Subgroups — C₂×C₁₃×#2561 #15721180

Order 3328.

4166 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2561	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#397	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#393	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#388	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#381	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#379	C₂	1	2	yes	maximal
9	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
11	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
12	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊Q₈	—	2	8	no	—
15	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₁₃×C₂²⋊C₄	—	2	8	no	—
19	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
26	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
27	C₁₃×#397	C₂²	1	16	yes	complemented
28	C₁₃×#393	C₂²	1	16	yes	complemented
29	C₁₃×#388	C₂²	1	32	yes	complemented
30	C₁₃×#381	C₂²	1	16	yes	complemented
31	C₁₃×#379	C₂²	1	16	yes	—
32	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
33	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
34	C₂×C₁₃×#95	C₂²	1	4	yes	complemented
35	C₂×C₁₃×#95	C₂²	1	4	yes	complemented
36	C₂⁵×C₁₃	—	2	4	no	—
37	C₂⁵×C₁₃	—	2	8	no	—
38	C₂⁵×C₁₃	—	2	8	no	—
39	C₂⁵×C₁₃	—	4	4	no	—
40	C₂⁵×C₁₃	C₂³	1	2	yes	—
41	C₂⁵×C₁₃	C₂³	1	4	yes	—
42	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₁₃	—	2	4	no	—
44	C₂²×Q₈×C₁₃	—	4	4	no	—
45	C₂²×Q₈×C₁₃	C₂³	1	4	yes	complemented
46	C₂³×C₄×C₁₃	—	2	4	no	—
47	C₂³×C₄×C₁₃	—	2	8	no	—
48	C₂³×C₄×C₁₃	—	4	4	no	—
49	C₂³×C₄×C₁₃	D₄	1	8	yes	—
50	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
51	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
58	C₁₃×C₂²⋊Q₈	—	2	32	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
63	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
64	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
65	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	32	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
70	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
71	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
72	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
73	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
74	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
75	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
76	C₂×C₄²×C₁₃	—	4	4	no	—
77	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
78	C₁₃×#95	C₂³	1	8	yes	complemented
79	C₁₃×#95	C₂³	1	16	yes	complemented
80	C₁₃×#95	C₂³	1	16	yes	complemented
81	C₂×#2561	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂⁴×C₁₃	—	2	4	no	—
83	C₂⁴×C₁₃	—	2	4	no	—
84	C₂⁴×C₁₃	—	2	32	no	—
85	C₂⁴×C₁₃	—	2	8	no	—
86	C₂⁴×C₁₃	—	2	4	no	—
87	C₂⁴×C₁₃	—	2	16	no	—
88	C₂⁴×C₁₃	—	2	4	no	—
89	C₂⁴×C₁₃	—	2	8	no	—
90	C₂⁴×C₁₃	—	2	8	no	—
91	C₂⁴×C₁₃	—	2	16	no	—
92	C₂⁴×C₁₃	—	4	8	no	—
93	C₂⁴×C₁₃	—	4	64	no	—
94	C₂⁴×C₁₃	—	4	16	no	—
95	C₂⁴×C₁₃	—	4	16	no	—
96	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
97	C₂⁴×C₁₃	#41	1	8	yes	—
98	C₂⁴×C₁₃	#41	1	8	yes	—
99	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
100	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
101	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
102	C₂×Q₈×C₁₃	—	2	8	no	—
103	C₂×Q₈×C₁₃	—	4	8	no	—
104	C₂×Q₈×C₁₃	—	4	16	no	—
105	C₂²×C₄×C₁₃	—	2	4	no	—
106	C₂²×C₄×C₁₃	—	2	4	no	—
