Subgroups — C₂×C₁₃×#2591 #15721189

Order 3328.

3438 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2591	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#400	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#394	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#388	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#386	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#386	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
11	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#121	—	2	8	no	—
16	C₂×C₁₃×#121	C₂²	1	8	yes	—
17	C₂²×C₁₃×C₄⋊C₄	—	2	8	no	—
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	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	—
27	C₁₃×#400	C₂²	1	16	yes	complemented
28	C₁₃×#394	C₂²	1	16	yes	complemented
29	C₁₃×#388	C₂²	1	32	yes	complemented
30	C₁₃×#386	C₂²	1	16	yes	complemented
31	C₁₃×#386	C₂²	1	16	yes	complemented
32	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
33	C₂×C₁₃×#95	C₂²	1	2	yes	—
34	C₂×C₁₃×#95	C₂²	1	4	yes	—
35	C₂×C₁₃×#95	C₂²	1	4	yes	—
36	C₂⁵×C₁₃	C₂³	1	2	yes	—
37	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
38	C₂²×D₄×C₁₃	—	2	8	no	—
39	C₂²×D₄×C₁₃	—	2	16	no	—
40	C₂²×D₄×C₁₃	—	2	4	no	—
41	C₂²×D₄×C₁₃	—	4	4	no	—
42	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
43	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
44	C₂³×C₄×C₁₃	—	2	4	no	—
45	C₂³×C₄×C₁₃	—	2	8	no	—
46	C₂³×C₄×C₁₃	—	2	4	no	—
47	C₂³×C₄×C₁₃	—	4	4	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	1	yes	characteristic
55	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
59	C₁₃×#121	—	2	32	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	32	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
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	16	yes	—
75	C₂×C₄²×C₁₃	—	4	4	no	—
76	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
77	C₁₃×#95	C₂³	1	8	yes	—
78	C₁₃×#95	C₂³	1	16	yes	—
79	C₁₃×#95	C₂³	1	16	yes	—
80	C₂×#2591	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂⁴×C₁₃	—	2	4	no	—
82	C₂⁴×C₁₃	—	2	4	no	—
83	C₂⁴×C₁₃	—	2	4	no	—
84	C₂⁴×C₁₃	—	2	8	no	—
85	C₂⁴×C₁₃	—	2	8	no	—
86	C₂⁴×C₁₃	—	2	8	no	—
87	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
88	C₂⁴×C₁₃	#41	1	8	yes	—
89	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
90	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
91	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
92	C₂×D₄×C₁₃	—	2	16	no	—
93	C₂×D₄×C₁₃	—	2	32	no	—
94	C₂×D₄×C₁₃	—	2	8	no	—
95	C₂×D₄×C₁₃	—	4	8	no	—
96	C₂×D₄×C₁₃	—	4	16	no	—
97	C₂×D₄×C₁₃	—	4	32	no	—
98	C₂²×C₄×C₁₃	—	2	32	no	—
99	C₂²×C₄×C₁₃	—	2	8	no	—
100	C₂²×C₄×C₁₃	—	2	4	no	—
101	C₂²×C₄×C₁₃	—	2	4	no	—
102	C₂²×C₄×C₁₃	—	2	4	no	—
103	C₂²×C₄×C₁₃	—	2	4	no	—
104	C₂²×C₄×C₁₃	—	2	16	no	—
105	C₂²×C₄×C₁₃	—	2	4	no	—
106	C₂²×C₄×C₁₃	—	2	8	no	—
107	C₂²×C₄×C₁₃	—	2	4	no	—
108	C₂²×C₄×C₁₃	—	2	8	no	—
109	C₂²×C₄×C₁₃	—	2	8	no	—
110	C₂²×C₄×C₁₃	—	2	8	no	—
111	C₂²×C₄×C₁₃	—	2	8	no	—
112	C₂²×C₄×C₁₃	—	2	8	no	—
113	C₂²×C₄×C₁₃	—	4	16	no	—
114	C₂²×C₄×C₁₃	—	4	8	no	—
115	C₂²×C₄×C₁₃	—	4	8	no	—
116	C₂²×C₄×C₁₃	—	4	16	no	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	—
120	C₂²×C₄×C₁₃	#41	1	8	yes	—
121	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
123	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
124	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
125	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
126	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
127	C₁₃×C₄⋊C₄	—	2	16	no	—
128	C₁₃×C₄⋊C₄	—	2	16	no	—
129	C₁₃×C₄⋊C₄	—	2	8	no	—
130	C₁₃×C₂²⋊C₄	—	2	16	no	—
131	C₁₃×C₂²⋊C₄	—	2	16	no	—
132	C₁₃×C₂²⋊C₄	—	2	32	no	—
133	C₁₃×C₂²⋊C₄	—	4	16	no	—
134	C₄²×C₁₃	—	4	8	no	—
135	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic
