Subgroups — C₁₃×#25882 #15712221

Order 3328.

1334 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2547	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2036	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1788	C₂	1	4	yes	maximal, complemented
9	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	C₂²	1	2	yes	—
11	C₁₃×#547	—	2	4	no	—
12	C₁₃×#547	—	2	4	no	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#124	—	2	1	no	—
16	C₂×C₁₃×#123	—	2	2	no	—
17	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₃×#121	—	2	1	no	—
19	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
22	C₁₃×#487	—	2	4	no	—
23	C₁₃×#474	—	2	4	no	—
24	C₂×C₁₃×#107	C₂²	1	2	yes	—
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	C₂²	1	4	yes	—
27	C₂×C₁₃×#103	C₂²	1	4	yes	—
28	C₂×C₁₃×#102	C₂²	1	2	yes	—
29	C₂×C₁₃×#102	C₂²	1	2	yes	—
30	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	—
31	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#397	—	2	2	no	—
33	C₁₃×#391	—	2	1	no	—
34	C₁₃×#380	C₂²	1	4	yes	—
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₂×C₁₃×#41	—	2	4	no	—
38	C₂×C₁₃×#41	—	2	4	no	—
39	C₂×C₁₃×#41	—	2	8	no	—
40	C₂×C₁₃×#41	—	4	4	no	—
41	C₂²×Q₈×C₁₃	—	2	1	no	—
42	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
43	C₂²×D₄×C₁₃	—	2	2	no	—
44	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
45	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	—	2	1	no	—
47	C₂³×C₄×C₁₃	—	2	2	no	—
48	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₁₃×C₄⋊Q₈	—	2	2	no	—
52	C₁₃×C₄⋊Q₈	—	2	2	no	—
53	C₁₃×C₄⋊Q₈	—	2	2	no	—
54	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
55	C₁₃×#124	—	4	4	no	—
56	C₁₃×#123	—	2	16	no	—
57	C₁₃×C₂²⋊Q₈	—	2	4	no	—
58	C₁₃×C₂²⋊Q₈	—	2	4	no	—
59	C₁₃×#121	—	2	8	no	—
60	C₄×D₄×C₁₃	—	2	2	no	—
61	C₄×D₄×C₁₃	—	2	2	no	—
62	C₄×D₄×C₁₃	—	2	2	no	—
63	C₄×D₄×C₁₃	D₄	1	4	yes	—
64	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
76	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
77	C₂×C₄²×C₁₃	—	2	1	no	—
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×#107	—	2	4	no	—
80	C₁₃×C₄⋊C₈	—	2	2	no	—
81	C₁₃×#103	—	2	8	no	—
82	C₁₃×#103	—	4	4	no	—
83	C₁₃×#102	—	2	4	no	—
84	C₁₃×#102	—	2	4	no	—
85	C₁₃×C₂²⋊C₈	—	4	4	no	—
86	C₄×C₈×C₁₃	—	2	2	no	—
87	C₁₃×#95	—	2	1	no	—
88	C₁₃×#95	—	2	4	no	—
89	#25882	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	—	2	1	no	—
91	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
92	C₁₃×#41	—	4	16	no	—
93	C₁₃×#41	—	4	8	no	—
94	C₁₃×#41	—	4	8	no	—
95	C₂×Q₈×C₁₃	—	2	2	no	—
96	C₂×Q₈×C₁₃	—	2	4	no	—
97	C₂×Q₈×C₁₃	—	2	4	no	—
98	C₂×Q₈×C₁₃	—	4	2	no	—
99	C₂×Q₈×C₁₃	—	4	2	no	—
100	C₂×Q₈×C₁₃	—	4	2	no	—
101	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
102	C₂×D₄×C₁₃	—	2	8	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	2	2	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	2	1	no	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	4	8	no	—
109	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
110	C₂×D₄×C₁₃	#41	1	4	yes	—
