Subgroups — C₁₃×#34219 #15720558

Order 3328.

2230 conjugacy classes of subgroups.

The subgroup lattice has 620 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×#2356	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2353	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2346	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2343	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2329	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2325	C₂	1	2	yes	maximal
11	C₁₃×#2318	C₂	1	2	yes	maximal, complemented
12	C₄×C₁₃×#123	C₂	1	4	yes	maximal, complemented
13	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2275	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	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
29	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#391	C₂²	1	4	yes	—
31	C₁₃×#389	C₂²	1	4	yes	—
32	C₁₃×#388	C₂²	1	4	yes	—
33	C₁₃×#388	C₂²	1	4	yes	—
34	C₁₃×#388	C₂²	1	4	yes	—
35	C₁₃×#388	C₂²	1	4	yes	—
36	C₁₃×#387	C₂²	1	4	yes	—
37	C₁₃×#387	C₂²	1	4	yes	—
38	C₁₃×#387	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×#386	C₂²	1	4	yes	—
43	C₁₃×#386	C₂²	1	4	yes	—
44	C₁₃×#385	C₂²	1	4	yes	—
45	C₁₃×#385	C₂²	1	4	yes	—
46	C₁₃×#383	C₂²	1	2	yes	—
47	C₁₃×#383	C₂²	1	2	yes	—
48	C₁₃×#382	C₂²	1	1	yes	characteristic
49	C₁₃×#382	C₂²	1	1	yes	characteristic
50	C₁₃×#382	C₂²	1	2	yes	—
51	C₁₃×#381	C₂²	1	2	yes	—
52	C₁₃×#381	C₂²	1	2	yes	—
53	C₁₃×#380	C₂²	1	2	yes	—
54	C₁₃×#380	C₂²	1	2	yes	—
55	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
56	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
57	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
58	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
59	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
60	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
61	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
62	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
63	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
64	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
65	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
66	C₁₃×#376	C₂²	1	2	yes	—
67	C₁₃×#376	C₂²	1	2	yes	—
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	1	yes	characteristic
73	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
74	C₂×C₁₃×#95	C₂²	1	2	yes	—
75	C₂×C₁₃×#95	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	1	yes	characteristic
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	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
86	C₁₃×#126	C₂×C₄	1	16	yes	complemented
87	C₁₃×#125	C₂×C₄	1	8	yes	complemented
88	C₁₃×#124	C₂×C₄	1	8	yes	complemented
89	C₁₃×#123	C₂×C₄	1	16	yes	complemented
90	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
91	C₁₃×#121	C₂×C₄	1	8	yes	—
92	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
93	C₄×D₄×C₁₃	—	2	16	no	—
94	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
95	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
96	C₁₃×#117	C₂×C₄	1	16	yes	complemented
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	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	4	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×C₄²×C₁₃	—	2	8	no	—
118	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
119	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
120	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
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	1	yes	characteristic
126	C₂×C₄²×C₁₃	C₂³	1	2	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	1	yes	characteristic
130	C₁₃×#95	C₂³	1	2	yes	—
131	C₁₃×#95	C₂³	1	2	yes	—
132	C₁₃×#95	C₂³	1	2	yes	—
133	C₁₃×#95	C₂³	1	4	yes	—
134	C₁₃×#95	C₂³	1	4	yes	—
135	C₁₃×#95	C₂³	1	2	yes	—
136	C₁₃×#95	C₂³	1	4	yes	—
137	C₁₃×#95	C₂³	1	2	yes	—
138	C₁₃×#95	C₂³	1	4	yes	—
139	C₁₃×#95	C₂³	1	4	yes	—
140	C₁₃×#95	C₂³	1	2	yes	—
141	C₁₃×#95	C₂³	1	4	yes	—
142	C₁₃×#95	C₂³	1	4	yes	—
143	C₁₃×#95	C₂³	1	2	yes	—
144	C₁₃×#95	C₂³	1	4	yes	—
145	C₁₃×#95	C₂³	1	4	yes	—
146	C₁₃×#95	C₂³	1	4	yes	—
147	C₁₃×#95	C₂³	1	2	yes	—
148	#34219	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
150	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
151	C₂×Q₈×C₁₃	—	4	1	no	—
152	C₂×Q₈×C₁₃	—	4	1	no	—
