Subgroups — C₁₃×#34814 #15721153

Order 3328.

1994 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2497	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2496	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2495	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2494	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2493	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2480	C₂	1	4	yes	maximal
7	C₁₃×#2401	C₂	1	4	yes	maximal, complemented
8	C₄×C₁₃×#126	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2280	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#2280	C₂	1	1	yes	maximal, characteristic
14	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
16	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#126	C₂²	1	4	yes	—
18	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#401	C₂²	1	4	yes	complemented
26	C₁₃×#400	C₂²	1	4	yes	complemented
27	C₁₃×#400	C₂²	1	4	yes	complemented
28	C₁₃×#400	C₂²	1	4	yes	complemented
29	C₁₃×#397	C₂²	1	4	yes	—
30	C₁₃×#397	C₂²	1	4	yes	—
31	C₁₃×#397	C₂²	1	4	yes	—
32	C₁₃×#396	C₂²	1	4	yes	—
33	C₁₃×#389	C₂²	1	2	yes	complemented
34	C₁₃×#389	C₂²	1	2	yes	complemented
35	C₁₃×#389	C₂²	1	2	yes	complemented
36	C₁₃×#389	C₂²	1	2	yes	complemented
37	C₁₃×#388	C₂²	1	4	yes	—
38	C₁₃×#388	C₂²	1	4	yes	—
39	C₁₃×#388	C₂²	1	4	yes	—
40	C₁₃×#387	C₂²	1	4	yes	complemented
41	C₁₃×#387	C₂²	1	4	yes	complemented
42	C₁₃×#387	C₂²	1	4	yes	complemented
43	C₁₃×#385	C₂²	1	4	yes	—
44	C₁₃×#385	C₂²	1	4	yes	—
45	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#383	C₂²	1	4	yes	complemented
48	C₁₃×#382	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#382	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#381	C₂²	1	2	yes	—
51	C₁₃×#381	C₂²	1	2	yes	—
52	C₁₃×#380	C₂²	1	2	yes	—
53	C₁₃×#380	C₂²	1	2	yes	—
54	C₁₃×#380	C₂²	1	2	yes	—
55	C₁₃×#380	C₂²	1	2	yes	—
56	C₁₃×#380	C₂²	1	4	yes	—
57	C₁₃×#379	C₂²	1	2	yes	—
58	C₁₃×#379	C₂²	1	2	yes	—
59	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
60	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
61	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
62	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
63	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
64	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
65	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
66	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
67	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
68	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
69	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
70	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
71	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
72	C₁₃×#376	C₂²	1	2	yes	complemented
73	C₂×C₁₃×#95	C₂²	1	2	yes	—
74	C₄³×C₁₃	C₂²	1	2	yes	complemented
75	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₃	—	2	4	no	—
77	C₂³×C₄×C₁₃	—	2	4	no	—
78	C₂³×C₄×C₁₃	—	2	4	no	—
79	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
80	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
82	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₁₃×#126	—	2	16	no	—
86	C₁₃×#117	—	2	4	no	—
87	C₁₃×#117	—	2	4	no	—
88	C₁₃×#117	—	2	4	no	—
89	C₁₃×#117	—	2	4	no	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	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×C₂²⋊C₄	—	2	8	no	—
103	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
107	C₂×C₁₃×C₂²⋊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	2	yes	—
