Subgroups — C₁₃×#35019 #15721358

Order 3328.

2994 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2850	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2639	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2591	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2561	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2504	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2503	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2436	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2435	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2308	C₂	1	4	yes	maximal, complemented
12	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
14	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
15	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
18	C₂×C₁₃×C₂²⋊Q₈	—	2	8	no	—
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#121	—	2	8	no	—
24	C₂×C₁₃×#121	C₂²	1	2	yes	—
25	C₂×C₁₃×#121	C₂²	1	2	yes	—
26	C₂×C₁₃×#121	C₂²	1	2	yes	—
27	C₂×C₁₃×#121	C₂²	1	2	yes	—
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
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×C₄²×C₁₃	C₂²	1	2	yes	complemented
35	C₁₃×#400	C₂²	1	8	yes	complemented
36	C₁₃×#397	C₂²	1	8	yes	complemented
37	C₁₃×#394	C₂²	1	8	yes	complemented
38	C₁₃×#393	C₂²	1	8	yes	complemented
39	C₁₃×#391	C₂²	1	4	yes	complemented
40	C₁₃×#390	C₂²	1	4	yes	complemented
41	C₁₃×#388	C₂²	1	16	yes	complemented
42	C₁₃×#386	C₂²	1	8	yes	complemented
43	C₁₃×#386	C₂²	1	8	yes	complemented
44	C₁₃×#386	C₂²	1	16	yes	complemented
45	C₁₃×#382	C₂²	1	4	yes	complemented
46	C₁₃×#381	C₂²	1	8	yes	—
47	C₁₃×#379	C₂²	1	8	yes	—
48	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
49	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
50	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
51	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
52	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
53	C₂⁵×C₁₃	C₂³	1	2	yes	—
54	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₁₃	—	2	4	no	—
56	C₂²×Q₈×C₁₃	—	4	4	no	—
57	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
58	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
59	C₂²×D₄×C₁₃	—	2	8	no	—
60	C₂²×D₄×C₁₃	—	2	16	no	—
61	C₂²×D₄×C₁₃	—	2	4	no	—
62	C₂²×D₄×C₁₃	—	4	4	no	—
63	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
64	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
65	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
66	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₃	—	4	4	no	—
68	C₂³×C₄×C₁₃	D₄	1	8	yes	—
69	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
74	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×#124	—	4	8	no	—
80	C₁₃×C₂²⋊Q₈	—	2	8	no	—
81	C₁₃×C₂²⋊Q₈	—	2	8	no	—
82	C₁₃×C₂²⋊Q₈	—	2	8	no	—
83	C₁₃×C₂²⋊Q₈	—	2	8	no	—
84	C₁₃×#121	—	2	8	no	—
85	C₁₃×#121	—	2	8	no	—
86	C₁₃×#121	—	2	8	no	—
87	C₁₃×#121	—	2	8	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
100	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
103	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
108	C₂×C₄²×C₁₃	—	4	4	no	—
109	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
110	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
111	C₁₃×#95	C₂³	1	4	yes	—
112	C₁₃×#95	C₂³	1	4	yes	—
113	C₁₃×#95	C₂³	1	16	yes	—
114	C₁₃×#95	C₂³	1	16	yes	—
