Subgroups — C₁₃×#34276 #15720615

Order 3328.

2930 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#536	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#520	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#519	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2362	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2360	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2359	C₂	1	8	yes	maximal, complemented
7	C₁₃×#2327	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2326	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2317	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₃×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#124	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic
13	C₂×C₁₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
16	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#536	C₄	1	16	yes	complemented
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#124	C₂²	1	2	yes	—
20	C₂×C₁₃×#123	C₂²	1	4	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
22	C₁₃×#520	—	2	8	no	—
23	C₁₃×#519	—	2	8	no	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
31	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#117	C₂²	1	4	yes	—
33	C₂×C₁₃×#117	C₂²	1	2	yes	—
34	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
36	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
38	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#391	C₂²	1	2	yes	—
40	C₁₃×#391	C₂²	1	2	yes	—
41	C₁₃×#391	C₂²	1	4	yes	—
42	C₁₃×#391	C₂²	1	1	yes	characteristic
43	C₁₃×#391	C₂²	1	1	yes	characteristic
44	C₁₃×#390	C₂²	1	1	yes	characteristic
45	C₁₃×#390	C₂²	1	1	yes	characteristic
46	C₁₃×#389	C₂²	1	8	yes	—
47	C₁₃×#389	C₂²	1	4	yes	—
48	C₁₃×#388	C₂²	1	8	yes	—
49	C₁₃×#388	C₂²	1	8	yes	—
50	C₁₃×#387	C₂²	1	8	yes	—
51	C₁₃×#387	C₂²	1	8	yes	—
52	C₁₃×#386	C₂²	1	4	yes	—
53	C₁₃×#385	C₂²	1	4	yes	—
54	C₁₃×#385	C₂²	1	8	yes	—
55	C₁₃×#384	C₂²	1	2	yes	—
56	C₁₃×#382	C₂²	1	2	yes	—
57	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
58	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
59	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
60	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
61	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
62	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
63	C₁₃×#376	C₂²	1	2	yes	—
64	C₂×C₁₃×#95	C₂²	1	4	yes	—
65	C₄³×C₁₃	C₂²	1	2	yes	—
66	C₂×C₁₃×#41	—	2	4	no	—
67	C₂×C₁₃×#41	—	2	4	no	—
68	C₂×C₁₃×#41	C₂×C₄	1	8	yes	—
69	C₂²×Q₈×C₁₃	—	2	4	no	—
70	C₂²×Q₈×C₁₃	—	2	4	no	—
71	C₂²×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
72	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
73	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
74	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
76	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
78	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
80	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
81	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
82	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₁₃×C₄⋊Q₈	C₂×C₄	1	16	yes	complemented
84	C₁₃×#124	C₂×C₄	1	16	yes	complemented
85	C₁₃×#123	C₂×C₄	1	32	yes	complemented
86	C₁₃×C₂²⋊Q₈	C₂×C₄	1	32	yes	complemented
87	C₄×Q₈×C₁₃	—	2	8	no	—
88	C₄×Q₈×C₁₃	—	2	8	no	—
89	C₄×Q₈×C₁₃	—	2	8	no	—
90	C₄×Q₈×C₁₃	—	2	8	no	—
91	C₄×Q₈×C₁₃	—	2	8	no	—
92	C₄×D₄×C₁₃	—	2	16	no	—
93	C₄×D₄×C₁₃	—	2	8	no	—
94	C₁₃×#117	—	2	4	no	—
95	C₁₃×#117	—	2	8	no	—
96	C₁₃×#117	—	2	16	no	—
97	C₁₃×#117	C₂×C₄	1	8	yes	complemented
98	C₁₃×#117	D₄	1	8	yes	—
99	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
114	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
116	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
117	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
118	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
119	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
120	C₂×C₄²×C₁₃	—	2	4	no	—
121	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
122	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
123	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
125	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
126	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
127	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
130	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
