Subgroups — C₁₃×#34266 #15720605

Order 3328.

2946 conjugacy classes of subgroups.

The subgroup lattice has 582 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	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2367	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2365	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2362	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2360	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2322	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2310	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₃×#123	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
15	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#536	C₄	1	16	yes	complemented
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₃×#124	C₂²	1	2	yes	—
19	C₂×C₁₃×#123	C₂²	1	4	yes	—
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
21	C₁₃×#520	—	2	8	no	—
22	C₂×C₄×Q₈×C₁₃	—	2	8	no	—
23	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
28	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#117	C₂²	1	2	yes	—
31	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
32	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
37	C₁₃×#391	C₂²	1	2	yes	—
38	C₁₃×#391	C₂²	1	2	yes	—
39	C₁₃×#391	C₂²	1	2	yes	—
40	C₁₃×#391	C₂²	1	4	yes	—
41	C₁₃×#390	C₂²	1	2	yes	—
42	C₁₃×#389	C₂²	1	2	yes	—
43	C₁₃×#389	C₂²	1	2	yes	—
44	C₁₃×#389	C₂²	1	8	yes	—
45	C₁₃×#388	C₂²	1	8	yes	—
46	C₁₃×#388	C₂²	1	8	yes	—
47	C₁₃×#387	C₂²	1	8	yes	—
48	C₁₃×#387	C₂²	1	8	yes	—
49	C₁₃×#386	C₂²	1	2	yes	—
50	C₁₃×#386	C₂²	1	2	yes	—
51	C₁₃×#385	C₂²	1	2	yes	—
52	C₁₃×#385	C₂²	1	2	yes	—
53	C₁₃×#385	C₂²	1	8	yes	—
54	C₁₃×#381	C₂²	1	4	yes	—
55	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
56	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
57	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
58	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
59	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
60	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
61	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
62	C₂×C₁₃×#41	—	2	4	no	—
63	C₂×C₁₃×#41	—	2	4	no	—
64	C₂×C₁₃×#41	C₂×C₄	1	8	yes	—
65	C₂²×Q₈×C₁₃	—	2	4	no	—
66	C₂²×Q₈×C₁₃	—	2	4	no	—
67	C₂²×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
68	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
69	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
70	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
72	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
77	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×C₄⋊Q₈	C₂×C₄	1	16	yes	complemented
81	C₁₃×#124	C₂×C₄	1	16	yes	complemented
82	C₁₃×#123	C₂×C₄	1	32	yes	complemented
83	C₁₃×C₂²⋊Q₈	C₂×C₄	1	32	yes	complemented
84	C₄×Q₈×C₁₃	—	2	16	no	—
85	C₄×Q₈×C₁₃	—	2	16	no	—
86	C₄×Q₈×C₁₃	—	2	8	no	—
87	C₄×D₄×C₁₃	—	2	16	no	—
88	C₄×D₄×C₁₃	—	2	8	no	—
89	C₁₃×#117	—	2	4	no	—
90	C₁₃×#117	—	2	4	no	—
91	C₁₃×#117	—	2	8	no	—
92	C₁₃×#117	C₂×C₄	1	8	yes	complemented
93	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
95	C₂×C₁₃×C₄⋊C₄	D₄	1	8	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
110	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
111	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
112	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
113	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
114	C₂×C₄²×C₁₃	—	2	8	no	—
115	C₂×C₄²×C₁₃	—	2	4	no	—
116	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
117	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
119	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
120	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
122	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
123	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
124	C₁₃×#95	C₂³	1	4	yes	—
125	C₁₃×#95	C₂³	1	8	yes	—
126	C₁₃×#95	C₂³	1	4	yes	—
127	C₁₃×#95	C₂³	1	8	yes	—
128	C₁₃×#95	C₂³	1	4	yes	—
129	C₁₃×#95	C₂³	1	8	yes	—
130	C₁₃×#95	C₂³	1	4	yes	—
131	#34266	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