136	C₂³×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
137	#2591	C₂×C₁₃	1	16	yes	direct product factor
138	C₂×#400	C₂×C₁₃	1	2	yes	complemented
139	C₂×#394	C₂×C₁₃	1	2	yes	complemented
140	C₂×#388	C₂×C₁₃	1	4	yes	complemented
141	C₂×#386	C₂×C₁₃	1	2	yes	complemented
142	C₂×#386	C₂×C₁₃	1	2	yes	complemented
143	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
144	C₂³×C₁₃	—	2	8	no	—
145	C₂³×C₁₃	—	2	8	no	—
146	C₂³×C₁₃	—	2	32	no	—
147	C₂³×C₁₃	—	2	4	no	—
148	C₂³×C₁₃	—	2	4	no	—
149	C₂³×C₁₃	—	2	4	no	—
150	C₂³×C₁₃	—	2	8	no	—
151	C₂³×C₁₃	—	2	8	no	—
152	C₂³×C₁₃	—	2	8	no	—
153	C₂³×C₁₃	—	4	8	no	—
154	C₂³×C₁₃	—	4	8	no	—
155	C₂³×C₁₃	—	4	8	no	—
156	C₂³×C₁₃	—	4	32	no	—
157	C₂³×C₁₃	#124	1	16	yes	—
158	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
159	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
160	C₂³×C₁₃	C₂×#41	1	8	yes	—
161	C₂³×C₁₃	C₂×#41	1	4	yes	—
162	C₂³×C₁₃	C₂×#41	1	4	yes	—
163	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
164	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
165	D₄×C₁₃	—	4	16	no	—
166	D₄×C₁₃	—	4	32	no	—
167	C₂×C₄×C₁₃	—	2	32	no	—
168	C₂×C₄×C₁₃	—	2	16	no	—
169	C₂×C₄×C₁₃	—	2	8	no	—
170	C₂×C₄×C₁₃	—	2	8	no	—
171	C₂×C₄×C₁₃	—	2	4	no	—
172	C₂×C₄×C₁₃	—	2	4	no	—
173	C₂×C₄×C₁₃	—	2	4	no	—
174	C₂×C₄×C₁₃	—	2	4	no	—
175	C₂×C₄×C₁₃	—	2	4	no	—
176	C₂×C₄×C₁₃	—	2	4	no	—
177	C₂×C₄×C₁₃	—	2	8	no	—
178	C₂×C₄×C₁₃	—	2	8	no	—
179	C₂×C₄×C₁₃	—	2	8	no	—
180	C₂×C₄×C₁₃	—	2	8	no	—
181	C₂×C₄×C₁₃	—	2	8	no	—
182	C₂×C₄×C₁₃	—	4	16	no	—
183	C₂×C₄×C₁₃	—	4	16	no	—
184	C₂×C₄×C₁₃	—	4	8	no	—
185	C₂×C₄×C₁₃	—	4	8	no	—
186	C₂×C₄×C₁₃	—	4	16	no	—
187	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
188	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
189	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
190	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
191	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
192	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
193	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
194	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×#121	—	2	8	no	—
196	C₂×#121	C₂²×C₁₃	1	8	yes	—
197	C₂²×C₄⋊C₄	—	2	8	no	—
198	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
199	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
200	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
201	C₂²×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
202	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
203	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
204	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
205	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
206	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
207	#400	C₂²×C₁₃	1	16	yes	complemented
208	#394	C₂²×C₁₃	1	16	yes	complemented
209	#388	C₂²×C₁₃	1	32	yes	complemented
210	#386	C₂²×C₁₃	1	16	yes	complemented
211	#386	C₂²×C₁₃	1	16	yes	complemented
212	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
213	C₂×#95	C₂²×C₁₃	1	2	yes	—
214	C₂×#95	C₂²×C₁₃	1	4	yes	—
215	C₂×#95	C₂²×C₁₃	1	4	yes	—
216	C₂²×C₁₃	—	2	32	no	—
217	C₂²×C₁₃	—	2	4	no	—
218	C₂²×C₁₃	—	2	4	no	—
219	C₂²×C₁₃	—	2	16	no	—
220	C₂²×C₁₃	—	4	4	no	—
221	C₂²×C₁₃	—	4	4	no	—
222	C₂²×C₁₃	—	4	4	no	—
223	C₂²×C₁₃	—	4	16	no	—
224	C₂²×C₁₃	—	8	16	no	—
225	C₂²×C₁₃	#525	1	4	yes	—
226	C₂²×C₁₃	C₂×#124	1	8	yes	—
227	C₂²×C₁₃	C₂×#124	1	4	yes	—
228	C₂²×C₁₃	#534	1	4	yes	—
229	C₂²×C₁₃	#553	1	16	yes	—
230	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
231	C₂²×C₁₃	C₂²×#41	1	2	yes	—
232	C₂²×C₁₃	C₂²×#41	1	2	yes	—
233	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
234	C₄×C₁₃	—	2	8	no	—
235	C₄×C₁₃	—	2	4	no	—
236	C₄×C₁₃	—	2	4	no	—
237	C₄×C₁₃	—	4	4	no	—
238	C₄×C₁₃	—	4	4	no	—