115	#35019	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂⁴×C₁₃	—	2	4	no	—
117	C₂⁴×C₁₃	—	2	8	no	—
118	C₂⁴×C₁₃	—	4	2	no	—
119	C₂⁴×C₁₃	—	4	2	no	—
120	C₂⁴×C₁₃	—	4	4	no	—
121	C₂⁴×C₁₃	—	4	4	no	—
122	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
123	C₂⁴×C₁₃	#41	1	8	yes	—
124	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
125	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
126	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
127	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
128	C₂×Q₈×C₁₃	—	2	4	no	—
129	C₂×Q₈×C₁₃	—	2	4	no	—
130	C₂×Q₈×C₁₃	—	2	8	no	—
131	C₂×Q₈×C₁₃	—	4	4	no	—
132	C₂×Q₈×C₁₃	—	4	16	no	—
133	C₂×D₄×C₁₃	—	2	8	no	—
134	C₂×D₄×C₁₃	—	2	8	no	—
135	C₂×D₄×C₁₃	—	2	16	no	—
136	C₂×D₄×C₁₃	—	2	16	no	—
137	C₂×D₄×C₁₃	—	2	4	no	—
138	C₂×D₄×C₁₃	—	2	4	no	—
139	C₂×D₄×C₁₃	—	2	8	no	—
140	C₂×D₄×C₁₃	—	4	4	no	—
141	C₂×D₄×C₁₃	—	4	16	no	—
142	C₂×D₄×C₁₃	—	4	32	no	—
143	C₂²×C₄×C₁₃	—	2	4	no	—
144	C₂²×C₄×C₁₃	—	2	4	no	—
145	C₂²×C₄×C₁₃	—	2	4	no	—
146	C₂²×C₄×C₁₃	—	2	4	no	—
147	C₂²×C₄×C₁₃	—	2	4	no	—
148	C₂²×C₄×C₁₃	—	2	4	no	—
149	C₂²×C₄×C₁₃	—	2	8	no	—
150	C₂²×C₄×C₁₃	—	2	8	no	—
151	C₂²×C₄×C₁₃	—	4	16	no	—
152	C₂²×C₄×C₁₃	—	4	4	no	—
153	C₂²×C₄×C₁₃	—	4	2	no	—
154	C₂²×C₄×C₁₃	—	4	2	no	—
155	C₂²×C₄×C₁₃	—	4	2	no	—
156	C₂²×C₄×C₁₃	—	4	4	no	—
157	C₂²×C₄×C₁₃	—	4	4	no	—
158	C₂²×C₄×C₁₃	—	4	4	no	—
159	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
162	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
163	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
164	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
165	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₁₃×C₄⋊C₄	—	2	4	no	—
174	C₁₃×C₄⋊C₄	—	2	4	no	—
175	C₁₃×C₄⋊C₄	—	2	4	no	—
176	C₁₃×C₄⋊C₄	—	2	4	no	—
177	C₁₃×C₄⋊C₄	—	2	8	no	—
178	C₁₃×C₄⋊C₄	—	2	8	no	—
179	C₁₃×C₂²⋊C₄	—	2	8	no	—
180	C₁₃×C₂²⋊C₄	—	2	8	no	—
181	C₁₃×C₂²⋊C₄	—	2	8	no	—
182	C₁₃×C₂²⋊C₄	—	2	8	no	—
183	C₁₃×C₂²⋊C₄	—	2	8	no	—
184	C₁₃×C₂²⋊C₄	—	2	8	no	—
185	C₁₃×C₂²⋊C₄	—	4	16	no	—
186	C₁₃×C₂²⋊C₄	—	4	16	no	—
187	C₄²×C₁₃	—	2	8	no	—
188	C₄²×C₁₃	—	4	4	no	—
189	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
190	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic
191	#2850	C₂×C₁₃	1	4	yes	complemented
192	#2639	C₂×C₁₃	1	4	yes	complemented
193	#2591	C₂×C₁₃	1	4	yes	complemented
194	#2561	C₂×C₁₃	1	4	yes	complemented
195	#2504	C₂×C₁₃	1	2	yes	complemented
196	#2503	C₂×C₁₃	1	2	yes	complemented
197	#2436	C₂×C₁₃	1	2	yes	complemented
198	#2435	C₂×C₁₃	1	2	yes	complemented
199	#2308	C₂×C₁₃	1	4	yes	complemented
200	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
201	C₂³×C₁₃	—	2	2	no	—
202	C₂³×C₁₃	—	2	2	no	—
203	C₂³×C₁₃	—	2	2	no	—
204	C₂³×C₁₃	—	2	2	no	—
205	C₂³×C₁₃	—	2	2	no	—
206	C₂³×C₁₃	—	2	2	no	—
207	C₂³×C₁₃	—	2	4	no	—
208	C₂³×C₁₃	—	2	8	no	—
209	C₂³×C₁₃	—	2	8	no	—
210	C₂³×C₁₃	—	2	8	no	—
211	C₂³×C₁₃	—	4	4	no	—
212	C₂³×C₁₃	—	4	4	no	—
213	C₂³×C₁₃	—	4	16	no	—
214	C₂³×C₁₃	—	4	8	no	—
215	C₂³×C₁₃	—	4	8	no	—
216	C₂³×C₁₃	—	4	8	no	—
217	C₂³×C₁₃	—	8	16	no	—
218	C₂³×C₁₃	#124	1	16	yes	complemented
219	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
220	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
221	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
222	C₂³×C₁₃	C₂×#41	1	4	yes	—
223	C₂³×C₁₃	C₂×#41	1	4	yes	—
224	C₂³×C₁₃	C₂×#41	1	4	yes	—
225	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