111	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
113	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
114	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
115	C₂×C₄²×C₁₃	—	2	4	no	—
116	C₂×C₄²×C₁₃	—	2	4	no	—
117	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
121	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
122	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
123	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	C₁₃×#95	C₂³	1	2	yes	—
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	4	yes	—
136	C₁₃×#95	C₂³	1	4	yes	—
137	C₁₃×#95	C₂³	1	4	yes	—
138	C₁₃×#95	C₂³	1	4	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	4	yes	—
145	#34814	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
146	C₂⁴×C₁₃	—	2	4	no	—
147	C₂⁴×C₁₃	—	2	2	no	—
148	C₂⁴×C₁₃	—	2	2	no	—
149	C₂⁴×C₁₃	—	2	2	no	—
150	C₂⁴×C₁₃	—	4	2	no	—
151	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
152	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	—	2	4	no	—
154	C₂²×C₄×C₁₃	—	2	4	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	4	no	—
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	—	4	2	no	—
167	C₂²×C₄×C₁₃	—	4	2	no	—
168	C₂²×C₄×C₁₃	—	4	16	no	—
169	C₂²×C₄×C₁₃	#41	1	4	yes	—
170	C₂²×C₄×C₁₃	#41	1	4	yes	—
171	C₂²×C₄×C₁₃	#41	1	4	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
184	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
185	C₁₃×C₄⋊C₄	—	2	4	no	—
186	C₁₃×C₄⋊C₄	—	2	4	no	—
187	C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₁₃×C₄⋊C₄	—	2	2	no	—
189	C₁₃×C₄⋊C₄	—	2	2	no	—
190	C₁₃×C₄⋊C₄	—	2	2	no	—
191	C₁₃×C₄⋊C₄	—	2	8	no	—
192	C₁₃×C₄⋊C₄	—	2	8	no	—
193	C₁₃×C₄⋊C₄	—	2	8	no	—
194	C₁₃×C₄⋊C₄	—	4	4	no	—
195	C₁₃×C₄⋊C₄	—	4	4	no	—
196	C₁₃×C₄⋊C₄	—	4	4	no	—
197	C₁₃×C₂²⋊C₄	—	2	4	no	—
198	C₁₃×C₂²⋊C₄	—	2	4	no	—
199	C₁₃×C₂²⋊C₄	—	2	4	no	—
200	C₁₃×C₂²⋊C₄	—	2	4	no	—
201	C₁₃×C₂²⋊C₄	—	2	4	no	—
202	C₁₃×C₂²⋊C₄	—	2	8	no	—
203	C₁₃×C₂²⋊C₄	—	2	8	no	—
204	C₁₃×C₂²⋊C₄	—	2	4	no	—
205	C₁₃×C₂²⋊C₄	—	2	4	no	—
206	C₁₃×C₂²⋊C₄	—	4	4	no	—
207	C₁₃×C₂²⋊C₄	—	4	4	no	—
208	C₁₃×C₂²⋊C₄	#41	1	8	yes	—
209	C₄²×C₁₃	—	2	2	no	—
210	C₄²×C₁₃	—	2	2	no	—
211	C₄²×C₁₃	—	2	4	no	—
212	C₄²×C₁₃	—	2	4	no	—
213	C₄²×C₁₃	—	2	2	no	—
214	C₄²×C₁₃	—	2	2	no	—
215	C₄²×C₁₃	—	2	4	no	—
216	C₄²×C₁₃	—	2	4	no	—
217	C₄²×C₁₃	—	2	4	no	—
218	C₄²×C₁₃	—	2	4	no	—
219	C₄²×C₁₃	—	2	8	no	—
220	C₄²×C₁₃	—	4	4	no	—
221	#2497	C₂×C₁₃	1	2	yes	complemented
222	#2496	C₂×C₁₃	1	2	yes	complemented
223	#2495	C₂×C₁₃	1	2	yes	complemented
224	#2494	C₂×C₁₃	1	2	yes	complemented
225	#2493	C₂×C₁₃	1	4	yes	complemented
226	#2480	C₂×C₁₃	1	4	yes	—
227	#2401	C₂×C₁₃	1	4	yes	complemented
228	C₄×#126	C₂×C₁₃	1	4	yes	complemented
229	#2296	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#2296	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#2285	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#2280	C₂×C₁₃	1	1	yes	characteristic
233	#2280	C₂×C₁₃	1	1	yes	characteristic
234	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
235	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
236	C₂³×C₁₃	—	2	2	no	—
237	C₂³×C₁₃	—	2	2	no	—
238	C₂³×C₁₃	—	2	8	no	—
239	C₂³×C₁₃	—	2	2	no	—
240	C₂³×C₁₃	—	2	2	no	—
241	C₂³×C₁₃	—	2	2	no	—
242	C₂³×C₁₃	—	2	2	no	—
243	C₂³×C₁₃	—	2	2	no	—
244	C₂³×C₁₃	—	2	2	no	—
245	C₂³×C₁₃	—	4	8	no	—
246	C₂³×C₁₃	—	4	8	no	—
247	C₂³×C₁₃	—	4	4	no	—
248	C₂³×C₁₃	—	4	4	no	—
249	C₂³×C₁₃	C₂×#41	1	4	yes	—
250	C₂³×C₁₃	C₂×#41	1	2	yes	—
251	C₂³×C₁₃	C₂×#41	1	2	yes	—
