Subgroups — C₁₃×#34985 #15721324

Order 3328.

2866 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2855	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2848	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2627	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2626	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2450	C₂	1	8	yes	maximal, complemented
8	C₁₃×#2449	C₂	1	8	yes	maximal, complemented
9	C₁₃×#2315	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2308	C₂	1	2	yes	maximal
11	C₂×C₁₃×#385	C₂	1	2	yes	maximal, complemented
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#543	—	2	8	no	—
16	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
21	C₂×C₄×D₄×C₁₃	—	2	8	no	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#400	C₂²	1	4	yes	complemented
31	C₁₃×#399	C₂²	1	4	yes	complemented
32	C₁₃×#398	C₂²	1	8	yes	complemented
33	C₁₃×#396	C₂²	1	8	yes	complemented
34	C₁₃×#395	C₂²	1	4	yes	complemented
35	C₁₃×#393	C₂²	1	4	yes	complemented
36	C₁₃×#391	C₂²	1	4	yes	complemented
37	C₁₃×#389	C₂²	1	4	yes	complemented
38	C₁₃×#387	C₂²	1	8	yes	complemented
39	C₁₃×#386	C₂²	1	4	yes	—
40	C₁₃×#386	C₂²	1	8	yes	—
41	C₁₃×#386	C₂²	1	4	yes	—
42	C₁₃×#385	C₂²	1	4	yes	—
43	C₁₃×#385	C₂²	1	4	yes	—
44	C₁₃×#385	C₂²	1	8	yes	complemented
45	C₁₃×#385	C₂²	1	8	yes	complemented
46	C₁₃×#385	C₂²	1	8	yes	complemented
47	C₁₃×#381	C₂²	1	4	yes	—
48	C₁₃×#380	C₂²	1	2	yes	—
49	C₁₃×#380	C₂²	1	2	yes	—
50	C₁₃×#380	C₂²	1	4	yes	complemented
51	C₁₃×#379	C₂²	1	4	yes	—
52	C₂×C₁₃×#95	C₂²	1	4	yes	complemented
53	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
54	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
56	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
57	C₂²×D₄×C₁₃	—	2	4	no	—
58	C₂²×D₄×C₁₃	—	2	4	no	—
59	C₂²×D₄×C₁₃	Q₈	1	8	yes	complemented
60	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
61	C₂³×C₄×C₁₃	—	2	4	no	—
62	C₂³×C₄×C₁₃	—	2	4	no	—
63	C₂³×C₄×C₁₃	—	4	4	no	—
64	C₂³×C₄×C₁₃	—	4	4	no	—
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
71	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
72	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×C₂²⋊Q₈	—	2	8	no	—
76	C₁₃×C₂²⋊Q₈	—	2	8	no	—
77	C₁₃×C₂²⋊Q₈	—	2	16	no	—
78	C₁₃×C₂²⋊Q₈	—	2	16	no	—
79	C₁₃×C₂²⋊Q₈	—	4	8	no	—
80	C₄×D₄×C₁₃	—	2	32	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
82	C₂×C₁₃×C₄⋊C₄	—	4	8	no	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
95	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	—
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
97	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
100	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	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	4	no	—
105	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
106	C₁₃×#95	C₂³	1	4	yes	—
107	C₁₃×#95	C₂³	1	4	yes	—
108	C₁₃×#95	C₂³	1	8	yes	—
109	C₁₃×#95	C₂³	1	8	yes	—
110	C₁₃×#95	C₂³	1	8	yes	—
111	C₁₃×#95	C₂³	1	8	yes	—
112	#34985	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂⁴×C₁₃	—	2	2	no	—
114	C₂⁴×C₁₃	—	2	2	no	—
115	C₂⁴×C₁₃	—	4	2	no	—
116	C₂⁴×C₁₃	—	4	2	no	—
117	C₂⁴×C₁₃	—	4	2	no	—
118	C₂⁴×C₁₃	—	4	2	no	—
119	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
120	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