226	Q₈×C₁₃	—	4	8	no	—
227	Q₈×C₁₃	—	4	8	no	—
228	D₄×C₁₃	—	4	8	no	—
229	D₄×C₁₃	—	4	16	no	—
230	D₄×C₁₃	—	4	16	no	—
231	D₄×C₁₃	—	4	8	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	8	no	—
236	C₂×C₄×C₁₃	—	2	8	no	—
237	C₂×C₄×C₁₃	—	2	8	no	—
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	—	2	4	no	—
240	C₂×C₄×C₁₃	—	2	4	no	—
241	C₂×C₄×C₁₃	—	2	8	no	—
242	C₂×C₄×C₁₃	—	2	8	no	—
243	C₂×C₄×C₁₃	—	2	8	no	—
244	C₂×C₄×C₁₃	—	2	8	no	—
245	C₂×C₄×C₁₃	—	2	8	no	—
246	C₂×C₄×C₁₃	—	2	8	no	—
247	C₂×C₄×C₁₃	—	4	4	no	—
248	C₂×C₄×C₁₃	—	4	4	no	—
249	C₂×C₄×C₁₃	—	4	4	no	—
250	C₂×C₄×C₁₃	—	4	8	no	—
251	C₂×C₄×C₁₃	—	4	16	no	—
252	C₂×C₄×C₁₃	—	4	8	no	—
253	C₂×C₄×C₁₃	—	4	8	no	—
254	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
255	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
256	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
259	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
260	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
261	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
262	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
264	C₂×C₂²⋊Q₈	—	2	8	no	—
265	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
266	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
267	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
268	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
269	C₂×#121	—	2	8	no	—
270	C₂×#121	C₂²×C₁₃	1	2	yes	—
271	C₂×#121	C₂²×C₁₃	1	2	yes	—
272	C₂×#121	C₂²×C₁₃	1	2	yes	—
273	C₂×#121	C₂²×C₁₃	1	2	yes	—
274	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
275	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
276	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
277	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
278	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
279	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
280	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
281	#400	C₂²×C₁₃	1	8	yes	complemented
282	#397	C₂²×C₁₃	1	8	yes	complemented
283	#394	C₂²×C₁₃	1	8	yes	complemented
284	#393	C₂²×C₁₃	1	8	yes	complemented
285	#391	C₂²×C₁₃	1	4	yes	complemented
286	#390	C₂²×C₁₃	1	4	yes	complemented
287	#388	C₂²×C₁₃	1	16	yes	complemented
288	#386	C₂²×C₁₃	1	8	yes	complemented
289	#386	C₂²×C₁₃	1	8	yes	complemented
290	#386	C₂²×C₁₃	1	16	yes	complemented
291	#382	C₂²×C₁₃	1	4	yes	complemented
292	#381	C₂²×C₁₃	1	8	yes	—
293	#379	C₂²×C₁₃	1	8	yes	—
294	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
295	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
296	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
297	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
298	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
299	C₂²×C₁₃	—	2	2	no	—
300	C₂²×C₁₃	—	2	2	no	—
301	C₂²×C₁₃	—	2	2	no	—
302	C₂²×C₁₃	—	2	2	no	—
303	C₂²×C₁₃	—	2	2	no	—
304	C₂²×C₁₃	—	2	2	no	—
305	C₂²×C₁₃	—	2	8	no	—
306	C₂²×C₁₃	—	2	8	no	—
307	C₂²×C₁₃	—	2	8	no	—
308	C₂²×C₁₃	—	4	16	no	—
309	C₂²×C₁₃	—	4	4	no	—
310	C₂²×C₁₃	—	4	4	no	—
311	C₂²×C₁₃	—	4	4	no	—
312	C₂²×C₁₃	—	4	16	no	—
313	C₂²×C₁₃	—	8	16	no	—
314	C₂²×C₁₃	C₂×#124	1	4	yes	—
315	C₂²×C₁₃	C₂×#124	1	4	yes	—
316	C₂²×C₁₃	C₂×#124	1	4	yes	—
317	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
318	C₂²×C₁₃	C₂²×#41	1	2	yes	—
319	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
320	C₂²×C₁₃	#585	1	2	yes	—
