Subgroups — C₁₃×#34149 #15720488

Order 3328.

2442 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2373	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2372	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2371	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2368	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2364	C₂	1	2	yes	maximal
7	C₁₃×#2359	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2298	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2295	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2290	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2290	C₂	1	2	yes	maximal, complemented
12	C₄²×D₄×C₁₃	C₂	1	2	yes	maximal, complemented
13	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₃×#117	C₂	1	2	yes	maximal, complemented
15	C₂×C₁₃×#376	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#529	C₄	1	16	yes	complemented
17	C₂×C₁₃×#126	C₂²	1	2	yes	—
18	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#123	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#117	C₂²	1	2	yes	—
28	C₂×C₁₃×#117	C₂²	1	2	yes	—
29	C₂×C₁₃×#117	C₂²	1	2	yes	—
30	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
31	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#391	C₂²	1	4	yes	—
34	C₁₃×#389	C₂²	1	4	yes	—
35	C₁₃×#388	C₂²	1	4	yes	—
36	C₁₃×#388	C₂²	1	4	yes	—
37	C₁₃×#388	C₂²	1	4	yes	—
38	C₁₃×#388	C₂²	1	4	yes	—
39	C₁₃×#387	C₂²	1	4	yes	—
40	C₁₃×#387	C₂²	1	4	yes	—
41	C₁₃×#387	C₂²	1	4	yes	—
42	C₁₃×#387	C₂²	1	4	yes	—
43	C₁₃×#387	C₂²	1	4	yes	—
44	C₁₃×#387	C₂²	1	4	yes	—
45	C₁₃×#386	C₂²	1	4	yes	—
46	C₁₃×#386	C₂²	1	4	yes	—
47	C₁₃×#385	C₂²	1	4	yes	—
48	C₁₃×#385	C₂²	1	4	yes	—
49	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
50	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
51	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
52	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
53	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
54	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
55	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
56	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
57	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
58	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
59	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
60	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
61	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
62	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
63	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
64	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
65	C₁₃×#376	C₂²	1	1	yes	characteristic
66	C₁₃×#376	C₂²	1	2	yes	—
67	C₁₃×#376	C₂²	1	1	yes	characteristic
68	C₁₃×#376	C₂²	1	2	yes	—
69	C₁₃×#376	C₂²	1	2	yes	—
70	C₁₃×#376	C₂²	1	2	yes	—
71	C₁₃×#376	C₂²	1	2	yes	—
72	C₂×C₁₃×#95	C₂²	1	2	yes	—
73	C₂×C₁₃×#95	C₂²	1	2	yes	—
74	C₄³×C₁₃	C₂²	1	2	yes	—
75	C₄³×C₁₃	C₂²	1	2	yes	—
76	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
78	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
80	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
81	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₁₃×#126	C₂×C₄	1	16	yes	complemented
86	C₁₃×#125	C₂×C₄	1	8	yes	complemented
87	C₁₃×#124	C₂×C₄	1	8	yes	complemented
88	C₁₃×#123	C₂×C₄	1	16	yes	complemented
89	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
90	C₁₃×#121	C₂×C₄	1	8	yes	—
91	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
92	C₄×D₄×C₁₃	—	2	16	no	—
93	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
94	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
95	C₁₃×#117	—	2	8	no	—
96	C₁₃×#117	—	2	8	no	—
97	C₁₃×#117	C₂×C₄	1	16	yes	complemented
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	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	2	yes	—
114	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
116	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
117	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₃	—	2	8	no	—
119	C₂×C₄²×C₁₃	—	2	8	no	—
120	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
121	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
122	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
123	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
124	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
125	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
126	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
127	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
