Subgroups — C₂×C₁₃×#2540 #15721226

Order 3328.

4566 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
3	C₂²×C₁₃×#121	C₂	1	2	yes	maximal, complemented
4	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2540	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₁₃×#399	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#392	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#390	C₂	1	4	yes	maximal, complemented
9	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₃	C₂²	1	4	yes	—
14	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
15	C₂×C₁₃×#124	—	2	8	no	—
16	C₂×C₁₃×#124	C₂²	1	8	yes	complemented
17	C₂×C₁₃×C₂²⋊Q₈	—	2	16	no	—
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	16	yes	complemented
19	C₂×C₁₃×#121	—	2	16	no	—
20	C₂×C₁₃×#121	C₂²	1	16	yes	complemented
21	C₂×C₄×D₄×C₁₃	—	2	8	no	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#399	C₂²	1	16	yes	complemented
34	C₁₃×#392	C₂²	1	16	yes	complemented
35	C₁₃×#390	C₂²	1	32	yes	complemented
36	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
37	C₂×C₁₃×#95	C₂²	1	2	yes	—
38	C₂⁵×C₁₃	C₂³	1	2	yes	—
39	C₂⁵×C₁₃	C₂³	1	2	yes	—
40	C₂²×Q₈×C₁₃	—	2	8	no	—
41	C₂²×Q₈×C₁₃	—	2	4	no	—
42	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
43	C₂²×D₄×C₁₃	—	2	8	no	—
44	C₂²×D₄×C₁₃	—	2	16	no	—
45	C₂²×D₄×C₁₃	—	2	4	no	—
46	C₂²×D₄×C₁₃	—	2	16	no	—
47	C₂²×D₄×C₁₃	—	2	8	no	—
48	C₂²×D₄×C₁₃	—	2	4	no	—
49	C₂²×D₄×C₁₃	—	4	8	no	—
50	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
51	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
52	C₂²×D₄×C₁₃	C₂³	1	16	yes	—
53	C₂³×C₄×C₁₃	—	2	8	no	—
54	C₂³×C₄×C₁₃	—	2	8	no	—
55	C₂³×C₄×C₁₃	—	2	8	no	—
56	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₁₃×#124	—	2	32	no	—
64	C₁₃×C₂²⋊Q₈	—	2	64	no	—
65	C₁₃×#121	—	2	64	no	—
66	C₄×D₄×C₁₃	—	2	32	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
69	C₂×C₁₃×C₄⋊C₄	D₄	1	16	yes	complemented
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
78	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
79	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
80	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
81	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
82	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
83	C₂×C₄²×C₁₃	—	4	4	no	—
84	C₂×C₄²×C₁₃	D₄	1	8	yes	complemented
85	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
86	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
87	C₁₃×#95	C₂³	1	8	yes	—
88	C₂×#2540	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	—	2	4	no	—
90	C₂⁴×C₁₃	—	2	4	no	—
91	C₂⁴×C₁₃	—	2	4	no	—
92	C₂⁴×C₁₃	—	2	4	no	—
93	C₂⁴×C₁₃	—	2	4	no	—
94	C₂⁴×C₁₃	—	2	4	no	—
95	C₂⁴×C₁₃	—	2	4	no	—
96	C₂⁴×C₁₃	—	2	8	no	—
97	C₂⁴×C₁₃	—	2	8	no	—
98	C₂⁴×C₁₃	—	2	4	no	—
99	C₂⁴×C₁₃	—	2	4	no	—
100	C₂⁴×C₁₃	#41	1	8	yes	—
101	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
102	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
103	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
104	C₂×Q₈×C₁₃	—	2	16	no	—
105	C₂×Q₈×C₁₃	—	2	8	no	—
106	C₂×Q₈×C₁₃	—	4	16	no	—
107	C₂×D₄×C₁₃	—	2	32	no	—
108	C₂×D₄×C₁₃	—	2	16	no	—
109	C₂×D₄×C₁₃	—	2	32	no	—
110	C₂×D₄×C₁₃	—	2	8	no	—
111	C₂×D₄×C₁₃	—	2	32	no	—
112	C₂×D₄×C₁₃	—	2	16	no	—
113	C₂×D₄×C₁₃	—	2	8	no	—
114	C₂×D₄×C₁₃	—	4	16	no	—
115	C₂×D₄×C₁₃	—	4	64	no	—
116	C₂×D₄×C₁₃	—	4	16	no	—
117	C₂²×C₄×C₁₃	—	2	4	no	—
118	C₂²×C₄×C₁₃	—	2	8	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	8	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	4	no	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₃	—	2	8	no	—