111	C₂²×C₄×C₁₃	—	2	8	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	4	no	—
118	C₂²×C₄×C₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	4	8	no	—
122	C₂²×C₄×C₁₃	—	4	2	no	—
123	C₂²×C₄×C₁₃	—	4	2	no	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	—	2	4	no	—
133	C₁₃×C₄⋊C₄	—	2	8	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	4	no	—
136	C₁₃×C₄⋊C₄	—	2	4	no	—
137	C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
143	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
144	C₁₃×C₂²⋊C₄	—	2	8	no	—
145	C₁₃×C₂²⋊C₄	—	2	4	no	—
146	C₁₃×C₂²⋊C₄	—	2	4	no	—
147	C₁₃×C₂²⋊C₄	—	4	8	no	—
148	C₄²×C₁₃	—	4	2	no	—
149	C₄²×C₁₃	C₂×D₄	1	2	yes	—
150	C₄²×C₁₃	C₂×D₄	1	2	yes	—
151	C₂×#547	C₂×C₁₃	1	1	yes	characteristic
152	C₂×#487	C₂×C₁₃	1	1	yes	characteristic, complemented
153	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#2547	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#2036	C₂×C₁₃	1	4	yes	complemented
156	#1981	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#1954	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#1788	C₂×C₁₃	1	4	yes	complemented
159	C₄×#102	C₂×C₁₃	1	1	yes	characteristic, complemented
160	C₂³×C₁₃	—	2	2	no	—
161	C₂³×C₁₃	—	2	4	no	—
162	C₂³×C₁₃	—	2	2	no	—
163	C₂³×C₁₃	—	2	4	no	—
164	C₂³×C₁₃	—	2	2	no	—
165	C₂³×C₁₃	—	2	2	no	—
166	C₂³×C₁₃	—	2	4	no	—
167	C₂³×C₁₃	—	4	1	no	—
168	C₂³×C₁₃	—	4	1	no	—
169	C₂³×C₁₃	—	4	2	no	—
170	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₁₃	—	2	8	no	—
172	Q₈×C₁₃	—	4	2	no	—
173	Q₈×C₁₃	—	4	2	no	—
174	Q₈×C₁₃	—	8	4	no	—
175	D₄×C₁₃	—	2	2	no	—
176	D₄×C₁₃	—	2	4	no	—
177	D₄×C₁₃	—	4	16	no	—
178	D₄×C₁₃	—	4	4	no	—
179	D₄×C₁₃	#124	1	4	yes	complemented
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	4	16	no	—
186	C₂×C₄×C₁₃	—	4	4	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	4	no	—
192	C₂×C₄×C₁₃	—	4	8	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	#120	1	2	yes	—
200	C₂×C₄×C₁₃	#120	1	2	yes	—
201	C₂×C₄×C₁₃	#135	1	2	yes	—
202	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
203	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
206	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
207	C₈×C₁₃	—	4	2	no	—
208	C₈×C₁₃	—	4	2	no	—
209	C₂²×#41	C₂²×C₁₃	1	2	yes	—
210	#547	—	2	4	no	—
211	#547	—	2	4	no	—
212	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×#124	—	2	1	no	—
215	C₂×#123	—	2	2	no	—
216	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
217	C₂×#121	—	2	1	no	—
218	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
220	C₂²×C₄⋊C₄	—	2	1	no	—
221	#487	—	2	4	no	—
222	#474	—	2	4	no	—
223	C₂×#107	C₂²×C₁₃	1	2	yes	—
224	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×#103	C₂²×C₁₃	1	4	yes	—
226	C₂×#103	C₂²×C₁₃	1	4	yes	—
227	C₂×#102	C₂²×C₁₃	1	2	yes	—
228	C₂×#102	C₂²×C₁₃	1	2	yes	—
229	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	—
230	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
231	#397	—	2	2	no	—
232	#391	—	2	1	no	—
233	#380	C₂²×C₁₃	1	4	yes	—
234	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
235	#340	C₂²×C₁₃	1	2	yes	—