121	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
122	C₂⁴×C₁₃	#41	1	4	yes	—
123	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
124	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
126	C₂×Q₈×C₁₃	—	2	4	no	—
127	C₂×Q₈×C₁₃	—	2	4	no	—
128	C₂×Q₈×C₁₃	—	4	4	no	—
129	C₂×Q₈×C₁₃	—	4	4	no	—
130	C₂×D₄×C₁₃	—	2	32	no	—
131	C₂×D₄×C₁₃	—	2	8	no	—
132	C₂×D₄×C₁₃	—	2	8	no	—
133	C₂×D₄×C₁₃	C₂×Q₈	1	16	yes	—
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	8	no	—
140	C₂²×C₄×C₁₃	—	2	8	no	—
141	C₂²×C₄×C₁₃	—	2	4	no	—
142	C₂²×C₄×C₁₃	—	2	4	no	—
143	C₂²×C₄×C₁₃	—	2	8	no	—
144	C₂²×C₄×C₁₃	—	2	8	no	—
145	C₂²×C₄×C₁₃	—	2	8	no	—
146	C₂²×C₄×C₁₃	—	4	4	no	—
147	C₂²×C₄×C₁₃	—	4	2	no	—
148	C₂²×C₄×C₁₃	—	4	4	no	—
149	C₂²×C₄×C₁₃	—	4	4	no	—
150	C₂²×C₄×C₁₃	—	4	2	no	—
151	C₂²×C₄×C₁₃	—	4	2	no	—
152	C₂²×C₄×C₁₃	—	4	4	no	—
153	C₂²×C₄×C₁₃	—	4	4	no	—
154	C₂²×C₄×C₁₃	—	4	4	no	—
155	C₂²×C₄×C₁₃	—	4	16	no	—
156	C₂²×C₄×C₁₃	—	4	16	no	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
159	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
160	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	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	2	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
168	C₁₃×C₄⋊C₄	—	2	8	no	—
169	C₁₃×C₄⋊C₄	—	2	8	no	—
170	C₁₃×C₄⋊C₄	—	2	4	no	—
171	C₁₃×C₄⋊C₄	—	2	4	no	—
172	C₁₃×C₄⋊C₄	—	2	8	no	—
173	C₁₃×C₄⋊C₄	—	2	16	no	—
174	C₁₃×C₄⋊C₄	—	4	8	no	—
175	C₁₃×C₄⋊C₄	—	4	4	no	—
176	C₁₃×C₄⋊C₄	—	4	4	no	—
177	C₁₃×C₂²⋊C₄	—	2	8	no	—
178	C₁₃×C₂²⋊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	—	4	8	no	—
183	C₁₃×C₂²⋊C₄	—	4	8	no	—
184	C₁₃×C₂²⋊C₄	C₂×D₄	1	16	yes	—
185	C₄²×C₁₃	—	2	8	no	—
186	C₂×#543	C₂×C₁₃	1	1	yes	characteristic, complemented
187	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic
188	#2855	C₂×C₁₃	1	2	yes	complemented
189	#2848	C₂×C₁₃	1	2	yes	complemented
190	#2627	C₂×C₁₃	1	2	yes	complemented
191	#2626	C₂×C₁₃	1	2	yes	complemented
192	#2450	C₂×C₁₃	1	8	yes	complemented
193	#2449	C₂×C₁₃	1	8	yes	complemented
194	#2315	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#2308	C₂×C₁₃	1	2	yes	—
196	C₂×#385	C₂×C₁₃	1	2	yes	complemented
197	C₂³×C₁₃	—	2	4	no	—
198	C₂³×C₁₃	—	2	2	no	—
199	C₂³×C₁₃	—	2	4	no	—
200	C₂³×C₁₃	—	2	2	no	—
201	C₂³×C₁₃	—	2	8	no	—
202	C₂³×C₁₃	—	2	2	no	—
203	C₂³×C₁₃	—	2	2	no	—
204	C₂³×C₁₃	—	2	4	no	—
205	C₂³×C₁₃	—	2	4	no	—
206	C₂³×C₁₃	—	4	4	no	—
207	C₂³×C₁₃	—	4	4	no	—
208	C₂³×C₁₃	—	4	8	no	—
209	C₂³×C₁₃	—	4	8	no	—
210	C₂³×C₁₃	—	4	8	no	—
211	C₂³×C₁₃	—	4	4	no	—
212	C₂³×C₁₃	—	4	8	no	—
213	C₂³×C₁₃	—	4	4	no	—
214	C₂³×C₁₃	C₂²⋊Q₈	1	16	yes	complemented
215	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
216	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
217	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
218	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
219	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
220	C₂³×C₁₃	C₂×#41	1	2	yes	—
221	C₂³×C₁₃	C₂×#41	1	4	yes	—
222	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
223	Q₈×C₁₃	—	8	4	no	—
224	Q₈×C₁₃	—	8	4	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	2	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	4	no	—
234	C₂×C₄×C₁₃	—	2	4	no	—
235	C₂×C₄×C₁₃	—	2	4	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	8	no	—