128	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
129	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
130	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
134	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
136	C₁₃×#95	C₂³	1	2	yes	—
137	C₁₃×#95	C₂³	1	2	yes	—
138	C₁₃×#95	C₂³	1	2	yes	—
139	C₁₃×#95	C₂³	1	4	yes	—
140	C₁₃×#95	C₂³	1	4	yes	—
141	C₁₃×#95	C₂³	1	4	yes	—
142	C₁₃×#95	C₂³	1	4	yes	—
143	C₁₃×#95	C₂³	1	4	yes	—
144	C₁₃×#95	C₂³	1	2	yes	—
145	C₁₃×#95	C₂³	1	4	yes	—
146	C₁₃×#95	C₂³	1	4	yes	—
147	C₁₃×#95	C₂³	1	4	yes	—
148	C₁₃×#95	C₂³	1	4	yes	—
149	C₁₃×#95	C₂³	1	2	yes	—
150	C₁₃×#95	C₂³	1	2	yes	—
151	#34149	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
153	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
154	C₂×Q₈×C₁₃	—	4	2	no	—
155	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
156	C₂×D₄×C₁₃	—	2	8	no	—
157	C₂×D₄×C₁₃	—	4	2	no	—
158	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
159	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
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	8	no	—
165	C₂²×C₄×C₁₃	—	2	8	no	—
166	C₂²×C₄×C₁₃	—	2	8	no	—
167	C₂²×C₄×C₁₃	—	2	8	no	—
168	C₂²×C₄×C₁₃	—	4	4	no	—
169	C₂²×C₄×C₁₃	—	4	2	no	—
170	C₂²×C₄×C₁₃	—	4	4	no	—
171	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
172	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
173	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
174	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
185	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
188	C₁₃×C₄⋊C₄	—	2	8	no	—
189	C₁₃×C₄⋊C₄	—	2	8	no	—
190	C₁₃×C₄⋊C₄	—	2	8	no	—
191	C₁₃×C₄⋊C₄	—	4	4	no	—
192	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
193	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
194	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
195	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
196	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
197	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
198	C₁₃×C₂²⋊C₄	—	2	4	no	—
199	C₁₃×C₂²⋊C₄	—	2	8	no	—
200	C₁₃×C₂²⋊C₄	—	2	8	no	—
201	C₁₃×C₂²⋊C₄	—	4	4	no	—
202	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
203	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
204	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
205	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
206	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
207	C₁₃×C₂²⋊C₄	#41	1	8	yes	—
208	C₄²×C₁₃	—	2	8	no	—
209	C₄²×C₁₃	—	2	4	no	—
210	C₄²×C₁₃	—	2	8	no	—
211	C₄²×C₁₃	—	2	4	no	—
212	C₄²×C₁₃	—	2	8	no	—
213	C₄²×C₁₃	—	2	4	no	—
214	C₄²×C₁₃	—	2	8	no	—
215	C₄²×C₁₃	—	4	4	no	—
216	C₄²×C₁₃	—	4	4	no	—
217	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
218	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
219	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
220	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
221	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
222	C₄²×C₁₃	#41	1	8	yes	—
223	C₂×#529	C₂×C₁₃	1	1	yes	characteristic
224	#2373	C₂×C₁₃	1	4	yes	complemented
225	#2372	C₂×C₁₃	1	2	yes	complemented
226	#2371	C₂×C₁₃	1	2	yes	complemented
227	#2368	C₂×C₁₃	1	2	yes	complemented
228	#2364	C₂×C₁₃	1	2	yes	—
229	#2359	C₂×C₁₃	1	4	yes	complemented
230	#2298	C₂×C₁₃	1	2	yes	complemented
231	#2295	C₂×C₁₃	1	2	yes	complemented
232	#2290	C₂×C₁₃	1	2	yes	complemented
233	#2290	C₂×C₁₃	1	2	yes	complemented
234	C₄²×D₄	C₂×C₁₃	1	2	yes	complemented
235	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
236	C₄×#117	C₂×C₁₃	1	2	yes	complemented
237	C₂×#376	C₂×C₁₃	1	1	yes	characteristic, complemented
238	C₂³×C₁₃	—	2	2	no	—
239	C₂³×C₁₃	—	2	2	no	—
240	C₂³×C₁₃	—	2	2	no	—
241	C₂³×C₁₃	—	2	4	no	—
242	C₂³×C₁₃	—	2	2	no	—
243	C₂³×C₁₃	—	2	4	no	—
244	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
245	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
246	C₂³×C₁₃	C₂×#41	1	4	yes	—
247	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
248	Q₈×C₁₃	—	4	4	no	—
249	D₄×C₁₃	—	2	16	no	—
250	D₄×C₁₃	—	4	4	no	—
251	C₂×C₄×C₁₃	—	2	8	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	4	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	4	no	—
258	C₂×C₄×C₁₃	—	2	2	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	4	no	—
263	C₂×C₄×C₁₃	—	2	4	no	—
264	C₂×C₄×C₁₃	—	2	2	no	—
265	C₂×C₄×C₁₃	—	2	8	no	—
266	C₂×C₄×C₁₃	—	2	16	no	—
267	C₂×C₄×C₁₃	—	2	4	no	—
268	C₂×C₄×C₁₃	—	2	4	no	—
269	C₂×C₄×C₁₃	—	2	4	no	—
270	C₂×C₄×C₁₃	—	2	4	no	—
271	C₂×C₄×C₁₃	—	2	4	no	—
272	C₂×C₄×C₁₃	—	2	4	no	—
273	C₂×C₄×C₁₃	—	4	4	no	—
