Subgroups — C₁₃×#22654 #15708993

Order 3328.

1010 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2352	C₂	1	2	yes	maximal
5	C₁₃×#1949	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1854	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1852	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1846	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1807	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1807	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#117	C₂²	1	2	yes	—
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
17	C₈×D₄×C₁₃	C₄	1	8	yes	complemented
18	C₁₃×#427	—	2	4	no	—
19	C₂×C₁₃×#107	C₂²	1	2	yes	—
20	C₂×C₁₃×#107	C₂²	1	2	yes	—
21	C₂×C₁₃×#106	—	2	4	no	—
22	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#106	C₂²	1	2	yes	—
26	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#388	—	2	2	no	—
32	C₁₃×#387	—	2	2	no	—
33	C₁₃×#386	—	2	2	no	—
34	C₁₃×#382	C₂²	1	2	yes	—
35	C₁₃×#380	C₂²	1	2	yes	—
36	C₁₃×#380	C₂²	1	2	yes	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
38	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	—	2	2	no	—
44	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	—	2	2	no	—
47	C₂²×C₈×C₁₃	—	2	2	no	—
48	C₂²×C₈×C₁₃	—	2	2	no	—
49	C₂²×C₈×C₁₃	—	2	2	no	—
50	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
51	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
57	C₄×D₄×C₁₃	Q₈	1	4	yes	—
58	C₁₃×#117	—	2	4	no	—
59	C₁₃×#117	—	4	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
63	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
72	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	—	2	2	no	—
74	C₂×C₄²×C₁₃	—	2	2	no	—
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#107	—	2	4	no	—
77	C₁₃×#107	—	4	2	no	—
78	C₁₃×#106	—	2	2	no	—
79	C₁₃×#106	—	2	2	no	—
80	C₁₃×#106	—	2	2	no	—
81	C₁₃×#106	—	2	4	no	—
82	C₁₃×#106	D₄	1	4	yes	complemented
83	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
84	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
85	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
86	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
87	C₁₃×#95	—	2	2	no	—
88	C₁₃×#95	—	2	2	no	—
89	C₁₃×#95	—	2	2	no	—
90	C₁₃×#95	—	2	2	no	—
91	C₁₃×#95	—	2	2	no	—
92	#22654	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
94	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂×D₄×C₁₃	—	2	4	no	—
96	C₂×D₄×C₁₃	C₄⋊C₄	1	4	yes	—
97	C₂²×C₄×C₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	4	4	no	—
110	C₂²×C₄×C₁₃	—	4	4	no	—
111	C₂²×C₄×C₁₃	—	8	2	no	—
112	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
119	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
120	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	2	8	no	—
128	C₂×C₈×C₁₃	—	2	8	no	—
129	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
131	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₁₃	#41	1	2	yes	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₁₃×C₄⋊C₄	—	4	4	no	—
143	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
144	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
145	C₁₃×C₂²⋊C₄	—	4	4	no	—
146	C₁₃×C₂²⋊C₄	—	4	4	no	—
147	C₁₃×C₂²⋊C₄	—	8	2	no	—
148	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
149	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
150	C₄²×C₁₃	—	4	4	no	—
151	C₄²×C₁₃	—	8	2	no	—
152	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
153	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
154	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic
155	C₂×#427	C₂×C₁₃	1	1	yes	characteristic, complemented
156	C₂²×#106	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#2352	C₂×C₁₃	1	2	yes	—
158	#1949	C₂×C₁₃	1	2	yes	complemented
159	#1854	C₂×C₁₃	1	2	yes	complemented
160	#1852	C₂×C₁₃	1	2	yes	complemented
161	#1846	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#1807	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#1807	C₂×C₁₃	1	1	yes	characteristic, complemented
164	C₄×#106	C₂×C₁₃	1	1	yes	characteristic, complemented
165	C₂³×C₁₃	—	2	1	no	—
166	C₂³×C₁₃	—	2	1	no	—
167	C₂³×C₁₃	—	2	2	no	—
168	C₂³×C₁₃	—	2	1	no	—
169	C₂³×C₁₃	—	2	1	no	—
170	C₂³×C₁₃	—	2	2	no	—
171	C₂³×C₁₃	—	2	2	no	—
172	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
173	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
174	C₂³×C₁₃	#135	1	4	yes	—
175	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
176	D₄×C₁₃	—	2	8	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	4	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	8	8	no	—
