Subgroups — C₂×C₁₃×#2535 #15721224

Order 3328.

4390 conjugacy classes of subgroups.

The subgroup lattice has 484 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	2	yes	maximal, complemented
2	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2535	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₃×#397	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#392	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#386	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₃×#382	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#380	C₂	1	2	yes	maximal, complemented
10	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₁₃	C₂²	1	4	yes	—
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
15	C₂×C₁₃×#121	—	2	16	no	—
16	C₂×C₁₃×#121	C₂²	1	16	yes	complemented
17	C₂×C₄×D₄×C₁₃	—	2	8	no	—
18	C₂×C₄×D₄×C₁₃	—	2	8	no	—
19	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
20	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
28	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#397	C₂²	1	16	yes	complemented
30	C₁₃×#392	C₂²	1	16	yes	complemented
31	C₁₃×#386	C₂²	1	32	yes	complemented
32	C₁₃×#382	C₂²	1	8	yes	complemented
33	C₁₃×#380	C₂²	1	16	yes	complemented
34	C₂×C₁₃×#95	C₂²	1	4	yes	—
35	C₂×C₁₃×#95	C₂²	1	2	yes	—
36	C₂×C₁₃×#95	C₂²	1	2	yes	—
37	C₂⁵×C₁₃	C₂³	1	2	yes	—
38	C₂⁵×C₁₃	C₂³	1	2	yes	—
39	C₂²×D₄×C₁₃	—	2	8	no	—
40	C₂²×D₄×C₁₃	—	2	16	no	—
41	C₂²×D₄×C₁₃	—	2	16	no	—
42	C₂²×D₄×C₁₃	—	2	4	no	—
43	C₂²×D₄×C₁₃	—	2	4	no	—
44	C₂²×D₄×C₁₃	—	2	4	no	—
45	C₂²×D₄×C₁₃	—	4	8	no	—
46	C₂²×D₄×C₁₃	D₄	1	8	yes	complemented
47	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
48	C₂²×D₄×C₁₃	C₂³	1	16	yes	—
49	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
50	C₂³×C₄×C₁₃	—	2	8	no	—
51	C₂³×C₄×C₁₃	—	2	8	no	—
52	C₂³×C₄×C₁₃	—	2	8	no	—
53	C₂³×C₄×C₁₃	—	2	8	no	—
54	C₂³×C₄×C₁₃	—	4	8	no	—
55	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
56	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
62	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₁₃×#121	—	2	64	no	—
64	C₄×D₄×C₁₃	—	2	32	no	—
65	C₄×D₄×C₁₃	—	2	32	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
76	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
77	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
78	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
79	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
80	C₂×C₄²×C₁₃	D₄	1	8	yes	complemented
81	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
82	C₁₃×#95	C₂³	1	16	yes	—
83	C₁₃×#95	C₂³	1	8	yes	—
84	C₁₃×#95	C₂³	1	8	yes	—
85	C₂×#2535	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₃	—	2	4	no	—
87	C₂⁴×C₁₃	—	2	4	no	—
88	C₂⁴×C₁₃	—	2	4	no	—
89	C₂⁴×C₁₃	—	2	4	no	—
90	C₂⁴×C₁₃	—	2	4	no	—
91	C₂⁴×C₁₃	—	2	4	no	—
92	C₂⁴×C₁₃	—	2	8	no	—
93	C₂⁴×C₁₃	—	2	4	no	—
94	C₂⁴×C₁₃	—	2	8	no	—
95	C₂⁴×C₁₃	—	2	4	no	—
96	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
97	C₂⁴×C₁₃	#41	1	8	yes	—
98	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
99	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
100	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
101	C₂×D₄×C₁₃	—	2	32	no	—
102	C₂×D₄×C₁₃	—	2	16	no	—
103	C₂×D₄×C₁₃	—	2	32	no	—
104	C₂×D₄×C₁₃	—	2	32	no	—
105	C₂×D₄×C₁₃	—	2	32	no	—
106	C₂×D₄×C₁₃	—	2	8	no	—
107	C₂×D₄×C₁₃	—	2	8	no	—
108	C₂×D₄×C₁₃	—	2	8	no	—
109	C₂×D₄×C₁₃	—	4	16	no	—
110	C₂×D₄×C₁₃	—	4	64	no	—
111	C₂×D₄×C₁₃	C₂×D₄	1	16	yes	complemented
