Subgroups — C₁₃×#32742 #15719081

Order 3328.

764 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2854	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2088	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2084	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2077	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2071	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2065	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2058	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2034	C₂	1	2	yes	maximal
10	C₁₃×#2023	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#123	—	2	1	no	—
14	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
15	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#106	C₂²	1	2	yes	—
18	C₂×C₁₃×#106	C₂²	1	2	yes	—
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₂×C₁₃×#102	C₂²	1	2	yes	—
22	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₁₃×#391	—	2	1	no	—
24	C₁₃×#390	C₂²	1	1	yes	characteristic
25	C₁₃×#390	C₂²	1	1	yes	characteristic
26	C₁₃×#389	—	2	1	no	—
27	C₁₃×#389	C₂²	1	1	yes	characteristic
28	C₁₃×#389	C₂²	1	2	yes	—
29	C₁₃×#389	C₂²	1	1	yes	characteristic
30	C₁₃×#388	—	2	1	no	—
31	C₁₃×#388	—	2	1	no	—
32	C₁₃×#386	—	2	1	no	—
33	C₁₃×#384	C₂²	1	1	yes	characteristic
34	C₁₃×#380	—	2	1	no	—
35	C₁₃×#380	C₂²	1	2	yes	—
36	C₁₃×#380	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#336	C₂²	1	1	yes	characteristic
42	C₁₃×#336	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	—	2	1	no	—
45	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₁₃×C₄⋊Q₈	—	4	2	no	—
52	C₁₃×#123	—	4	4	no	—
53	C₁₃×C₂²⋊Q₈	—	4	4	no	—
54	C₁₃×#121	—	4	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₄²×C₁₃	—	4	2	no	—
74	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×#106	—	4	2	no	—
79	C₁₃×#106	—	4	2	no	—
80	C₁₃×C₄⋊C₈	—	4	2	no	—
81	C₁₃×#102	—	4	2	no	—
82	C₁₃×#102	—	4	2	no	—
83	C₁₃×C₂²⋊C₈	—	4	2	no	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	—	2	1	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	—	2	1	no	—
88	C₁₃×#95	—	2	1	no	—
89	#32742	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	—	2	1	no	—
91	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
92	C₂×Q₈×C₁₃	—	4	2	no	—
93	C₂×Q₈×C₁₃	—	4	2	no	—
94	C₂×Q₈×C₁₃	—	4	2	no	—
95	C₂×D₄×C₁₃	—	2	1	no	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	2	1	no	—
99	C₂×D₄×C₁₃	—	4	2	no	—
100	C₂×D₄×C₁₃	—	4	2	no	—
101	C₂×D₄×C₁₃	—	4	2	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	4	1	no	—
113	C₂²×C₄×C₁₃	—	4	1	no	—
114	C₂²×C₄×C₁₃	—	4	1	no	—
115	C₂²×C₄×C₁₃	—	4	1	no	—
116	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₄⋊C₄	—	4	2	no	—
138	C₁₃×C₄⋊C₄	—	4	4	no	—
139	C₁₃×C₄⋊C₄	—	4	2	no	—
140	C₁₃×C₄⋊C₄	—	4	2	no	—
141	C₁₃×C₄⋊C₄	—	4	2	no	—
142	C₁₃×C₄⋊C₄	—	4	2	no	—
143	C₁₃×C₂²⋊C₄	—	4	2	no	—
144	C₁₃×C₂²⋊C₄	—	4	2	no	—
145	C₁₃×C₂²⋊C₄	—	4	4	no	—
146	C₁₃×C₂²⋊C₄	—	4	2	no	—
147	C₁₃×C₂²⋊C₄	—	4	2	no	—
148	C₁₃×C₂²⋊C₄	—	4	2	no	—
149	C₁₃×C₂²⋊C₄	—	4	2	no	—
150	C₄²×C₁₃	—	2	2	no	—
151	C₄²×C₁₃	—	2	2	no	—
152	C₄²×C₁₃	—	4	1	no	—
153	C₄²×C₁₃	—	4	1	no	—