153	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
154	C₂×D₄×C₁₃	—	2	8	no	—
155	C₂×D₄×C₁₃	—	4	1	no	—
156	C₂×D₄×C₁₃	—	4	1	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	8	no	—
162	C₂²×C₄×C₁₃	—	4	2	no	—
163	C₂²×C₄×C₁₃	—	4	4	no	—
164	C₂²×C₄×C₁₃	—	4	2	no	—
165	C₂²×C₄×C₁₃	—	4	2	no	—
166	C₂²×C₄×C₁₃	—	4	1	no	—
167	C₂²×C₄×C₁₃	—	4	1	no	—
168	C₂²×C₄×C₁₃	—	4	2	no	—
169	C₂²×C₄×C₁₃	—	4	2	no	—
170	C₂²×C₄×C₁₃	—	4	4	no	—
171	C₂²×C₄×C₁₃	—	4	4	no	—
172	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
173	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
174	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
175	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
176	C₂²×C₄×C₁₃	#41	1	8	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
182	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
184	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
185	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
190	C₁₃×C₄⋊C₄	—	2	8	no	—
191	C₁₃×C₄⋊C₄	—	4	4	no	—
192	C₁₃×C₄⋊C₄	—	4	2	no	—
193	C₁₃×C₄⋊C₄	—	4	2	no	—
194	C₁₃×C₄⋊C₄	—	4	4	no	—
195	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
196	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
197	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
198	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
199	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
200	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
201	C₁₃×C₂²⋊C₄	—	2	8	no	—
202	C₁₃×C₂²⋊C₄	—	2	8	no	—
203	C₁₃×C₂²⋊C₄	—	4	4	no	—
204	C₁₃×C₂²⋊C₄	—	4	4	no	—
205	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
206	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
207	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
208	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
209	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
210	C₄²×C₁₃	—	2	8	no	—
211	C₄²×C₁₃	—	2	8	no	—
212	C₄²×C₁₃	—	2	8	no	—
213	C₄²×C₁₃	—	4	4	no	—
214	C₄²×C₁₃	—	4	4	no	—
215	C₄²×C₁₃	—	4	4	no	—
216	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
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	8	yes	—
221	C₂×#529	C₂×C₁₃	1	1	yes	characteristic
222	#2373	C₂×C₁₃	1	4	yes	complemented
223	#2372	C₂×C₁₃	1	2	yes	complemented
224	#2371	C₂×C₁₃	1	2	yes	complemented
225	#2356	C₂×C₁₃	1	2	yes	complemented
226	#2353	C₂×C₁₃	1	2	yes	complemented
227	#2346	C₂×C₁₃	1	2	yes	complemented
228	#2343	C₂×C₁₃	1	2	yes	complemented
229	#2329	C₂×C₁₃	1	2	yes	complemented
230	#2325	C₂×C₁₃	1	2	yes	—
231	#2318	C₂×C₁₃	1	2	yes	complemented
232	C₄×#123	C₂×C₁₃	1	4	yes	complemented
233	#2283	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#2275	C₂×C₁₃	1	2	yes	complemented
235	C₂×#376	C₂×C₁₃	1	1	yes	characteristic, complemented
236	C₂³×C₁₃	—	2	1	no	—
237	C₂³×C₁₃	—	2	2	no	—
238	C₂³×C₁₃	—	2	1	no	—
239	C₂³×C₁₃	—	2	4	no	—
240	C₂³×C₁₃	—	2	2	no	—
241	C₂³×C₁₃	—	2	4	no	—
242	C₂³×C₁₃	—	2	2	no	—
243	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
244	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
245	C₂³×C₁₃	C₂×#41	1	4	yes	—
246	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
247	Q₈×C₁₃	—	4	4	no	—
248	D₄×C₁₃	—	2	16	no	—
249	D₄×C₁₃	—	4	4	no	—
250	C₂×C₄×C₁₃	—	2	8	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	2	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	4	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	2	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	4	no	—
266	C₂×C₄×C₁₃	—	2	4	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	—	2	4	no	—
274	C₂×C₄×C₁₃	—	4	4	no	—
275	C₂×C₄×C₁₃	—	4	8	no	—
276	C₂×C₄×C₁₃	—	4	4	no	—
277	C₂×C₄×C₁₃	—	4	8	no	—
278	C₂×C₄×C₁₃	—	4	8	no	—
279	C₂×C₄×C₁₃	—	8	8	no	—
280	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
281	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
282	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
283	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
284	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
285	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
286	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
287	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
288	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