252	C₂³×C₁₃	C₂×#41	1	2	yes	—
253	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	2	no	—
257	C₂×C₄×C₁₃	—	2	2	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	2	no	—
262	C₂×C₄×C₁₃	—	2	4	no	—
263	C₂×C₄×C₁₃	—	2	2	no	—
264	C₂×C₄×C₁₃	—	2	2	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	2	no	—
269	C₂×C₄×C₁₃	—	2	2	no	—
270	C₂×C₄×C₁₃	—	2	4	no	—
271	C₂×C₄×C₁₃	—	2	4	no	—
272	C₂×C₄×C₁₃	—	2	2	no	—
273	C₂×C₄×C₁₃	—	2	2	no	—
274	C₂×C₄×C₁₃	—	2	2	no	—
275	C₂×C₄×C₁₃	—	2	4	no	—
276	C₂×C₄×C₁₃	—	2	4	no	—
277	C₂×C₄×C₁₃	—	2	4	no	—
278	C₂×C₄×C₁₃	—	2	4	no	—
279	C₂×C₄×C₁₃	—	2	2	no	—
280	C₂×C₄×C₁₃	—	2	2	no	—
281	C₂×C₄×C₁₃	—	4	8	no	—
282	C₂×C₄×C₁₃	—	4	8	no	—
283	C₂×C₄×C₁₃	—	4	4	no	—
284	C₂×C₄×C₁₃	—	4	8	no	—
285	C₂×C₄×C₁₃	—	4	8	no	—
286	C₂×C₄×C₁₃	#126	1	16	yes	complemented
287	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
288	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
289	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
290	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
291	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
292	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
293	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
294	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
295	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×#126	C₂²×C₁₃	1	4	yes	—
297	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
301	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
302	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
303	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
304	#401	C₂²×C₁₃	1	4	yes	complemented
305	#400	C₂²×C₁₃	1	4	yes	complemented
306	#400	C₂²×C₁₃	1	4	yes	complemented
307	#400	C₂²×C₁₃	1	4	yes	complemented
308	#397	C₂²×C₁₃	1	4	yes	—
309	#397	C₂²×C₁₃	1	4	yes	—
310	#397	C₂²×C₁₃	1	4	yes	—
311	#396	C₂²×C₁₃	1	4	yes	—
312	#389	C₂²×C₁₃	1	2	yes	complemented
313	#389	C₂²×C₁₃	1	2	yes	complemented
314	#389	C₂²×C₁₃	1	2	yes	complemented
315	#389	C₂²×C₁₃	1	2	yes	complemented
316	#388	C₂²×C₁₃	1	4	yes	—
317	#388	C₂²×C₁₃	1	4	yes	—
318	#388	C₂²×C₁₃	1	4	yes	—
319	#387	C₂²×C₁₃	1	4	yes	complemented
320	#387	C₂²×C₁₃	1	4	yes	complemented
321	#387	C₂²×C₁₃	1	4	yes	complemented
322	#385	C₂²×C₁₃	1	4	yes	—
323	#385	C₂²×C₁₃	1	4	yes	—
324	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
325	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
326	#383	C₂²×C₁₃	1	4	yes	complemented
327	#382	C₂²×C₁₃	1	1	yes	characteristic, complemented
328	#382	C₂²×C₁₃	1	1	yes	characteristic, complemented
329	#381	C₂²×C₁₃	1	2	yes	—
330	#381	C₂²×C₁₃	1	2	yes	—
331	#380	C₂²×C₁₃	1	4	yes	—
332	#380	C₂²×C₁₃	1	2	yes	—
333	#380	C₂²×C₁₃	1	2	yes	—
334	#380	C₂²×C₁₃	1	2	yes	—
335	#380	C₂²×C₁₃	1	2	yes	—
336	#379	C₂²×C₁₃	1	2	yes	—
337	#379	C₂²×C₁₃	1	2	yes	—
338	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
339	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
340	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
341	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
342	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
343	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
344	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
345	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
346	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
347	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
348	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