126	C₂²×C₄×C₁₃	—	2	4	no	—
127	C₂²×C₄×C₁₃	—	2	16	no	—
128	C₂²×C₄×C₁₃	—	2	16	no	—
129	C₂²×C₄×C₁₃	—	2	16	no	—
130	C₂²×C₄×C₁₃	—	4	32	no	—
131	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
133	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
135	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
138	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
140	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
141	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
142	C₁₃×C₄⋊C₄	—	2	8	no	—
143	C₁₃×C₄⋊C₄	—	2	32	no	—
144	C₁₃×C₄⋊C₄	C₂×D₄	1	32	yes	complemented
145	C₁₃×C₂²⋊C₄	—	2	16	no	—
146	C₁₃×C₂²⋊C₄	—	2	32	no	—
147	C₁₃×C₂²⋊C₄	—	2	32	no	—
148	C₁₃×C₂²⋊C₄	—	2	16	no	—
149	C₁₃×C₂²⋊C₄	—	2	16	no	—
150	C₄²×C₁₃	—	4	8	no	—
151	C₄²×C₁₃	C₂×D₄	1	16	yes	complemented
152	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
153	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
154	C₂²×#121	C₂×C₁₃	1	2	yes	complemented
155	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#2540	C₂×C₁₃	1	16	yes	direct product factor
157	C₂×#399	C₂×C₁₃	1	2	yes	complemented
158	C₂×#392	C₂×C₁₃	1	2	yes	complemented
159	C₂×#390	C₂×C₁₃	1	4	yes	complemented
160	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
161	C₂³×C₁₃	—	2	16	no	—
162	C₂³×C₁₃	—	2	16	no	—
163	C₂³×C₁₃	—	2	16	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	4	no	—
169	C₂³×C₁₃	—	2	4	no	—
170	C₂³×C₁₃	—	2	4	no	—
171	C₂³×C₁₃	—	2	8	no	—
172	C₂³×C₁₃	—	2	8	no	—
173	C₂³×C₁₃	—	2	4	no	—
174	C₂³×C₁₃	—	2	4	no	—
175	C₂³×C₁₃	—	4	8	no	—
176	C₂³×C₁₃	—	4	8	no	—
177	C₂³×C₁₃	—	4	8	no	—
178	C₂³×C₁₃	—	4	8	no	—
179	C₂³×C₁₃	—	4	8	no	—
180	C₂³×C₁₃	—	4	8	no	—
181	C₂³×C₁₃	—	4	8	no	—
182	C₂³×C₁₃	—	4	16	no	—
183	C₂³×C₁₃	—	4	16	no	—
184	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
185	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
186	C₂³×C₁₃	C₂×#41	1	8	yes	—
187	C₂³×C₁₃	C₂×#41	1	4	yes	—
188	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
189	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
190	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
191	Q₈×C₁₃	—	4	16	no	—
192	D₄×C₁₃	—	2	32	no	—
193	D₄×C₁₃	—	4	64	no	—
194	D₄×C₁₃	—	4	16	no	—
195	C₂×C₄×C₁₃	—	2	8	no	—
196	C₂×C₄×C₁₃	—	2	8	no	—
197	C₂×C₄×C₁₃	—	2	32	no	—
198	C₂×C₄×C₁₃	—	2	4	no	—
199	C₂×C₄×C₁₃	—	2	8	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	8	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	4	no	—
204	C₂×C₄×C₁₃	—	2	4	no	—
205	C₂×C₄×C₁₃	—	2	4	no	—
206	C₂×C₄×C₁₃	—	2	8	no	—
207	C₂×C₄×C₁₃	—	2	4	no	—
208	C₂×C₄×C₁₃	—	4	8	no	—
209	C₂×C₄×C₁₃	—	4	8	no	—
210	C₂×C₄×C₁₃	—	4	32	no	—
211	C₂×C₄×C₁₃	#127	1	16	yes	—
212	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
213	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
214	C₂×C₄×C₁₃	C₂²×D₄	1	16	yes	—
215	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
216	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
217	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
218	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
219	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
220	C₂³×D₄	C₂²×C₁₃	1	4	yes	—
221	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
222	C₂×#124	—	2	8	no	—
223	C₂×#124	C₂²×C₁₃	1	8	yes	complemented
224	C₂×C₂²⋊Q₈	—	2	16	no	—
225	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	16	yes	complemented
226	C₂×#121	—	2	16	no	—
227	C₂×#121	C₂²×C₁₃	1	16	yes	complemented
228	C₂×C₄×D₄	—	2	8	no	—
229	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