204	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
205	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
206	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
207	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
208	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
213	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
214	C₈×C₁₃	—	2	2	no	—
215	C₈×C₁₃	—	2	2	no	—
216	C₈×C₁₃	—	2	2	no	—
217	C₈×C₁₃	C₄×D₄	1	4	yes	—
218	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
219	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×#117	C₂²×C₁₃	1	2	yes	—
222	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
223	C₈×D₄	C₄×C₁₃	1	8	yes	complemented
224	#427	—	2	4	no	—
225	C₂×#107	C₂²×C₁₃	1	2	yes	—
226	C₂×#107	C₂²×C₁₃	1	2	yes	—
227	C₂×#106	—	2	4	no	—
228	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
230	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
231	C₂×#106	C₂²×C₁₃	1	2	yes	—
232	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
235	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
237	#388	—	2	2	no	—
238	#387	—	2	2	no	—
239	#386	—	2	2	no	—
240	#382	C₂²×C₁₃	1	2	yes	—
241	#380	C₂²×C₁₃	1	2	yes	—
242	#380	C₂²×C₁₃	1	2	yes	—
243	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
244	C₄×C₂²⋊C₄	—	2	2	no	—
245	#340	C₂²×C₁₃	1	2	yes	—
246	#340	C₂²×C₁₃	1	2	yes	—
247	#340	C₂²×C₁₃	1	2	yes	—
248	C₂²×C₁₃	—	2	4	no	—
249	C₂²×C₁₃	—	2	2	no	—
250	C₂²×C₁₃	—	2	2	no	—
251	C₂²×C₁₃	—	2	4	no	—
252	C₂²×C₁₃	—	2	2	no	—
253	C₂²×C₁₃	—	2	2	no	—
254	C₂²×C₁₃	—	2	2	no	—
255	C₂²×C₁₃	—	4	2	no	—
256	C₂²×C₁₃	—	4	2	no	—
257	C₂²×C₁₃	#427	1	4	yes	complemented
258	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
259	C₂²×C₁₃	D₄²	1	1	yes	characteristic
260	C₂²×C₁₃	#547	1	1	yes	characteristic
261	C₂²×C₁₃	C₂×#135	1	2	yes	—
262	C₂²×C₁₃	#577	1	2	yes	—
263	C₄×C₁₃	—	2	2	no	—
264	C₄×C₁₃	—	2	2	no	—
265	C₄×C₁₃	—	2	2	no	—
266	C₄×C₁₃	—	2	2	no	—
267	C₄×C₁₃	—	4	4	no	—
268	C₄×C₁₃	—	8	2	no	—
269	C₄×C₁₃	—	8	2	no	—
270	C₄×C₁₃	—	8	2	no	—
271	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
272	C₄×C₁₃	#520	1	1	yes	characteristic
273	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
274	C₄×C₁₃	#554	1	1	yes	characteristic
275	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
276	C₂³×C₄	—	2	2	no	—
277	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
278	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
279	C₂²×C₈	—	2	2	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	—	2	2	no	—
282	C₂²×C₈	—	2	2	no	—
283	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
284	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	complemented
285	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
287	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
289	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
290	C₄×D₄	Q₈×C₁₃	1	4	yes	—
291	#117	—	2	4	no	—
292	#117	—	4	2	no	—
293	C₂×C₄⋊C₄	—	2	4	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	4	2	no	—
296	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
298	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
299	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
306	C₂×C₄²	—	2	2	no	—
307	C₂×C₄²	—	2	2	no	—
308	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
309	#107	—	2	4	no	—
310	#107	—	4	2	no	—
311	#106	—	2	2	no	—
312	#106	—	2	2	no	—
313	#106	—	2	2	no	—
314	#106	—	2	4	no	—
315	#106	D₄×C₁₃	1	4	yes	complemented
316	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	complemented
317	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
318	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	complemented
319	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	complemented
320	#95	—	2	2	no	—
321	#95	—	2	2	no	—
322	#95	—	2	2	no	—
323	#95	—	2	2	no	—
324	#95	—	2	2	no	—
325	C₂×C₁₃	—	2	4	no	—
326	C₂×C₁₃	—	4	2	no	—
327	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
328	C₂×C₁₃	C₂×#427	1	1	yes	characteristic
329	C₂×C₁₃	#2912	1	1	yes	characteristic
330	C₂×C₁₃	#3282	1	2	yes	—
331	C₂×C₁₃	#3337	1	2	yes	—
332	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
333	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	C₁₃×C₄⋊C₄	1	4	yes	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	4	4	no	—
349	C₂²×C₄	—	4	4	no	—
350	C₂²×C₄	—	8	2	no	—
351	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
352	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