236	C₂²×C₁₃	—	2	4	no	—
237	C₂²×C₁₃	—	4	4	no	—
238	C₂²×C₁₃	—	4	2	no	—
239	C₂²×C₁₃	—	4	2	no	—
240	C₂²×C₁₃	—	4	4	no	—
241	C₂²×C₁₃	—	4	4	no	—
242	C₂²×C₁₃	—	4	2	no	—
243	C₂²×C₁₃	—	4	2	no	—
244	C₂²×C₁₃	—	4	2	no	—
245	C₂²×C₁₃	—	4	4	no	—
246	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
247	C₂²×C₁₃	#546	1	2	yes	—
248	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
249	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
250	C₂²×C₁₃	#578	1	2	yes	—
251	C₄×C₁₃	—	2	2	no	—
252	C₄×C₁₃	—	4	2	no	—
253	C₄×C₁₃	—	4	4	no	—
254	C₄×C₁₃	—	4	2	no	—
255	C₄×C₁₃	—	8	2	no	—
256	C₄×C₁₃	—	8	2	no	—
257	C₄×C₁₃	#449	1	4	yes	—
258	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
259	C₄×C₁₃	#535	1	1	yes	characteristic
260	C₄×C₁₃	#546	1	2	yes	—
261	C₂×#41	—	2	4	no	—
262	C₂×#41	—	2	4	no	—
263	C₂×#41	—	2	8	no	—
264	C₂×#41	—	4	4	no	—
265	C₂²×Q₈	—	2	1	no	—
266	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
267	C₂²×D₄	—	2	2	no	—
268	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
269	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
270	C₂³×C₄	—	2	1	no	—
271	C₂³×C₄	—	2	2	no	—
272	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
273	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
274	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
275	C₄⋊Q₈	—	2	2	no	—
276	C₄⋊Q₈	—	2	2	no	—
277	C₄⋊Q₈	—	2	2	no	—
278	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
279	#124	—	4	4	no	—
280	#123	—	2	16	no	—
281	C₂²⋊Q₈	—	2	4	no	—
282	C₂²⋊Q₈	—	2	4	no	—
283	#121	—	2	8	no	—
284	C₄×D₄	—	2	2	no	—
285	C₄×D₄	—	2	2	no	—
286	C₄×D₄	—	2	2	no	—
287	C₄×D₄	D₄×C₁₃	1	4	yes	—
288	C₂×C₄⋊C₄	—	2	8	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
295	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
296	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₂²⋊C₄	—	2	4	no	—
300	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
303	#107	—	2	4	no	—
304	C₄⋊C₈	—	2	2	no	—
305	#103	—	2	8	no	—
306	#103	—	4	4	no	—
307	#102	—	2	4	no	—
308	#102	—	2	4	no	—
309	C₂²⋊C₈	—	4	4	no	—
310	C₄×C₈	—	2	2	no	—
311	#95	—	2	1	no	—
312	#95	—	2	4	no	—
313	C₂×C₁₃	—	4	4	no	—
314	C₂×C₁₃	—	8	2	no	—
315	C₂×C₁₃	#2435	1	1	yes	characteristic
316	C₂×C₁₃	C₂×#449	1	1	yes	characteristic
317	C₂×C₁₃	#3011	1	1	yes	characteristic
318	C₂×C₁₃	#3302	1	2	yes	—
319	C₂×C₁₃	#3330	1	2	yes	—
320	C₂⁴	—	2	1	no	—
321	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
322	#41	—	4	16	no	—
323	#41	—	4	8	no	—
324	#41	—	4	8	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	4	no	—
327	C₂×Q₈	—	2	4	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×Q₈	—	4	2	no	—
330	C₂×Q₈	—	4	2	no	—
331	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
332	C₂×D₄	—	2	8	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	4	8	no	—
339	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
340	C₂×D₄	C₁₃×#41	1	4	yes	—
341	C₂²×C₄	—	2	8	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	4	8	no	—
352	C₂²×C₄	—	4	2	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