131	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
132	C₁₃×#95	C₂³	1	4	yes	—
133	C₁₃×#95	C₂³	1	4	yes	—
134	C₁₃×#95	C₂³	1	4	yes	—
135	C₁₃×#95	C₂³	1	8	yes	—
136	C₁₃×#95	C₂³	1	8	yes	—
137	C₁₃×#95	C₂³	1	4	yes	—
138	C₁₃×#95	C₂³	1	8	yes	—
139	#34276	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
141	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
142	C₁₃×#41	—	2	32	no	—
143	C₂×Q₈×C₁₃	—	2	32	no	—
144	C₂×Q₈×C₁₃	—	2	4	no	—
145	C₂×Q₈×C₁₃	—	2	4	no	—
146	C₂×Q₈×C₁₃	—	2	2	no	—
147	C₂×Q₈×C₁₃	—	2	4	no	—
148	C₂×Q₈×C₁₃	—	2	4	no	—
149	C₂×Q₈×C₁₃	—	2	2	no	—
150	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
151	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
152	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
153	C₂×D₄×C₁₃	—	2	4	no	—
154	C₂×D₄×C₁₃	—	2	4	no	—
155	C₂×D₄×C₁₃	—	2	2	no	—
156	C₂×D₄×C₁₃	—	2	2	no	—
157	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
158	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
159	C₂²×C₄×C₁₃	—	2	4	no	—
160	C₂²×C₄×C₁₃	—	2	4	no	—
161	C₂²×C₄×C₁₃	—	2	4	no	—
162	C₂²×C₄×C₁₃	—	2	4	no	—
163	C₂²×C₄×C₁₃	—	2	4	no	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	2	4	no	—
166	C₂²×C₄×C₁₃	—	2	8	no	—
167	C₂²×C₄×C₁₃	—	4	2	no	—
168	C₂²×C₄×C₁₃	—	4	8	no	—
169	C₂²×C₄×C₁₃	—	4	4	no	—
170	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
171	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
172	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
173	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
174	C₂²×C₄×C₁₃	#41	1	4	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
187	C₁₃×C₄⋊C₄	—	2	4	no	—
188	C₁₃×C₄⋊C₄	—	2	8	no	—
189	C₁₃×C₄⋊C₄	—	2	4	no	—
190	C₁₃×C₄⋊C₄	—	2	8	no	—
191	C₁₃×C₄⋊C₄	—	2	8	no	—
192	C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₁₃×C₄⋊C₄	—	2	2	no	—
194	C₁₃×C₄⋊C₄	—	4	8	no	—
195	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
196	C₁₃×C₄⋊C₄	C₂²×C₄	1	32	yes	—
197	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
198	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
199	C₁₃×C₂²⋊C₄	—	2	4	no	—
200	C₁₃×C₂²⋊C₄	—	2	8	no	—
201	C₁₃×C₂²⋊C₄	—	2	8	no	—
202	C₁₃×C₂²⋊C₄	—	4	4	no	—
203	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
204	C₁₃×C₂²⋊C₄	C₂²×C₄	1	32	yes	—
205	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
206	C₄²×C₁₃	—	2	8	no	—
207	C₄²×C₁₃	—	2	8	no	—
208	C₄²×C₁₃	—	2	8	no	—
209	C₄²×C₁₃	—	2	4	no	—
210	C₄²×C₁₃	—	2	2	no	—
211	C₄²×C₁₃	—	2	4	no	—
212	C₄²×C₁₃	—	2	2	no	—
213	C₄²×C₁₃	—	2	8	no	—
214	C₄²×C₁₃	—	4	4	no	—
215	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
216	C₄²×C₁₃	C₂×D₄	1	8	yes	—
217	C₂×#536	C₂×C₁₃	1	1	yes	characteristic
218	C₂×#520	C₂×C₁₃	1	1	yes	characteristic
219	C₂×#519	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#2362	C₂×C₁₃	1	4	yes	complemented
221	#2360	C₂×C₁₃	1	4	yes	complemented
222	#2359	C₂×C₁₃	1	8	yes	complemented
223	#2327	C₂×C₁₃	1	2	yes	complemented
224	#2326	C₂×C₁₃	1	2	yes	complemented
225	#2317	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₄×C₄⋊Q₈	C₂×C₁₃	1	2	yes	complemented
227	C₄×#124	C₂×C₁₃	1	2	yes	complemented
228	#2297	C₂×C₁₃	1	1	yes	characteristic
229	C₂×#391	C₂×C₁₃	1	1	yes	characteristic, complemented
230	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
231	C₂³×C₁₃	—	2	2	no	—
232	C₂³×C₁₃	—	2	2	no	—
233	C₂³×C₁₃	—	2	2	no	—
234	C₂³×C₁₃	—	2	2	no	—
235	C₂³×C₁₃	—	2	4	no	—
236	C₂³×C₁₃	—	2	4	no	—
237	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
238	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
239	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
240	C₂³×C₁₃	C₂×#41	1	2	yes	—
241	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
242	Q₈×C₁₃	—	2	16	no	—
243	Q₈×C₁₃	—	2	16	no	—
244	Q₈×C₁₃	—	2	8	no	—
245	D₄×C₁₃	—	2	16	no	—
246	D₄×C₁₃	—	2	8	no	—
247	C₂×C₄×C₁₃	—	2	16	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	4	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	4	no	—
258	C₂×C₄×C₁₃	—	2	16	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	4	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	4	no	—
264	C₂×C₄×C₁₃	—	2	2	no	—
265	C₂×C₄×C₁₃	—	2	2	no	—
266	C₂×C₄×C₁₃	—	2	4	no	—
267	C₂×C₄×C₁₃	—	2	8	no	—
268	C₂×C₄×C₁₃	—	4	8	no	—
269	C₂×C₄×C₁₃	—	8	8	no	—
270	C₂×C₄×C₁₃	—	8	4	no	—
271	C₂×C₄×C₁₃	C₄×D₄	1	16	yes	—
272	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
273	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
