Subgroups — C₁₃×#34936 #15721275

Order 3328.

4138 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#525	C₂	1	4	yes	maximal, complemented
3	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2542	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2541	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2540	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2539	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2501	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2433	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2397	C₂	1	4	yes	maximal, complemented
11	C₄×C₁₃×#127	C₂	1	4	yes	maximal, complemented
12	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	2	yes	—
14	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
16	C₁₃×#532	—	2	8	no	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₁₃×#127	C₂²	1	4	yes	—
19	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
21	C₁₃×#525	—	2	32	no	—
22	C₂×C₁₃×#123	C₂²	1	8	yes	—
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
24	C₂×C₁₃×#121	C₂²	1	2	yes	—
25	C₂×C₁₃×#121	C₂²	1	2	yes	—
26	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
27	C₂×C₁₃×#120	C₂²	1	8	yes	—
28	C₂×C₄×D₄×C₁₃	—	2	8	no	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
34	C₂×C₄×D₄×C₁₃	C₂²	1	16	yes	complemented
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
36	C₂×C₁₃×#117	C₂²	1	2	yes	—
37	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
39	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
40	C₁₃×#399	C₂²	1	8	yes	complemented
41	C₁₃×#399	C₂²	1	8	yes	complemented
42	C₁₃×#392	C₂²	1	8	yes	—
43	C₁₃×#392	C₂²	1	8	yes	complemented
44	C₁₃×#390	C₂²	1	4	yes	—
45	C₁₃×#390	C₂²	1	4	yes	complemented
46	C₁₃×#390	C₂²	1	16	yes	complemented
47	C₁₃×#384	C₂²	1	4	yes	complemented
48	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
49	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
50	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
51	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
52	C₁₃×#376	C₂²	1	2	yes	complemented
53	C₄³×C₁₃	C₂²	1	2	yes	complemented
54	C₂⁵×C₁₃	C₂³	1	2	yes	—
55	C₂×C₁₃×#41	—	2	16	no	—
56	C₂×C₁₃×#41	—	2	8	no	—
57	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
58	C₂²×D₄×C₁₃	—	2	8	no	—
59	C₂²×D₄×C₁₃	—	2	4	no	—
60	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
61	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
62	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
63	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
64	C₂²×D₄×C₁₃	C₂³	1	16	yes	—
65	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
66	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₃	—	2	8	no	—
68	C₂³×C₄×C₁₃	—	2	16	no	—
69	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
70	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
71	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
72	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×C₄⋊Q₈	—	2	4	no	—
77	C₁₃×#127	—	2	16	no	—
78	C₁₃×#127	—	2	4	no	—
79	C₁₃×#124	—	2	8	no	—
80	C₁₃×#123	—	2	32	no	—
81	C₁₃×C₂²⋊Q₈	—	2	32	no	—
82	C₁₃×#121	—	2	8	no	—
83	C₁₃×#121	—	2	8	no	—
84	C₁₃×#121	—	2	32	no	—
85	C₁₃×#120	—	2	32	no	—
86	C₄×D₄×C₁₃	—	2	8	no	—
87	C₄×D₄×C₁₃	—	2	8	no	—
88	C₄×D₄×C₁₃	—	2	8	no	—
89	C₄×D₄×C₁₃	—	2	8	no	—
90	C₄×D₄×C₁₃	—	2	8	no	—
91	C₄×D₄×C₁₃	—	2	8	no	—
92	C₄×D₄×C₁₃	—	2	64	no	—
93	C₁₃×#117	D₄	1	16	yes	complemented