133	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₁₃×#41	—	2	32	no	—
135	C₂×Q₈×C₁₃	—	2	32	no	—
136	C₂×Q₈×C₁₃	—	2	4	no	—
137	C₂×Q₈×C₁₃	—	2	4	no	—
138	C₂×Q₈×C₁₃	—	2	2	no	—
139	C₂×Q₈×C₁₃	—	2	4	no	—
140	C₂×Q₈×C₁₃	—	2	4	no	—
141	C₂×Q₈×C₁₃	—	2	2	no	—
142	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
143	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
144	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
145	C₂×D₄×C₁₃	—	2	4	no	—
146	C₂×D₄×C₁₃	—	2	4	no	—
147	C₂×D₄×C₁₃	—	2	2	no	—
148	C₂×D₄×C₁₃	—	2	2	no	—
149	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
150	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
151	C₂²×C₄×C₁₃	—	2	2	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	4	no	—
156	C₂²×C₄×C₁₃	—	2	4	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	8	no	—
159	C₂²×C₄×C₁₃	—	4	4	no	—
160	C₂²×C₄×C₁₃	—	4	2	no	—
161	C₂²×C₄×C₁₃	—	4	8	no	—
162	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
163	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
164	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
165	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
166	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
167	C₂²×C₄×C₁₃	#41	1	4	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₁₃×C₄⋊C₄	—	2	2	no	—
180	C₁₃×C₄⋊C₄	—	2	8	no	—
181	C₁₃×C₄⋊C₄	—	2	16	no	—
182	C₁₃×C₄⋊C₄	—	2	2	no	—
183	C₁₃×C₄⋊C₄	—	2	4	no	—
184	C₁₃×C₄⋊C₄	—	2	8	no	—
185	C₁₃×C₄⋊C₄	—	4	4	no	—
186	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
187	C₁₃×C₄⋊C₄	C₂²×C₄	1	32	yes	—
188	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
189	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
190	C₁₃×C₂²⋊C₄	—	2	4	no	—
191	C₁₃×C₂²⋊C₄	—	2	4	no	—
192	C₁₃×C₂²⋊C₄	—	2	8	no	—
193	C₁₃×C₂²⋊C₄	—	2	8	no	—
194	C₁₃×C₂²⋊C₄	—	4	4	no	—
195	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
196	C₁₃×C₂²⋊C₄	C₂²×C₄	1	32	yes	—
197	C₄²×C₁₃	—	2	16	no	—
198	C₄²×C₁₃	—	2	4	no	—
199	C₄²×C₁₃	—	2	4	no	—
200	C₄²×C₁₃	—	2	8	no	—
201	C₄²×C₁₃	—	2	4	no	—
202	C₄²×C₁₃	—	2	4	no	—
203	C₄²×C₁₃	—	4	8	no	—
204	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
205	C₂×#536	C₂×C₁₃	1	1	yes	characteristic
206	C₂×#520	C₂×C₁₃	1	1	yes	characteristic
207	C₂²×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#2367	C₂×C₁₃	1	4	yes	complemented
209	#2365	C₂×C₁₃	1	4	yes	complemented
210	#2362	C₂×C₁₃	1	4	yes	complemented
211	#2360	C₂×C₁₃	1	4	yes	complemented
212	#2322	C₂×C₁₃	1	4	yes	complemented
213	#2310	C₂×C₁₃	1	1	yes	characteristic, complemented
214	C₄×#123	C₂×C₁₃	1	4	yes	complemented
215	#2297	C₂×C₁₃	1	1	yes	characteristic
216	#2296	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#2274	C₂×C₁₃	1	1	yes	characteristic, complemented
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	—	2	4	no	—
223	C₂³×C₁₃	—	2	4	no	—
224	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
225	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
226	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
227	C₂³×C₁₃	C₂×#41	1	2	yes	—
228	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
229	Q₈×C₁₃	—	2	16	no	—
230	Q₈×C₁₃	—	2	16	no	—
231	Q₈×C₁₃	—	2	8	no	—
232	D₄×C₁₃	—	2	16	no	—
233	D₄×C₁₃	—	2	8	no	—
234	C₂×C₄×C₁₃	—	2	8	no	—
235	C₂×C₄×C₁₃	—	2	16	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	4	no	—
241	C₂×C₄×C₁₃	—	2	4	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	4	no	—
244	C₂×C₄×C₁₃	—	2	8	no	—
245	C₂×C₄×C₁₃	—	2	16	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	4	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	4	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	4	no	—
256	C₂×C₄×C₁₃	—	4	8	no	—
257	C₂×C₄×C₁₃	—	4	4	no	—
258	C₂×C₄×C₁₃	—	8	8	no	—
259	C₂×C₄×C₁₃	C₄×D₄	1	16	yes	—
260	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
261	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
262	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
263	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
264	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
265	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
