Subgroups — C₂×C₁₃×#2491 #15721098

Order 3328.

3678 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#124	C₂	1	2	yes	maximal, complemented
3	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2491	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₃×#394	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#393	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#388	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
14	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊Q₈	—	2	8	no	—
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	8	yes	complemented
19	C₂×C₁₃×#124	—	2	16	no	—
20	C₂×C₁₃×#124	C₂²	1	16	yes	complemented
21	C₂×C₁₃×#121	—	2	8	no	—
22	C₂×C₁₃×#121	C₂²	1	8	yes	—
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
38	C₁₃×#394	C₂²	1	16	yes	complemented
39	C₁₃×#393	C₂²	1	16	yes	complemented
40	C₁₃×#390	C₂²	1	8	yes	complemented
41	C₁₃×#390	C₂²	1	8	yes	complemented
42	C₁₃×#388	C₂²	1	16	yes	complemented
43	C₁₃×#380	C₂²	1	8	yes	complemented
44	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
45	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
46	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#95	C₂²	1	2	yes	—
49	C₂×C₁₃×#95	C₂²	1	2	yes	—
50	C₂⁵×C₁₃	C₂³	1	2	yes	—
51	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×Q₈×C₁₃	—	2	8	no	—
53	C₂²×Q₈×C₁₃	—	2	8	no	—
54	C₂²×Q₈×C₁₃	—	4	4	no	—
55	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
56	C₂²×D₄×C₁₃	—	2	8	no	—
57	C₂²×D₄×C₁₃	—	2	8	no	—
58	C₂²×D₄×C₁₃	—	2	4	no	—
59	C₂²×D₄×C₁₃	—	2	4	no	—
60	C₂²×D₄×C₁₃	—	2	4	no	—
61	C₂²×D₄×C₁₃	—	4	4	no	—
62	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
63	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
64	C₂³×C₄×C₁₃	—	2	4	no	—
65	C₂³×C₄×C₁₃	—	2	4	no	—
66	C₂³×C₄×C₁₃	—	2	4	no	—
67	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
68	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
69	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₁₃×C₄⋊Q₈	—	2	32	no	—
78	C₁₃×#124	—	2	64	no	—
79	C₁₃×#121	—	2	32	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
83	C₂×C₁₃×C₄⋊C₄	D₄	1	8	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
88	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
90	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
95	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	complemented
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
97	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
98	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
99	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
100	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
103	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
104	C₂×C₄²×C₁₃	—	2	8	no	—
105	C₂×C₄²×C₁₃	—	2	4	no	—
106	C₂×C₄²×C₁₃	—	2	4	no	—
107	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
108	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
109	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
110	C₁₃×#95	C₂³	1	4	yes	—
111	C₁₃×#95	C₂³	1	4	yes	—
112	C₁₃×#95	C₂³	1	8	yes	—
113	C₁₃×#95	C₂³	1	8	yes	—
114	C₂×#2491	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂⁴×C₁₃	—	2	2	no	—
116	C₂⁴×C₁₃	—	2	2	no	—
117	C₂⁴×C₁₃	—	2	2	no	—
118	C₂⁴×C₁₃	—	2	2	no	—
119	C₂⁴×C₁₃	—	2	2	no	—
120	C₂⁴×C₁₃	—	2	2	no	—
121	C₂⁴×C₁₃	—	2	4	no	—
122	C₂⁴×C₁₃	—	2	4	no	—
123	C₂⁴×C₁₃	—	2	4	no	—
124	C₂⁴×C₁₃	—	2	4	no	—
125	C₂⁴×C₁₃	—	2	4	no	—
126	C₂⁴×C₁₃	—	2	4	no	—
127	C₂⁴×C₁₃	—	2	4	no	—
128	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
129	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
130	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
131	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