274	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
275	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
276	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
277	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
278	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
279	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
280	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
281	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
282	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
283	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
284	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
285	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
286	#536	C₄×C₁₃	1	16	yes	complemented
287	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
288	C₂×#124	C₂²×C₁₃	1	2	yes	—
289	C₂×#123	C₂²×C₁₃	1	4	yes	—
290	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
291	#520	—	2	8	no	—
292	#519	—	2	8	no	—
293	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
294	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
295	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
296	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
297	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
298	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
299	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
300	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×#117	C₂²×C₁₃	1	4	yes	—
302	C₂×#117	C₂²×C₁₃	1	2	yes	—
303	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
305	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
306	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
307	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
308	#391	C₂²×C₁₃	1	1	yes	characteristic
309	#391	C₂²×C₁₃	1	2	yes	—
310	#391	C₂²×C₁₃	1	2	yes	—
311	#391	C₂²×C₁₃	1	1	yes	characteristic
312	#391	C₂²×C₁₃	1	4	yes	—
313	#390	C₂²×C₁₃	1	1	yes	characteristic
314	#390	C₂²×C₁₃	1	1	yes	characteristic
315	#389	C₂²×C₁₃	1	8	yes	—
316	#389	C₂²×C₁₃	1	4	yes	—
317	#388	C₂²×C₁₃	1	8	yes	—
318	#388	C₂²×C₁₃	1	8	yes	—
319	#387	C₂²×C₁₃	1	8	yes	—
320	#387	C₂²×C₁₃	1	8	yes	—
321	#386	C₂²×C₁₃	1	4	yes	—
322	#385	C₂²×C₁₃	1	4	yes	—
323	#385	C₂²×C₁₃	1	8	yes	—
324	#384	C₂²×C₁₃	1	2	yes	—
325	#382	C₂²×C₁₃	1	2	yes	—
326	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
327	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
328	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
329	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
330	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
331	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
332	#376	C₂²×C₁₃	1	2	yes	—
333	C₂×#95	C₂²×C₁₃	1	4	yes	—
334	C₄³	C₂²×C₁₃	1	2	yes	—
335	C₂²×C₁₃	—	2	4	no	—
336	C₂²×C₁₃	—	2	4	no	—
337	C₂²×C₁₃	—	2	2	no	—
338	C₂²×C₁₃	—	2	2	no	—
339	C₂²×C₁₃	—	2	4	no	—
340	C₂²×C₁₃	—	2	8	no	—
341	C₂²×C₁₃	—	4	4	no	—
342	C₂²×C₁₃	—	4	2	no	—
343	C₂²×C₁₃	—	4	2	no	—
344	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
345	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
346	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
347	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
348	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
349	C₂²×C₁₃	#585	1	2	yes	—
350	C₄×C₁₃	—	2	4	no	—
351	C₄×C₁₃	—	2	8	no	—
352	C₄×C₁₃	—	2	8	no	—
353	C₄×C₁₃	—	2	4	no	—
354	C₄×C₁₃	—	2	4	no	—
355	C₄×C₁₃	—	2	4	no	—
356	C₄×C₁₃	—	4	2	no	—
357	C₄×C₁₃	—	4	2	no	—
358	C₄×C₁₃	—	4	2	no	—
359	C₄×C₁₃	—	4	4	no	—
360	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
361	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
362	C₂×#41	—	2	4	no	—
363	C₂×#41	—	2	4	no	—
364	C₂×#41	C₂×C₄×C₁₃	1	8	yes	—
365	C₂²×Q₈	—	2	4	no	—
366	C₂²×Q₈	—	2	4	no	—
367	C₂²×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
368	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
369	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
370	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
371	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
372	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
373	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
374	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
375	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
376	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