321	C₄×C₁₃	—	2	2	no	—
322	C₄×C₁₃	—	2	2	no	—
323	C₄×C₁₃	—	2	2	no	—
324	C₄×C₁₃	—	4	4	no	—
325	C₄×C₁₃	—	4	4	no	—
326	C₄×C₁₃	—	4	4	no	—
327	C₄×C₁₃	—	4	8	no	—
328	C₄×C₁₃	#534	1	4	yes	—
329	C₂⁵	C₂³×C₁₃	1	2	yes	—
330	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
331	C₂²×Q₈	—	2	4	no	—
332	C₂²×Q₈	—	4	4	no	—
333	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
334	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
335	C₂²×D₄	—	2	8	no	—
336	C₂²×D₄	—	2	16	no	—
337	C₂²×D₄	—	2	4	no	—
338	C₂²×D₄	—	4	4	no	—
339	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
340	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
341	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
342	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
343	C₂³×C₄	—	4	4	no	—
344	C₂³×C₄	D₄×C₁₃	1	8	yes	—
345	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
346	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
347	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
348	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
349	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
350	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
351	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
352	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
353	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
354	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
355	#124	—	4	8	no	—
356	C₂²⋊Q₈	—	2	8	no	—
357	C₂²⋊Q₈	—	2	8	no	—
358	C₂²⋊Q₈	—	2	8	no	—
359	C₂²⋊Q₈	—	2	8	no	—
360	#121	—	2	8	no	—
361	#121	—	2	8	no	—
362	#121	—	2	8	no	—
363	#121	—	2	8	no	—
364	C₂×C₄⋊C₄	—	2	4	no	—
365	C₂×C₄⋊C₄	—	2	4	no	—
366	C₂×C₄⋊C₄	—	2	8	no	—
367	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
371	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
372	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
373	C₂×C₂²⋊C₄	—	2	8	no	—
374	C₂×C₂²⋊C₄	—	2	8	no	—
375	C₂×C₂²⋊C₄	—	2	8	no	—
376	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
382	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
384	C₂×C₄²	—	4	4	no	—
385	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
386	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
387	#95	C₂³×C₁₃	1	4	yes	—
388	#95	C₂³×C₁₃	1	4	yes	—
389	#95	C₂³×C₁₃	1	16	yes	—
390	#95	C₂³×C₁₃	1	16	yes	—
391	C₂×C₁₃	—	2	4	no	—
392	C₂×C₁₃	—	2	4	no	—
393	C₂×C₁₃	—	2	4	no	—
394	C₂×C₁₃	—	8	4	no	—
395	C₂×C₁₃	C₂²×#124	1	1	yes	characteristic
396	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
397	C₂×C₁₃	#3449	1	1	yes	characteristic
398	C₂×C₁₃	#3505	1	4	yes	—
399	C₂⁴	—	2	4	no	—
400	C₂⁴	—	2	8	no	—
401	C₂⁴	—	4	2	no	—
402	C₂⁴	—	4	2	no	—
403	C₂⁴	—	4	4	no	—
404	C₂⁴	—	4	4	no	—
405	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
406	C₂⁴	C₁₃×#41	1	8	yes	—
407	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
408	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
409	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
410	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
411	C₂×Q₈	—	2	4	no	—
412	C₂×Q₈	—	2	4	no	—
413	C₂×Q₈	—	2	8	no	—
414	C₂×Q₈	—	4	4	no	—
415	C₂×Q₈	—	4	16	no	—
416	C₂×D₄	—	2	8	no	—
417	C₂×D₄	—	2	8	no	—
418	C₂×D₄	—	2	16	no	—
419	C₂×D₄	—	2	16	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	8	no	—
423	C₂×D₄	—	4	4	no	—
424	C₂×D₄	—	4	16	no	—