132	C₂×Q₈×C₁₃	—	2	16	no	—
133	C₂×Q₈×C₁₃	—	2	16	no	—
134	C₂×Q₈×C₁₃	—	4	8	no	—
135	C₂×Q₈×C₁₃	—	4	32	no	—
136	C₂×D₄×C₁₃	—	2	16	no	—
137	C₂×D₄×C₁₃	—	2	16	no	—
138	C₂×D₄×C₁₃	—	2	8	no	—
139	C₂×D₄×C₁₃	—	2	8	no	—
140	C₂×D₄×C₁₃	—	2	8	no	—
141	C₂×D₄×C₁₃	—	4	8	no	—
142	C₂×D₄×C₁₃	—	4	32	no	—
143	C₂×D₄×C₁₃	—	4	16	no	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	—	2	4	no	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	—	2	2	no	—
148	C₂²×C₄×C₁₃	—	2	4	no	—
149	C₂²×C₄×C₁₃	—	2	2	no	—
150	C₂²×C₄×C₁₃	—	2	2	no	—
151	C₂²×C₄×C₁₃	—	2	2	no	—
152	C₂²×C₄×C₁₃	—	2	4	no	—
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	—	2	4	no	—
155	C₂²×C₄×C₁₃	—	2	4	no	—
156	C₂²×C₄×C₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₃	—	2	4	no	—
158	C₂²×C₄×C₁₃	—	2	2	no	—
159	C₂²×C₄×C₁₃	—	2	4	no	—
160	C₂²×C₄×C₁₃	—	2	2	no	—
161	C₂²×C₄×C₁₃	—	2	2	no	—
162	C₂²×C₄×C₁₃	—	2	2	no	—
163	C₂²×C₄×C₁₃	—	2	4	no	—
164	C₂²×C₄×C₁₃	—	2	8	no	—
165	C₂²×C₄×C₁₃	—	2	8	no	—
166	C₂²×C₄×C₁₃	—	2	8	no	—
167	C₂²×C₄×C₁₃	—	4	16	no	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
170	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
171	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
172	C₂²×C₄×C₁₃	#41	1	4	yes	—
173	C₂²×C₄×C₁₃	#41	1	4	yes	—
174	C₂²×C₄×C₁₃	#41	1	4	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
184	C₁₃×C₄⋊C₄	—	2	16	no	—
185	C₁₃×C₄⋊C₄	—	2	8	no	—
186	C₁₃×C₄⋊C₄	—	2	8	no	—
187	C₁₃×C₄⋊C₄	C₂×D₄	1	16	yes	—
188	C₁₃×C₂²⋊C₄	—	2	16	no	—
189	C₁₃×C₂²⋊C₄	—	2	16	no	—
190	C₁₃×C₂²⋊C₄	—	2	16	no	—
191	C₁₃×C₂²⋊C₄	—	2	16	no	—
192	C₁₃×C₂²⋊C₄	—	2	8	no	—
193	C₁₃×C₂²⋊C₄	—	2	16	no	—
194	C₁₃×C₂²⋊C₄	—	4	8	no	—
195	C₁₃×C₂²⋊C₄	C₂×D₄	1	16	yes	complemented
196	C₄²×C₁₃	—	2	16	no	—
197	C₄²×C₁₃	—	2	8	no	—
198	C₄²×C₁₃	—	2	8	no	—
199	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
200	C₂²×#124	C₂×C₁₃	1	2	yes	complemented
201	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic
202	#2491	C₂×C₁₃	1	16	yes	direct product factor
203	C₂×#394	C₂×C₁₃	1	2	yes	complemented
204	C₂×#393	C₂×C₁₃	1	2	yes	complemented
205	C₂×#390	C₂×C₁₃	1	1	yes	characteristic, complemented
206	C₂×#390	C₂×C₁₃	1	1	yes	characteristic, complemented
207	C₂×#388	C₂×C₁₃	1	2	yes	complemented
208	C₂×#380	C₂×C₁₃	1	1	yes	characteristic, complemented
209	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
210	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
211	C₂³×C₁₃	—	2	8	no	—
212	C₂³×C₁₃	—	2	8	no	—
213	C₂³×C₁₃	—	2	8	no	—
214	C₂³×C₁₃	—	2	2	no	—
215	C₂³×C₁₃	—	2	2	no	—
216	C₂³×C₁₃	—	2	2	no	—
217	C₂³×C₁₃	—	2	2	no	—
218	C₂³×C₁₃	—	2	2	no	—
219	C₂³×C₁₃	—	2	2	no	—
220	C₂³×C₁₃	—	2	4	no	—
221	C₂³×C₁₃	—	2	4	no	—
222	C₂³×C₁₃	—	2	4	no	—
223	C₂³×C₁₃	—	2	4	no	—
224	C₂³×C₁₃	—	2	4	no	—
225	C₂³×C₁₃	—	2	4	no	—
226	C₂³×C₁₃	—	2	4	no	—
227	C₂³×C₁₃	—	4	4	no	—
228	C₂³×C₁₃	—	4	4	no	—
229	C₂³×C₁₃	—	4	4	no	—
230	C₂³×C₁₃	—	4	4	no	—
231	C₂³×C₁₃	—	4	8	no	—
232	C₂³×C₁₃	—	4	8	no	—
233	C₂³×C₁₃	—	4	8	no	—
234	C₂³×C₁₃	—	4	8	no	—
235	C₂³×C₁₃	—	4	8	no	—
236	C₂³×C₁₃	—	4	8	no	—
237	C₂³×C₁₃	—	4	8	no	—
238	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
239	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
240	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
241	C₂³×C₁₃	C₂×#41	1	2	yes	—
242	C₂³×C₁₃	C₂×#41	1	2	yes	—
243	C₂³×C₁₃	C₂×#41	1	2	yes	—
244	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
245	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
246	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
247	Q₈×C₁₃	—	4	32	no	—
248	D₄×C₁₃	—	4	32	no	—
249	D₄×C₁₃	—	4	16	no	—
250	C₂×C₄×C₁₃	—	2	16	no	—
251	C₂×C₄×C₁₃	—	2	8	no	—
252	C₂×C₄×C₁₃	—	2	8	no	—
253	C₂×C₄×C₁₃	—	2	8	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	4	no	—