266	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
268	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
269	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
270	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
271	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
272	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
273	#536	C₄×C₁₃	1	16	yes	complemented
274	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
275	C₂×#124	C₂²×C₁₃	1	2	yes	—
276	C₂×#123	C₂²×C₁₃	1	4	yes	—
277	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
278	#520	—	2	8	no	—
279	C₂×C₄×Q₈	—	2	8	no	—
280	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
281	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
282	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
283	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
284	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
285	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×#117	C₂²×C₁₃	1	2	yes	—
288	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
289	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
290	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
291	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
292	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
293	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
294	#391	C₂²×C₁₃	1	2	yes	—
295	#391	C₂²×C₁₃	1	2	yes	—
296	#391	C₂²×C₁₃	1	4	yes	—
297	#391	C₂²×C₁₃	1	2	yes	—
298	#390	C₂²×C₁₃	1	2	yes	—
299	#389	C₂²×C₁₃	1	8	yes	—
300	#389	C₂²×C₁₃	1	2	yes	—
301	#389	C₂²×C₁₃	1	2	yes	—
302	#388	C₂²×C₁₃	1	8	yes	—
303	#388	C₂²×C₁₃	1	8	yes	—
304	#387	C₂²×C₁₃	1	8	yes	—
305	#387	C₂²×C₁₃	1	8	yes	—
306	#386	C₂²×C₁₃	1	2	yes	—
307	#386	C₂²×C₁₃	1	2	yes	—
308	#385	C₂²×C₁₃	1	2	yes	—
309	#385	C₂²×C₁₃	1	8	yes	—
310	#385	C₂²×C₁₃	1	2	yes	—
311	#381	C₂²×C₁₃	1	4	yes	—
312	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
313	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
314	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
315	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
316	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
317	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
318	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
319	C₂²×C₁₃	—	2	4	no	—
320	C₂²×C₁₃	—	2	2	no	—
321	C₂²×C₁₃	—	2	2	no	—
322	C₂²×C₁₃	—	2	4	no	—
323	C₂²×C₁₃	—	2	4	no	—
324	C₂²×C₁₃	—	2	8	no	—
325	C₂²×C₁₃	—	4	2	no	—
326	C₂²×C₁₃	—	4	2	no	—
327	C₂²×C₁₃	—	4	4	no	—
328	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
329	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
330	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
331	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
332	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
333	C₂²×C₁₃	#585	1	2	yes	—
334	C₄×C₁₃	—	2	4	no	—
335	C₄×C₁₃	—	2	8	no	—
336	C₄×C₁₃	—	2	8	no	—
337	C₄×C₁₃	—	2	8	no	—
338	C₄×C₁₃	—	2	4	no	—
339	C₄×C₁₃	—	4	2	no	—
340	C₄×C₁₃	—	4	2	no	—
341	C₄×C₁₃	—	4	2	no	—
342	C₄×C₁₃	—	4	4	no	—
343	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
344	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
345	C₂×#41	—	2	4	no	—
346	C₂×#41	—	2	4	no	—
347	C₂×#41	C₂×C₄×C₁₃	1	8	yes	—
348	C₂²×Q₈	—	2	4	no	—
349	C₂²×Q₈	—	2	4	no	—
350	C₂²×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
351	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
352	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
353	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
354	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
355	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
356	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
357	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
358	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
359	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
360	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
361	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
362	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
363	C₄⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