289	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
290	#529	C₄×C₁₃	1	16	yes	complemented
291	C₂×#126	C₂²×C₁₃	1	2	yes	—
292	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×#123	C₂²×C₁₃	1	2	yes	—
295	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
299	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
300	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×#117	C₂²×C₁₃	1	2	yes	—
302	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
303	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
304	#391	C₂²×C₁₃	1	4	yes	—
305	#389	C₂²×C₁₃	1	4	yes	—
306	#388	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	#387	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	#386	C₂²×C₁₃	1	4	yes	—
317	#386	C₂²×C₁₃	1	4	yes	—
318	#385	C₂²×C₁₃	1	4	yes	—
319	#385	C₂²×C₁₃	1	4	yes	—
320	#383	C₂²×C₁₃	1	2	yes	—
321	#383	C₂²×C₁₃	1	2	yes	—
322	#382	C₂²×C₁₃	1	2	yes	—
323	#382	C₂²×C₁₃	1	1	yes	characteristic
324	#382	C₂²×C₁₃	1	1	yes	characteristic
325	#381	C₂²×C₁₃	1	2	yes	—
326	#381	C₂²×C₁₃	1	2	yes	—
327	#380	C₂²×C₁₃	1	2	yes	—
328	#380	C₂²×C₁₃	1	2	yes	—
329	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
330	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
331	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
332	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
333	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
334	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
335	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
336	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
337	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
338	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
339	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
340	#376	C₂²×C₁₃	1	2	yes	—
341	#376	C₂²×C₁₃	1	2	yes	—
342	#376	C₂²×C₁₃	1	2	yes	—
343	#376	C₂²×C₁₃	1	2	yes	—
344	#376	C₂²×C₁₃	1	2	yes	—
345	#376	C₂²×C₁₃	1	2	yes	—
346	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×#95	C₂²×C₁₃	1	2	yes	—
348	C₂×#95	C₂²×C₁₃	1	2	yes	—
349	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
350	C₂²×C₁₃	—	2	2	no	—
351	C₂²×C₁₃	—	2	2	no	—
352	C₂²×C₁₃	—	2	4	no	—
353	C₂²×C₁₃	—	2	4	no	—
354	C₂²×C₁₃	—	2	4	no	—
355	C₂²×C₁₃	—	2	4	no	—
356	C₂²×C₁₃	—	2	4	no	—
357	C₂²×C₁₃	—	4	4	no	—
358	C₂²×C₁₃	—	4	4	no	—
359	C₂²×C₁₃	C₄×#41	1	4	yes	—
360	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
361	C₂²×C₁₃	C₂²×#41	1	2	yes	—
362	C₂²×C₁₃	#585	1	1	yes	characteristic
363	C₂²×C₁₃	#585	1	2	yes	—
364	C₂²×C₁₃	#585	1	1	yes	characteristic
365	C₄×C₁₃	—	2	2	no	—
366	C₄×C₁₃	—	2	2	no	—
367	C₄×C₁₃	—	2	4	no	—
368	C₄×C₁₃	—	2	2	no	—
369	C₄×C₁₃	—	2	2	no	—
370	C₄×C₁₃	—	2	4	no	—
371	C₄×C₁₃	—	2	2	no	—
372	C₄×C₁₃	—	2	2	no	—
373	C₄×C₁₃	—	2	4	no	—
374	C₄×C₁₃	—	2	8	no	—
375	C₄×C₁₃	—	4	4	no	—
376	C₄×C₁₃	—	4	4	no	—
377	C₄×C₁₃	—	4	4	no	—
378	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
379	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
380	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
381	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
382	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
383	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
384	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
385	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
386	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
387	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
388	#126	C₂×C₄×C₁₃	1	16	yes	complemented
389	#125	C₂×C₄×C₁₃	1	8	yes	complemented
390	#124	C₂×C₄×C₁₃	1	8	yes	complemented
391	#123	C₂×C₄×C₁₃	1	16	yes	complemented
392	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
393	#121	C₂×C₄×C₁₃	1	8	yes	—
394	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
395	C₄×D₄	—	2	16	no	—
396	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
397	C₄×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
398	#117	C₂×C₄×C₁₃	1	16	yes	complemented
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	4	yes	—
403	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
404	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
405	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
409	C₂×C₄⋊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	4	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