256	C₂×C₄×C₁₃	—	2	2	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	2	4	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	2	no	—
262	C₂×C₄×C₁₃	—	2	4	no	—
263	C₂×C₄×C₁₃	—	2	2	no	—
264	C₂×C₄×C₁₃	—	2	4	no	—
265	C₂×C₄×C₁₃	—	2	4	no	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	2	4	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	2	4	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	2	2	no	—
273	C₂×C₄×C₁₃	—	2	4	no	—
274	C₂×C₄×C₁₃	—	4	4	no	—
275	C₂×C₄×C₁₃	—	4	8	no	—
276	C₂×C₄×C₁₃	—	4	8	no	—
277	C₂×C₄×C₁₃	—	4	4	no	—
278	C₂×C₄×C₁₃	—	4	16	no	—
279	C₂×C₄×C₁₃	#124	1	16	yes	complemented
280	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
281	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
282	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
283	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
284	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
285	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
286	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
287	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
288	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
289	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
290	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×C₄⋊Q₈	—	2	8	no	—
292	C₂×C₄⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
293	C₂×#124	—	2	16	no	—
294	C₂×#124	C₂²×C₁₃	1	16	yes	complemented
295	C₂×#121	—	2	8	no	—
296	C₂×#121	C₂²×C₁₃	1	8	yes	—
297	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
298	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
299	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
300	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
301	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
302	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
303	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
304	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
305	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
306	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
307	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
308	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
309	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
310	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
311	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
312	#394	C₂²×C₁₃	1	16	yes	complemented
313	#393	C₂²×C₁₃	1	16	yes	complemented
314	#390	C₂²×C₁₃	1	8	yes	complemented
315	#390	C₂²×C₁₃	1	8	yes	complemented
316	#388	C₂²×C₁₃	1	16	yes	complemented
317	#380	C₂²×C₁₃	1	8	yes	complemented
318	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
319	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
320	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#95	C₂²×C₁₃	1	2	yes	—
322	C₂×#95	C₂²×C₁₃	1	2	yes	—
323	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
324	C₂²×C₁₃	—	2	4	no	—
325	C₂²×C₁₃	—	2	4	no	—
326	C₂²×C₁₃	—	2	4	no	—
327	C₂²×C₁₃	—	4	2	no	—
328	C₂²×C₁₃	—	4	2	no	—
329	C₂²×C₁₃	—	4	2	no	—
330	C₂²×C₁₃	—	4	2	no	—
331	C₂²×C₁₃	—	4	16	no	—
332	C₂²×C₁₃	—	4	4	no	—
333	C₂²×C₁₃	—	4	4	no	—
334	C₂²×C₁₃	—	4	4	no	—
335	C₂²×C₁₃	—	4	4	no	—
336	C₂²×C₁₃	—	4	4	no	—
337	C₂²×C₁₃	—	4	4	no	—
338	C₂²×C₁₃	—	4	4	no	—
339	C₂²×C₁₃	—	8	16	no	—
340	C₂²×C₁₃	C₂×#124	1	4	yes	—
341	C₂²×C₁₃	#532	1	4	yes	—
342	C₂²×C₁₃	#542	1	4	yes	—
343	C₂²×C₁₃	D₄²	1	4	yes	—
344	C₂²×C₁₃	#547	1	4	yes	—
345	C₂²×C₁₃	#548	1	4	yes	—
346	C₂²×C₁₃	#555	1	4	yes	—
347	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
348	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
349	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