239	C₄×C₁₃	—	4	8	no	—
240	C₂⁵	C₂³×C₁₃	1	2	yes	—
241	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
242	C₂²×D₄	—	2	8	no	—
243	C₂²×D₄	—	2	16	no	—
244	C₂²×D₄	—	2	4	no	—
245	C₂²×D₄	—	4	4	no	—
246	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
247	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
248	C₂³×C₄	—	2	4	no	—
249	C₂³×C₄	—	2	8	no	—
250	C₂³×C₄	—	2	4	no	—
251	C₂³×C₄	—	4	4	no	—
252	C₂³×C₄	—	4	4	no	—
253	C₂³×C₄	D₄×C₁₃	1	8	yes	—
254	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
255	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
256	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
257	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
258	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
259	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
260	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
261	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
262	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
263	#121	—	2	32	no	—
264	C₂×C₄⋊C₄	—	2	8	no	—
265	C₂×C₄⋊C₄	—	2	8	no	—
266	C₂×C₄⋊C₄	—	2	32	no	—
267	C₂×C₄⋊C₄	—	2	4	no	—
268	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
270	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
271	C₂×C₂²⋊C₄	—	2	8	no	—
272	C₂×C₂²⋊C₄	—	2	8	no	—
273	C₂×C₂²⋊C₄	—	2	16	no	—
274	C₂×C₂²⋊C₄	—	4	8	no	—
275	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
276	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
277	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
278	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
279	C₂×C₄²	—	4	4	no	—
280	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
281	#95	C₂³×C₁₃	1	8	yes	—
282	#95	C₂³×C₁₃	1	16	yes	—
283	#95	C₂³×C₁₃	1	16	yes	—
284	C₂×C₁₃	—	2	8	no	—
285	C₂×C₁₃	—	8	4	no	—
286	C₂×C₁₃	#2591	1	8	yes	direct product factor
287	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
288	C₂×C₁₃	C₂²×#124	1	1	yes	characteristic
289	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
290	C₂×C₁₃	C₂×#553	1	4	yes	—
291	C₂⁴	—	2	4	no	—
292	C₂⁴	—	2	4	no	—
293	C₂⁴	—	2	4	no	—
294	C₂⁴	—	2	8	no	—
295	C₂⁴	—	2	8	no	—
296	C₂⁴	—	2	8	no	—
297	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
298	C₂⁴	C₁₃×#41	1	8	yes	—
299	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
300	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
301	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
302	C₂×D₄	—	2	16	no	—
303	C₂×D₄	—	2	32	no	—
304	C₂×D₄	—	2	8	no	—
305	C₂×D₄	—	4	8	no	—
306	C₂×D₄	—	4	16	no	—
307	C₂×D₄	—	4	32	no	—
308	C₂²×C₄	—	2	32	no	—
309	C₂²×C₄	—	2	8	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	16	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	8	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	8	no	—
319	C₂²×C₄	—	2	8	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	2	8	no	—
322	C₂²×C₄	—	2	8	no	—
323	C₂²×C₄	—	4	16	no	—
324	C₂²×C₄	—	4	8	no	—
325	C₂²×C₄	—	4	8	no	—
326	C₂²×C₄	—	4	16	no	—
327	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
328	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
329	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	—
330	C₂²×C₄	C₁₃×#41	1	8	yes	—
331	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
332	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
333	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
334	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
335	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
336	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
337	C₄⋊C₄	—	2	16	no	—
338	C₄⋊C₄	—	2	16	no	—
339	C₄⋊C₄	—	2	8	no	—
340	C₂²⋊C₄	—	2	16	no	—
341	C₂²⋊C₄	—	2	16	no	—
342	C₂²⋊C₄	—	2	32	no	—
343	C₂²⋊C₄	—	4	16	no	—
344	C₄²	—	4	8	no	—