357	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	4	no	—
363	C₄⋊C₄	—	2	8	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
374	C₂²⋊C₄	—	2	8	no	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₂²⋊C₄	—	2	4	no	—
377	C₂²⋊C₄	—	4	8	no	—
378	C₄²	—	4	2	no	—
379	C₄²	C₂×D₄×C₁₃	1	2	yes	—
380	C₄²	C₂×D₄×C₁₃	1	2	yes	—
381	C₁₃	#25882	1	1	yes	characteristic, direct product factor, Sylow
382	C₂³	—	2	2	no	—
383	C₂³	—	2	4	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	2	no	—
392	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
393	Q₈	—	2	8	no	—
394	Q₈	—	4	2	no	—
395	Q₈	—	4	2	no	—
396	Q₈	—	8	4	no	—
397	D₄	—	2	2	no	—
398	D₄	—	2	4	no	—
399	D₄	—	4	16	no	—
400	D₄	—	4	4	no	—
401	D₄	C₁₃×#124	1	4	yes	complemented
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	4	16	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	8	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	C₁₃×#120	1	2	yes	—
422	C₂×C₄	C₁₃×#120	1	2	yes	—
423	C₂×C₄	C₁₃×#135	1	2	yes	—
424	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
425	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
426	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
427	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
428	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
429	C₈	—	4	2	no	—
430	C₈	—	4	2	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
442	C₂²	C₁₃×#546	1	2	yes	—
443	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
444	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
445	C₂²	C₁₃×#578	1	2	yes	—
446	C₄	—	2	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	4	no	—
449	C₄	—	4	2	no	—
450	C₄	—	8	2	no	—
451	C₄	—	8	2	no	—
452	C₄	C₁₃×#449	1	4	yes	—
453	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
454	C₄	C₁₃×#535	1	1	yes	characteristic
455	C₄	C₁₃×#546	1	2	yes	—
456	C₂	—	4	4	no	—
457	C₂	—	8	2	no	—
458	C₂	C₁₃×#2435	1	1	yes	characteristic
459	C₂	C₂×C₁₃×#449	1	1	yes	characteristic
460	C₂	C₁₃×#3011	1	1	yes	characteristic
461	C₂	C₁₃×#3302	1	2	yes	—
462	C₂	C₁₃×#3330	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#547	C₂
LCS	G ▷ C₂²×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×#487	C₂	semidirect
3. C₂×C₁₃×#474	C₂	semidirect
4. C₁₃×#2547	C₂	semidirect
5. C₁₃×#2036	C₂	semidirect
6. C₁₃×#1981	C₂	semidirect
7. C₁₃×#1954	C₂	semidirect
8. C₁₃×#1788	C₂	semidirect
9. C₄×C₁₃×#102	C₂	semidirect
89. #25882	C₁₃	direct (N × H)
152. C₂×#487	C₂×C₁₃	semidirect
153. C₂×#474	C₂×C₁₃	semidirect
154. #2547	C₂×C₁₃	semidirect
155. #2036	C₂×C₁₃	semidirect
156. #1981	C₂×C₁₃	semidirect
157. #1954	C₂×C₁₃	semidirect
158. #1788	C₂×C₁₃	semidirect
159. C₄×#102	C₂×C₁₃	semidirect
179. D₄×C₁₃	#124	semidirect
381. C₁₃	#25882	direct (N × H)
401. D₄	C₁₃×#124	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#547	2
C₂×C₁₃×#487	2
C₂×C₁₃×#474	2
C₁₃×#2547	2
C₁₃×#2036	2
C₁₃×#1981	2
C₁₃×#1954	2
C₁₃×#1788	2
C₄×C₁₃×#102	2
#25882	13

Subgroups — C13×#25882 #15712221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25882 #15712221