364	#124	C₂×C₄×C₁₃	1	16	yes	complemented
365	#123	C₂×C₄×C₁₃	1	32	yes	complemented
366	C₂²⋊Q₈	C₂×C₄×C₁₃	1	32	yes	complemented
367	C₄×Q₈	—	2	16	no	—
368	C₄×Q₈	—	2	16	no	—
369	C₄×Q₈	—	2	8	no	—
370	C₄×D₄	—	2	16	no	—
371	C₄×D₄	—	2	8	no	—
372	#117	—	2	4	no	—
373	#117	—	2	4	no	—
374	#117	—	2	8	no	—
375	#117	C₂×C₄×C₁₃	1	8	yes	complemented
376	C₂×C₄⋊C₄	—	2	8	no	—
377	C₂×C₄⋊C₄	—	2	8	no	—
378	C₂×C₄⋊C₄	D₄×C₁₃	1	8	yes	—
379	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
381	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
382	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
384	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
385	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
387	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
388	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
389	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
397	C₂×C₄²	—	2	8	no	—
398	C₂×C₄²	—	2	4	no	—
399	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
400	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
401	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
402	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
403	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
404	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
405	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
406	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
407	#95	C₂³×C₁₃	1	4	yes	—
408	#95	C₂³×C₁₃	1	8	yes	—
409	#95	C₂³×C₁₃	1	4	yes	—
410	#95	C₂³×C₁₃	1	8	yes	—
411	#95	C₂³×C₁₃	1	4	yes	—
412	#95	C₂³×C₁₃	1	8	yes	—
413	#95	C₂³×C₁₃	1	4	yes	—
414	C₂×C₁₃	—	2	4	no	—
415	C₂×C₁₃	—	4	4	no	—
416	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
417	C₂×C₁₃	C₄×2₋¹⁺⁴	1	2	yes	—
418	C₂×C₁₃	#3485	1	1	yes	characteristic
419	C₂×C₁₃	#3486	1	1	yes	characteristic
420	C₂×C₁₃	#3507	1	2	yes	—
421	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
422	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
423	#41	—	2	32	no	—
424	C₂×Q₈	—	2	32	no	—
425	C₂×Q₈	—	2	4	no	—
426	C₂×Q₈	—	2	4	no	—
427	C₂×Q₈	—	2	2	no	—
428	C₂×Q₈	—	2	4	no	—
429	C₂×Q₈	—	2	4	no	—
430	C₂×Q₈	—	2	2	no	—
431	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
432	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
433	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
439	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	8	no	—
448	C₂²×C₄	—	4	4	no	—
449	C₂²×C₄	—	4	2	no	—
450	C₂²×C₄	—	4	8	no	—
451	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
452	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
453	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
454	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
455	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
456	C₂²×C₄	C₁₃×#41	1	4	yes	—
457	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
458	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
459	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
460	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
461	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
462	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
463	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
464	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
465	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
466	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
467	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	8	no	—
470	C₄⋊C₄	—	2	16	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	8	no	—
474	C₄⋊C₄	—	4	4	no	—
475	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
476	C₄⋊C₄	C₂²×C₄×C₁₃	1	32	yes	—
477	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
478	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	2	8	no	—
482	C₂²⋊C₄	—	2	8	no	—
483	C₂²⋊C₄	—	4	4	no	—
484	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
485	C₂²⋊C₄	C₂²×C₄×C₁₃	1	32	yes	—
486	C₄²	—	2	16	no	—
487	C₄²	—	2	4	no	—
488	C₄²	—	2	4	no	—
489	C₄²	—	2	8	no	—
490	C₄²	—	2	4	no	—
491	C₄²	—	2	4	no	—