345	C₁₃	C₂×#2591	1	1	yes	characteristic, direct product factor, Sylow
346	C₂³	—	2	8	no	—
347	C₂³	—	2	8	no	—
348	C₂³	—	2	32	no	—
349	C₂³	—	2	4	no	—
350	C₂³	—	2	4	no	—
351	C₂³	—	2	4	no	—
352	C₂³	—	2	8	no	—
353	C₂³	—	2	8	no	—
354	C₂³	—	2	8	no	—
355	C₂³	—	4	8	no	—
356	C₂³	—	4	8	no	—
357	C₂³	—	4	8	no	—
358	C₂³	—	4	32	no	—
359	C₂³	C₁₃×#124	1	16	yes	—
360	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
361	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
362	C₂³	C₂×C₁₃×#41	1	8	yes	—
363	C₂³	C₂×C₁₃×#41	1	4	yes	—
364	C₂³	C₂×C₁₃×#41	1	4	yes	—
365	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
366	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
367	D₄	—	4	16	no	—
368	D₄	—	4	32	no	—
369	C₂×C₄	—	2	32	no	—
370	C₂×C₄	—	2	16	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	8	no	—
380	C₂×C₄	—	2	8	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	4	16	no	—
385	C₂×C₄	—	4	16	no	—
386	C₂×C₄	—	4	8	no	—
387	C₂×C₄	—	4	8	no	—
388	C₂×C₄	—	4	16	no	—
389	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
390	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
391	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
392	C₂²	—	2	32	no	—
393	C₂²	—	2	4	no	—
394	C₂²	—	2	4	no	—
395	C₂²	—	2	16	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	4	4	no	—
398	C₂²	—	4	4	no	—
399	C₂²	—	4	16	no	—
400	C₂²	—	8	16	no	—
401	C₂²	C₁₃×#525	1	4	yes	—
402	C₂²	C₂×C₁₃×#124	1	8	yes	—
403	C₂²	C₂×C₁₃×#124	1	4	yes	—
404	C₂²	C₁₃×#534	1	4	yes	—
405	C₂²	C₁₃×#553	1	16	yes	—
406	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
407	C₂²	C₂²×C₁₃×#41	1	2	yes	—
408	C₂²	C₂²×C₁₃×#41	1	2	yes	—
409	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
410	C₄	—	2	8	no	—
411	C₄	—	2	4	no	—
412	C₄	—	2	4	no	—
413	C₄	—	4	4	no	—
414	C₄	—	4	4	no	—
415	C₄	—	4	8	no	—
416	C₂	—	2	8	no	—
417	C₂	—	8	4	no	—
418	C₂	C₁₃×#2591	1	8	yes	direct product factor
419	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
420	C₂	C₂²×C₁₃×#124	1	1	yes	characteristic
421	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
422	C₂	C₂×C₁₃×#553	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#121	C₂
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
2. C₂³×C₁₃×C₄⋊C₄	C₂	semidirect
3. C₁₃×#2591	C₂	direct (N × H)
4. C₂×C₁₃×#400	C₂	semidirect
5. C₂×C₁₃×#394	C₂	semidirect
6. C₂×C₁₃×#388	C₂	semidirect
7. C₂×C₁₃×#386	C₂	semidirect
8. C₂×C₁₃×#386	C₂	semidirect
9. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
21. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
27. C₁₃×#400	C₂²	semidirect
28. C₁₃×#394	C₂²	semidirect
29. C₁₃×#388	C₂²	semidirect
30. C₁₃×#386	C₂²	semidirect
31. C₁₃×#386	C₂²	semidirect
32. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
80. C₂×#2591	C₁₃	direct (N × H)
136. C₂³×C₄⋊C₄	C₂×C₁₃	semidirect
137. #2591	C₂×C₁₃	direct (N × H)
138. C₂×#400	C₂×C₁₃	semidirect
139. C₂×#394	C₂×C₁₃	semidirect
140. C₂×#388	C₂×C₁₃	semidirect
141. C₂×#386	C₂×C₁₃	semidirect
142. C₂×#386	C₂×C₁₃	semidirect
143. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
201. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
207. #400	C₂²×C₁₃	semidirect
208. #394	C₂²×C₁₃	semidirect
209. #388	C₂²×C₁₃	semidirect
210. #386	C₂²×C₁₃	semidirect
211. #386	C₂²×C₁₃	semidirect
212. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
286. C₂×C₁₃	#2591	direct (N × H)
345. C₁₃	C₂×#2591	direct (N × H)
418. C₂	C₁₃×#2591	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×#121	2
C₂³×C₁₃×C₄⋊C₄	2
C₁₃×#2591	2
C₂×C₁₃×#400	2
C₂×C₁₃×#394	2
C₂×C₁₃×#388	2
C₂×C₁₃×#386	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂×#2591	13

Subgroups — C2×C13×#2591 #15721189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2591 #15721189