238	C₂×C₄×C₁₃	—	2	8	no	—
239	C₂×C₄×C₁₃	—	2	8	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	—	4	4	no	—
244	C₂×C₄×C₁₃	—	4	4	no	—
245	C₂×C₄×C₁₃	—	4	16	no	—
246	C₂×C₄×C₁₃	—	4	16	no	—
247	C₂×C₄×C₁₃	—	4	16	no	—
248	C₂×C₄×C₁₃	—	4	4	no	—
249	C₂×C₄×C₁₃	—	8	4	no	—
250	C₂×C₄×C₁₃	—	8	4	no	—
251	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
252	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
253	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
254	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
255	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
256	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
257	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
258	#543	—	2	8	no	—
259	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
260	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
261	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
262	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
263	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
264	C₂×C₄×D₄	—	2	8	no	—
265	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
266	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
267	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
268	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
269	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
270	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
271	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
272	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
273	#400	C₂²×C₁₃	1	4	yes	complemented
274	#399	C₂²×C₁₃	1	4	yes	complemented
275	#398	C₂²×C₁₃	1	8	yes	complemented
276	#396	C₂²×C₁₃	1	8	yes	complemented
277	#395	C₂²×C₁₃	1	4	yes	complemented
278	#393	C₂²×C₁₃	1	4	yes	complemented
279	#391	C₂²×C₁₃	1	4	yes	complemented
280	#389	C₂²×C₁₃	1	4	yes	complemented
281	#387	C₂²×C₁₃	1	8	yes	complemented
282	#386	C₂²×C₁₃	1	4	yes	—
283	#386	C₂²×C₁₃	1	8	yes	—
284	#386	C₂²×C₁₃	1	4	yes	—
285	#385	C₂²×C₁₃	1	4	yes	—
286	#385	C₂²×C₁₃	1	4	yes	—
287	#385	C₂²×C₁₃	1	8	yes	complemented
288	#385	C₂²×C₁₃	1	8	yes	complemented
289	#385	C₂²×C₁₃	1	8	yes	complemented
290	#381	C₂²×C₁₃	1	4	yes	—
291	#380	C₂²×C₁₃	1	2	yes	—
292	#380	C₂²×C₁₃	1	2	yes	—
293	#380	C₂²×C₁₃	1	4	yes	complemented
294	#379	C₂²×C₁₃	1	4	yes	—
295	C₂×#95	C₂²×C₁₃	1	4	yes	complemented
296	C₂²×C₁₃	—	2	8	no	—
297	C₂²×C₁₃	—	2	4	no	—
298	C₂²×C₁₃	—	2	2	no	—
299	C₂²×C₁₃	—	2	4	no	—
300	C₂²×C₁₃	—	2	2	no	—
301	C₂²×C₁₃	—	2	4	no	—
302	C₂²×C₁₃	—	2	4	no	—
303	C₂²×C₁₃	—	2	8	no	—
304	C₂²×C₁₃	—	2	4	no	—
305	C₂²×C₁₃	—	2	8	no	—
306	C₂²×C₁₃	—	4	16	no	—
307	C₂²×C₁₃	—	4	16	no	—
308	C₂²×C₁₃	—	4	4	no	—
309	C₂²×C₁₃	—	4	2	no	—
310	C₂²×C₁₃	—	4	2	no	—
311	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
312	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	8	yes	—
313	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
314	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
315	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
316	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
317	C₂²×C₁₃	#585	1	2	yes	—
318	C₄×C₁₃	—	2	4	no	—
319	C₄×C₁₃	—	2	4	no	—
320	C₄×C₁₃	—	2	4	no	—
321	C₄×C₁₃	—	2	4	no	—
322	C₄×C₁₃	—	4	8	no	—
323	C₄×C₁₃	—	4	2	no	—
