Subgroups — C₂×C₁₃×#2452 #15721019

Order 3328.

3614 conjugacy classes of subgroups.

The subgroup lattice has 592 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×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2452	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₃×#396	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
8	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#385	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₁₃×C₄⋊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	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊Q₈	—	2	8	no	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	8	yes	complemented
18	C₂×C₁₃×C₂²⋊Q₈	—	2	16	no	—
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	16	yes	complemented
20	C₂×C₄×D₄×C₁₃	—	2	8	no	—
21	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	—
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
38	C₁₃×#396	C₂²	1	16	yes	complemented
39	C₁₃×#393	C₂²	1	16	yes	complemented
40	C₁₃×#390	C₂²	1	8	yes	—
41	C₁₃×#390	C₂²	1	8	yes	—
42	C₁₃×#389	C₂²	1	8	yes	complemented
43	C₁₃×#389	C₂²	1	8	yes	complemented
44	C₁₃×#385	C₂²	1	16	yes	complemented
45	C₄×C₁₃×C₄⋊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	C₂²×Q₈×C₁₃	—	2	8	no	—
52	C₂²×Q₈×C₁₃	—	2	8	no	—
53	C₂²×Q₈×C₁₃	—	4	4	no	—
54	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
55	C₂²×D₄×C₁₃	—	2	4	no	—
56	C₂²×D₄×C₁₃	—	2	4	no	—
57	C₂²×D₄×C₁₃	Q₈	1	8	yes	complemented
58	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
59	C₂³×C₄×C₁₃	—	2	8	no	—
60	C₂³×C₄×C₁₃	—	2	8	no	—
61	C₂³×C₄×C₁₃	—	4	4	no	—
62	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
66	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
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	C₁₃×C₄⋊Q₈	—	2	32	no	—
74	C₁₃×C₂²⋊Q₈	—	2	64	no	—
75	C₄×D₄×C₁₃	—	2	32	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
82	C₂×C₁₃×C₄⋊C₄	D₄	1	8	yes	—
83	C₂×C₁₃×C₄⋊C₄	D₄	1	8	yes	complemented
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
96	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
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×C₄²×C₁₃	—	2	4	no	—
103	C₂×C₄²×C₁₃	—	2	4	no	—
104	C₂×C₄²×C₁₃	—	2	4	no	—
105	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
106	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
107	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
108	C₁₃×#95	C₂³	1	4	yes	—
109	C₁₃×#95	C₂³	1	4	yes	—
110	C₁₃×#95	C₂³	1	8	yes	—
111	C₁₃×#95	C₂³	1	8	yes	—
112	C₂×#2452	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂⁴×C₁₃	—	2	4	no	—
114	C₂⁴×C₁₃	—	2	4	no	—
115	C₂⁴×C₁₃	—	2	4	no	—
116	C₂⁴×C₁₃	—	2	4	no	—
117	C₂⁴×C₁₃	—	2	4	no	—
118	C₂⁴×C₁₃	—	2	4	no	—
119	C₂⁴×C₁₃	C₂×Q₈	1	8	yes	—
120	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
121	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
122	C₂×Q₈×C₁₃	—	2	16	no	—
123	C₂×Q₈×C₁₃	—	2	16	no	—
124	C₂×Q₈×C₁₃	—	4	8	no	—
125	C₂×Q₈×C₁₃	—	4	32	no	—
126	C₂×D₄×C₁₃	—	2	32	no	—
127	C₂×D₄×C₁₃	—	2	8	no	—
128	C₂×D₄×C₁₃	—	2	8	no	—
129	C₂×D₄×C₁₃	C₂×Q₈	1	16	yes	complemented
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	4	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	4	no	—
138	C₂²×C₄×C₁₃	—	2	2	no	—
139	C₂²×C₄×C₁₃	—	2	2	no	—
140	C₂²×C₄×C₁₃	—	2	2	no	—
141	C₂²×C₄×C₁₃	—	2	4	no	—
142	C₂²×C₄×C₁₃	—	2	4	no	—
143	C₂²×C₄×C₁₃	—	2	4	no	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	—	2	4	no	—
146	C₂²×C₄×C₁₃	—	2	4	no	—
147	C₂²×C₄×C₁₃	—	2	2	no	—
148	C₂²×C₄×C₁₃	—	2	2	no	—
149	C₂²×C₄×C₁₃	—	2	4	no	—
150	C₂²×C₄×C₁₃	—	2	2	no	—
151	C₂²×C₄×C₁₃	—	2	2	no	—
152	C₂²×C₄×C₁₃	—	2	16	no	—
153	C₂²×C₄×C₁₃	—	2	16	no	—
154	C₂²×C₄×C₁₃	—	4	8	no	—
155	C₂²×C₄×C₁₃	—	4	32	no	—
156	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
159	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
162	C₂²×C₄×C₁₃	#41	1	4	yes	—
163	C₂²×C₄×C₁₃	#41	1	4	yes	—
164	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
174	C₁₃×C₄⋊C₄	—	2	16	no	—