230	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
231	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
232	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
233	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
234	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
235	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
236	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
237	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
238	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
239	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
240	#399	C₂²×C₁₃	1	16	yes	complemented
241	#392	C₂²×C₁₃	1	16	yes	complemented
242	#390	C₂²×C₁₃	1	32	yes	complemented
243	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
244	C₂×#95	C₂²×C₁₃	1	2	yes	—
245	C₂²×C₁₃	—	2	8	no	—
246	C₂²×C₁₃	—	2	8	no	—
247	C₂²×C₁₃	—	2	8	no	—
248	C₂²×C₁₃	—	4	4	no	—
249	C₂²×C₁₃	—	4	4	no	—
250	C₂²×C₁₃	—	4	4	no	—
251	C₂²×C₁₃	—	4	4	no	—
252	C₂²×C₁₃	—	4	32	no	—
253	C₂²×C₁₃	—	4	4	no	—
254	C₂²×C₁₃	—	4	4	no	—
255	C₂²×C₁₃	—	4	4	no	—
256	C₂²×C₁₃	—	4	8	no	—
257	C₂²×C₁₃	—	4	8	no	—
258	C₂²×C₁₃	—	8	16	no	—
259	C₂²×C₁₃	#525	1	4	yes	—
260	C₂²×C₁₃	C₂×#127	1	4	yes	—
261	C₂²×C₁₃	#537	1	4	yes	—
262	C₂²×C₁₃	#546	1	8	yes	—
263	C₂²×C₁₃	#548	1	8	yes	—
264	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
265	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
266	C₂²×C₁₃	C₂²×#41	1	2	yes	—
267	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
268	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
269	C₄×C₁₃	—	2	4	no	—
270	C₄×C₁₃	—	2	4	no	—
271	C₄×C₁₃	—	2	16	no	—
272	C₄×C₁₃	—	4	4	no	—
273	C₄×C₁₃	—	4	4	no	—
274	C₄×C₁₃	C₂×#127	1	8	yes	—
275	C₂⁵	C₂³×C₁₃	1	2	yes	—
276	C₂⁵	C₂³×C₁₃	1	2	yes	—
277	C₂²×Q₈	—	2	8	no	—
278	C₂²×Q₈	—	2	4	no	—
279	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
280	C₂²×D₄	—	2	8	no	—
281	C₂²×D₄	—	2	16	no	—
282	C₂²×D₄	—	2	4	no	—
283	C₂²×D₄	—	2	16	no	—
284	C₂²×D₄	—	2	8	no	—
285	C₂²×D₄	—	2	4	no	—
286	C₂²×D₄	—	4	8	no	—
287	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
288	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
289	C₂²×D₄	C₂³×C₁₃	1	16	yes	—
290	C₂³×C₄	—	2	8	no	—
291	C₂³×C₄	—	2	8	no	—
292	C₂³×C₄	—	2	8	no	—
293	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
294	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
295	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
296	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
297	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
298	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
299	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
300	#124	—	2	32	no	—
301	C₂²⋊Q₈	—	2	64	no	—
302	#121	—	2	64	no	—
303	C₄×D₄	—	2	32	no	—
304	C₂×C₄⋊C₄	—	2	4	no	—
305	C₂×C₄⋊C₄	—	2	16	no	—
306	C₂×C₄⋊C₄	D₄×C₁₃	1	16	yes	complemented
307	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
308	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
309	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
310	C₂×C₂²⋊C₄	—	2	8	no	—
311	C₂×C₂²⋊C₄	—	2	16	no	—
312	C₂×C₂²⋊C₄	—	2	16	no	—
313	C₂×C₂²⋊C₄	—	2	8	no	—
314	C₂×C₂²⋊C₄	—	2	8	no	—
315	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
316	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
317	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
318	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
319	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
320	C₂×C₄²	—	4	4	no	—
321	C₂×C₄²	D₄×C₁₃	1	8	yes	complemented