492	C₄²	—	4	8	no	—
493	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
494	C₁₃	#34266	1	1	yes	characteristic, direct product factor, Sylow
495	C₂³	—	2	2	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	4	no	—
501	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
502	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
503	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
504	C₂³	C₂×C₁₃×#41	1	2	yes	—
505	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
506	Q₈	—	2	16	no	—
507	Q₈	—	2	16	no	—
508	Q₈	—	2	8	no	—
509	D₄	—	2	16	no	—
510	D₄	—	2	8	no	—
511	C₂×C₄	—	2	8	no	—
512	C₂×C₄	—	2	16	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	8	no	—
522	C₂×C₄	—	2	16	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	4	8	no	—
534	C₂×C₄	—	4	4	no	—
535	C₂×C₄	—	8	8	no	—
536	C₂×C₄	C₄×D₄×C₁₃	1	16	yes	—
537	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
538	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
539	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
540	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
541	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
542	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
543	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
544	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
545	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
546	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
547	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
548	C₂²	—	2	4	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	4	no	—
552	C₂²	—	2	4	no	—
553	C₂²	—	2	8	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	4	no	—
557	C₂²	C₂×C₄×D₄×C₁₃	1	4	yes	—
558	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
559	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
560	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
561	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
562	C₂²	C₁₃×#585	1	2	yes	—
563	C₄	—	2	4	no	—
564	C₄	—	2	8	no	—
565	C₄	—	2	8	no	—
566	C₄	—	2	8	no	—
567	C₄	—	2	4	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	2	no	—
570	C₄	—	4	2	no	—
571	C₄	—	4	4	no	—
572	C₄	C₂×C₄×D₄×C₁₃	1	4	yes	—
573	C₄	C₂×C₄×D₄×C₁₃	1	4	yes	—
574	C₂	—	2	4	no	—
575	C₂	—	4	4	no	—
576	C₂	C₂²×C₄×D₄×C₁₃	1	1	yes	characteristic
577	C₂	C₄×C₁₃×2₋¹⁺⁴	1	2	yes	—
578	C₂	C₁₃×#3485	1	1	yes	characteristic
579	C₂	C₁₃×#3486	1	1	yes	characteristic
580	C₂	C₁₃×#3507	1	2	yes	—

	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. C₂²×C₄×Q₈×C₁₃	C₂	semidirect
4. C₁₃×#2367	C₂	semidirect
5. C₁₃×#2365	C₂	semidirect
6. C₁₃×#2362	C₂	semidirect
7. C₁₃×#2360	C₂	semidirect
8. C₁₃×#2322	C₂	semidirect
9. C₁₃×#2310	C₂	semidirect
10. C₄×C₁₃×#123	C₂	semidirect
12. C₁₃×#2296	C₂	semidirect
13. C₁₃×#2274	C₂	semidirect
16. C₁₃×#536	C₄	semidirect
67. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
80. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
81. C₁₃×#124	C₂×C₄	semidirect
82. C₁₃×#123	C₂×C₄	semidirect
83. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
92. C₁₃×#117	C₂×C₄	semidirect
131. #34266	C₁₃	direct (N × H)
207. C₂²×C₄×Q₈	C₂×C₁₃	semidirect
208. #2367	C₂×C₁₃	semidirect
209. #2365	C₂×C₁₃	semidirect
210. #2362	C₂×C₁₃	semidirect
211. #2360	C₂×C₁₃	semidirect
212. #2322	C₂×C₁₃	semidirect
213. #2310	C₂×C₁₃	semidirect
214. C₄×#123	C₂×C₁₃	semidirect
216. #2296	C₂×C₁₃	semidirect
217. #2274	C₂×C₁₃	semidirect
273. #536	C₄×C₁₃	semidirect
350. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
363. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
364. #124	C₂×C₄×C₁₃	semidirect
365. #123	C₂×C₄×C₁₃	semidirect
366. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
375. #117	C₂×C₄×C₁₃	semidirect
494. C₁₃	#34266	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
C₂²×C₄×Q₈×C₁₃	2
C₁₃×#2367	2
C₁₃×#2365	2
C₁₃×#2362	2
C₁₃×#2360	2
C₁₃×#2322	2
C₁₃×#2310	2
C₄×C₁₃×#123	2
C₁₃×#2297	2
C₁₃×#2296	2
C₁₃×#2274	2
#34266	13

Subgroups — C13×#34266 #15720605

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34266 #15720605