C₂×Q₈	C₁₃×#41	1	2	yes	—
416	C₂×Q₈	C₁₃×#41	1	2	yes	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
435	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
436	C₂²×C₄	C₁₃×#41	1	2	yes	—
437	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	4	2	no	—
457	C₄⋊C₄	—	8	2	no	—
458	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
459	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
460	C₂²⋊C₄	—	2	4	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₂²⋊C₄	—	8	2	no	—
464	C₄²	—	2	4	no	—
465	C₄²	—	2	4	no	—
466	C₄²	—	2	4	no	—
467	C₄²	—	2	4	no	—
468	C₄²	—	2	4	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	C₂×D₄×C₁₃	1	2	yes	—
472	C₄²	C₂×D₄×C₁₃	1	2	yes	—
473	C₁₃	#32964	1	1	yes	characteristic, direct product factor, Sylow
474	C₂³	—	2	1	no	—
475	C₂³	—	2	1	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
479	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
480	Q₈	—	2	16	no	—
481	Q₈	—	2	2	no	—
482	Q₈	—	2	2	no	—
483	Q₈	—	2	2	no	—
484	Q₈	—	2	2	no	—
485	Q₈	—	2	2	no	—
486	Q₈	—	2	2	no	—
487	Q₈	—	8	4	no	—
488	Q₈	C₁₃×C₂²⋊Q₈	1	4	yes	—
489	Q₈	C₁₃×C₂²⋊Q₈	1	4	yes	—
490	C₂×C₄	—	2	16	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	C₁₃×#120	1	2	yes	—
520	C₂×C₄	C₁₃×#120	1	2	yes	—
521	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
522	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
524	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
525	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
526	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
527	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
528	C₈	—	4	2	no	—
529	C₈	—	4	2	no	—
530	C₂²	—	2	4	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	2	no	—
535	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
536	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
537	C₂²	C₁₃×#525	1	1	yes	characteristic
538	C₂²	C₁₃×#577	1	2	yes	—
539	C₂²	C₁₃×#578	1	2	yes	—
540	C₄	—	2	2	no	—
541	C₄	—	2	2	no	—
542	C₄	—	2	4	no	—
543	C₄	—	2	4	no	—
544	C₄	—	2	2	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	2	no	—
549	C₄	—	8	2	no	—
550	C₄	—	8	2	no	—
551	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
552	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
553	C₄	C₁₃×#525	1	1	yes	characteristic
554	C₄	C₁₃×#525	1	1	yes	characteristic
555	C₂	—	4	2	no	—
556	C₂	C₁₃×#2848	1	1	yes	characteristic
557	C₂	C₁₃×#3010	1	1	yes	characteristic
558	C₂	C₁₃×#3011	1	1	yes	characteristic
559	C₂	C₁₃×#3082	1	2	yes	—
560	C₂	C₁₃×#3121	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
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×#475	C₂	semidirect
5. C₁₃×#1865	C₂	semidirect
6. C₁₃×#1863	C₂	semidirect
8. C₁₃×#1805	C₂	semidirect
9. C₁₃×#1805	C₂	semidirect
54. C₂²×Q₈×C₁₃	Q₈	semidirect
115. #32964	C₁₃	direct (N × H)
195. C₂×#477	C₂×C₁₃	semidirect
196. C₂×#475	C₂×C₁₃	semidirect
198. #1865	C₂×C₁₃	semidirect
199. #1863	C₂×C₁₃	semidirect
201. #1805	C₂×C₁₃	semidirect
202. #1805	C₂×C₁₃	semidirect
328. C₂²×Q₈	Q₈×C₁₃	semidirect
473. C₁₃	#32964	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×#519	2
C₂×C₁₃×#477	2
C₂×C₁₃×#475	2
C₁₃×#2628	2
C₁₃×#1865	2
C₁₃×#1863	2
C₁₃×#1854	2
C₁₃×#1805	2
C₁₃×#1798	2
C₁₃×#1787	2
#32964	13

Subgroups — C13×#32964 #15719303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32964 #15719303