349	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
350	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
351	#376	C₂²×C₁₃	1	2	yes	complemented
352	C₂×#95	C₂²×C₁₃	1	2	yes	—
353	C₄³	C₂²×C₁₃	1	2	yes	complemented
354	C₂²×C₁₃	—	2	2	no	—
355	C₂²×C₁₃	—	2	2	no	—
356	C₂²×C₁₃	—	2	4	no	—
357	C₂²×C₁₃	—	2	4	no	—
358	C₂²×C₁₃	—	2	4	no	—
359	C₂²×C₁₃	—	2	4	no	—
360	C₂²×C₁₃	—	2	4	no	—
361	C₂²×C₁₃	—	4	16	no	—
362	C₂²×C₁₃	—	4	2	no	—
363	C₂²×C₁₃	—	4	2	no	—
364	C₂²×C₁₃	—	4	2	no	—
365	C₂²×C₁₃	—	4	2	no	—
366	C₂²×C₁₃	C₂×#126	1	4	yes	—
367	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
368	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
369	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
370	C₂²×C₁₃	C₂²×#41	1	2	yes	—
371	C₂²×C₁₃	#585	1	2	yes	—
372	C₄×C₁₃	—	2	4	no	—
373	C₄×C₁₃	—	2	4	no	—
374	C₄×C₁₃	—	4	2	no	—
375	C₄×C₁₃	—	4	2	no	—
376	C₄×C₁₃	—	4	2	no	—
377	C₄×C₁₃	—	4	2	no	—
378	C₄×C₁₃	—	4	2	no	—
379	C₄×C₁₃	—	4	4	no	—
380	C₄×C₁₃	—	4	4	no	—
381	C₄×C₁₃	—	4	2	no	—
382	C₄×C₁₃	—	4	2	no	—
383	C₄×C₁₃	C₂×#126	1	4	yes	—
384	C₄×C₁₃	C₂×#126	1	4	yes	—
385	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
386	C₂³×C₄	—	2	4	no	—
387	C₂³×C₄	—	2	4	no	—
388	C₂³×C₄	—	2	4	no	—
389	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
390	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
391	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
392	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
393	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
394	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
395	#126	—	2	16	no	—
396	#117	—	2	4	no	—
397	#117	—	2	4	no	—
398	#117	—	2	4	no	—
399	#117	—	2	4	no	—
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	2	yes	—
403	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
407	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
408	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
409	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
410	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
411	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
412	C₂×C₂²⋊C₄	—	2	8	no	—
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×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×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
425	C₂×C₄²	—	2	4	no	—
426	C₂×C₄²	—	2	4	no	—
427	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
428	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
429	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
430	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
431	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
432	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
433	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
434	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
435	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
436	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
437	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
438	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
439	#95	C₂³×C₁₃	1	2	yes	—
440	#95	C₂³×C₁₃	1	2	yes	—
441	#95	C₂³×C₁₃	1	2	yes	—
442	#95	C₂³×C₁₃	1	2	yes	—
443	#95	C₂³×C₁₃	1	4	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	#95	C₂³×C₁₃	1	4	yes	—
451	#95	C₂³×C₁₃	1	4	yes	—
452	#95	C₂³×C₁₃	1	4	yes	—
453	#95	C₂³×C₁₃	1	4	yes	—
454	#95	C₂³×C₁₃	1	4	yes	—
455	C₂×C₁₃	—	2	4	no	—
456	C₂×C₁₃	—	4	4	no	—
457	C₂×C₁₃	C₂²×#126	1	1	yes	characteristic
458	C₂×C₁₃	#3444	1	1	yes	characteristic