274	C₂×C₄×C₁₃	—	4	16	no	—
275	C₂×C₄×C₁₃	—	4	16	no	—
276	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
277	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
278	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
279	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
280	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
281	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
282	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
283	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
284	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
285	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
286	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
287	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
288	#529	C₄×C₁₃	1	16	yes	complemented
289	C₂×#126	C₂²×C₁₃	1	2	yes	—
290	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×#123	C₂²×C₁₃	1	2	yes	—
293	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
297	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
298	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×#117	C₂²×C₁₃	1	2	yes	—
300	C₂×#117	C₂²×C₁₃	1	2	yes	—
301	C₂×#117	C₂²×C₁₃	1	2	yes	—
302	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
303	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
304	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
305	#391	C₂²×C₁₃	1	4	yes	—
306	#389	C₂²×C₁₃	1	4	yes	—
307	#388	C₂²×C₁₃	1	4	yes	—
308	#388	C₂²×C₁₃	1	4	yes	—
309	#388	C₂²×C₁₃	1	4	yes	—
310	#388	C₂²×C₁₃	1	4	yes	—
311	#387	C₂²×C₁₃	1	4	yes	—
312	#387	C₂²×C₁₃	1	4	yes	—
313	#387	C₂²×C₁₃	1	4	yes	—
314	#387	C₂²×C₁₃	1	4	yes	—
315	#387	C₂²×C₁₃	1	4	yes	—
316	#387	C₂²×C₁₃	1	4	yes	—
317	#386	C₂²×C₁₃	1	4	yes	—
318	#386	C₂²×C₁₃	1	4	yes	—
319	#385	C₂²×C₁₃	1	4	yes	—
320	#385	C₂²×C₁₃	1	4	yes	—
321	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
322	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
323	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
324	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
325	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
326	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
327	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
328	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
329	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
330	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
331	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
332	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
333	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
334	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
335	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
336	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
337	#376	C₂²×C₁₃	1	2	yes	—
338	#376	C₂²×C₁₃	1	2	yes	—
339	#376	C₂²×C₁₃	1	2	yes	—
340	#376	C₂²×C₁₃	1	1	yes	characteristic
341	#376	C₂²×C₁₃	1	2	yes	—
342	#376	C₂²×C₁₃	1	1	yes	characteristic
343	#376	C₂²×C₁₃	1	2	yes	—
344	C₂×#95	C₂²×C₁₃	1	2	yes	—
345	C₂×#95	C₂²×C₁₃	1	2	yes	—
346	C₄³	C₂²×C₁₃	1	2	yes	—
347	C₄³	C₂²×C₁₃	1	2	yes	—
348	C₂²×C₁₃	—	2	2	no	—
349	C₂²×C₁₃	—	2	2	no	—
350	C₂²×C₁₃	—	2	8	no	—
351	C₂²×C₁₃	—	2	4	no	—
352	C₂²×C₁₃	—	2	4	no	—
353	C₂²×C₁₃	—	2	4	no	—
354	C₂²×C₁₃	—	4	4	no	—
355	C₂²×C₁₃	—	4	4	no	—
356	C₂²×C₁₃	C₄×#41	1	4	yes	—
357	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
358	C₂²×C₁₃	C₂²×#41	1	2	yes	—
359	C₂²×C₁₃	C₂²×#41	1	2	yes	—
360	C₂²×C₁₃	#585	1	2	yes	—
361	C₄×C₁₃	—	2	2	no	—
362	C₄×C₁₃	—	2	2	no	—
363	C₄×C₁₃	—	2	2	no	—
364	C₄×C₁₃	—	2	4	no	—
365	C₄×C₁₃	—	2	4	no	—
366	C₄×C₁₃	—	2	2	no	—
367	C₄×C₁₃	—	2	2	no	—
368	C₄×C₁₃	—	2	4	no	—
369	C₄×C₁₃	—	2	8	no	—
370	C₄×C₁₃	—	2	8	no	—
371	C₄×C₁₃	—	4	4	no	—
372	C₄×C₁₃	—	4	4	no	—
373	C₄×C₁₃	C₄×#41	1	4	yes	—
374	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
375	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
376	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
377	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
378	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
379	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
380	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
381	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
382	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
383	#126	C₂×C₄×C₁₃	1	16	yes	complemented
384	#125	C₂×C₄×C₁₃	1	8	yes	complemented
385	#124	C₂×C₄×C₁₃	1	8	yes	complemented
386	#123	C₂×C₄×C₁₃	1	16	yes	complemented
387	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