154	#2857	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#2854	C₂×C₁₃	1	1	yes	characteristic
156	#2088	C₂×C₁₃	1	2	yes	complemented
157	#2084	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#2077	C₂×C₁₃	1	2	yes	complemented
159	#2071	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#2065	C₂×C₁₃	1	2	yes	complemented
161	#2058	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#2034	C₂×C₁₃	1	2	yes	—
163	#2023	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#1797	C₂×C₁₃	1	1	yes	characteristic, complemented
165	C₂³×C₁₃	—	2	1	no	—
166	C₂³×C₁₃	—	2	1	no	—
167	C₂³×C₁₃	—	2	1	no	—
168	C₂³×C₁₃	—	2	1	no	—
169	C₂³×C₁₃	—	2	1	no	—
170	C₂³×C₁₃	—	2	1	no	—
171	C₂³×C₁₃	—	4	1	no	—
172	C₂³×C₁₃	—	4	1	no	—
173	C₂³×C₁₃	—	4	1	no	—
174	C₂³×C₁₃	—	4	1	no	—
175	C₂³×C₁₃	—	4	1	no	—
176	C₂³×C₁₃	—	4	1	no	—
177	C₂³×C₁₃	—	4	1	no	—
178	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
179	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
180	Q₈×C₁₃	—	8	4	no	—
181	D₄×C₁₃	—	4	2	no	—
182	D₄×C₁₃	—	4	2	no	—
183	D₄×C₁₃	—	8	4	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	4	4	no	—
197	C₂×C₄×C₁₃	—	4	4	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	1	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	4	1	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	2	no	—
205	C₂×C₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	1	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	4	2	no	—
210	C₂×C₄×C₁₃	—	4	1	no	—
211	C₂×C₄×C₁₃	—	4	1	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
216	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
217	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
218	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
219	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
220	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
221	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
222	C₈×C₁₃	—	4	2	no	—
223	C₈×C₁₃	—	4	2	no	—
224	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×#123	—	2	1	no	—
226	C₂×C₂²⋊Q₈	—	2	1	no	—
227	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
228	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×#106	C₂²×C₁₃	1	2	yes	—
230	C₂×#106	C₂²×C₁₃	1	2	yes	—
231	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
232	C₂×#102	C₂²×C₁₃	1	2	yes	—
233	C₂×#102	C₂²×C₁₃	1	2	yes	—
234	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
235	#391	—	2	1	no	—
236	#390	C₂²×C₁₃	1	1	yes	characteristic
237	#390	C₂²×C₁₃	1	1	yes	characteristic
238	#389	—	2	1	no	—
239	#389	C₂²×C₁₃	1	1	yes	characteristic
240	#389	C₂²×C₁₃	1	2	yes	—
241	#389	C₂²×C₁₃	1	1	yes	characteristic
242	#388	—	2	1	no	—
243	#388	—	2	1	no	—
244	#386	—	2	1	no	—
245	#384	C₂²×C₁₃	1	1	yes	characteristic
246	#380	—	2	1	no	—
247	#380	C₂²×C₁₃	1	1	yes	characteristic
248	#380	C₂²×C₁₃	1	2	yes	—
249	#340	C₂²×C₁₃	1	2	yes	—
250	#340	C₂²×C₁₃	1	2	yes	—
251	#340	C₂²×C₁₃	1	2	yes	—
252	#340	C₂²×C₁₃	1	2	yes	—
253	#336	C₂²×C₁₃	1	1	yes	characteristic
254	#336	C₂²×C₁₃	1	1	yes	characteristic
255	C₂²×C₁₃	—	2	2	no	—