94	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	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×C₂²⋊C₄	—	2	8	no	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
103	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
109	C₂×C₄²×C₁₃	D₄	1	8	yes	complemented
110	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
111	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
112	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
117	C₁₃×#95	C₂³	1	4	yes	—
118	C₁₃×#95	C₂³	1	4	yes	—
119	#34936	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂⁴×C₁₃	—	2	4	no	—
121	C₂⁴×C₁₃	—	2	8	no	—
122	C₂⁴×C₁₃	—	2	8	no	—
123	C₂⁴×C₁₃	—	4	4	no	—
124	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
125	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
126	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
127	C₁₃×#41	—	4	32	no	—
128	C₂×Q₈×C₁₃	—	2	8	no	—
129	C₂×Q₈×C₁₃	—	2	4	no	—
130	C₂×D₄×C₁₃	—	2	32	no	—
131	C₂×D₄×C₁₃	—	2	8	no	—
132	C₂×D₄×C₁₃	—	2	16	no	—
133	C₂×D₄×C₁₃	—	2	8	no	—
134	C₂×D₄×C₁₃	—	2	32	no	—
135	C₂×D₄×C₁₃	—	2	4	no	—
136	C₂×D₄×C₁₃	—	2	4	no	—
137	C₂×D₄×C₁₃	—	2	32	no	—
138	C₂×D₄×C₁₃	—	2	4	no	—
139	C₂×D₄×C₁₃	—	2	4	no	—
140	C₂×D₄×C₁₃	—	2	8	no	—
141	C₂×D₄×C₁₃	—	2	4	no	—
142	C₂×D₄×C₁₃	—	2	4	no	—
143	C₂×D₄×C₁₃	—	2	8	no	—
144	C₂×D₄×C₁₃	—	4	16	no	—
145	C₂×D₄×C₁₃	—	4	4	no	—
146	C₂×D₄×C₁₃	#41	1	8	yes	complemented
147	C₂²×C₄×C₁₃	—	2	4	no	—
148	C₂²×C₄×C₁₃	—	2	4	no	—
149	C₂²×C₄×C₁₃	—	2	8	no	—
150	C₂²×C₄×C₁₃	—	2	8	no	—
151	C₂²×C₄×C₁₃	—	2	8	no	—
152	C₂²×C₄×C₁₃	—	2	16	no	—
153	C₂²×C₄×C₁₃	—	2	8	no	—
154	C₂²×C₄×C₁₃	—	2	16	no	—
155	C₂²×C₄×C₁₃	—	2	16	no	—
156	C₂²×C₄×C₁₃	—	4	2	no	—
157	C₂²×C₄×C₁₃	—	4	32	no	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
159	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
164	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
171	C₁₃×C₄⋊C₄	—	2	4	no	—
172	C₁₃×C₄⋊C₄	—	2	4	no	—
173	C₁₃×C₄⋊C₄	—	2	4	no	—
174	C₁₃×C₄⋊C₄	—	2	4	no	—
175	C₁₃×C₄⋊C₄	—	2	32	no	—
176	C₁₃×C₄⋊C₄	C₂×D₄	1	16	yes	complemented
177	C₁₃×C₂²⋊C₄	—	2	8	no	—
178	C₁₃×C₂²⋊C₄	—	2	8	no	—
179	C₁₃×C₂²⋊C₄	—	2	32	no	—
180	C₁₃×C₂²⋊C₄	—	2	32	no	—
181	C₁₃×C₂²⋊C₄	—	2	8	no	—
182	C₁₃×C₂²⋊C₄	—	2	8	no	—
183	C₁₃×C₂²⋊C₄	C₂×D₄	1	16	yes	—
184	C₄²×C₁₃	—	2	8	no	—
185	C₄²×C₁₃	—	4	4	no	—
186	C₄²×C₁₃	C₂×D₄	1	4	yes	—
187	C₄²×C₁₃	C₂×D₄	1	4	yes	—
188	C₄²×C₁₃	C₂×D₄	1	4	yes	—
189	C₄²×C₁₃	C₂×D₄	1	4	yes	—
190	C₄²×C₁₃	C₂×D₄	1	16	yes	complemented
191	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
192	C₂×#525	C₂×C₁₃	1	4	yes	complemented
193	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#2542	C₂×C₁₃	1	2	yes	complemented
195	#2541	C₂×C₁₃	1	2	yes	complemented
196	#2540	C₂×C₁₃	1	4	yes	complemented
197	#2539	C₂×C₁₃	1	4	yes	complemented
198	#2501	C₂×C₁₃	1	2	yes	complemented
199	#2433	C₂×C₁₃	1	2	yes	complemented
200	#2397	C₂×C₁₃	1	4	yes	complemented
201	C₄×#127	C₂×C₁₃	1	4	yes	complemented
202	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
203	C₂³×C₁₃	—	2	2	no	—
204	C₂³×C₁₃	—	2	2	no	—
205	C₂³×C₁₃	—	2	16	no	—
206	C₂³×C₁₃	—	2	4	no	—
207	C₂³×C₁₃	—	2	8	no	—
208	C₂³×C₁₃	—	2	4	no	—
209	C₂³×C₁₃	—	2	8	no	—
210	C₂³×C₁₃	—	2	4	no	—
211	C₂³×C₁₃	—	2	8	no	—
212	C₂³×C₁₃	—	2	8	no	—
213	C₂³×C₁₃	—	2	8	no	—
214	C₂³×C₁₃	—	4	32	no	—
215	C₂³×C₁₃	—	4	8	no	—
216	C₂³×C₁₃	—	4	8	no	—
217	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
218	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
219	C₂³×C₁₃	C₂×#41	1	8	yes	—
220	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
221	Q₈×C₁₃	—	4	8	no	—
222	D₄×C₁₃	—	2	16	no	—