377	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
378	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
379	C₄⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
380	#124	C₂×C₄×C₁₃	1	16	yes	complemented
381	#123	C₂×C₄×C₁₃	1	32	yes	complemented
382	C₂²⋊Q₈	C₂×C₄×C₁₃	1	32	yes	complemented
383	C₄×Q₈	—	2	8	no	—
384	C₄×Q₈	—	2	8	no	—
385	C₄×Q₈	—	2	8	no	—
386	C₄×Q₈	—	2	8	no	—
387	C₄×Q₈	—	2	8	no	—
388	C₄×D₄	—	2	16	no	—
389	C₄×D₄	—	2	8	no	—
390	#117	—	2	4	no	—
391	#117	—	2	8	no	—
392	#117	—	2	16	no	—
393	#117	C₂×C₄×C₁₃	1	8	yes	complemented
394	#117	D₄×C₁₃	1	8	yes	—
395	C₂×C₄⋊C₄	—	2	4	no	—
396	C₂×C₄⋊C₄	—	2	8	no	—
397	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
398	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
403	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
404	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
405	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
407	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
409	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
416	C₂×C₄²	—	2	4	no	—
417	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
418	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
419	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
420	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
421	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
423	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
425	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
426	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
427	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
428	#95	C₂³×C₁₃	1	8	yes	—
429	#95	C₂³×C₁₃	1	8	yes	—
430	#95	C₂³×C₁₃	1	4	yes	—
431	#95	C₂³×C₁₃	1	4	yes	—
432	#95	C₂³×C₁₃	1	4	yes	—
433	#95	C₂³×C₁₃	1	8	yes	—
434	#95	C₂³×C₁₃	1	4	yes	—
435	C₂×C₁₃	—	2	4	no	—
436	C₂×C₁₃	—	4	4	no	—
437	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
438	C₂×C₁₃	C₄×2₋¹⁺⁴	1	2	yes	—
439	C₂×C₁₃	#3495	1	2	yes	—
440	C₂×C₁₃	#3499	1	1	yes	characteristic
441	C₂×C₁₃	#3500	1	1	yes	characteristic
442	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
443	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
444	#41	—	2	32	no	—
445	C₂×Q₈	—	2	32	no	—
446	C₂×Q₈	—	2	4	no	—
447	C₂×Q₈	—	2	4	no	—
448	C₂×Q₈	—	2	2	no	—
449	C₂×Q₈	—	2	4	no	—
450	C₂×Q₈	—	2	4	no	—
451	C₂×Q₈	—	2	2	no	—
452	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
453	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
454	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
460	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	8	no	—
469	C₂²×C₄	—	4	2	no	—
470	C₂²×C₄	—	4	8	no	—
471	C₂²×C₄	—	4	4	no	—
472	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
473	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
474	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
475	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
476	C₂²×C₄	C₁₃×#41	1	4	yes	—
477	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
478	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
479	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
480	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
481	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
482	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
483	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
484	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
485	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
486	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
487	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
488	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	2	8	no	—
491	C₄⋊C₄	—	2	4	no	—
492	C₄⋊C₄	—	2	8	no	—
493	C₄⋊C₄	—	2	8	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	4	8	no	—
497	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
498	C₄⋊C₄	C₂²×C₄×C₁₃	1	32	yes	—
499	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
500	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
501	C₂²⋊C₄	—	2	4	no	—
502	C₂²⋊C₄	—	2	8	no	—
503	C₂²⋊C₄	—	2	8	no	—
504	C₂²⋊C₄	—	4	4	no	—
505	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
506	C₂²⋊C₄	C₂²×C₄×C₁₃	1	32	yes	—
507	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
508	C₄²	—	2	8	no	—
509	C₄²	—	2	8	no	—
510	C₄²	—	2	8	no	—
511	C₄²	—	2	4	no	—
512	C₄²	—	2	2	no	—
513	C₄²	—	2	4	no	—
514	C₄²	—	2	2	no	—