322	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
323	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
324	#95	C₂³×C₁₃	1	8	yes	—
325	C₂×C₁₃	—	4	8	no	—
326	C₂×C₁₃	—	8	4	no	—
327	C₂×C₁₃	#2540	1	8	yes	direct product factor
328	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
329	C₂×C₁₃	C₂²×#127	1	1	yes	characteristic
330	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
331	C₂×C₁₃	C₂×#546	1	2	yes	—
332	C₂×C₁₃	C₂×#548	1	2	yes	—
333	C₂⁴	—	2	4	no	—
334	C₂⁴	—	2	4	no	—
335	C₂⁴	—	2	4	no	—
336	C₂⁴	—	2	4	no	—
337	C₂⁴	—	2	4	no	—
338	C₂⁴	—	2	4	no	—
339	C₂⁴	—	2	4	no	—
340	C₂⁴	—	2	8	no	—
341	C₂⁴	—	2	8	no	—
342	C₂⁴	—	2	4	no	—
343	C₂⁴	—	2	4	no	—
344	C₂⁴	C₁₃×#41	1	8	yes	—
345	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
346	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
347	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
348	C₂×Q₈	—	2	16	no	—
349	C₂×Q₈	—	2	8	no	—
350	C₂×Q₈	—	4	16	no	—
351	C₂×D₄	—	2	32	no	—
352	C₂×D₄	—	2	16	no	—
353	C₂×D₄	—	2	32	no	—
354	C₂×D₄	—	2	8	no	—
355	C₂×D₄	—	2	32	no	—
356	C₂×D₄	—	2	16	no	—
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	—	4	16	no	—
359	C₂×D₄	—	4	64	no	—
360	C₂×D₄	—	4	16	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	8	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	8	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	16	no	—
372	C₂²×C₄	—	2	16	no	—
373	C₂²×C₄	—	2	16	no	—
374	C₂²×C₄	—	4	32	no	—
375	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
376	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
377	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	—
378	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
379	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
380	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
381	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
382	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
383	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
384	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
385	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
386	C₄⋊C₄	—	2	8	no	—
387	C₄⋊C₄	—	2	32	no	—
388	C₄⋊C₄	C₂×D₄×C₁₃	1	32	yes	complemented
389	C₂²⋊C₄	—	2	16	no	—
390	C₂²⋊C₄	—	2	32	no	—
391	C₂²⋊C₄	—	2	32	no	—
392	C₂²⋊C₄	—	2	16	no	—
393	C₂²⋊C₄	—	2	16	no	—
394	C₄²	—	4	8	no	—
395	C₄²	C₂×D₄×C₁₃	1	16	yes	complemented
396	C₁₃	C₂×#2540	1	1	yes	characteristic, direct product factor, Sylow
397	C₂³	—	2	16	no	—
398	C₂³	—	2	16	no	—
399	C₂³	—	2	16	no	—
400	C₂³	—	2	4	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	2	4	no	—
403	C₂³	—	2	4	no	—
404	C₂³	—	2	4	no	—
405	C₂³	—	2	4	no	—
406	C₂³	—	2	4	no	—
407	C₂³	—	2	8	no	—
408	C₂³	—	2	8	no	—
409	C₂³	—	2	4	no	—
410	C₂³	—	2	4	no	—
411	C₂³	—	4	8	no	—
412	C₂³	—	4	8	no	—
413	C₂³	—	4	8	no	—
414	C₂³	—	4	8	no	—
415	C₂³	—	4	8	no	—
416	C₂³	—	4	8	no	—
417	C₂³	—	4	8	no	—
418	C₂³	—	4	16	no	—
419	C₂³	—	4	16	no	—
420	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
421	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
422	C₂³	C₂×C₁₃×#41	1	8	yes	—
423	C₂³	C₂×C₁₃×#41	1	4	yes	—
424	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
425	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
426	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
427	Q₈	—	4	16	no	—
428	D₄	—	2	32	no	—
429	D₄	—	4	64	no	—
430	D₄	—	4	16	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	32	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	8	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	8	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	4	8	no	—