459	C₂×C₁₃	#3455	1	1	yes	characteristic
460	C₂×C₁₃	#3475	1	2	yes	—
461	C₂×C₁₃	#3475	1	2	yes	—
462	C₂⁴	—	2	4	no	—
463	C₂⁴	—	2	2	no	—
464	C₂⁴	—	2	2	no	—
465	C₂⁴	—	2	2	no	—
466	C₂⁴	—	4	2	no	—
467	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
468	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	4	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	4	2	no	—
483	C₂²×C₄	—	4	2	no	—
484	C₂²×C₄	—	4	16	no	—
485	C₂²×C₄	C₁₃×#41	1	4	yes	—
486	C₂²×C₄	C₁₃×#41	1	4	yes	—
487	C₂²×C₄	C₁₃×#41	1	4	yes	—
488	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
489	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
490	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
491	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
492	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
493	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
494	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
495	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
496	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
497	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
498	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
499	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
500	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	—	2	4	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	8	no	—
508	C₄⋊C₄	—	2	8	no	—
509	C₄⋊C₄	—	2	8	no	—
510	C₄⋊C₄	—	4	4	no	—
511	C₄⋊C₄	—	4	4	no	—
512	C₄⋊C₄	—	4	4	no	—
513	C₂²⋊C₄	—	2	4	no	—
514	C₂²⋊C₄	—	2	4	no	—
515	C₂²⋊C₄	—	2	4	no	—
516	C₂²⋊C₄	—	2	4	no	—
517	C₂²⋊C₄	—	2	4	no	—
518	C₂²⋊C₄	—	2	8	no	—
519	C₂²⋊C₄	—	2	8	no	—
520	C₂²⋊C₄	—	2	4	no	—
521	C₂²⋊C₄	—	2	4	no	—
522	C₂²⋊C₄	—	4	4	no	—
523	C₂²⋊C₄	—	4	4	no	—
524	C₂²⋊C₄	C₁₃×#41	1	8	yes	—
525	C₄²	—	2	2	no	—
526	C₄²	—	2	2	no	—
527	C₄²	—	2	4	no	—
528	C₄²	—	2	4	no	—
529	C₄²	—	2	2	no	—
530	C₄²	—	2	2	no	—
531	C₄²	—	2	4	no	—
532	C₄²	—	2	4	no	—
533	C₄²	—	2	4	no	—
534	C₄²	—	2	4	no	—
535	C₄²	—	2	8	no	—
536	C₄²	—	4	4	no	—
537	C₁₃	#34814	1	1	yes	characteristic, direct product factor, Sylow
538	C₂³	—	2	2	no	—
539	C₂³	—	2	2	no	—
540	C₂³	—	2	8	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	4	8	no	—
548	C₂³	—	4	8	no	—
549	C₂³	—	4	4	no	—
550	C₂³	—	4	4	no	—
551	C₂³	C₂×C₁₃×#41	1	4	yes	—
552	C₂³	C₂×C₁₃×#41	1	2	yes	—
553	C₂³	C₂×C₁₃×#41	1	2	yes	—
554	C₂³	C₂×C₁₃×#41	1	2	yes	—
555	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	4	8	no	—
584	C₂×C₄	—	4	8	no	—
585	C₂×C₄	—	4	4	no	—
586	C₂×C₄	—	4	8	no	—
587	C₂×C₄	—	4	8	no	—
588	C₂×C₄	C₁₃×#126	1	16	yes	complemented
589	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
590	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
591	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
592	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
593	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
594	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
595	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
596	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	4	no	—
600	C₂²	—	2	4	no	—
601	C₂²	—	2	4	no	—
602	C₂²	—	2	4	no	—
603	C₂²	—	2	4	no	—
604	C₂²	—	4	16	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	C₂×C₁₃×#126	1	4	yes	—
610	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
611	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
612	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
613	C₂²	C₂²×C₁₃×#41	1	2	yes	—
614	C₂²	C₁₃×#585	1	2	yes	—
615	C₄	—	2	4	no	—