425	C₂×D₄	—	4	32	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	8	no	—
433	C₂²×C₄	—	2	8	no	—
434	C₂²×C₄	—	4	16	no	—
435	C₂²×C₄	—	4	4	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	—	4	2	no	—
439	C₂²×C₄	—	4	4	no	—
440	C₂²×C₄	—	4	4	no	—
441	C₂²×C₄	—	4	4	no	—
442	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
443	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
444	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
445	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
446	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
447	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
448	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
449	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
450	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
451	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
452	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
453	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
454	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
455	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	2	8	no	—
461	C₄⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	2	8	no	—
463	C₂²⋊C₄	—	2	8	no	—
464	C₂²⋊C₄	—	2	8	no	—
465	C₂²⋊C₄	—	2	8	no	—
466	C₂²⋊C₄	—	2	8	no	—
467	C₂²⋊C₄	—	2	8	no	—
468	C₂²⋊C₄	—	4	16	no	—
469	C₂²⋊C₄	—	4	16	no	—
470	C₄²	—	2	8	no	—
471	C₄²	—	4	4	no	—
472	C₁₃	#35019	1	1	yes	characteristic, direct product factor, Sylow
473	C₂³	—	2	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	2	8	no	—
481	C₂³	—	2	8	no	—
482	C₂³	—	2	8	no	—
483	C₂³	—	4	4	no	—
484	C₂³	—	4	4	no	—
485	C₂³	—	4	16	no	—
486	C₂³	—	4	8	no	—
487	C₂³	—	4	8	no	—
488	C₂³	—	4	8	no	—
489	C₂³	—	8	16	no	—
490	C₂³	C₁₃×#124	1	16	yes	complemented
491	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
492	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
493	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
494	C₂³	C₂×C₁₃×#41	1	4	yes	—
495	C₂³	C₂×C₁₃×#41	1	4	yes	—
496	C₂³	C₂×C₁₃×#41	1	4	yes	—
497	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
498	Q₈	—	4	8	no	—
499	Q₈	—	4	8	no	—
500	D₄	—	4	8	no	—
501	D₄	—	4	16	no	—
502	D₄	—	4	16	no	—
503	D₄	—	4	8	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	8	no	—
508	C₂×C₄	—	2	8	no	—
509	C₂×C₄	—	2	8	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	8	no	—
514	C₂×C₄	—	2	8	no	—
515	C₂×C₄	—	2	8	no	—
516	C₂×C₄	—	2	8	no	—
517	C₂×C₄	—	2	8	no	—
518	C₂×C₄	—	2	8	no	—
519	C₂×C₄	—	4	4	no	—
520	C₂×C₄	—	4	4	no	—
521	C₂×C₄	—	4	4	no	—
522	C₂×C₄	—	4	8	no	—
523	C₂×C₄	—	4	16	no	—
524	C₂×C₄	—	4	8	no	—
525	C₂×C₄	—	4	8	no	—
526	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
527	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
528	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
529	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
530	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	2	2	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	8	no	—
538	C₂²	—	2	8	no	—
539	C₂²	—	2	8	no	—
540	C₂²	—	4	16	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	4	4	no	—
544	C₂²	—	4	16	no	—
545	C₂²	—	8	16	no	—
546	C₂²	C₂×C₁₃×#124	1	4	yes	—
547	C₂²	C₂×C₁₃×#124	1	4	yes	—
548	C₂²	C₂×C₁₃×#124	1	4	yes	—
549	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
550	C₂²	C₂²×C₁₃×#41	1	2	yes	—
551	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