445	C₂×C₄	—	4	8	no	—
446	C₂×C₄	—	4	32	no	—
447	C₂×C₄	C₁₃×#127	1	16	yes	—
448	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
449	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
450	C₂×C₄	C₂²×D₄×C₁₃	1	16	yes	—
451	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
452	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
453	C₂²	—	2	8	no	—
454	C₂²	—	2	8	no	—
455	C₂²	—	2	8	no	—
456	C₂²	—	4	32	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	4	4	no	—
464	C₂²	—	4	8	no	—
465	C₂²	—	4	8	no	—
466	C₂²	—	8	16	no	—
467	C₂²	C₁₃×#525	1	4	yes	—
468	C₂²	C₂×C₁₃×#127	1	4	yes	—
469	C₂²	C₁₃×#537	1	4	yes	—
470	C₂²	C₁₃×#546	1	8	yes	—
471	C₂²	C₁₃×#548	1	8	yes	—
472	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
473	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
474	C₂²	C₂²×C₁₃×#41	1	2	yes	—
475	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
476	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
477	C₄	—	2	4	no	—
478	C₄	—	2	4	no	—
479	C₄	—	2	16	no	—
480	C₄	—	4	4	no	—
481	C₄	—	4	4	no	—
482	C₄	C₂×C₁₃×#127	1	8	yes	—
483	C₂	—	4	8	no	—
484	C₂	—	8	4	no	—
485	C₂	C₁₃×#2540	1	8	yes	direct product factor
486	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
487	C₂	C₂²×C₁₃×#127	1	1	yes	characteristic
488	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
489	C₂	C₂×C₁₃×#546	1	2	yes	—
490	C₂	C₂×C₁₃×#548	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×#124	C₂	semidirect
2. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
3. C₂²×C₁₃×#121	C₂	semidirect
4. C₂²×C₄×D₄×C₁₃	C₂	semidirect
5. C₁₃×#2540	C₂	direct (N × H)
6. C₂×C₁₃×#399	C₂	semidirect
7. C₂×C₁₃×#392	C₂	semidirect
8. C₂×C₁₃×#390	C₂	semidirect
9. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
16. C₂×C₁₃×#124	C₂²	semidirect
18. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
20. C₂×C₁₃×#121	C₂²	semidirect
22. C₂×C₄×D₄×C₁₃	C₂²	semidirect
33. C₁₃×#399	C₂²	semidirect
34. C₁₃×#392	C₂²	semidirect
35. C₁₃×#390	C₂²	semidirect
36. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
69. C₂×C₁₃×C₄⋊C₄	D₄	semidirect
84. C₂×C₄²×C₁₃	D₄	semidirect
88. C₂×#2540	C₁₃	direct (N × H)
144. C₁₃×C₄⋊C₄	C₂×D₄	semidirect
151. C₄²×C₁₃	C₂×D₄	semidirect
152. C₂²×#124	C₂×C₁₃	semidirect
153. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
154. C₂²×#121	C₂×C₁₃	semidirect
155. C₂²×C₄×D₄	C₂×C₁₃	semidirect
156. #2540	C₂×C₁₃	direct (N × H)
157. C₂×#399	C₂×C₁₃	semidirect
158. C₂×#392	C₂×C₁₃	semidirect
159. C₂×#390	C₂×C₁₃	semidirect
160. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
223. C₂×#124	C₂²×C₁₃	semidirect
225. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
227. C₂×#121	C₂²×C₁₃	semidirect
229. C₂×C₄×D₄	C₂²×C₁₃	semidirect
240. #399	C₂²×C₁₃	semidirect
241. #392	C₂²×C₁₃	semidirect
242. #390	C₂²×C₁₃	semidirect
243. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
306. C₂×C₄⋊C₄	D₄×C₁₃	semidirect
321. C₂×C₄²	D₄×C₁₃	semidirect
327. C₂×C₁₃	#2540	direct (N × H)
388. C₄⋊C₄	C₂×D₄×C₁₃	semidirect
395. C₄²	C₂×D₄×C₁₃	semidirect
396. C₁₃	C₂×#2540	direct (N × H)
485. C₂	C₁₃×#2540	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×#124	2
C₂²×C₁₃×C₂²⋊Q₈	2
C₂²×C₁₃×#121	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2540	2
C₂×C₁₃×#399	2
C₂×C₁₃×#392	2
C₂×C₁₃×#390	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×#2540	13

Subgroups — C2×C13×#2540 #15721226

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2540 #15721226