223	D₄×C₁₃	—	2	16	no	—
224	D₄×C₁₃	—	4	64	no	—
225	D₄×C₁₃	—	4	8	no	—
226	D₄×C₁₃	—	4	16	no	—
227	D₄×C₁₃	—	4	8	no	—
228	D₄×C₁₃	—	4	8	no	—
229	C₂×C₄×C₁₃	—	2	8	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	8	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	8	no	—
235	C₂×C₄×C₁₃	—	2	4	no	—
236	C₂×C₄×C₁₃	—	2	8	no	—
237	C₂×C₄×C₁₃	—	2	4	no	—
238	C₂×C₄×C₁₃	—	2	8	no	—
239	C₂×C₄×C₁₃	—	4	4	no	—
240	C₂×C₄×C₁₃	—	4	8	no	—
241	C₂×C₄×C₁₃	—	4	16	no	—
242	C₂×C₄×C₁₃	—	4	16	no	—
243	C₂×C₄×C₁₃	—	4	16	no	—
244	C₂×C₄×C₁₃	#127	1	16	yes	complemented
245	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₁₃	C₂²×D₄	1	16	yes	—
249	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
250	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
251	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
252	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
253	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
254	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
255	C₂²×#41	C₂²×C₁₃	1	2	yes	—
256	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
257	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
258	#532	—	2	8	no	—
259	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
260	C₂×#127	C₂²×C₁₃	1	4	yes	—
261	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
262	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
263	#525	—	2	32	no	—
264	C₂×#123	C₂²×C₁₃	1	8	yes	—
265	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
266	C₂×#121	C₂²×C₁₃	1	2	yes	—
267	C₂×#121	C₂²×C₁₃	1	2	yes	—
268	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
269	C₂×#120	C₂²×C₁₃	1	8	yes	—
270	C₂×C₄×D₄	—	2	8	no	—
271	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
272	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
273	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
274	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
275	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
276	C₂×C₄×D₄	C₂²×C₁₃	1	16	yes	complemented
277	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
278	C₂×#117	C₂²×C₁₃	1	2	yes	—
279	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
280	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
281	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
282	#399	C₂²×C₁₃	1	8	yes	complemented
283	#399	C₂²×C₁₃	1	8	yes	complemented
284	#392	C₂²×C₁₃	1	8	yes	—
285	#392	C₂²×C₁₃	1	8	yes	complemented
286	#390	C₂²×C₁₃	1	4	yes	—
287	#390	C₂²×C₁₃	1	4	yes	complemented
288	#390	C₂²×C₁₃	1	16	yes	complemented
289	#384	C₂²×C₁₃	1	4	yes	complemented
290	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
291	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
292	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
293	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
294	#376	C₂²×C₁₃	1	2	yes	complemented
295	C₄³	C₂²×C₁₃	1	2	yes	complemented
296	C₂²×C₁₃	—	2	2	no	—
297	C₂²×C₁₃	—	2	2	no	—
298	C₂²×C₁₃	—	2	8	no	—
299	C₂²×C₁₃	—	2	8	no	—
300	C₂²×C₁₃	—	2	16	no	—
301	C₂²×C₁₃	—	4	32	no	—
302	C₂²×C₁₃	—	4	4	no	—
303	C₂²×C₁₃	—	4	4	no	—
304	C₂²×C₁₃	—	4	8	no	—
305	C₂²×C₁₃	—	4	4	no	—
306	C₂²×C₁₃	—	4	4	no	—
307	C₂²×C₁₃	—	4	4	no	—
308	C₂²×C₁₃	—	4	16	no	—
309	C₂²×C₁₃	C₂×#127	1	4	yes	—
310	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
311	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
312	C₂²×C₁₃	C₂²×#41	1	2	yes	—
313	C₂²×C₁₃	#585	1	2	yes	—
314	C₄×C₁₃	—	2	2	no	—
315	C₄×C₁₃	—	2	2	no	—