107	C₂²×C₄×C₁₃	—	2	8	no	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	2	4	no	—
111	C₂²×C₄×C₁₃	—	2	8	no	—
112	C₂²×C₄×C₁₃	—	2	8	no	—
113	C₂²×C₄×C₁₃	—	2	8	no	—
114	C₂²×C₄×C₁₃	—	2	16	no	—
115	C₂²×C₄×C₁₃	—	2	8	no	—
116	C₂²×C₄×C₁₃	—	2	8	no	—
117	C₂²×C₄×C₁₃	—	2	8	no	—
118	C₂²×C₄×C₁₃	—	4	16	no	—
119	C₂²×C₄×C₁₃	—	4	8	no	—
120	C₂²×C₄×C₁₃	—	4	16	no	—
121	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
122	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
123	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	—
124	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
125	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
126	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
127	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
128	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
130	C₁₃×C₄⋊C₄	—	2	8	no	—
131	C₁₃×C₄⋊C₄	—	2	16	no	—
132	C₁₃×C₂²⋊C₄	—	2	16	no	—
133	C₁₃×C₂²⋊C₄	—	2	32	no	—
134	C₁₃×C₂²⋊C₄	—	2	16	no	—
135	C₁₃×C₂²⋊C₄	—	2	16	no	—
136	C₁₃×C₂²⋊C₄	—	2	16	no	—
137	C₁₃×C₂²⋊C₄	—	4	16	no	—
138	C₄²×C₁₃	—	4	8	no	—
139	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
140	C₂³×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
141	#2561	C₂×C₁₃	1	16	yes	direct product factor
142	C₂×#397	C₂×C₁₃	1	2	yes	complemented
143	C₂×#393	C₂×C₁₃	1	2	yes	complemented
144	C₂×#388	C₂×C₁₃	1	4	yes	complemented
145	C₂×#381	C₂×C₁₃	1	2	yes	complemented
146	C₂×#379	C₂×C₁₃	1	2	yes	—
147	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
148	C₂³×C₁₃	—	2	8	no	—
149	C₂³×C₁₃	—	2	8	no	—
150	C₂³×C₁₃	—	2	32	no	—
151	C₂³×C₁₃	—	2	4	no	—
152	C₂³×C₁₃	—	2	4	no	—
153	C₂³×C₁₃	—	2	32	no	—
154	C₂³×C₁₃	—	2	16	no	—
155	C₂³×C₁₃	—	2	32	no	—
156	C₂³×C₁₃	—	2	4	no	—
157	C₂³×C₁₃	—	2	4	no	—
158	C₂³×C₁₃	—	2	8	no	—
159	C₂³×C₁₃	—	2	8	no	—
160	C₂³×C₁₃	—	4	64	no	—
161	C₂³×C₁₃	—	4	128	no	—
162	C₂³×C₁₃	—	4	16	no	—
163	C₂³×C₁₃	—	4	16	no	—
164	C₂³×C₁₃	—	4	8	no	—
165	C₂³×C₁₃	—	4	8	no	—
166	C₂³×C₁₃	—	4	16	no	—
167	C₂³×C₁₃	#124	1	16	yes	—
168	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
169	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
170	C₂³×C₁₃	C₂×#41	1	8	yes	—
171	C₂³×C₁₃	C₂×#41	1	8	yes	—
172	C₂³×C₁₃	C₂×#41	1	4	yes	—
173	C₂³×C₁₃	C₂×#41	1	4	yes	—
174	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
175	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
176	Q₈×C₁₃	—	4	16	no	—
177	C₂×C₄×C₁₃	—	2	8	no	—
178	C₂×C₄×C₁₃	—	2	8	no	—
179	C₂×C₄×C₁₃	—	2	4	no	—
180	C₂×C₄×C₁₃	—	2	4	no	—
181	C₂×C₄×C₁₃	—	2	4	no	—
182	C₂×C₄×C₁₃	—	2	4	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	2	8	no	—
185	C₂×C₄×C₁₃	—	2	8	no	—
186	C₂×C₄×C₁₃	—	2	8	no	—
187	C₂×C₄×C₁₃	—	2	8	no	—
188	C₂×C₄×C₁₃	—	2	8	no	—
189	C₂×C₄×C₁₃	—	2	8	no	—
190	C₂×C₄×C₁₃	—	4	16	no	—
191	C₂×C₄×C₁₃	—	4	8	no	—
192	C₂×C₄×C₁₃	—	4	16	no	—
193	C₂×C₄×C₁₃	—	4	8	no	—
194	C₂×C₄×C₁₃	—	4	8	no	—
195	C₂×C₄×C₁₃	—	4	16	no	—
196	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
197	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
198	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
199	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
200	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
201	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
202	C₂×C₂²⋊Q₈	—	2	8	no	—
203	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
204	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