350	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
351	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
352	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
353	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
354	C₄×C₁₃	—	2	8	no	—
355	C₄×C₁₃	—	2	4	no	—
356	C₄×C₁₃	—	2	4	no	—
357	C₄×C₁₃	—	2	4	no	—
358	C₄×C₁₃	—	4	2	no	—
359	C₄×C₁₃	—	4	4	no	—
360	C₄×C₁₃	—	4	4	no	—
361	C₄×C₁₃	—	4	2	no	—
362	C₄×C₁₃	C₂×#124	1	8	yes	complemented
363	C₂⁵	C₂³×C₁₃	1	2	yes	—
364	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
365	C₂²×Q₈	—	2	8	no	—
366	C₂²×Q₈	—	2	8	no	—
367	C₂²×Q₈	—	4	4	no	—
368	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
369	C₂²×D₄	—	2	8	no	—
370	C₂²×D₄	—	2	8	no	—
371	C₂²×D₄	—	2	4	no	—
372	C₂²×D₄	—	2	4	no	—
373	C₂²×D₄	—	2	4	no	—
374	C₂²×D₄	—	4	4	no	—
375	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
376	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
377	C₂³×C₄	—	2	4	no	—
378	C₂³×C₄	—	2	4	no	—
379	C₂³×C₄	—	2	4	no	—
380	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
381	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
382	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
383	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
384	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
385	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
386	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
387	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
388	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
389	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
390	C₄⋊Q₈	—	2	32	no	—
391	#124	—	2	64	no	—
392	#121	—	2	32	no	—
393	C₂×C₄⋊C₄	—	2	8	no	—
394	C₂×C₄⋊C₄	—	2	4	no	—
395	C₂×C₄⋊C₄	—	2	4	no	—
396	C₂×C₄⋊C₄	D₄×C₁₃	1	8	yes	—
397	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
398	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
399	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
401	C₂×C₂²⋊C₄	—	2	8	no	—
402	C₂×C₂²⋊C₄	—	2	8	no	—
403	C₂×C₂²⋊C₄	—	2	8	no	—
404	C₂×C₂²⋊C₄	—	2	8	no	—
405	C₂×C₂²⋊C₄	—	2	4	no	—
406	C₂×C₂²⋊C₄	—	2	8	no	—
407	C₂×C₂²⋊C₄	—	4	4	no	—
408	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	complemented
409	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
417	C₂×C₄²	—	2	8	no	—
418	C₂×C₄²	—	2	4	no	—
419	C₂×C₄²	—	2	4	no	—
420	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
421	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
422	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
423	#95	C₂³×C₁₃	1	4	yes	—
424	#95	C₂³×C₁₃	1	4	yes	—
425	#95	C₂³×C₁₃	1	8	yes	—
426	#95	C₂³×C₁₃	1	8	yes	—
427	C₂×C₁₃	—	4	4	no	—
428	C₂×C₁₃	—	8	4	no	—
429	C₂×C₁₃	#2491	1	8	yes	direct product factor
430	C₂×C₁₃	C₂²×#124	1	1	yes	characteristic
431	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
432	C₂×C₁₃	C₂×#542	1	1	yes	characteristic
433	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
434	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
435	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
436	C₂×C₁₃	C₂×#555	1	1	yes	characteristic
437	C₂⁴	—	2	2	no	—
438	C₂⁴	—	2	2	no	—
439	C₂⁴	—	2	2	no	—
440	C₂⁴	—	2	2	no	—
441	C₂⁴	—	2	2	no	—
442	C₂⁴	—	2	2	no	—
443	C₂⁴	—	2	4	no	—
444	C₂⁴	—	2	4	no	—
445	C₂⁴	—	2	4	no	—
446	C₂⁴	—	2	4	no	—
447	C₂⁴	—	2	4	no	—
448	C₂⁴	—	2	4	no	—
449	C₂⁴	—	2	4	no	—
450	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
451	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
452	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
453	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
454	C₂×Q₈	—	2	16	no	—
455	C₂×Q₈	—	2	16	no	—
456	C₂×Q₈	—	4	8	no	—
457	C₂×Q₈	—	4	32	no	—
458	C₂×D₄	—	2	16	no	—
459	C₂×D₄	—	2	16	no	—
460	C₂×D₄	—	2	8	no	—