353	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
357	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
358	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
359	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	8	no	—
367	C₂×C₈	—	2	8	no	—
368	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
369	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
370	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
371	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
372	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
373	C₂×C₈	C₁₃×#41	1	2	yes	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	4	4	no	—
382	C₄⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
383	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
384	C₂²⋊C₄	—	4	4	no	—
385	C₂²⋊C₄	—	4	4	no	—
386	C₂²⋊C₄	—	8	2	no	—
387	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
388	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
389	C₄²	—	4	4	no	—
390	C₄²	—	8	2	no	—
391	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
392	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
393	C₁₃	#22654	1	1	yes	characteristic, direct product factor, Sylow
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	1	no	—
398	C₂³	—	2	1	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
402	C₂³	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
403	C₂³	C₁₃×#135	1	4	yes	—
404	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
405	D₄	—	2	8	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	8	8	no	—
433	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
434	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
435	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
436	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
437	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
438	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
439	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
440	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
441	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
442	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
443	C₈	—	2	2	no	—
444	C₈	—	2	2	no	—
445	C₈	—	2	2	no	—
446	C₈	C₄×D₄×C₁₃	1	4	yes	—
447	C₂²	—	2	4	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	C₁₃×#427	1	4	yes	complemented
457	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
458	C₂²	D₄²×C₁₃	1	1	yes	characteristic
459	C₂²	C₁₃×#547	1	1	yes	characteristic
460	C₂²	C₂×C₁₃×#135	1	2	yes	—
461	C₂²	C₁₃×#577	1	2	yes	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	2	no	—
466	C₄	—	4	4	no	—
467	C₄	—	8	2	no	—
468	C₄	—	8	2	no	—
469	C₄	—	8	2	no	—
470	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
471	C₄	C₁₃×#520	1	1	yes	characteristic
472	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
473	C₄	C₁₃×#554	1	1	yes	characteristic
474	C₂	—	2	4	no	—
475	C₂	—	4	2	no	—
476	C₂	D₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
477	C₂	C₂×C₁₃×#427	1	1	yes	characteristic
478	C₂	C₁₃×#2912	1	1	yes	characteristic
479	C₂	C₁₃×#3282	1	2	yes	—
480	C₂	C₁₃×#3337	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#427	C₂	semidirect
3. C₂²×C₁₃×#106	C₂	semidirect
5. C₁₃×#1949	C₂	semidirect
6. C₁₃×#1854	C₂	semidirect
7. C₁₃×#1852	C₂	semidirect
8. C₁₃×#1846	C₂	semidirect
9. C₁₃×#1807	C₂	semidirect
10. C₁₃×#1807	C₂	semidirect
11. C₄×C₁₃×#106	C₂	semidirect
17. C₈×D₄×C₁₃	C₄	semidirect
51. C₂²×C₈×C₁₃	C₂×C₄	semidirect
82. C₁₃×#106	D₄	semidirect
83. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
85. C₁₃×C₂²⋊C₈	C₂×C₄	semidirect
86. C₄×C₈×C₁₃	C₂×C₄	semidirect
92. #22654	C₁₃	direct (N × H)
155. C₂×#427	C₂×C₁₃	semidirect
156. C₂²×#106	C₂×C₁₃	semidirect
158. #1949	C₂×C₁₃	semidirect
159. #1854	C₂×C₁₃	semidirect
160. #1852	C₂×C₁₃	semidirect
161. #1846	C₂×C₁₃	semidirect
162. #1807	C₂×C₁₃	semidirect
163. #1807	C₂×C₁₃	semidirect
164. C₄×#106	C₂×C₁₃	semidirect
223. C₈×D₄	C₄×C₁₃	semidirect
257. C₂²×C₁₃	#427	semidirect
284. C₂²×C₈	C₂×C₄×C₁₃	semidirect
315. #106	D₄×C₁₃	semidirect
316. C₄⋊C₈	C₂×C₄×C₁₃	semidirect
318. C₂²⋊C₈	C₂×C₄×C₁₃	semidirect
319. C₄×C₈	C₂×C₄×C₁₃	semidirect
393. C₁₃	#22654	direct (N × H)
456. C₂²	C₁₃×#427	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₄×C₁₃	2
C₂×C₁₃×#427	2
C₂²×C₁₃×#106	2
C₁₃×#2352	2
C₁₃×#1949	2
C₁₃×#1854	2
C₁₃×#1852	2
C₁₃×#1846	2
C₁₃×#1807	2
C₄×C₁₃×#106	2
#22654	13

Subgroups — C13×#22654 #15708993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22654 #15708993