112	C₂²×C₄×C₁₃	—	2	4	no	—
113	C₂²×C₄×C₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₃	—	2	4	no	—
117	C₂²×C₄×C₁₃	—	2	8	no	—
118	C₂²×C₄×C₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₃	—	2	8	no	—
120	C₂²×C₄×C₁₃	—	2	8	no	—
121	C₂²×C₄×C₁₃	—	2	8	no	—
122	C₂²×C₄×C₁₃	—	2	16	no	—
123	C₂²×C₄×C₁₃	—	2	16	no	—
124	C₂²×C₄×C₁₃	—	2	16	no	—
125	C₂²×C₄×C₁₃	—	2	16	no	—
126	C₂²×C₄×C₁₃	—	4	16	no	—
127	C₂²×C₄×C₁₃	—	4	32	no	—
128	C₂²×C₄×C₁₃	—	4	32	no	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
133	C₂²×C₄×C₁₃	#41	1	4	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
140	C₁₃×C₄⋊C₄	—	2	8	no	—
141	C₁₃×C₄⋊C₄	—	2	8	no	—
142	C₁₃×C₄⋊C₄	—	2	16	no	—
143	C₁₃×C₂²⋊C₄	—	2	32	no	—
144	C₁₃×C₂²⋊C₄	—	2	16	no	—
145	C₁₃×C₂²⋊C₄	—	2	16	no	—
146	C₁₃×C₂²⋊C₄	—	4	16	no	—
147	C₄²×C₁₃	C₂×D₄	1	16	yes	complemented
148	C₂²×#121	C₂×C₁₃	1	2	yes	complemented
149	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
150	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#2535	C₂×C₁₃	1	16	yes	direct product factor
152	C₂×#397	C₂×C₁₃	1	2	yes	complemented
153	C₂×#392	C₂×C₁₃	1	2	yes	complemented
154	C₂×#386	C₂×C₁₃	1	4	yes	complemented
155	C₂×#382	C₂×C₁₃	1	1	yes	characteristic, complemented
156	C₂×#380	C₂×C₁₃	1	2	yes	complemented
157	C₂³×C₁₃	—	2	16	no	—
158	C₂³×C₁₃	—	2	16	no	—
159	C₂³×C₁₃	—	2	16	no	—
160	C₂³×C₁₃	—	2	32	no	—
161	C₂³×C₁₃	—	2	16	no	—
162	C₂³×C₁₃	—	2	4	no	—
163	C₂³×C₁₃	—	2	4	no	—
164	C₂³×C₁₃	—	2	4	no	—
165	C₂³×C₁₃	—	2	4	no	—
166	C₂³×C₁₃	—	2	4	no	—
167	C₂³×C₁₃	—	2	4	no	—
168	C₂³×C₁₃	—	2	8	no	—
169	C₂³×C₁₃	—	2	4	no	—
170	C₂³×C₁₃	—	2	8	no	—
171	C₂³×C₁₃	—	2	4	no	—
172	C₂³×C₁₃	—	4	8	no	—
173	C₂³×C₁₃	—	4	8	no	—
174	C₂³×C₁₃	—	4	8	no	—
175	C₂³×C₁₃	—	4	8	no	—
176	C₂³×C₁₃	—	4	8	no	—
177	C₂³×C₁₃	—	4	8	no	—
178	C₂³×C₁₃	—	4	16	no	—
179	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
180	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
181	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
182	C₂³×C₁₃	C₂×#41	1	8	yes	—
183	C₂³×C₁₃	C₂×#41	1	2	yes	—
184	C₂³×C₁₃	C₂×#41	1	4	yes	—
185	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
186	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
187	D₄×C₁₃	—	2	32	no	—
188	D₄×C₁₃	—	2	32	no	—
189	D₄×C₁₃	—	4	64	no	—
190	C₂×C₄×C₁₃	—	2	8	no	—
191	C₂×C₄×C₁₃	—	2	8	no	—
192	C₂×C₄×C₁₃	—	2	4	no	—
193	C₂×C₄×C₁₃	—	2	4	no	—
194	C₂×C₄×C₁₃	—	2	4	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	2	4	no	—
197	C₂×C₄×C₁₃	—	2	8	no	—
198	C₂×C₄×C₁₃	—	2	4	no	—
199	C₂×C₄×C₁₃	—	2	8	no	—
200	C₂×C₄×C₁₃	—	2	8	no	—
201	C₂×C₄×C₁₃	—	2	8	no	—
202	C₂×C₄×C₁₃	—	4	32	no	—
203	C₂×C₄×C₁₃	—	4	8	no	—
204	C₂×C₄×C₁₃	—	4	8	no	—
205	C₂×C₄×C₁₃	—	4	16	no	—
206	C₂×C₄×C₁₃	—	4	32	no	—
207	C₂×C₄×C₁₃	#121	1	16	yes	—
208	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
209	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
210	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
211	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
212	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
213	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
214	C₂³×D₄	C₂²×C₁₃	1	4	yes	—
215	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
216	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
217	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
218	C₂×#121	—	2	16	no	—
219	C₂×#121	C₂²×C₁₃	1	16	yes	complemented
220	C₂×C₄×D₄	—	2	8	no	—
221	C₂×C₄×D₄	—	2	8	no	—