205	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
206	C₂²×C₂²⋊C₄	—	2	8	no	—
207	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
208	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
209	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
210	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
211	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
212	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
213	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
214	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
215	#397	C₂²×C₁₃	1	16	yes	complemented
216	#393	C₂²×C₁₃	1	16	yes	complemented
217	#388	C₂²×C₁₃	1	32	yes	complemented
218	#381	C₂²×C₁₃	1	16	yes	complemented
219	#379	C₂²×C₁₃	1	16	yes	—
220	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
221	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
222	C₂×#95	C₂²×C₁₃	1	4	yes	complemented
223	C₂×#95	C₂²×C₁₃	1	4	yes	complemented
224	C₂²×C₁₃	—	2	32	no	—
225	C₂²×C₁₃	—	2	4	no	—
226	C₂²×C₁₃	—	2	4	no	—
227	C₂²×C₁₃	—	2	16	no	—
228	C₂²×C₁₃	—	2	8	no	—
229	C₂²×C₁₃	—	2	16	no	—
230	C₂²×C₁₃	—	4	64	no	—
231	C₂²×C₁₃	—	4	32	no	—
232	C₂²×C₁₃	—	4	4	no	—
233	C₂²×C₁₃	—	4	4	no	—
234	C₂²×C₁₃	—	4	8	no	—
235	C₂²×C₁₃	#525	1	4	yes	—
236	C₂²×C₁₃	C₂×#124	1	8	yes	—
237	C₂²×C₁₃	C₂×#124	1	4	yes	—
238	C₂²×C₁₃	#534	1	4	yes	—
239	C₂²×C₁₃	#551	1	16	yes	—
240	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
241	C₂²×C₁₃	C₂²×#41	1	2	yes	—
242	C₂²×C₁₃	C₂²×#41	1	2	yes	—
243	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
244	C₄×C₁₃	—	2	4	no	—
245	C₄×C₁₃	—	2	4	no	—
246	C₄×C₁₃	—	4	4	no	—
247	C₄×C₁₃	—	4	4	no	—
248	C₄×C₁₃	—	4	4	no	—
249	C₄×C₁₃	—	4	8	no	—
250	C₂⁵	—	2	4	no	—
251	C₂⁵	—	2	8	no	—
252	C₂⁵	—	2	8	no	—
253	C₂⁵	—	4	4	no	—
254	C₂⁵	C₂³×C₁₃	1	2	yes	—
255	C₂⁵	C₂³×C₁₃	1	4	yes	—
256	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
257	C₂²×Q₈	—	2	4	no	—
258	C₂²×Q₈	—	4	4	no	—
259	C₂²×Q₈	C₂³×C₁₃	1	4	yes	complemented
260	C₂³×C₄	—	2	4	no	—
261	C₂³×C₄	—	2	8	no	—
262	C₂³×C₄	—	4	4	no	—
263	C₂³×C₄	D₄×C₁₃	1	8	yes	—
264	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
265	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
266	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
267	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
268	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
269	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
270	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
271	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
272	C₂²⋊Q₈	—	2	32	no	—
273	C₂×C₄⋊C₄	—	2	4	no	—
274	C₂×C₄⋊C₄	—	2	8	no	—
275	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
276	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
277	C₂×C₂²⋊C₄	—	2	8	no	—
278	C₂×C₂²⋊C₄	—	2	16	no	—
279	C₂×C₂²⋊C₄	—	2	8	no	—
280	C₂×C₂²⋊C₄	—	2	8	no	—
281	C₂×C₂²⋊C₄	—	2	8	no	—
282	C₂×C₂²⋊C₄	—	2	32	no	—
283	C₂×C₂²⋊C₄	—	4	8	no	—
284	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
285	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
286	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
287	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
288	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
289	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
290	C₂×C₄²	—	4	4	no	—
291	C₂×C₄²	C₂³×C₁₃	1	8	yes	complemented
292	#95	C₂³×C₁₃	1	8	yes	complemented
293	#95	C₂³×C₁₃	1	16	yes	complemented