388	#121	C₂×C₄×C₁₃	1	8	yes	—
389	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
390	C₄×D₄	—	2	16	no	—
391	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
392	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
393	#117	—	2	8	no	—
394	#117	—	2	8	no	—
395	#117	C₂×C₄×C₁₃	1	16	yes	complemented
396	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
397	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
398	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
399	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
401	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
402	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
404	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
406	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
416	C₂×C₄²	—	2	8	no	—
417	C₂×C₄²	—	2	8	no	—
418	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	complemented
419	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
420	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
421	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
422	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
423	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
424	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
425	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
426	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
427	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
428	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
429	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
430	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
431	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
433	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
434	#95	C₂³×C₁₃	1	2	yes	—
435	#95	C₂³×C₁₃	1	2	yes	—
436	#95	C₂³×C₁₃	1	4	yes	—
437	#95	C₂³×C₁₃	1	4	yes	—
438	#95	C₂³×C₁₃	1	2	yes	—
439	#95	C₂³×C₁₃	1	2	yes	—
440	#95	C₂³×C₁₃	1	2	yes	—
441	#95	C₂³×C₁₃	1	4	yes	—
442	#95	C₂³×C₁₃	1	4	yes	—
443	#95	C₂³×C₁₃	1	4	yes	—
444	#95	C₂³×C₁₃	1	2	yes	—
445	#95	C₂³×C₁₃	1	4	yes	—
446	#95	C₂³×C₁₃	1	4	yes	—
447	#95	C₂³×C₁₃	1	4	yes	—
448	#95	C₂³×C₁₃	1	4	yes	—
449	C₂×C₁₃	—	2	4	no	—
450	C₂×C₁₃	—	4	4	no	—
451	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
452	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
453	C₂×C₁₃	#3428	1	1	yes	characteristic
454	C₂×C₁₃	#3475	1	4	yes	—
455	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
456	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
457	C₂×Q₈	—	4	2	no	—
458	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
459	C₂×D₄	—	2	8	no	—
460	C₂×D₄	—	4	2	no	—
461	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
462	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
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	8	no	—
468	C₂²×C₄	—	2	8	no	—
469	C₂²×C₄	—	2	8	no	—
470	C₂²×C₄	—	2	8	no	—
471	C₂²×C₄	—	4	4	no	—
472	C₂²×C₄	—	4	2	no	—
473	C₂²×C₄	—	4	4	no	—
474	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
475	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
476	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
477	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
478	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
479	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
480	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
481	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
482	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
483	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
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	4	yes	—
489	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
490	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
491	C₄⋊C₄	—	2	8	no	—
492	C₄⋊C₄	—	2	8	no	—
493	C₄⋊C₄	—	2	8	no	—
494	C₄⋊C₄	—	4	4	no	—
495	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
496	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
497	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
498	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
499	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
500	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	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	8	yes	—
507	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
508	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
509	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
510	C₂²⋊C₄	C₁₃×#41	1	8	yes	—
511	C₄²	—	2	8	no	—
512	C₄²	—	2	4	no	—
513	C₄²	—	2	8	no	—
514	C₄²	—	2	4	no	—
515	C₄²	—	2	8	no	—