461	C₂×D₄	—	2	8	no	—
462	C₂×D₄	—	2	8	no	—
463	C₂×D₄	—	4	8	no	—
464	C₂×D₄	—	4	32	no	—
465	C₂×D₄	—	4	16	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	4	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	8	no	—
487	C₂²×C₄	—	2	8	no	—
488	C₂²×C₄	—	2	8	no	—
489	C₂²×C₄	—	4	16	no	—
490	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
491	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
492	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
493	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
494	C₂²×C₄	C₁₃×#41	1	4	yes	—
495	C₂²×C₄	C₁₃×#41	1	4	yes	—
496	C₂²×C₄	C₁₃×#41	1	4	yes	—
497	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
498	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
499	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
500	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
501	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
502	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
503	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
504	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
505	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
506	C₄⋊C₄	—	2	16	no	—
507	C₄⋊C₄	—	2	8	no	—
508	C₄⋊C₄	—	2	8	no	—
509	C₄⋊C₄	C₂×D₄×C₁₃	1	16	yes	—
510	C₂²⋊C₄	—	2	16	no	—
511	C₂²⋊C₄	—	2	16	no	—
512	C₂²⋊C₄	—	2	16	no	—
513	C₂²⋊C₄	—	2	16	no	—
514	C₂²⋊C₄	—	2	8	no	—
515	C₂²⋊C₄	—	2	16	no	—
516	C₂²⋊C₄	—	4	8	no	—
517	C₂²⋊C₄	C₂×D₄×C₁₃	1	16	yes	complemented
518	C₄²	—	2	16	no	—
519	C₄²	—	2	8	no	—
520	C₄²	—	2	8	no	—
521	C₁₃	C₂×#2491	1	1	yes	characteristic, direct product factor, Sylow
522	C₂³	—	2	8	no	—
523	C₂³	—	2	8	no	—
524	C₂³	—	2	8	no	—
525	C₂³	—	2	2	no	—
526	C₂³	—	2	2	no	—
527	C₂³	—	2	2	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	2	no	—
530	C₂³	—	2	2	no	—
531	C₂³	—	2	4	no	—
532	C₂³	—	2	4	no	—
533	C₂³	—	2	4	no	—
534	C₂³	—	2	4	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	4	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	4	4	no	—
539	C₂³	—	4	4	no	—
540	C₂³	—	4	4	no	—
541	C₂³	—	4	4	no	—
542	C₂³	—	4	8	no	—
543	C₂³	—	4	8	no	—
544	C₂³	—	4	8	no	—
545	C₂³	—	4	8	no	—
546	C₂³	—	4	8	no	—
547	C₂³	—	4	8	no	—
548	C₂³	—	4	8	no	—
549	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
550	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
551	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
552	C₂³	C₂×C₁₃×#41	1	2	yes	—
553	C₂³	C₂×C₁₃×#41	1	2	yes	—
554	C₂³	C₂×C₁₃×#41	1	2	yes	—
555	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
556	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
557	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
558	Q₈	—	4	32	no	—
559	D₄	—	4	32	no	—
560	D₄	—	4	16	no	—
561	C₂×C₄	—	2	16	no	—
562	C₂×C₄	—	2	8	no	—
563	C₂×C₄	—	2	8	no	—
564	C₂×C₄	—	2	8	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	4	4	no	—
586	C₂×C₄	—	4	8	no	—
587	C₂×C₄	—	4	8	no	—
588	C₂×C₄	—	4	4	no	—
589	C₂×C₄	—	4	16	no	—
590	C₂×C₄	C₁₃×#124	1	16	yes	complemented
591	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
592	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
593	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
594	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
595	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
596	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
597	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
598	C₂²	—	2	4	no	—
599	C₂²	—	2	4	no	—
600	C₂²	—	2	4	no	—
601	C₂²	—	4	2	no	—
602	C₂²	—	4	2	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	16	no	—
606	C₂²	—	4	4	no	—
607	C₂²	—	4	4	no	—
608	C₂²	—	4	4	no	—
609	C₂²	—	4	4	no	—
610	C₂²	—	4	4	no	—
611	C₂²	—	4	4	no	—
612	C₂²	—	4	4	no	—