175	C₁₃×C₄⋊C₄	—	2	16	no	—
176	C₁₃×C₄⋊C₄	—	2	16	no	—
177	C₁₃×C₄⋊C₄	—	2	8	no	—
178	C₁₃×C₄⋊C₄	—	2	8	no	—
179	C₁₃×C₄⋊C₄	—	2	8	no	—
180	C₁₃×C₄⋊C₄	C₂×D₄	1	16	yes	—
181	C₁₃×C₄⋊C₄	C₂×D₄	1	16	yes	complemented
182	C₁₃×C₂²⋊C₄	—	2	16	no	—
183	C₁₃×C₂²⋊C₄	—	2	16	no	—
184	C₁₃×C₂²⋊C₄	—	2	16	no	—
185	C₁₃×C₂²⋊C₄	—	2	16	no	—
186	C₁₃×C₂²⋊C₄	—	4	8	no	—
187	C₄²×C₁₃	—	2	8	no	—
188	C₄²×C₁₃	—	2	8	no	—
189	C₄²×C₁₃	—	2	8	no	—
190	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
191	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
192	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic
193	#2452	C₂×C₁₃	1	16	yes	direct product factor
194	C₂×#396	C₂×C₁₃	1	2	yes	complemented
195	C₂×#393	C₂×C₁₃	1	2	yes	complemented
196	C₂×#390	C₂×C₁₃	1	1	yes	characteristic
197	C₂×#390	C₂×C₁₃	1	1	yes	characteristic
198	C₂×#389	C₂×C₁₃	1	1	yes	characteristic, complemented
199	C₂×#389	C₂×C₁₃	1	1	yes	characteristic, complemented
200	C₂×#385	C₂×C₁₃	1	2	yes	complemented
201	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
202	C₂³×C₁₃	—	2	16	no	—
203	C₂³×C₁₃	—	2	16	no	—
204	C₂³×C₁₃	—	2	16	no	—
205	C₂³×C₁₃	—	2	4	no	—
206	C₂³×C₁₃	—	2	4	no	—
207	C₂³×C₁₃	—	2	4	no	—
208	C₂³×C₁₃	—	2	4	no	—
209	C₂³×C₁₃	—	2	4	no	—
210	C₂³×C₁₃	—	2	4	no	—
211	C₂³×C₁₃	—	4	8	no	—
212	C₂³×C₁₃	—	4	8	no	—
213	C₂³×C₁₃	—	4	8	no	—
214	C₂³×C₁₃	—	4	8	no	—
215	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
216	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
217	C₂³×C₁₃	C₂²×Q₈	1	8	yes	—
218	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
219	C₂³×C₁₃	C₂×#41	1	2	yes	—
220	C₂³×C₁₃	C₂×#41	1	2	yes	—
221	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
222	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
223	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
224	Q₈×C₁₃	—	4	32	no	—
225	D₄×C₁₃	—	2	32	no	—
226	C₂×C₄×C₁₃	—	2	8	no	—
227	C₂×C₄×C₁₃	—	2	8	no	—
228	C₂×C₄×C₁₃	—	2	16	no	—
229	C₂×C₄×C₁₃	—	2	8	no	—
230	C₂×C₄×C₁₃	—	2	8	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	4	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	4	no	—
243	C₂×C₄×C₁₃	—	2	4	no	—
244	C₂×C₄×C₁₃	—	2	4	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	4	no	—
247	C₂×C₄×C₁₃	—	2	4	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	4	32	no	—
254	C₂×C₄×C₁₃	—	4	8	no	—
255	C₂×C₄×C₁₃	—	4	4	no	—
256	C₂×C₄×C₁₃	—	4	8	no	—
257	C₂×C₄×C₁₃	—	4	4	no	—
258	C₂×C₄×C₁₃	C₂²⋊Q₈	1	16	yes	complemented
259	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
260	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
261	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
262	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
263	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
264	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
265	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
266	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
267	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
268	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
269	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
270	C₂×C₄⋊Q₈	—	2	8	no	—
271	C₂×C₄⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
272	C₂×C₂²⋊Q₈	—	2	16	no	—
273	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	16	yes	complemented
274	C₂×C₄×D₄	—	2	8	no	—
275	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
276	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
277	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
278	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
279	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
280	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
281	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
282	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
283	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
284	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
285	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