419	C₂×C₄²	—	2	8	no	—
420	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	complemented
421	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
422	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
423	C₂×C₄²	C₂³×C₁₃	1	4	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	1	yes	characteristic
428	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
429	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
430	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
431	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
432	#95	C₂³×C₁₃	1	2	yes	—
433	#95	C₂³×C₁₃	1	2	yes	—
434	#95	C₂³×C₁₃	1	2	yes	—
435	#95	C₂³×C₁₃	1	4	yes	—
436	#95	C₂³×C₁₃	1	4	yes	—
437	#95	C₂³×C₁₃	1	2	yes	—
438	#95	C₂³×C₁₃	1	2	yes	—
439	#95	C₂³×C₁₃	1	4	yes	—
440	#95	C₂³×C₁₃	1	2	yes	—
441	#95	C₂³×C₁₃	1	2	yes	—
442	#95	C₂³×C₁₃	1	4	yes	—
443	#95	C₂³×C₁₃	1	2	yes	—
444	#95	C₂³×C₁₃	1	4	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	#95	C₂³×C₁₃	1	4	yes	—
450	C₂×C₁₃	—	2	4	no	—
451	C₂×C₁₃	—	4	4	no	—
452	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
453	C₂×C₁₃	#3428	1	1	yes	characteristic
454	C₂×C₁₃	#3428	1	1	yes	characteristic
455	C₂×C₁₃	#3491	1	2	yes	—
456	C₂×C₁₃	#3493	1	2	yes	—
457	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
458	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
459	C₂×Q₈	—	4	1	no	—
460	C₂×Q₈	—	4	1	no	—
461	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
462	C₂×D₄	—	2	8	no	—
463	C₂×D₄	—	4	1	no	—
464	C₂×D₄	—	4	1	no	—
465	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
466	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	2	8	no	—
470	C₂²×C₄	—	4	2	no	—
471	C₂²×C₄	—	4	4	no	—
472	C₂²×C₄	—	4	2	no	—
473	C₂²×C₄	—	4	2	no	—
474	C₂²×C₄	—	4	1	no	—
475	C₂²×C₄	—	4	1	no	—
476	C₂²×C₄	—	4	2	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	4	4	no	—
479	C₂²×C₄	—	4	4	no	—
480	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
481	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
482	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
483	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
484	C₂²×C₄	C₁₃×#41	1	8	yes	—
485	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
486	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
487	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
488	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
489	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
490	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
491	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
492	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
493	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
494	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
495	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
496	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
497	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
498	C₄⋊C₄	—	2	8	no	—
499	C₄⋊C₄	—	4	4	no	—
500	C₄⋊C₄	—	4	2	no	—
501	C₄⋊C₄	—	4	2	no	—
502	C₄⋊C₄	—	4	4	no	—
503	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
504	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
505	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
506	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
507	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
508	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
509	C₂²⋊C₄	—	2	8	no	—
510	C₂²⋊C₄	—	2	8	no	—
511	C₂²⋊C₄	—	4	4	no	—
512	C₂²⋊C₄	—	4	4	no	—
513	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
514	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
515	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
516	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
517	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
518	C₄²	—	2	8	no	—
519	C₄²	—	2	8	no	—
520	C₄²	—	2	8	no	—
521	C₄²	—	4	4	no	—
522	C₄²	—	4	4	no	—
523	C₄²	—	4	4	no	—
524	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
525	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
526	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
527	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
528	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