294	#95	C₂³×C₁₃	1	16	yes	complemented
295	C₂×C₁₃	—	2	8	no	—
296	C₂×C₁₃	—	4	8	no	—
297	C₂×C₁₃	#2561	1	8	yes	direct product factor
298	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
299	C₂×C₁₃	C₂²×#124	1	1	yes	characteristic
300	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
301	C₂×C₁₃	C₂×#551	1	4	yes	—
302	C₂⁴	—	2	4	no	—
303	C₂⁴	—	2	4	no	—
304	C₂⁴	—	2	32	no	—
305	C₂⁴	—	2	8	no	—
306	C₂⁴	—	2	4	no	—
307	C₂⁴	—	2	16	no	—
308	C₂⁴	—	2	4	no	—
309	C₂⁴	—	2	8	no	—
310	C₂⁴	—	2	8	no	—
311	C₂⁴	—	2	16	no	—
312	C₂⁴	—	4	8	no	—
313	C₂⁴	—	4	64	no	—
314	C₂⁴	—	4	16	no	—
315	C₂⁴	—	4	16	no	—
316	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
317	C₂⁴	C₁₃×#41	1	8	yes	—
318	C₂⁴	C₁₃×#41	1	8	yes	—
319	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
320	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
321	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
322	C₂×Q₈	—	2	8	no	—
323	C₂×Q₈	—	4	8	no	—
324	C₂×Q₈	—	4	16	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	2	16	no	—
335	C₂²×C₄	—	2	8	no	—
336	C₂²×C₄	—	2	8	no	—
337	C₂²×C₄	—	2	8	no	—
338	C₂²×C₄	—	4	16	no	—
339	C₂²×C₄	—	4	8	no	—
340	C₂²×C₄	—	4	16	no	—
341	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
342	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
343	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	—
344	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
345	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
346	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
347	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
348	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
349	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
350	C₄⋊C₄	—	2	8	no	—
351	C₄⋊C₄	—	2	16	no	—
352	C₂²⋊C₄	—	2	16	no	—
353	C₂²⋊C₄	—	2	32	no	—
354	C₂²⋊C₄	—	2	16	no	—
355	C₂²⋊C₄	—	2	16	no	—
356	C₂²⋊C₄	—	2	16	no	—
357	C₂²⋊C₄	—	4	16	no	—
358	C₄²	—	4	8	no	—
359	C₁₃	C₂×#2561	1	1	yes	characteristic, direct product factor, Sylow
360	C₂³	—	2	8	no	—
361	C₂³	—	2	8	no	—
362	C₂³	—	2	32	no	—
363	C₂³	—	2	4	no	—
364	C₂³	—	2	4	no	—
365	C₂³	—	2	32	no	—
366	C₂³	—	2	16	no	—
367	C₂³	—	2	32	no	—
368	C₂³	—	2	4	no	—
369	C₂³	—	2	4	no	—
370	C₂³	—	2	8	no	—
371	C₂³	—	2	8	no	—
372	C₂³	—	4	64	no	—
373	C₂³	—	4	128	no	—
374	C₂³	—	4	16	no	—
375	C₂³	—	4	16	no	—
376	C₂³	—	4	8	no	—
377	C₂³	—	4	8	no	—
378	C₂³	—	4	16	no	—
379	C₂³	C₁₃×#124	1	16	yes	—
380	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
381	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
382	C₂³	C₂×C₁₃×#41	1	8	yes	—
383	C₂³	C₂×C₁₃×#41	1	8	yes	—
384	C₂³	C₂×C₁₃×#41	1	4	yes	—
385	C₂³	C₂×C₁₃×#41	1	4	yes	—
386	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
387	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
388	Q₈	—	4	16	no	—
389	C₂×C₄	—	2	8	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	8	no	—
397	C₂×C₄	—	2	8	no	—
398	C₂×C₄	—	2	8	no	—
399	C₂×C₄	—	2	8	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	8	no	—
402	C₂×C₄	—	4	16	no	—
403	C₂×C₄	—	4	8	no	—
404	C₂×C₄	—	4	16	no	—
405	C₂×C₄	—	4	8	no	—
406	C₂×C₄	—	4	8	no	—
407	C₂×C₄	—	4	16	no	—
408	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
409	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
410	C₂²	—	2	32	no	—
411	C₂²	—	2	4	no	—
412	C₂²	—	2	4	no	—
413	C₂²	—	2	16	no	—
414	C₂²	—	2	8	no	—
415	C₂²	—	2	16	no	—
416	C₂²	—	4	64	no	—