613	C₂²	—	8	16	no	—
614	C₂²	C₂×C₁₃×#124	1	4	yes	—
615	C₂²	C₁₃×#532	1	4	yes	—
616	C₂²	C₁₃×#542	1	4	yes	—
617	C₂²	D₄²×C₁₃	1	4	yes	—
618	C₂²	C₁₃×#547	1	4	yes	—
619	C₂²	C₁₃×#548	1	4	yes	—
620	C₂²	C₁₃×#555	1	4	yes	—
621	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
622	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
623	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
624	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
625	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
626	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
627	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
628	C₄	—	2	8	no	—
629	C₄	—	2	4	no	—
630	C₄	—	2	4	no	—
631	C₄	—	2	4	no	—
632	C₄	—	4	2	no	—
633	C₄	—	4	4	no	—
634	C₄	—	4	4	no	—
635	C₄	—	4	2	no	—
636	C₄	C₂×C₁₃×#124	1	8	yes	complemented
637	C₂	—	4	4	no	—
638	C₂	—	8	4	no	—
639	C₂	C₁₃×#2491	1	8	yes	direct product factor
640	C₂	C₂²×C₁₃×#124	1	1	yes	characteristic
641	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
642	C₂	C₂×C₁₃×#542	1	1	yes	characteristic
643	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
644	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
645	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
646	C₂	C₂×C₁₃×#555	1	1	yes	characteristic

	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
1. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
2. C₂²×C₁₃×#124	C₂	semidirect
4. C₁₃×#2491	C₂	direct (N × H)
5. C₂×C₁₃×#394	C₂	semidirect
6. C₂×C₁₃×#393	C₂	semidirect
7. C₂×C₁₃×#390	C₂	semidirect
8. C₂×C₁₃×#390	C₂	semidirect
9. C₂×C₁₃×#388	C₂	semidirect
10. C₂×C₁₃×#380	C₂	semidirect
11. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
12. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
18. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
20. C₂×C₁₃×#124	C₂²	semidirect
38. C₁₃×#394	C₂²	semidirect
39. C₁₃×#393	C₂²	semidirect
40. C₁₃×#390	C₂²	semidirect
41. C₁₃×#390	C₂²	semidirect
42. C₁₃×#388	C₂²	semidirect
43. C₁₃×#380	C₂²	semidirect
44. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
45. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
95. C₂×C₁₃×C₂²⋊C₄	D₄	semidirect
114. C₂×#2491	C₁₃	direct (N × H)
195. C₁₃×C₂²⋊C₄	C₂×D₄	semidirect
199. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
200. C₂²×#124	C₂×C₁₃	semidirect
202. #2491	C₂×C₁₃	direct (N × H)
203. C₂×#394	C₂×C₁₃	semidirect
204. C₂×#393	C₂×C₁₃	semidirect
205. C₂×#390	C₂×C₁₃	semidirect
206. C₂×#390	C₂×C₁₃	semidirect
207. C₂×#388	C₂×C₁₃	semidirect
208. C₂×#380	C₂×C₁₃	semidirect
209. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
210. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
279. C₂×C₄×C₁₃	#124	semidirect
292. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
294. C₂×#124	C₂²×C₁₃	semidirect
312. #394	C₂²×C₁₃	semidirect
313. #393	C₂²×C₁₃	semidirect
314. #390	C₂²×C₁₃	semidirect
315. #390	C₂²×C₁₃	semidirect
316. #388	C₂²×C₁₃	semidirect
317. #380	C₂²×C₁₃	semidirect
318. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
319. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
362. C₄×C₁₃	C₂×#124	semidirect
408. C₂×C₂²⋊C₄	D₄×C₁₃	semidirect
429. C₂×C₁₃	#2491	direct (N × H)
517. C₂²⋊C₄	C₂×D₄×C₁₃	semidirect
521. C₁₃	C₂×#2491	direct (N × H)
590. C₂×C₄	C₁₃×#124	semidirect
636. C₄	C₂×C₁₃×#124	semidirect
639. C₂	C₁₃×#2491	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×C₄⋊Q₈	2
C₂²×C₁₃×#124	2
C₂²×C₁₃×#121	2
C₁₃×#2491	2
C₂×C₁₃×#394	2
C₂×C₁₃×#393	2
C₂×C₁₃×#390	2
C₂×C₁₃×#388	2
C₂×C₁₃×#380	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂×#2491	13

Subgroups — C2×C13×#2491 #15721098

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2491 #15721098