286	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
287	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
288	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
289	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
290	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
291	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
292	#396	C₂²×C₁₃	1	16	yes	complemented
293	#393	C₂²×C₁₃	1	16	yes	complemented
294	#390	C₂²×C₁₃	1	8	yes	—
295	#390	C₂²×C₁₃	1	8	yes	—
296	#389	C₂²×C₁₃	1	8	yes	complemented
297	#389	C₂²×C₁₃	1	8	yes	complemented
298	#385	C₂²×C₁₃	1	16	yes	complemented
299	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
300	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×#95	C₂²×C₁₃	1	2	yes	—
302	C₂×#95	C₂²×C₁₃	1	2	yes	—
303	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
304	C₂²×C₁₃	—	2	8	no	—
305	C₂²×C₁₃	—	2	8	no	—
306	C₂²×C₁₃	—	2	8	no	—
307	C₂²×C₁₃	—	4	4	no	—
308	C₂²×C₁₃	—	4	4	no	—
309	C₂²×C₁₃	—	4	4	no	—
310	C₂²×C₁₃	—	4	4	no	—
311	C₂²×C₁₃	—	4	32	no	—
312	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
313	C₂²×C₁₃	#532	1	4	yes	—
314	C₂²×C₁₃	#542	1	4	yes	—
315	C₂²×C₁₃	D₄²	1	4	yes	—
316	C₂²×C₁₃	#548	1	4	yes	—
317	C₂²×C₁₃	D₄×Q₈	1	4	yes	—
318	C₂²×C₁₃	#554	1	4	yes	—
319	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
320	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
321	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
322	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
323	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
324	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
325	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
326	C₄×C₁₃	—	2	4	no	—
327	C₄×C₁₃	—	2	4	no	—
328	C₄×C₁₃	—	2	8	no	—
329	C₄×C₁₃	—	2	4	no	—
330	C₄×C₁₃	—	2	4	no	—
331	C₄×C₁₃	—	4	4	no	—
332	C₄×C₁₃	—	4	2	no	—
333	C₄×C₁₃	—	4	4	no	—
334	C₄×C₁₃	—	4	2	no	—
335	C₄×C₁₃	C₂×C₂²⋊Q₈	1	8	yes	complemented
336	C₂⁵	C₂³×C₁₃	1	2	yes	—
337	C₂²×Q₈	—	2	8	no	—
338	C₂²×Q₈	—	2	8	no	—
339	C₂²×Q₈	—	4	4	no	—
340	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
341	C₂²×D₄	—	2	4	no	—
342	C₂²×D₄	—	2	4	no	—
343	C₂²×D₄	Q₈×C₁₃	1	8	yes	complemented
344	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
345	C₂³×C₄	—	2	8	no	—
346	C₂³×C₄	—	2	8	no	—
347	C₂³×C₄	—	4	4	no	—
348	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
349	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
350	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
351	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
352	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
353	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
354	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
355	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
356	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
357	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
359	C₄⋊Q₈	—	2	32	no	—
360	C₂²⋊Q₈	—	2	64	no	—
361	C₄×D₄	—	2	32	no	—
362	C₂×C₄⋊C₄	—	2	8	no	—
363	C₂×C₄⋊C₄	—	2	8	no	—
364	C₂×C₄⋊C₄	—	2	8	no	—
365	C₂×C₄⋊C₄	—	2	4	no	—
366	C₂×C₄⋊C₄	—	2	4	no	—
367	C₂×C₄⋊C₄	—	2	4	no	—
368	C₂×C₄⋊C₄	D₄×C₁₃	1	8	yes	—
369	C₂×C₄⋊C₄	D₄×C₁₃	1	8	yes	complemented
370	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
371	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
372	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
373	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
374	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
378	C₂×C₂²⋊C₄	—	2	8	no	—
379	C₂×C₂²⋊C₄	—	2	8	no	—
380	C₂×C₂²⋊C₄	—	2	8	no	—
381	C₂×C₂²⋊C₄	—	2	8	no	—
382	C₂×C₂²⋊C₄	—	4	4	no	—
383	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
388	C₂×C₄²	—	2	4	no	—
389	C₂×C₄²	—	2	4	no	—
390	C₂×C₄²	—	2	4	no	—
391	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
392	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
393	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
394	#95	C₂³×C₁₃	1	4	yes	—