417	C₂²	—	4	32	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	4	4	no	—
420	C₂²	—	4	8	no	—
421	C₂²	C₁₃×#525	1	4	yes	—
422	C₂²	C₂×C₁₃×#124	1	8	yes	—
423	C₂²	C₂×C₁₃×#124	1	4	yes	—
424	C₂²	C₁₃×#534	1	4	yes	—
425	C₂²	C₁₃×#551	1	16	yes	—
426	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
427	C₂²	C₂²×C₁₃×#41	1	2	yes	—
428	C₂²	C₂²×C₁₃×#41	1	2	yes	—
429	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
430	C₄	—	2	4	no	—
431	C₄	—	2	4	no	—
432	C₄	—	4	4	no	—
433	C₄	—	4	4	no	—
434	C₄	—	4	4	no	—
435	C₄	—	4	8	no	—
436	C₂	—	2	8	no	—
437	C₂	—	4	8	no	—
438	C₂	C₁₃×#2561	1	8	yes	direct product factor
439	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
440	C₂	C₂²×C₁₃×#124	1	1	yes	characteristic
441	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
442	C₂	C₂×C₁₃×#551	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁶×C₁₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
3. C₁₃×#2561	C₂	direct (N × H)
4. C₂×C₁₃×#397	C₂	semidirect
5. C₂×C₁₃×#393	C₂	semidirect
6. C₂×C₁₃×#388	C₂	semidirect
7. C₂×C₁₃×#381	C₂	semidirect
9. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
11. C₂³×Q₈×C₁₃	C₂²	semidirect
15. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
16. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
17. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
26. C₂²×C₄²×C₁₃	C₂²	semidirect
27. C₁₃×#397	C₂²	semidirect
28. C₁₃×#393	C₂²	semidirect
29. C₁₃×#388	C₂²	semidirect
30. C₁₃×#381	C₂²	semidirect
32. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
33. C₂×C₁₃×#95	C₂²	semidirect
34. C₂×C₁₃×#95	C₂²	semidirect
35. C₂×C₁₃×#95	C₂²	semidirect
45. C₂²×Q₈×C₁₃	C₂³	semidirect
61. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
62. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
77. C₂×C₄²×C₁₃	C₂³	semidirect
78. C₁₃×#95	C₂³	semidirect
79. C₁₃×#95	C₂³	semidirect
80. C₁₃×#95	C₂³	semidirect
81. C₂×#2561	C₁₃	direct (N × H)
139. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
141. #2561	C₂×C₁₃	direct (N × H)
142. C₂×#397	C₂×C₁₃	semidirect
143. C₂×#393	C₂×C₁₃	semidirect
144. C₂×#388	C₂×C₁₃	semidirect
145. C₂×#381	C₂×C₁₃	semidirect
147. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
199. C₂³×Q₈	C₂²×C₁₃	semidirect
203. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
204. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
205. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
214. C₂²×C₄²	C₂²×C₁₃	semidirect
215. #397	C₂²×C₁₃	semidirect
216. #393	C₂²×C₁₃	semidirect
217. #388	C₂²×C₁₃	semidirect
218. #381	C₂²×C₁₃	semidirect
220. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
221. C₂×#95	C₂²×C₁₃	semidirect
222. C₂×#95	C₂²×C₁₃	semidirect
223. C₂×#95	C₂²×C₁₃	semidirect
259. C₂²×Q₈	C₂³×C₁₃	semidirect
275. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
276. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
291. C₂×C₄²	C₂³×C₁₃	semidirect
292. #95	C₂³×C₁₃	semidirect
293. #95	C₂³×C₁₃	semidirect
294. #95	C₂³×C₁₃	semidirect
297. C₂×C₁₃	#2561	direct (N × H)
359. C₁₃	C₂×#2561	direct (N × H)
438. C₂	C₁₃×#2561	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×C₂²⋊Q₈	2
C₂³×C₁₃×C₂²⋊C₄	2
C₁₃×#2561	2
C₂×C₁₃×#397	2
C₂×C₁₃×#393	2
C₂×C₁₃×#388	2
C₂×C₁₃×#381	2
C₂×C₁₃×#379	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂×#2561	13

Subgroups — C2×C13×#2561 #15721180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2561 #15721180