256	C₂²×C₁₃	—	2	2	no	—
257	C₂²×C₁₃	—	2	2	no	—
258	C₂²×C₁₃	—	4	1	no	—
259	C₂²×C₁₃	—	4	1	no	—
260	C₂²×C₁₃	—	4	1	no	—
261	C₂²×C₁₃	—	4	1	no	—
262	C₂²×C₁₃	—	8	1	no	—
263	C₂²×C₁₃	—	8	1	no	—
264	C₂²×C₁₃	—	8	1	no	—
265	C₂²×C₁₃	—	8	1	no	—
266	C₂²×C₁₃	—	8	1	no	—
267	C₂²×C₁₃	—	8	1	no	—
268	C₂²×C₁₃	—	8	1	no	—
269	C₂²×C₁₃	#534	1	1	yes	characteristic
270	C₂²×C₁₃	#536	1	1	yes	characteristic
271	C₂²×C₁₃	#537	1	1	yes	characteristic
272	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
273	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
274	C₂²×C₁₃	#575	1	1	yes	characteristic
275	C₂²×C₁₃	#575	1	1	yes	characteristic
276	C₄×C₁₃	—	2	2	no	—
277	C₄×C₁₃	—	2	2	no	—
278	C₄×C₁₃	—	2	2	no	—
279	C₄×C₁₃	—	4	1	no	—
280	C₄×C₁₃	—	4	1	no	—
281	C₄×C₁₃	—	8	1	no	—
282	C₄×C₁₃	—	8	2	no	—
283	C₄×C₁₃	—	8	1	no	—
284	C₄×C₁₃	—	8	1	no	—
285	C₄×C₁₃	—	8	2	no	—
286	C₄×C₁₃	#562	1	2	yes	—
287	C₄×C₁₃	#563	1	2	yes	—
288	C₂²×Q₈	—	2	1	no	—
289	C₂²×D₄	—	2	1	no	—
290	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
291	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
292	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
293	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
294	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
295	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
296	C₄⋊Q₈	—	4	2	no	—
297	#123	—	4	4	no	—
298	C₂²⋊Q₈	—	4	4	no	—
299	#121	—	4	2	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
308	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₂²⋊C₄	—	2	1	no	—
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₄²	—	4	2	no	—
319	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
320	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
322	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
323	#106	—	4	2	no	—
324	#106	—	4	2	no	—
325	C₄⋊C₈	—	4	2	no	—
326	#102	—	4	2	no	—
327	#102	—	4	2	no	—
328	C₂²⋊C₈	—	4	2	no	—
329	#95	—	2	2	no	—
330	#95	—	2	1	no	—
331	#95	—	2	2	no	—
332	#95	—	2	1	no	—
333	#95	—	2	1	no	—
334	C₂×C₁₃	—	4	2	no	—
335	C₂×C₁₃	—	16	1	no	—
336	C₂×C₁₃	#2814	1	1	yes	characteristic
337	C₂×C₁₃	#3187	1	1	yes	characteristic
338	C₂×C₁₃	#3194	1	1	yes	characteristic
339	C₂×C₁₃	#3227	1	1	yes	characteristic
340	C₂×C₁₃	#3240	1	1	yes	characteristic
341	C₂×C₁₃	#3246	1	1	yes	characteristic
342	C₂×C₁₃	#3251	1	1	yes	characteristic
343	C₂⁴	—	2	1	no	—
344	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
345	C₂×Q₈	—	4	2	no	—
346	C₂×Q₈	—	4	2	no	—
347	C₂×Q₈	—	4	2	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	—	4	2	no	—
354	C₂×D₄	—	4	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	4	1	no	—
366	C₂²×C₄	—	4	1	no	—
367	C₂²×C₄	—	4	1	no	—
368	C₂²×C₄	—	4	1	no	—
369	C₂²×C₄	C₁₃×SD₁₆	1	4	yes	—
370	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
375	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	4	4	no	—
391	C₄⋊C₄	—	4	2	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₄⋊C₄	—	4	2	no	—
394	C₄⋊C₄	—	4	2	no	—
395	C₄⋊C₄	—	4	2	no	—
396	C₂²⋊C₄	—	4	2	no	—
397	C₂²⋊C₄	—	4	2	no	—
398	C₂²⋊C₄	—	4	4	no	—
399	C₂²⋊C₄	—	4	2	no	—