324	C₄×C₁₃	—	4	4	no	—
325	C₄×C₁₃	—	4	4	no	—
326	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
327	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
328	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
329	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
330	C₂²×D₄	—	2	4	no	—
331	C₂²×D₄	—	2	4	no	—
332	C₂²×D₄	Q₈×C₁₃	1	8	yes	complemented
333	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
334	C₂³×C₄	—	2	4	no	—
335	C₂³×C₄	—	2	4	no	—
336	C₂³×C₄	—	4	4	no	—
337	C₂³×C₄	—	4	4	no	—
338	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
339	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
340	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
341	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
342	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
343	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
344	C₂³×C₄	C₂³×C₁₃	1	4	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	C₂²⋊Q₈	—	2	8	no	—
349	C₂²⋊Q₈	—	2	8	no	—
350	C₂²⋊Q₈	—	2	16	no	—
351	C₂²⋊Q₈	—	2	16	no	—
352	C₂²⋊Q₈	—	4	8	no	—
353	C₄×D₄	—	2	32	no	—
354	C₂×C₄⋊C₄	—	2	4	no	—
355	C₂×C₄⋊C₄	—	4	8	no	—
356	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
357	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
358	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
359	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
360	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
361	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
365	C₂×C₂²⋊C₄	—	2	8	no	—
366	C₂×C₂²⋊C₄	—	2	8	no	—
367	C₂×C₂²⋊C₄	—	2	4	no	—
368	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	—
369	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
370	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
376	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
377	C₂×C₄²	—	2	4	no	—
378	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
379	#95	C₂³×C₁₃	1	8	yes	—
380	#95	C₂³×C₁₃	1	8	yes	—
381	#95	C₂³×C₁₃	1	4	yes	—
382	#95	C₂³×C₁₃	1	4	yes	—
383	#95	C₂³×C₁₃	1	8	yes	—
384	#95	C₂³×C₁₃	1	8	yes	—
385	C₂×C₁₃	—	2	4	no	—
386	C₂×C₁₃	—	2	8	no	—
387	C₂×C₁₃	—	4	4	no	—
388	C₂×C₁₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
389	C₂×C₁₃	#3459	1	2	yes	—
390	C₂×C₁₃	#3484	1	1	yes	characteristic
391	C₂×C₁₃	#3485	1	1	yes	characteristic
392	C₂×C₁₃	#3501	1	2	yes	—
393	C₂⁴	—	2	2	no	—
394	C₂⁴	—	2	2	no	—
395	C₂⁴	—	4	2	no	—
396	C₂⁴	—	4	2	no	—
397	C₂⁴	—	4	2	no	—
398	C₂⁴	—	4	2	no	—
399	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
400	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
401	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
402	C₂⁴	C₁₃×#41	1	4	yes	—
403	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
404	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
405	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
406	C₂×Q₈	—	2	4	no	—
407	C₂×Q₈	—	2	4	no	—
408	C₂×Q₈	—	4	4	no	—
409	C₂×Q₈	—	4	4	no	—
410	C₂×D₄	—	2	32	no	—
411	C₂×D₄	—	2	8	no	—
412	C₂×D₄	—	2	8	no	—
413	C₂×D₄	C₂×Q₈×C₁₃	1	16	yes	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	8	no	—
420	C₂²×C₄	—	2	8	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	8	no	—
424	C₂²×C₄	—	2	8	no	—
425	C₂²×C₄	—	2	8	no	—
426	C₂²×C₄	—	4	4	no	—
427	C₂²×C₄	—	4	2	no	—