222	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
223	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
224	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
225	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
226	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
227	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
228	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
229	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
230	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
231	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
232	#397	C₂²×C₁₃	1	16	yes	complemented
233	#392	C₂²×C₁₃	1	16	yes	complemented
234	#386	C₂²×C₁₃	1	32	yes	complemented
235	#382	C₂²×C₁₃	1	8	yes	complemented
236	#380	C₂²×C₁₃	1	16	yes	complemented
237	C₂×#95	C₂²×C₁₃	1	2	yes	—
238	C₂×#95	C₂²×C₁₃	1	4	yes	—
239	C₂×#95	C₂²×C₁₃	1	2	yes	—
240	C₂²×C₁₃	—	2	8	no	—
241	C₂²×C₁₃	—	2	8	no	—
242	C₂²×C₁₃	—	2	8	no	—
243	C₂²×C₁₃	—	2	16	no	—
244	C₂²×C₁₃	—	2	8	no	—
245	C₂²×C₁₃	—	4	4	no	—
246	C₂²×C₁₃	—	4	4	no	—
247	C₂²×C₁₃	—	4	4	no	—
248	C₂²×C₁₃	—	4	4	no	—
249	C₂²×C₁₃	—	4	4	no	—
250	C₂²×C₁₃	—	4	4	no	—
251	C₂²×C₁₃	—	4	8	no	—
252	C₂²×C₁₃	—	4	32	no	—
253	C₂²×C₁₃	—	4	32	no	—
254	C₂²×C₁₃	C₂×#121	1	4	yes	—
255	C₂²×C₁₃	#525	1	4	yes	—
256	C₂²×C₁₃	#535	1	4	yes	—
257	C₂²×C₁₃	#546	1	8	yes	—
258	C₂²×C₁₃	#553	1	8	yes	—
259	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
260	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
261	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
262	C₂²×C₁₃	C₂²×#41	1	2	yes	—
263	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
264	C₄×C₁₃	—	2	4	no	—
265	C₄×C₁₃	—	2	4	no	—
266	C₄×C₁₃	—	4	4	no	—
267	C₄×C₁₃	—	4	4	no	—
268	C₄×C₁₃	—	4	8	no	—
269	C₄×C₁₃	C₂×#121	1	8	yes	—
270	C₂⁵	C₂³×C₁₃	1	2	yes	—
271	C₂⁵	C₂³×C₁₃	1	2	yes	—
272	C₂²×D₄	—	2	8	no	—
273	C₂²×D₄	—	2	16	no	—
274	C₂²×D₄	—	2	16	no	—
275	C₂²×D₄	—	2	4	no	—
276	C₂²×D₄	—	2	4	no	—
277	C₂²×D₄	—	2	4	no	—
278	C₂²×D₄	—	4	8	no	—
279	C₂²×D₄	D₄×C₁₃	1	8	yes	complemented
280	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
281	C₂²×D₄	C₂³×C₁₃	1	16	yes	—
282	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
283	C₂³×C₄	—	2	8	no	—
284	C₂³×C₄	—	2	8	no	—
285	C₂³×C₄	—	2	8	no	—
286	C₂³×C₄	—	2	8	no	—
287	C₂³×C₄	—	4	8	no	—
288	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
289	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
290	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
291	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
292	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
293	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
294	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
295	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
296	#121	—	2	64	no	—
297	C₄×D₄	—	2	32	no	—
298	C₄×D₄	—	2	32	no	—
299	C₂×C₄⋊C₄	—	2	4	no	—
300	C₂×C₄⋊C₄	—	2	4	no	—
301	C₂×C₄⋊C₄	—	2	8	no	—
302	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
303	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
304	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
305	C₂×C₂²⋊C₄	—	2	16	no	—
306	C₂×C₂²⋊C₄	—	2	8	no	—
307	C₂×C₂²⋊C₄	—	2	8	no	—
308	C₂×C₂²⋊C₄	—	4	8	no	—
309	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
310	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
311	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
312	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