552	C₂²	C₁₃×#585	1	2	yes	—
553	C₄	—	2	2	no	—
554	C₄	—	2	2	no	—
555	C₄	—	2	2	no	—
556	C₄	—	4	4	no	—
557	C₄	—	4	4	no	—
558	C₄	—	4	4	no	—
559	C₄	—	4	8	no	—
560	C₄	C₁₃×#534	1	4	yes	—
561	C₂	—	2	4	no	—
562	C₂	—	2	4	no	—
563	C₂	—	2	4	no	—
564	C₂	—	8	4	no	—
565	C₂	C₂²×C₁₃×#124	1	1	yes	characteristic
566	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
567	C₂	C₁₃×#3449	1	1	yes	characteristic
568	C₂	C₁₃×#3505	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#121	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
3. C₁₃×#2850	C₂	semidirect
4. C₁₃×#2639	C₂	semidirect
5. C₁₃×#2591	C₂	semidirect
6. C₁₃×#2561	C₂	semidirect
7. C₁₃×#2504	C₂	semidirect
8. C₁₃×#2503	C₂	semidirect
9. C₁₃×#2436	C₂	semidirect
10. C₁₃×#2435	C₂	semidirect
11. C₁₃×#2308	C₂	semidirect
12. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
13. C₂³×Q₈×C₁₃	C₂²	semidirect
17. C₂×C₁₃×#124	C₂²	semidirect
21. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
22. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
29. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
30. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
34. C₂²×C₄²×C₁₃	C₂²	semidirect
35. C₁₃×#400	C₂²	semidirect
36. C₁₃×#397	C₂²	semidirect
37. C₁₃×#394	C₂²	semidirect
38. C₁₃×#393	C₂²	semidirect
39. C₁₃×#391	C₂²	semidirect
40. C₁₃×#390	C₂²	semidirect
41. C₁₃×#388	C₂²	semidirect
42. C₁₃×#386	C₂²	semidirect
43. C₁₃×#386	C₂²	semidirect
44. C₁₃×#386	C₂²	semidirect
45. C₁₃×#382	C₂²	semidirect
50. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
51. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
52. C₂×C₁₃×#95	C₂²	semidirect
115. #35019	C₁₃	direct (N × H)
189. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
191. #2850	C₂×C₁₃	semidirect
192. #2639	C₂×C₁₃	semidirect
193. #2591	C₂×C₁₃	semidirect
194. #2561	C₂×C₁₃	semidirect
195. #2504	C₂×C₁₃	semidirect
196. #2503	C₂×C₁₃	semidirect
197. #2436	C₂×C₁₃	semidirect
198. #2435	C₂×C₁₃	semidirect
199. #2308	C₂×C₁₃	semidirect
200. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
218. C₂³×C₁₃	#124	semidirect
259. C₂³×Q₈	C₂²×C₁₃	semidirect
263. C₂×#124	C₂²×C₁₃	semidirect
267. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
268. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
275. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
276. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
280. C₂²×C₄²	C₂²×C₁₃	semidirect
281. #400	C₂²×C₁₃	semidirect
282. #397	C₂²×C₁₃	semidirect
283. #394	C₂²×C₁₃	semidirect
284. #393	C₂²×C₁₃	semidirect
285. #391	C₂²×C₁₃	semidirect
286. #390	C₂²×C₁₃	semidirect
287. #388	C₂²×C₁₃	semidirect
288. #386	C₂²×C₁₃	semidirect
289. #386	C₂²×C₁₃	semidirect
290. #386	C₂²×C₁₃	semidirect
291. #382	C₂²×C₁₃	semidirect
296. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
297. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
298. C₂×#95	C₂²×C₁₃	semidirect
472. C₁₃	#35019	direct (N × H)
490. C₂³	C₁₃×#124	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₁₃×C₂²⋊Q₈	2
C₂²×C₁₃×#121	2
C₁₃×#2850	2
C₁₃×#2639	2
C₁₃×#2591	2
C₁₃×#2561	2
C₁₃×#2504	2
C₁₃×#2503	2
C₁₃×#2436	2
C₁₃×#2435	2
C₁₃×#2308	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
#35019	13

Subgroups — C13×#35019 #15721358

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#35019 #15721358