428	C₂²×C₄	—	4	4	no	—
429	C₂²×C₄	—	4	4	no	—
430	C₂²×C₄	—	4	2	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	4	4	no	—
433	C₂²×C₄	—	4	4	no	—
434	C₂²×C₄	—	4	4	no	—
435	C₂²×C₄	—	4	16	no	—
436	C₂²×C₄	—	4	16	no	—
437	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
438	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
439	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
440	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
441	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
442	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
443	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
444	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
445	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
446	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
447	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
448	C₄⋊C₄	—	2	8	no	—
449	C₄⋊C₄	—	2	8	no	—
450	C₄⋊C₄	—	2	4	no	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	—	2	8	no	—
453	C₄⋊C₄	—	2	16	no	—
454	C₄⋊C₄	—	4	8	no	—
455	C₄⋊C₄	—	4	4	no	—
456	C₄⋊C₄	—	4	4	no	—
457	C₂²⋊C₄	—	2	8	no	—
458	C₂²⋊C₄	—	2	8	no	—
459	C₂²⋊C₄	—	2	8	no	—
460	C₂²⋊C₄	—	2	8	no	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	4	8	no	—
463	C₂²⋊C₄	—	4	8	no	—
464	C₂²⋊C₄	C₂×D₄×C₁₃	1	16	yes	—
465	C₄²	—	2	8	no	—
466	C₁₃	#34985	1	1	yes	characteristic, direct product factor, Sylow
467	C₂³	—	2	4	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	4	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	2	8	no	—
472	C₂³	—	2	2	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	4	no	—
476	C₂³	—	4	4	no	—
477	C₂³	—	4	4	no	—
478	C₂³	—	4	8	no	—
479	C₂³	—	4	8	no	—
480	C₂³	—	4	8	no	—
481	C₂³	—	4	4	no	—
482	C₂³	—	4	8	no	—
483	C₂³	—	4	4	no	—
484	C₂³	C₁₃×C₂²⋊Q₈	1	16	yes	complemented
485	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
486	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
487	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
488	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
489	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
490	C₂³	C₂×C₁₃×#41	1	2	yes	—
491	C₂³	C₂×C₁₃×#41	1	4	yes	—
492	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
493	Q₈	—	8	4	no	—
494	Q₈	—	8	4	no	—
495	D₄	—	2	32	no	—
496	C₂×C₄	—	2	8	no	—
497	C₂×C₄	—	2	8	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	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	8	no	—
512	C₂×C₄	—	2	8	no	—
513	C₂×C₄	—	4	4	no	—
514	C₂×C₄	—	4	4	no	—
515	C₂×C₄	—	4	16	no	—
516	C₂×C₄	—	4	16	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	4	16	no	—
519	C₂×C₄	—	8	4	no	—
520	C₂×C₄	—	8	4	no	—
521	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
522	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
523	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
524	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
525	C₂²	—	2	8	no	—
526	C₂²	—	2	4	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	4	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	4	no	—
531	C₂²	—	2	4	no	—
532	C₂²	—	2	8	no	—
533	C₂²	—	2	4	no	—
534	C₂²	—	2	8	no	—
535	C₂²	—	4	16	no	—
536	C₂²	—	4	16	no	—
537	C₂²	—	4	4	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	2	no	—