316	C₄×C₁₃	—	2	2	no	—
317	C₄×C₁₃	—	2	16	no	—
318	C₄×C₁₃	—	4	4	no	—
319	C₄×C₁₃	—	4	4	no	—
320	C₄×C₁₃	#525	1	4	yes	complemented
321	C₄×C₁₃	C₂×#127	1	4	yes	—
322	C₄×C₁₃	C₂×#127	1	4	yes	—
323	C₂⁵	C₂³×C₁₃	1	2	yes	—
324	C₂×#41	—	2	16	no	—
325	C₂×#41	—	2	8	no	—
326	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
327	C₂²×D₄	—	2	8	no	—
328	C₂²×D₄	—	2	4	no	—
329	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
330	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
331	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
332	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
333	C₂²×D₄	C₂³×C₁₃	1	16	yes	—
334	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
335	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
336	C₂³×C₄	—	2	8	no	—
337	C₂³×C₄	—	2	16	no	—
338	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
339	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
340	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
341	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
342	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
343	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
344	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
345	C₄⋊Q₈	—	2	4	no	—
346	#127	—	2	16	no	—
347	#127	—	2	4	no	—
348	#124	—	2	8	no	—
349	#123	—	2	32	no	—
350	C₂²⋊Q₈	—	2	32	no	—
351	#121	—	2	8	no	—
352	#121	—	2	8	no	—
353	#121	—	2	32	no	—
354	#120	—	2	32	no	—
355	C₄×D₄	—	2	8	no	—
356	C₄×D₄	—	2	8	no	—
357	C₄×D₄	—	2	8	no	—
358	C₄×D₄	—	2	8	no	—
359	C₄×D₄	—	2	8	no	—
360	C₄×D₄	—	2	8	no	—
361	C₄×D₄	—	2	64	no	—
362	#117	D₄×C₁₃	1	16	yes	complemented
363	C₂×C₄⋊C₄	—	2	4	no	—
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
367	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
370	C₂×C₂²⋊C₄	—	2	8	no	—
371	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
376	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
378	C₂×C₄²	D₄×C₁₃	1	8	yes	complemented
379	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
380	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
381	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
382	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
383	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
384	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
385	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
386	#95	C₂³×C₁₃	1	4	yes	—
387	#95	C₂³×C₁₃	1	4	yes	—
388	C₂×C₁₃	—	2	4	no	—
389	C₂×C₁₃	—	4	8	no	—
390	C₂×C₁₃	—	8	4	no	—
391	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
392	C₂×C₁₃	C₂²×#127	1	1	yes	characteristic
393	C₂×C₁₃	#3449	1	1	yes	characteristic
394	C₂×C₁₃	D₄×#41	1	4	yes	—
395	C₂⁴	—	2	4	no	—
396	C₂⁴	—	2	8	no	—
397	C₂⁴	—	2	8	no	—
398	C₂⁴	—	4	4	no	—
399	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
400	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
401	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
402	#41	—	4	32	no	—
403	C₂×Q₈	—	2	8	no	—
404	C₂×Q₈	—	2	4	no	—
405	C₂×D₄	—	2	32	no	—
406	C₂×D₄	—	2	8	no	—
407	C₂×D₄	—	2	16	no	—
408	C₂×D₄	—	2	8	no	—
409	C₂×D₄	—	2	32	no	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	2	4	no	—
412	C₂×D₄	—	2	32	no	—
413	C₂×D₄	—	2	4	no	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	8	no	—
416	C₂×D₄	—	2	4	no	—
417	C₂×D₄	—	2	4	no	—
418	C₂×D₄	—	2	8	no	—
419	C₂×D₄	—	4	16	no	—
420	C₂×D₄	—	4	4	no	—
421	C₂×D₄	C₁₃×#41	1	8	yes	complemented
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	8	no	—