313	C₂×C₄²	D₄×C₁₃	1	8	yes	complemented
314	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
315	#95	C₂³×C₁₃	1	16	yes	—
316	#95	C₂³×C₁₃	1	8	yes	—
317	#95	C₂³×C₁₃	1	8	yes	—
318	C₂×C₁₃	—	4	8	no	—
319	C₂×C₁₃	—	4	8	no	—
320	C₂×C₁₃	#2535	1	8	yes	direct product factor
321	C₂×C₁₃	C₂²×#121	1	1	yes	characteristic
322	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
323	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
324	C₂×C₁₃	C₂×#546	1	2	yes	—
325	C₂×C₁₃	C₂×#553	1	2	yes	—
326	C₂⁴	—	2	4	no	—
327	C₂⁴	—	2	4	no	—
328	C₂⁴	—	2	4	no	—
329	C₂⁴	—	2	4	no	—
330	C₂⁴	—	2	4	no	—
331	C₂⁴	—	2	4	no	—
332	C₂⁴	—	2	8	no	—
333	C₂⁴	—	2	4	no	—
334	C₂⁴	—	2	8	no	—
335	C₂⁴	—	2	4	no	—
336	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
337	C₂⁴	C₁₃×#41	1	8	yes	—
338	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
339	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
340	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
341	C₂×D₄	—	2	32	no	—
342	C₂×D₄	—	2	16	no	—
343	C₂×D₄	—	2	32	no	—
344	C₂×D₄	—	2	32	no	—
345	C₂×D₄	—	2	32	no	—
346	C₂×D₄	—	2	8	no	—
347	C₂×D₄	—	2	8	no	—
348	C₂×D₄	—	2	8	no	—
349	C₂×D₄	—	4	16	no	—
350	C₂×D₄	—	4	64	no	—
351	C₂×D₄	C₂×D₄×C₁₃	1	16	yes	complemented
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	8	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	8	no	—
360	C₂²×C₄	—	2	8	no	—
361	C₂²×C₄	—	2	8	no	—
362	C₂²×C₄	—	2	16	no	—
363	C₂²×C₄	—	2	16	no	—
364	C₂²×C₄	—	2	16	no	—
365	C₂²×C₄	—	2	16	no	—
366	C₂²×C₄	—	4	16	no	—
367	C₂²×C₄	—	4	32	no	—
368	C₂²×C₄	—	4	32	no	—
369	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
370	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
371	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
372	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
373	C₂²×C₄	C₁₃×#41	1	4	yes	—
374	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
375	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
376	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
377	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
378	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
379	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
380	C₄⋊C₄	—	2	8	no	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	2	16	no	—
383	C₂²⋊C₄	—	2	32	no	—
384	C₂²⋊C₄	—	2	16	no	—
385	C₂²⋊C₄	—	2	16	no	—
386	C₂²⋊C₄	—	4	16	no	—
387	C₄²	C₂×D₄×C₁₃	1	16	yes	complemented
388	C₁₃	C₂×#2535	1	1	yes	characteristic, direct product factor, Sylow
389	C₂³	—	2	16	no	—
390	C₂³	—	2	16	no	—
391	C₂³	—	2	16	no	—
392	C₂³	—	2	32	no	—
393	C₂³	—	2	16	no	—
394	C₂³	—	2	4	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	2	4	no	—
398	C₂³	—	2	4	no	—
399	C₂³	—	2	4	no	—
400	C₂³	—	2	8	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	2	8	no	—
403	C₂³	—	2	4	no	—
404	C₂³	—	4	8	no	—
405	C₂³	—	4	8	no	—
406	C₂³	—	4	8	no	—
407	C₂³	—	4	8	no	—
408	C₂³	—	4	8	no	—
409	C₂³	—	4	8	no	—
410	C₂³	—	4	16	no	—
411	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
412	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
413	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
414	C₂³	C₂×C₁₃×#41	1	8	yes	—
415	C₂³	C₂×C₁₃×#41	1	2	yes	—
416	C₂³	C₂×C₁₃×#41	1	4	yes	—
417	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
418	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
419	D₄	—	2	32	no	—
420	D₄	—	2	32	no	—