540	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
541	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	8	yes	—
542	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
543	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
544	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
545	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
546	C₂²	C₁₃×#585	1	2	yes	—
547	C₄	—	2	4	no	—
548	C₄	—	2	4	no	—
549	C₄	—	2	4	no	—
550	C₄	—	2	4	no	—
551	C₄	—	4	8	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	4	no	—
554	C₄	—	4	4	no	—
555	C₂	—	2	4	no	—
556	C₂	—	2	8	no	—
557	C₂	—	4	4	no	—
558	C₂	C₂²×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
559	C₂	C₁₃×#3459	1	2	yes	—
560	C₂	C₁₃×#3484	1	1	yes	characteristic
561	C₂	C₁₃×#3485	1	1	yes	characteristic
562	C₂	C₁₃×#3501	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
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. C₂×C₁₃×#543	C₂	semidirect
3. C₁₃×#2855	C₂	semidirect
4. C₁₃×#2848	C₂	semidirect
5. C₁₃×#2627	C₂	semidirect
6. C₁₃×#2626	C₂	semidirect
7. C₁₃×#2450	C₂	semidirect
8. C₁₃×#2449	C₂	semidirect
9. C₁₃×#2315	C₂	semidirect
11. C₂×C₁₃×#385	C₂	semidirect
18. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
19. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
20. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
24. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
30. C₁₃×#400	C₂²	semidirect
31. C₁₃×#399	C₂²	semidirect
32. C₁₃×#398	C₂²	semidirect
33. C₁₃×#396	C₂²	semidirect
34. C₁₃×#395	C₂²	semidirect
35. C₁₃×#393	C₂²	semidirect
36. C₁₃×#391	C₂²	semidirect
37. C₁₃×#389	C₂²	semidirect
38. C₁₃×#387	C₂²	semidirect
44. C₁₃×#385	C₂²	semidirect
45. C₁₃×#385	C₂²	semidirect
46. C₁₃×#385	C₂²	semidirect
50. C₁₃×#380	C₂²	semidirect
52. C₂×C₁₃×#95	C₂²	semidirect
59. C₂²×D₄×C₁₃	Q₈	semidirect
112. #34985	C₁₃	direct (N × H)
186. C₂×#543	C₂×C₁₃	semidirect
188. #2855	C₂×C₁₃	semidirect
189. #2848	C₂×C₁₃	semidirect
190. #2627	C₂×C₁₃	semidirect
191. #2626	C₂×C₁₃	semidirect
192. #2450	C₂×C₁₃	semidirect
193. #2449	C₂×C₁₃	semidirect
194. #2315	C₂×C₁₃	semidirect
196. C₂×#385	C₂×C₁₃	semidirect
214. C₂³×C₁₃	C₂²⋊Q₈	semidirect
261. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
262. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
263. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
267. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
273. #400	C₂²×C₁₃	semidirect
274. #399	C₂²×C₁₃	semidirect
275. #398	C₂²×C₁₃	semidirect
276. #396	C₂²×C₁₃	semidirect
277. #395	C₂²×C₁₃	semidirect
278. #393	C₂²×C₁₃	semidirect
279. #391	C₂²×C₁₃	semidirect
280. #389	C₂²×C₁₃	semidirect
281. #387	C₂²×C₁₃	semidirect
287. #385	C₂²×C₁₃	semidirect
288. #385	C₂²×C₁₃	semidirect
289. #385	C₂²×C₁₃	semidirect
293. #380	C₂²×C₁₃	semidirect
295. C₂×#95	C₂²×C₁₃	semidirect
332. C₂²×D₄	Q₈×C₁₃	semidirect
466. C₁₃	#34985	direct (N × H)
484. C₂³	C₁₃×C₂²⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#543	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2855	2
C₁₃×#2848	2
C₁₃×#2627	2
C₁₃×#2626	2
C₁₃×#2450	2
C₁₃×#2449	2
C₁₃×#2315	2
C₁₃×#2308	2
C₂×C₁₃×#385	2
#34985	13

Subgroups — C13×#34985 #15721324

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34985 #15721324