529	C₁₃	#34219	1	1	yes	characteristic, direct product factor, Sylow
530	C₂³	—	2	1	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	4	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	2	no	—
537	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
538	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
539	C₂³	C₂×C₁₃×#41	1	4	yes	—
540	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
541	Q₈	—	4	4	no	—
542	D₄	—	2	16	no	—
543	D₄	—	4	4	no	—
544	C₂×C₄	—	2	8	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	4	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	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	4	4	no	—
569	C₂×C₄	—	4	8	no	—
570	C₂×C₄	—	4	4	no	—
571	C₂×C₄	—	4	8	no	—
572	C₂×C₄	—	4	8	no	—
573	C₂×C₄	—	8	8	no	—
574	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
575	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
576	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
577	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
578	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
579	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
580	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
581	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
582	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
583	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
584	C₂²	—	2	2	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	2	4	no	—
587	C₂²	—	2	4	no	—
588	C₂²	—	2	4	no	—
589	C₂²	—	2	4	no	—
590	C₂²	—	2	4	no	—
591	C₂²	—	4	4	no	—
592	C₂²	—	4	4	no	—
593	C₂²	C₄×C₁₃×#41	1	4	yes	—
594	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
595	C₂²	C₂²×C₁₃×#41	1	2	yes	—
596	C₂²	C₁₃×#585	1	1	yes	characteristic
597	C₂²	C₁₃×#585	1	2	yes	—
598	C₂²	C₁₃×#585	1	1	yes	characteristic
599	C₄	—	2	2	no	—
600	C₄	—	2	2	no	—
601	C₄	—	2	4	no	—
602	C₄	—	2	2	no	—
603	C₄	—	2	2	no	—
604	C₄	—	2	4	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	4	no	—
608	C₄	—	2	8	no	—
609	C₄	—	4	4	no	—
610	C₄	—	4	4	no	—
611	C₄	—	4	4	no	—
612	C₂	—	2	4	no	—
613	C₂	—	4	4	no	—
614	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
615	C₂	C₁₃×#3428	1	1	yes	characteristic
616	C₂	C₁₃×#3428	1	1	yes	characteristic
617	C₂	C₁₃×#3491	1	2	yes	—
618	C₂	C₁₃×#3493	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#121	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
2. C₁₃×#2373	C₂	semidirect
3. C₁₃×#2372	C₂	semidirect
4. C₁₃×#2371	C₂	semidirect
5. C₁₃×#2356	C₂	semidirect
6. C₁₃×#2353	C₂	semidirect
7. C₁₃×#2346	C₂	semidirect
8. C₁₃×#2343	C₂	semidirect
9. C₁₃×#2329	C₂	semidirect
11. C₁₃×#2318	C₂	semidirect
12. C₄×C₁₃×#123	C₂	semidirect
13. C₁₃×#2283	C₂	semidirect
14. C₁₃×#2275	C₂	semidirect
15. C₂×C₁₃×#376	C₂	semidirect
16. C₁₃×#529	C₄	semidirect
86. C₁₃×#126	C₂×C₄	semidirect
87. C₁₃×#125	C₂×C₄	semidirect
88. C₁₃×#124	C₂×C₄	semidirect
89. C₁₃×#123	C₂×C₄	semidirect
90. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
92. C₄×Q₈×C₁₃	C₂×C₄	semidirect
94. C₄×D₄×C₁₃	C₂×C₄	semidirect
95. C₄×D₄×C₁₃	C₂×C₄	semidirect
96. C₁₃×#117	C₂×C₄	semidirect
118. C₂×C₄²×C₁₃	C₂×C₄	semidirect
148. #34219	C₁₃	direct (N × H)
222. #2373	C₂×C₁₃	semidirect
223. #2372	C₂×C₁₃	semidirect
224. #2371	C₂×C₁₃	semidirect
225. #2356	C₂×C₁₃	semidirect
226. #2353	C₂×C₁₃	semidirect
227. #2346	C₂×C₁₃	semidirect
228. #2343	C₂×C₁₃	semidirect
229. #2329	C₂×C₁₃	semidirect
231. #2318	C₂×C₁₃	semidirect
232. C₄×#123	C₂×C₁₃	semidirect
233. #2283	C₂×C₁₃	semidirect
234. #2275	C₂×C₁₃	semidirect
235. C₂×#376	C₂×C₁₃	semidirect
290. #529	C₄×C₁₃	semidirect
388. #126	C₂×C₄×C₁₃	semidirect
389. #125	C₂×C₄×C₁₃	semidirect
390. #124	C₂×C₄×C₁₃	semidirect
391. #123	C₂×C₄×C₁₃	semidirect
392. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
394. C₄×Q₈	C₂×C₄×C₁₃	semidirect
396. C₄×D₄	C₂×C₄×C₁₃	semidirect
397. C₄×D₄	C₂×C₄×C₁₃	semidirect
398. #117	C₂×C₄×C₁₃	semidirect
420. C₂×C₄²	C₂×C₄×C₁₃	semidirect
529. C₁₃	#34219	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×#2356	2
C₁₃×#2353	2
C₁₃×#2346	2
C₁₃×#2343	2
C₁₃×#2329	2
C₁₃×#2325	2
C₁₃×#2318	2
C₄×C₁₃×#123	2
C₁₃×#2283	2
C₁₃×#2275	2
C₂×C₁₃×#376	2
#34219	13

Subgroups — C13×#34219 #15720558

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34219 #15720558