395	#95	C₂³×C₁₃	1	4	yes	—
396	#95	C₂³×C₁₃	1	8	yes	—
397	#95	C₂³×C₁₃	1	8	yes	—
398	C₂×C₁₃	—	4	8	no	—
399	C₂×C₁₃	#2452	1	8	yes	direct product factor
400	C₂×C₁₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
401	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
402	C₂×C₁₃	C₂×#542	1	1	yes	characteristic
403	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
404	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
405	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
406	C₂×C₁₃	C₂×#554	1	1	yes	characteristic
407	C₂⁴	—	2	4	no	—
408	C₂⁴	—	2	4	no	—
409	C₂⁴	—	2	4	no	—
410	C₂⁴	—	2	4	no	—
411	C₂⁴	—	2	4	no	—
412	C₂⁴	—	2	4	no	—
413	C₂⁴	C₂×Q₈×C₁₃	1	8	yes	—
414	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
415	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
416	C₂×Q₈	—	2	16	no	—
417	C₂×Q₈	—	2	16	no	—
418	C₂×Q₈	—	4	8	no	—
419	C₂×Q₈	—	4	32	no	—
420	C₂×D₄	—	2	32	no	—
421	C₂×D₄	—	2	8	no	—
422	C₂×D₄	—	2	8	no	—
423	C₂×D₄	C₂×Q₈×C₁₃	1	16	yes	complemented
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	16	no	—
447	C₂²×C₄	—	2	16	no	—
448	C₂²×C₄	—	4	8	no	—
449	C₂²×C₄	—	4	32	no	—
450	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
451	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
452	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
453	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
454	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
455	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
456	C₂²×C₄	C₁₃×#41	1	4	yes	—
457	C₂²×C₄	C₁₃×#41	1	4	yes	—
458	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
459	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
460	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
461	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
462	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
463	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
464	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
465	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
466	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
467	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
468	C₄⋊C₄	—	2	16	no	—
469	C₄⋊C₄	—	2	16	no	—
470	C₄⋊C₄	—	2	16	no	—
471	C₄⋊C₄	—	2	8	no	—
472	C₄⋊C₄	—	2	8	no	—
473	C₄⋊C₄	—	2	8	no	—
474	C₄⋊C₄	C₂×D₄×C₁₃	1	16	yes	—
475	C₄⋊C₄	C₂×D₄×C₁₃	1	16	yes	complemented
476	C₂²⋊C₄	—	2	16	no	—
477	C₂²⋊C₄	—	2	16	no	—
478	C₂²⋊C₄	—	2	16	no	—
479	C₂²⋊C₄	—	2	16	no	—
480	C₂²⋊C₄	—	4	8	no	—
481	C₄²	—	2	8	no	—
482	C₄²	—	2	8	no	—
483	C₄²	—	2	8	no	—
484	C₁₃	C₂×#2452	1	1	yes	characteristic, direct product factor, Sylow
485	C₂³	—	2	16	no	—
486	C₂³	—	2	16	no	—
487	C₂³	—	2	16	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	4	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	2	4	no	—
493	C₂³	—	2	4	no	—
494	C₂³	—	4	8	no	—
495	C₂³	—	4	8	no	—
496	C₂³	—	4	8	no	—
497	C₂³	—	4	8	no	—
498	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
499	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
500	C₂³	C₂²×Q₈×C₁₃	1	8	yes	—
501	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
502	C₂³	C₂×C₁₃×#41	1	2	yes	—
503	C₂³	C₂×C₁₃×#41	1	2	yes	—
504	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
505	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
506	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
507	Q₈	—	4	32	no	—
508	D₄	—	2	32	no	—
509	C₂×C₄	—	2	8	no	—
510	C₂×C₄	—	2	8	no	—
511	C₂×C₄	—	2	16	no	—
512	C₂×C₄	—	2	8	no	—
513	C₂×C₄	—	2	8	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	4	32	no	—
537	C₂×C₄	—	4	8	no	—
538	C₂×C₄	—	4	4	no	—
539	C₂×C₄	—	4	8	no	—
540	C₂×C₄	—	4	4	no	—
541	C₂×C₄	C₁₃×C₂²⋊Q₈	1	16	yes	complemented
542	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
543	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
544	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
545	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
546	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