421	D₄	—	4	64	no	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	8	no	—
434	C₂×C₄	—	4	32	no	—
435	C₂×C₄	—	4	8	no	—
436	C₂×C₄	—	4	8	no	—
437	C₂×C₄	—	4	16	no	—
438	C₂×C₄	—	4	32	no	—
439	C₂×C₄	C₁₃×#121	1	16	yes	—
440	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
441	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
442	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
443	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
444	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
445	C₂²	—	2	8	no	—
446	C₂²	—	2	8	no	—
447	C₂²	—	2	8	no	—
448	C₂²	—	2	16	no	—
449	C₂²	—	2	8	no	—
450	C₂²	—	4	32	no	—
451	C₂²	—	4	32	no	—
452	C₂²	—	4	4	no	—
453	C₂²	—	4	4	no	—
454	C₂²	—	4	4	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	4	8	no	—
459	C₂²	C₂×C₁₃×#121	1	4	yes	—
460	C₂²	C₁₃×#525	1	4	yes	—
461	C₂²	C₁₃×#535	1	4	yes	—
462	C₂²	C₁₃×#546	1	8	yes	—
463	C₂²	C₁₃×#553	1	8	yes	—
464	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
465	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
466	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
467	C₂²	C₂²×C₁₃×#41	1	2	yes	—
468	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
469	C₄	—	2	4	no	—
470	C₄	—	2	4	no	—
471	C₄	—	4	4	no	—
472	C₄	—	4	4	no	—
473	C₄	—	4	8	no	—
474	C₄	C₂×C₁₃×#121	1	8	yes	—
475	C₂	—	4	8	no	—
476	C₂	—	4	8	no	—
477	C₂	C₁₃×#2535	1	8	yes	direct product factor
478	C₂	C₂²×C₁₃×#121	1	1	yes	characteristic
479	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
480	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
481	C₂	C₂×C₁₃×#546	1	2	yes	—
482	C₂	C₂×C₁₃×#553	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
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×#121	C₂	semidirect
2. C₂²×C₄×D₄×C₁₃	C₂	semidirect
3. C₂²×C₄×D₄×C₁₃	C₂	semidirect
4. C₁₃×#2535	C₂	direct (N × H)
5. C₂×C₁₃×#397	C₂	semidirect
6. C₂×C₁₃×#392	C₂	semidirect
7. C₂×C₁₃×#386	C₂	semidirect
8. C₂×C₁₃×#382	C₂	semidirect
9. C₂×C₁₃×#380	C₂	semidirect
16. C₂×C₁₃×#121	C₂²	semidirect
19. C₂×C₄×D₄×C₁₃	C₂²	semidirect
20. C₂×C₄×D₄×C₁₃	C₂²	semidirect
29. C₁₃×#397	C₂²	semidirect
30. C₁₃×#392	C₂²	semidirect
31. C₁₃×#386	C₂²	semidirect
32. C₁₃×#382	C₂²	semidirect
33. C₁₃×#380	C₂²	semidirect
46. C₂²×D₄×C₁₃	D₄	semidirect
80. C₂×C₄²×C₁₃	D₄	semidirect
85. C₂×#2535	C₁₃	direct (N × H)
111. C₂×D₄×C₁₃	C₂×D₄	semidirect
147. C₄²×C₁₃	C₂×D₄	semidirect
148. C₂²×#121	C₂×C₁₃	semidirect
149. C₂²×C₄×D₄	C₂×C₁₃	semidirect
150. C₂²×C₄×D₄	C₂×C₁₃	semidirect
151. #2535	C₂×C₁₃	direct (N × H)
152. C₂×#397	C₂×C₁₃	semidirect
153. C₂×#392	C₂×C₁₃	semidirect
154. C₂×#386	C₂×C₁₃	semidirect
155. C₂×#382	C₂×C₁₃	semidirect
156. C₂×#380	C₂×C₁₃	semidirect
219. C₂×#121	C₂²×C₁₃	semidirect
222. C₂×C₄×D₄	C₂²×C₁₃	semidirect
223. C₂×C₄×D₄	C₂²×C₁₃	semidirect
232. #397	C₂²×C₁₃	semidirect
233. #392	C₂²×C₁₃	semidirect
234. #386	C₂²×C₁₃	semidirect
235. #382	C₂²×C₁₃	semidirect
236. #380	C₂²×C₁₃	semidirect
279. C₂²×D₄	D₄×C₁₃	semidirect
313. C₂×C₄²	D₄×C₁₃	semidirect
320. C₂×C₁₃	#2535	direct (N × H)
351. C₂×D₄	C₂×D₄×C₁₃	semidirect
387. C₄²	C₂×D₄×C₁₃	semidirect
388. C₁₃	C₂×#2535	direct (N × H)
477. C₂	C₁₃×#2535	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
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2535	2
C₂×C₁₃×#397	2
C₂×C₁₃×#392	2
C₂×C₁₃×#386	2
C₂×C₁₃×#382	2
C₂×C₁₃×#380	2
C₂×#2535	13

Subgroups — C2×C13×#2535 #15721224

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2535 #15721224