400	C₂²⋊C₄	—	4	2	no	—
401	C₂²⋊C₄	—	4	2	no	—
402	C₂²⋊C₄	—	4	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	4	1	no	—
406	C₄²	—	4	1	no	—
407	C₁₃	#32742	1	1	yes	characteristic, direct product factor, Sylow
408	C₂³	—	2	1	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	1	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	4	1	no	—
415	C₂³	—	4	1	no	—
416	C₂³	—	4	1	no	—
417	C₂³	—	4	1	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	4	1	no	—
420	C₂³	—	4	1	no	—
421	C₂³	C₂×C₁₃×SD₁₆	1	2	yes	—
422	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
423	Q₈	—	8	4	no	—
424	D₄	—	4	2	no	—
425	D₄	—	4	2	no	—
426	D₄	—	8	4	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
459	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
460	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
461	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
462	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
463	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
464	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
465	C₈	—	4	2	no	—
466	C₈	—	4	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	8	1	no	—
475	C₂²	—	8	1	no	—
476	C₂²	—	8	1	no	—
477	C₂²	—	8	1	no	—
478	C₂²	—	8	1	no	—
479	C₂²	—	8	1	no	—
480	C₂²	—	8	1	no	—
481	C₂²	C₁₃×#534	1	1	yes	characteristic
482	C₂²	C₁₃×#536	1	1	yes	characteristic
483	C₂²	C₁₃×#537	1	1	yes	characteristic
484	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
485	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
486	C₂²	C₁₃×#575	1	1	yes	characteristic
487	C₂²	C₁₃×#575	1	1	yes	characteristic
488	C₄	—	2	2	no	—
489	C₄	—	2	2	no	—
490	C₄	—	2	2	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	1	no	—
493	C₄	—	8	1	no	—
494	C₄	—	8	2	no	—
495	C₄	—	8	1	no	—
496	C₄	—	8	1	no	—
497	C₄	—	8	2	no	—
498	C₄	C₁₃×#562	1	2	yes	—
499	C₄	C₁₃×#563	1	2	yes	—
500	C₂	—	4	2	no	—
501	C₂	—	16	1	no	—
502	C₂	C₁₃×#2814	1	1	yes	characteristic
503	C₂	C₁₃×#3187	1	1	yes	characteristic
504	C₂	C₁₃×#3194	1	1	yes	characteristic
505	C₂	C₁₃×#3227	1	1	yes	characteristic
506	C₂	C₁₃×#3240	1	1	yes	characteristic
507	C₂	C₁₃×#3246	1	1	yes	characteristic
508	C₂	C₁₃×#3251	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2857	C₂	semidirect
3. C₁₃×#2088	C₂	semidirect
4. C₁₃×#2084	C₂	semidirect
5. C₁₃×#2077	C₂	semidirect
6. C₁₃×#2071	C₂	semidirect
7. C₁₃×#2065	C₂	semidirect
8. C₁₃×#2058	C₂	semidirect
10. C₁₃×#2023	C₂	semidirect
11. C₁₃×#1797	C₂	semidirect
89. #32742	C₁₃	direct (N × H)
154. #2857	C₂×C₁₃	semidirect
156. #2088	C₂×C₁₃	semidirect
157. #2084	C₂×C₁₃	semidirect
158. #2077	C₂×C₁₃	semidirect
159. #2071	C₂×C₁₃	semidirect
160. #2065	C₂×C₁₃	semidirect
161. #2058	C₂×C₁₃	semidirect
163. #2023	C₂×C₁₃	semidirect
164. #1797	C₂×C₁₃	semidirect
407. C₁₃	#32742	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2857	2
C₁₃×#2854	2
C₁₃×#2088	2
C₁₃×#2084	2
C₁₃×#2077	2
C₁₃×#2071	2
C₁₃×#2065	2
C₁₃×#2058	2
C₁₃×#2034	2
C₁₃×#2023	2
C₁₃×#1797	2
#32742	13

Subgroups — C13×#32742 #15719081

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32742 #15719081