547	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
548	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
549	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
550	C₂²	—	2	8	no	—
551	C₂²	—	2	8	no	—
552	C₂²	—	2	8	no	—
553	C₂²	—	4	4	no	—
554	C₂²	—	4	4	no	—
555	C₂²	—	4	4	no	—
556	C₂²	—	4	4	no	—
557	C₂²	—	4	32	no	—
558	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
559	C₂²	C₁₃×#532	1	4	yes	—
560	C₂²	C₁₃×#542	1	4	yes	—
561	C₂²	D₄²×C₁₃	1	4	yes	—
562	C₂²	C₁₃×#548	1	4	yes	—
563	C₂²	D₄×Q₈×C₁₃	1	4	yes	—
564	C₂²	C₁₃×#554	1	4	yes	—
565	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
566	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
567	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
568	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
569	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
570	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
571	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
572	C₄	—	2	4	no	—
573	C₄	—	2	4	no	—
574	C₄	—	2	8	no	—
575	C₄	—	2	4	no	—
576	C₄	—	2	4	no	—
577	C₄	—	4	4	no	—
578	C₄	—	4	2	no	—
579	C₄	—	4	4	no	—
580	C₄	—	4	2	no	—
581	C₄	C₂×C₁₃×C₂²⋊Q₈	1	8	yes	complemented
582	C₂	—	4	8	no	—
583	C₂	C₁₃×#2452	1	8	yes	direct product factor
584	C₂	C₂²×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
585	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
586	C₂	C₂×C₁₃×#542	1	1	yes	characteristic
587	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
588	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
589	C₂	C₂×D₄×Q₈×C₁₃	1	1	yes	characteristic
590	C₂	C₂×C₁₃×#554	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×D₄×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×C₄⋊Q₈	C₂	semidirect
2. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
4. C₁₃×#2452	C₂	direct (N × H)
5. C₂×C₁₃×#396	C₂	semidirect
6. C₂×C₁₃×#393	C₂	semidirect
9. C₂×C₁₃×#389	C₂	semidirect
10. C₂×C₁₃×#389	C₂	semidirect
11. C₂×C₁₃×#385	C₂	semidirect
12. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
17. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
19. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
38. C₁₃×#396	C₂²	semidirect
39. C₁₃×#393	C₂²	semidirect
42. C₁₃×#389	C₂²	semidirect
43. C₁₃×#389	C₂²	semidirect
44. C₁₃×#385	C₂²	semidirect
45. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
57. C₂²×D₄×C₁₃	Q₈	semidirect
83. C₂×C₁₃×C₄⋊C₄	D₄	semidirect
112. C₂×#2452	C₁₃	direct (N × H)
129. C₂×D₄×C₁₃	C₂×Q₈	semidirect
181. C₁₃×C₄⋊C₄	C₂×D₄	semidirect
190. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
191. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
193. #2452	C₂×C₁₃	direct (N × H)
194. C₂×#396	C₂×C₁₃	semidirect
195. C₂×#393	C₂×C₁₃	semidirect
198. C₂×#389	C₂×C₁₃	semidirect
199. C₂×#389	C₂×C₁₃	semidirect
200. C₂×#385	C₂×C₁₃	semidirect
201. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
258. C₂×C₄×C₁₃	C₂²⋊Q₈	semidirect
271. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
273. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
292. #396	C₂²×C₁₃	semidirect
293. #393	C₂²×C₁₃	semidirect
296. #389	C₂²×C₁₃	semidirect
297. #389	C₂²×C₁₃	semidirect
298. #385	C₂²×C₁₃	semidirect
299. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
335. C₄×C₁₃	C₂×C₂²⋊Q₈	semidirect
343. C₂²×D₄	Q₈×C₁₃	semidirect
369. C₂×C₄⋊C₄	D₄×C₁₃	semidirect
399. C₂×C₁₃	#2452	direct (N × H)
423. C₂×D₄	C₂×Q₈×C₁₃	semidirect
475. C₄⋊C₄	C₂×D₄×C₁₃	semidirect
484. C₁₃	C₂×#2452	direct (N × H)
541. C₂×C₄	C₁₃×C₂²⋊Q₈	semidirect
581. C₄	C₂×C₁₃×C₂²⋊Q₈	semidirect
583. C₂	C₁₃×#2452	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×C₂²⋊Q₈	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2452	2
C₂×C₁₃×#396	2
C₂×C₁₃×#393	2
C₂×C₁₃×#390	2
C₂×C₁₃×#389	2
C₂×C₁₃×#385	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×#2452	13

Subgroups — C2×C13×#2452 #15721019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2452 #15721019