616	C₄	—	2	4	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	2	no	—
619	C₄	—	4	2	no	—
620	C₄	—	4	2	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	4	no	—
623	C₄	—	4	4	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	2	no	—
626	C₄	C₂×C₁₃×#126	1	4	yes	—
627	C₄	C₂×C₁₃×#126	1	4	yes	—
628	C₂	—	2	4	no	—
629	C₂	—	4	4	no	—
630	C₂	C₂²×C₁₃×#126	1	1	yes	characteristic
631	C₂	C₁₃×#3444	1	1	yes	characteristic
632	C₂	C₁₃×#3455	1	1	yes	characteristic
633	C₂	C₁₃×#3475	1	2	yes	—
634	C₂	C₁₃×#3475	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2497	C₂	semidirect
2. C₁₃×#2496	C₂	semidirect
3. C₁₃×#2495	C₂	semidirect
4. C₁₃×#2494	C₂	semidirect
5. C₁₃×#2493	C₂	semidirect
7. C₁₃×#2401	C₂	semidirect
8. C₄×C₁₃×#126	C₂	semidirect
9. C₁₃×#2296	C₂	semidirect
10. C₁₃×#2296	C₂	semidirect
11. C₁₃×#2285	C₂	semidirect
14. C₄×C₁₃×#117	C₂	semidirect
25. C₁₃×#401	C₂²	semidirect
26. C₁₃×#400	C₂²	semidirect
27. C₁₃×#400	C₂²	semidirect
28. C₁₃×#400	C₂²	semidirect
33. C₁₃×#389	C₂²	semidirect
34. C₁₃×#389	C₂²	semidirect
35. C₁₃×#389	C₂²	semidirect
36. C₁₃×#389	C₂²	semidirect
40. C₁₃×#387	C₂²	semidirect
41. C₁₃×#387	C₂²	semidirect
42. C₁₃×#387	C₂²	semidirect
45. C₁₃×#384	C₂²	semidirect
46. C₁₃×#384	C₂²	semidirect
47. C₁₃×#383	C₂²	semidirect
48. C₁₃×#382	C₂²	semidirect
49. C₁₃×#382	C₂²	semidirect
59. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
60. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
61. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
62. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
63. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
64. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
72. C₁₃×#376	C₂²	semidirect
74. C₄³×C₁₃	C₂²	semidirect
145. #34814	C₁₃	direct (N × H)
221. #2497	C₂×C₁₃	semidirect
222. #2496	C₂×C₁₃	semidirect
223. #2495	C₂×C₁₃	semidirect
224. #2494	C₂×C₁₃	semidirect
225. #2493	C₂×C₁₃	semidirect
227. #2401	C₂×C₁₃	semidirect
228. C₄×#126	C₂×C₁₃	semidirect
229. #2296	C₂×C₁₃	semidirect
230. #2296	C₂×C₁₃	semidirect
231. #2285	C₂×C₁₃	semidirect
234. C₄×#117	C₂×C₁₃	semidirect
286. C₂×C₄×C₁₃	#126	semidirect
304. #401	C₂²×C₁₃	semidirect
305. #400	C₂²×C₁₃	semidirect
306. #400	C₂²×C₁₃	semidirect
307. #400	C₂²×C₁₃	semidirect
312. #389	C₂²×C₁₃	semidirect
313. #389	C₂²×C₁₃	semidirect
314. #389	C₂²×C₁₃	semidirect
315. #389	C₂²×C₁₃	semidirect
319. #387	C₂²×C₁₃	semidirect
320. #387	C₂²×C₁₃	semidirect
321. #387	C₂²×C₁₃	semidirect
324. #384	C₂²×C₁₃	semidirect
325. #384	C₂²×C₁₃	semidirect
326. #383	C₂²×C₁₃	semidirect
327. #382	C₂²×C₁₃	semidirect
328. #382	C₂²×C₁₃	semidirect
338. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
339. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
340. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
341. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
342. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
343. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
351. #376	C₂²×C₁₃	semidirect
353. C₄³	C₂²×C₁₃	semidirect
537. C₁₃	#34814	direct (N × H)
588. C₂×C₄	C₁₃×#126	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#2497	2
C₁₃×#2496	2
C₁₃×#2495	2
C₁₃×#2494	2
C₁₃×#2493	2
C₁₃×#2480	2
C₁₃×#2401	2
C₄×C₁₃×#126	2
C₁₃×#2296	2
C₁₃×#2285	2
C₁₃×#2280	2
C₄×C₁₃×#117	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
#34814	13

Subgroups — C13×#34814 #15721153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34814 #15721153