515	C₄²	—	2	8	no	—
516	C₄²	—	4	4	no	—
517	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
518	C₄²	C₂×D₄×C₁₃	1	8	yes	—
519	C₁₃	#34276	1	1	yes	characteristic, direct product factor, Sylow
520	C₂³	—	2	2	no	—
521	C₂³	—	2	2	no	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	2	no	—
524	C₂³	—	2	4	no	—
525	C₂³	—	2	4	no	—
526	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
527	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
528	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
529	C₂³	C₂×C₁₃×#41	1	2	yes	—
530	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
531	Q₈	—	2	16	no	—
532	Q₈	—	2	16	no	—
533	Q₈	—	2	8	no	—
534	D₄	—	2	16	no	—
535	D₄	—	2	8	no	—
536	C₂×C₄	—	2	16	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	16	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	8	no	—
557	C₂×C₄	—	4	8	no	—
558	C₂×C₄	—	8	8	no	—
559	C₂×C₄	—	8	4	no	—
560	C₂×C₄	C₄×D₄×C₁₃	1	16	yes	—
561	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
562	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
563	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
564	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
565	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
566	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
567	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
568	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
569	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
570	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
571	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
572	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
573	C₂²	—	2	4	no	—
574	C₂²	—	2	4	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	2	8	no	—
579	C₂²	—	4	4	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	C₂×C₄×D₄×C₁₃	1	4	yes	—
583	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
584	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
585	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
586	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
587	C₂²	C₁₃×#585	1	2	yes	—
588	C₄	—	2	4	no	—
589	C₄	—	2	8	no	—
590	C₄	—	2	8	no	—
591	C₄	—	2	4	no	—
592	C₄	—	2	4	no	—
593	C₄	—	2	4	no	—
594	C₄	—	4	2	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	2	no	—
597	C₄	—	4	4	no	—
598	C₄	C₂×C₄×D₄×C₁₃	1	4	yes	—
599	C₄	C₂×C₄×D₄×C₁₃	1	4	yes	—
600	C₂	—	2	4	no	—
601	C₂	—	4	4	no	—
602	C₂	C₂²×C₄×D₄×C₁₃	1	1	yes	characteristic
603	C₂	C₄×C₁₃×2₋¹⁺⁴	1	2	yes	—
604	C₂	C₁₃×#3495	1	2	yes	—
605	C₂	C₁₃×#3499	1	1	yes	characteristic
606	C₂	C₁₃×#3500	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₃×#519	C₂	semidirect
4. C₁₃×#2362	C₂	semidirect
5. C₁₃×#2360	C₂	semidirect
6. C₁₃×#2359	C₂	semidirect
7. C₁₃×#2327	C₂	semidirect
8. C₁₃×#2326	C₂	semidirect
9. C₁₃×#2317	C₂	semidirect
10. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
11. C₄×C₁₃×#124	C₂	semidirect
13. C₂×C₁₃×#391	C₂	semidirect
14. C₄×C₁₃×#117	C₂	semidirect
17. C₁₃×#536	C₄	semidirect
71. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
83. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
84. C₁₃×#124	C₂×C₄	semidirect
85. C₁₃×#123	C₂×C₄	semidirect
86. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
97. C₁₃×#117	C₂×C₄	semidirect
139. #34276	C₁₃	direct (N × H)
219. C₂×#519	C₂×C₁₃	semidirect
220. #2362	C₂×C₁₃	semidirect
221. #2360	C₂×C₁₃	semidirect
222. #2359	C₂×C₁₃	semidirect
223. #2327	C₂×C₁₃	semidirect
224. #2326	C₂×C₁₃	semidirect
225. #2317	C₂×C₁₃	semidirect
226. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
227. C₄×#124	C₂×C₁₃	semidirect
229. C₂×#391	C₂×C₁₃	semidirect
230. C₄×#117	C₂×C₁₃	semidirect
286. #536	C₄×C₁₃	semidirect
367. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
379. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
380. #124	C₂×C₄×C₁₃	semidirect
381. #123	C₂×C₄×C₁₃	semidirect
382. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
393. #117	C₂×C₄×C₁₃	semidirect
519. C₁₃	#34276	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×#536	2
C₂×C₁₃×#520	2
C₂×C₁₃×#519	2
C₁₃×#2362	2
C₁₃×#2360	2
C₁₃×#2359	2
C₁₃×#2327	2
C₁₃×#2326	2
C₁₃×#2317	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×#124	2
C₁₃×#2297	2
C₂×C₁₃×#391	2
C₄×C₁₃×#117	2
#34276	13

Subgroups — C13×#34276 #15720615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34276 #15720615