425	C₂²×C₄	—	2	8	no	—
426	C₂²×C₄	—	2	8	no	—
427	C₂²×C₄	—	2	16	no	—
428	C₂²×C₄	—	2	8	no	—
429	C₂²×C₄	—	2	16	no	—
430	C₂²×C₄	—	2	16	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	4	32	no	—
433	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
434	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
435	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
436	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
437	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
438	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
439	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
440	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
441	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
442	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
443	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
444	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
445	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	32	no	—
451	C₄⋊C₄	C₂×D₄×C₁₃	1	16	yes	complemented
452	C₂²⋊C₄	—	2	8	no	—
453	C₂²⋊C₄	—	2	8	no	—
454	C₂²⋊C₄	—	2	32	no	—
455	C₂²⋊C₄	—	2	32	no	—
456	C₂²⋊C₄	—	2	8	no	—
457	C₂²⋊C₄	—	2	8	no	—
458	C₂²⋊C₄	C₂×D₄×C₁₃	1	16	yes	—
459	C₄²	—	2	8	no	—
460	C₄²	—	4	4	no	—
461	C₄²	C₂×D₄×C₁₃	1	4	yes	—
462	C₄²	C₂×D₄×C₁₃	1	4	yes	—
463	C₄²	C₂×D₄×C₁₃	1	4	yes	—
464	C₄²	C₂×D₄×C₁₃	1	4	yes	—
465	C₄²	C₂×D₄×C₁₃	1	16	yes	complemented
466	C₁₃	#34936	1	1	yes	characteristic, direct product factor, Sylow
467	C₂³	—	2	2	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	16	no	—
470	C₂³	—	2	4	no	—
471	C₂³	—	2	8	no	—
472	C₂³	—	2	4	no	—
473	C₂³	—	2	8	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	8	no	—
476	C₂³	—	2	8	no	—
477	C₂³	—	2	8	no	—
478	C₂³	—	4	32	no	—
479	C₂³	—	4	8	no	—
480	C₂³	—	4	8	no	—
481	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
482	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
483	C₂³	C₂×C₁₃×#41	1	8	yes	—
484	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
485	Q₈	—	4	8	no	—
486	D₄	—	2	16	no	—
487	D₄	—	2	16	no	—
488	D₄	—	4	64	no	—
489	D₄	—	4	8	no	—
490	D₄	—	4	16	no	—
491	D₄	—	4	8	no	—
492	D₄	—	4	8	no	—
493	C₂×C₄	—	2	8	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	8	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	8	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	8	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	8	no	—
503	C₂×C₄	—	4	4	no	—
504	C₂×C₄	—	4	8	no	—
505	C₂×C₄	—	4	16	no	—
506	C₂×C₄	—	4	16	no	—
507	C₂×C₄	—	4	16	no	—
508	C₂×C₄	C₁₃×#127	1	16	yes	complemented
509	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
510	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
511	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
512	C₂×C₄	C₂²×D₄×C₁₃	1	16	yes	—
513	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
514	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
515	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
516	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
517	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
518	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	8	no	—
522	C₂²	—	2	8	no	—
523	C₂²	—	2	16	no	—
524	C₂²	—	4	32	no	—
525	C₂²	—	4	4	no	—
526	C₂²	—	4	4	no	—
527	C₂²	—	4	8	no	—
528	C₂²	—	4	4	no	—
529	C₂²	—	4	4	no	—
530	C₂²	—	4	4	no	—
531	C₂²	—	4	16	no	—
532	C₂²	C₂×C₁₃×#127	1	4	yes	—
533	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
534	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