516	C₄²	—	2	4	no	—
517	C₄²	—	2	8	no	—
518	C₄²	—	4	4	no	—
519	C₄²	—	4	4	no	—
520	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
521	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
522	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
523	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
524	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
525	C₄²	C₁₃×#41	1	8	yes	—
526	C₁₃	#34149	1	1	yes	characteristic, direct product factor, Sylow
527	C₂³	—	2	2	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	2	no	—
530	C₂³	—	2	4	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	4	no	—
533	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
534	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
535	C₂³	C₂×C₁₃×#41	1	4	yes	—
536	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
537	Q₈	—	4	4	no	—
538	D₄	—	2	16	no	—
539	D₄	—	4	4	no	—
540	C₂×C₄	—	2	8	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	8	no	—
555	C₂×C₄	—	2	16	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	4	4	no	—
563	C₂×C₄	—	4	16	no	—
564	C₂×C₄	—	4	16	no	—
565	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
566	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
567	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
568	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
569	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
570	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
571	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
572	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
573	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
574	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
575	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
576	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	8	no	—
580	C₂²	—	2	4	no	—
581	C₂²	—	2	4	no	—
582	C₂²	—	2	4	no	—
583	C₂²	—	4	4	no	—
584	C₂²	—	4	4	no	—
585	C₂²	C₄×C₁₃×#41	1	4	yes	—
586	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
587	C₂²	C₂²×C₁₃×#41	1	2	yes	—
588	C₂²	C₂²×C₁₃×#41	1	2	yes	—
589	C₂²	C₁₃×#585	1	2	yes	—
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	4	no	—
594	C₄	—	2	4	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	2	no	—
597	C₄	—	2	4	no	—
598	C₄	—	2	8	no	—
599	C₄	—	2	8	no	—
600	C₄	—	4	4	no	—
601	C₄	—	4	4	no	—
602	C₄	C₄×C₁₃×#41	1	4	yes	—
603	C₂	—	2	4	no	—
604	C₂	—	4	4	no	—
605	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
606	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
607	C₂	C₁₃×#3428	1	1	yes	characteristic
608	C₂	C₁₃×#3475	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2373	C₂	semidirect
3. C₁₃×#2372	C₂	semidirect
4. C₁₃×#2371	C₂	semidirect
5. C₁₃×#2368	C₂	semidirect
7. C₁₃×#2359	C₂	semidirect
8. C₁₃×#2298	C₂	semidirect
9. C₁₃×#2295	C₂	semidirect
10. C₁₃×#2290	C₂	semidirect
11. C₁₃×#2290	C₂	semidirect
12. C₄²×D₄×C₁₃	C₂	semidirect
13. C₄×C₁₃×#117	C₂	semidirect
14. C₄×C₁₃×#117	C₂	semidirect
15. C₂×C₁₃×#376	C₂	semidirect
16. C₁₃×#529	C₄	semidirect
85. C₁₃×#126	C₂×C₄	semidirect
86. C₁₃×#125	C₂×C₄	semidirect
87. C₁₃×#124	C₂×C₄	semidirect
88. C₁₃×#123	C₂×C₄	semidirect
89. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
91. C₄×Q₈×C₁₃	C₂×C₄	semidirect
93. C₄×D₄×C₁₃	C₂×C₄	semidirect
94. C₄×D₄×C₁₃	C₂×C₄	semidirect
97. C₁₃×#117	C₂×C₄	semidirect
120. C₂×C₄²×C₁₃	C₂×C₄	semidirect
151. #34149	C₁₃	direct (N × H)
224. #2373	C₂×C₁₃	semidirect
225. #2372	C₂×C₁₃	semidirect
226. #2371	C₂×C₁₃	semidirect
227. #2368	C₂×C₁₃	semidirect
229. #2359	C₂×C₁₃	semidirect
230. #2298	C₂×C₁₃	semidirect
231. #2295	C₂×C₁₃	semidirect
232. #2290	C₂×C₁₃	semidirect
233. #2290	C₂×C₁₃	semidirect
234. C₄²×D₄	C₂×C₁₃	semidirect
235. C₄×#117	C₂×C₁₃	semidirect
236. C₄×#117	C₂×C₁₃	semidirect
237. C₂×#376	C₂×C₁₃	semidirect
288. #529	C₄×C₁₃	semidirect
383. #126	C₂×C₄×C₁₃	semidirect
384. #125	C₂×C₄×C₁₃	semidirect
385. #124	C₂×C₄×C₁₃	semidirect
386. #123	C₂×C₄×C₁₃	semidirect
387. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
389. C₄×Q₈	C₂×C₄×C₁₃	semidirect
391. C₄×D₄	C₂×C₄×C₁₃	semidirect
392. C₄×D₄	C₂×C₄×C₁₃	semidirect
395. #117	C₂×C₄×C₁₃	semidirect
418. C₂×C₄²	C₂×C₄×C₁₃	semidirect
526. C₁₃	#34149	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×#529	2
C₁₃×#2373	2
C₁₃×#2372	2
C₁₃×#2371	2
C₁₃×#2368	2
C₁₃×#2364	2
C₁₃×#2359	2
C₁₃×#2298	2
C₁₃×#2295	2
C₁₃×#2290	2
C₄²×D₄×C₁₃	2
C₄×C₁₃×#117	2
C₂×C₁₃×#376	2
#34149	13

Subgroups — C13×#34149 #15720488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34149 #15720488