535	C₂²	C₂²×C₁₃×#41	1	2	yes	—
536	C₂²	C₁₃×#585	1	2	yes	—
537	C₄	—	2	2	no	—
538	C₄	—	2	2	no	—
539	C₄	—	2	2	no	—
540	C₄	—	2	16	no	—
541	C₄	—	4	4	no	—
542	C₄	—	4	4	no	—
543	C₄	C₁₃×#525	1	4	yes	complemented
544	C₄	C₂×C₁₃×#127	1	4	yes	—
545	C₄	C₂×C₁₃×#127	1	4	yes	—
546	C₂	—	2	4	no	—
547	C₂	—	4	8	no	—
548	C₂	—	8	4	no	—
549	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
550	C₂	C₂²×C₁₃×#127	1	1	yes	characteristic
551	C₂	C₁₃×#3449	1	1	yes	characteristic
552	C₂	D₄×C₁₃×#41	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
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. C₂×C₁₃×#532	C₂	semidirect
2. C₂×C₁₃×#525	C₂	semidirect
3. C₂²×C₄×D₄×C₁₃	C₂	semidirect
4. C₁₃×#2542	C₂	semidirect
5. C₁₃×#2541	C₂	semidirect
6. C₁₃×#2540	C₂	semidirect
7. C₁₃×#2539	C₂	semidirect
8. C₁₃×#2501	C₂	semidirect
9. C₁₃×#2433	C₂	semidirect
10. C₁₃×#2397	C₂	semidirect
11. C₄×C₁₃×#127	C₂	semidirect
12. C₄×C₁₃×#117	C₂	semidirect
17. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
19. C₂×C₁₃×#127	C₂²	semidirect
20. C₂×C₁₃×#124	C₂²	semidirect
23. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₁₃×#121	C₂²	semidirect
33. C₂×C₄×D₄×C₁₃	C₂²	semidirect
34. C₂×C₄×D₄×C₁₃	C₂²	semidirect
35. C₂×C₄×D₄×C₁₃	C₂²	semidirect
40. C₁₃×#399	C₂²	semidirect
41. C₁₃×#399	C₂²	semidirect
43. C₁₃×#392	C₂²	semidirect
45. C₁₃×#390	C₂²	semidirect
46. C₁₃×#390	C₂²	semidirect
47. C₁₃×#384	C₂²	semidirect
48. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
49. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
52. C₁₃×#376	C₂²	semidirect
53. C₄³×C₁₃	C₂²	semidirect
93. C₁₃×#117	D₄	semidirect
109. C₂×C₄²×C₁₃	D₄	semidirect
119. #34936	C₁₃	direct (N × H)
146. C₂×D₄×C₁₃	#41	semidirect
176. C₁₃×C₄⋊C₄	C₂×D₄	semidirect
190. C₄²×C₁₃	C₂×D₄	semidirect
191. C₂×#532	C₂×C₁₃	semidirect
192. C₂×#525	C₂×C₁₃	semidirect
193. C₂²×C₄×D₄	C₂×C₁₃	semidirect
194. #2542	C₂×C₁₃	semidirect
195. #2541	C₂×C₁₃	semidirect
196. #2540	C₂×C₁₃	semidirect
197. #2539	C₂×C₁₃	semidirect
198. #2501	C₂×C₁₃	semidirect
199. #2433	C₂×C₁₃	semidirect
200. #2397	C₂×C₁₃	semidirect
201. C₄×#127	C₂×C₁₃	semidirect
202. C₄×#117	C₂×C₁₃	semidirect
244. C₂×C₄×C₁₃	#127	semidirect
259. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
261. C₂×#127	C₂²×C₁₃	semidirect
262. C₂×#124	C₂²×C₁₃	semidirect
265. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
268. C₂×#121	C₂²×C₁₃	semidirect
275. C₂×C₄×D₄	C₂²×C₁₃	semidirect
276. C₂×C₄×D₄	C₂²×C₁₃	semidirect
277. C₂×C₄×D₄	C₂²×C₁₃	semidirect
282. #399	C₂²×C₁₃	semidirect
283. #399	C₂²×C₁₃	semidirect
285. #392	C₂²×C₁₃	semidirect
287. #390	C₂²×C₁₃	semidirect
288. #390	C₂²×C₁₃	semidirect
289. #384	C₂²×C₁₃	semidirect
290. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
291. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
294. #376	C₂²×C₁₃	semidirect
295. C₄³	C₂²×C₁₃	semidirect
320. C₄×C₁₃	#525	semidirect
362. #117	D₄×C₁₃	semidirect
378. C₂×C₄²	D₄×C₁₃	semidirect
421. C₂×D₄	C₁₃×#41	semidirect
451. C₄⋊C₄	C₂×D₄×C₁₃	semidirect
465. C₄²	C₂×D₄×C₁₃	semidirect
466. C₁₃	#34936	direct (N × H)
508. C₂×C₄	C₁₃×#127	semidirect
543. C₄	C₁₃×#525	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#532	2
C₂×C₁₃×#525	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2542	2
C₁₃×#2541	2
C₁₃×#2540	2
C₁₃×#2539	2
C₁₃×#2501	2
C₁₃×#2433	2
C₁₃×#2397	2
C₄×C₁₃×#127	2
C₄×C₁₃×#117	2
#34936	13

Subgroups — C13×#34936 #15721275

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34936 #15721275