Subgroups — C₁₃×#25035 #15711374

Order 3328.

810 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2423	C₂	1	2	yes	maximal
4	C₁₃×#2072	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2036	C₂	1	2	yes	maximal
6	C₁₃×#1969	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1863	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1845	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1808	C₂	1	1	yes	maximal, characteristic
11	C₈×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
16	C₁₃×#467	—	2	4	no	—
17	C₄×C₁₃×Q₁₆	—	2	4	no	—
18	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#107	C₂²	1	2	yes	—
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#399	—	2	2	no	—
29	C₁₃×#398	—	2	2	no	—
30	C₁₃×#391	C₂²	1	2	yes	—
31	C₁₃×#389	C₂²	1	2	yes	—
32	C₁₃×#388	—	2	2	no	—
33	C₁₃×#387	—	2	2	no	—
34	C₁₃×#384	C₂²	1	2	yes	—
35	C₁₃×#380	C₂²	1	2	yes	—
36	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	1	yes	characteristic
40	C₁₃×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂×C₁₃×Q₁₆	—	2	2	no	—
44	C₂×C₁₃×Q₁₆	—	2	2	no	—
45	C₂×C₁₃×Q₁₆	D₄	1	4	yes	—
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	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₁₃×C₂²⋊Q₈	—	2	4	no	—
54	C₁₃×C₂²⋊Q₈	—	4	2	no	—
55	C₄×Q₈×C₁₃	—	2	4	no	—
56	C₄×Q₈×C₁₃	—	4	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
68	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	—	2	2	no	—
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
72	C₁₃×#107	—	2	2	no	—
73	C₁₃×#107	—	2	2	no	—
74	C₁₃×#107	—	2	2	no	—
75	C₁₃×#107	—	4	2	no	—
76	C₁₃×#103	—	2	4	no	—
77	C₁₃×#103	—	2	4	no	—
78	C₁₃×#103	—	2	4	no	—
79	C₁₃×C₂²⋊C₈	—	2	2	no	—
80	C₄×C₈×C₁₃	—	2	2	no	—
81	C₄×C₈×C₁₃	—	2	2	no	—
82	C₁₃×#95	—	2	2	no	—
83	C₁₃×#95	—	2	2	no	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	D₄	1	1	yes	characteristic
87	C₁₃×#95	D₄	1	1	yes	characteristic
88	#25035	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
90	C₂×Q₈×C₁₃	—	2	2	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
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	2	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
112	C₁₃×Q₁₆	—	2	8	no	—
113	C₂×C₈×C₁₃	—	2	1	no	—
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	2	1	no	—
116	C₂×C₈×C₁₃	—	2	1	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	—	2	1	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	4	4	no	—
122	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₁₃	#41	1	2	yes	—
124	C₂×C₈×C₁₃	#41	1	2	yes	—
125	C₂×C₈×C₁₃	#41	1	2	yes	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	4	4	no	—
133	C₁₃×C₄⋊C₄	—	4	4	no	—
134	C₁₃×C₄⋊C₄	—	4	4	no	—
135	C₁₃×C₄⋊C₄	—	8	2	no	—
136	C₁₃×C₄⋊C₄	—	8	2	no	—
137	C₁₃×C₂²⋊C₄	—	2	2	no	—
138	C₁₃×C₂²⋊C₄	—	4	4	no	—
139	C₁₃×C₂²⋊C₄	—	8	2	no	—
140	C₁₃×C₂²⋊C₄	Q₁₆	1	4	yes	complemented
141	C₄²×C₁₃	—	2	1	no	—
142	C₄²×C₁₃	—	2	1	no	—
143	C₄²×C₁₃	—	2	1	no	—
144	C₄²×C₁₃	—	2	1	no	—
145	C₄²×C₁₃	—	4	4	no	—
146	C₂×#467	C₂×C₁₃	1	1	yes	characteristic
147	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#2423	C₂×C₁₃	1	2	yes	—
149	#2072	C₂×C₁₃	1	2	yes	complemented
150	#2036	C₂×C₁₃	1	2	yes	—
151	#1969	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#1863	C₂×C₁₃	1	2	yes	complemented
154	#1845	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#1808	C₂×C₁₃	1	1	yes	characteristic
156	C₈×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
157	C₂³×C₁₃	—	2	1	no	—
158	C₂³×C₁₃	—	2	1	no	—
159	C₂³×C₁₃	—	2	1	no	—
160	C₂³×C₁₃	—	2	1	no	—
161	C₂³×C₁₃	—	2	1	no	—
162	C₂³×C₁₃	—	2	1	no	—
163	C₂³×C₁₃	C₂×Q₁₆	1	2	yes	—
164	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₁₃	—	2	4	no	—
166	Q₈×C₁₃	—	2	4	no	—
167	Q₈×C₁₃	—	4	2	no	—
168	Q₈×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	4	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	1	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	1	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	2	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	C₂×Q₁₆	1	2	yes	—
198	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
199	C₂×C₄×C₁₃	#135	1	2	yes	—
200	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
205	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
206	C₈×C₁₃	—	2	2	no	—
207	C₈×C₁₃	—	4	1	no	—
208	C₈×C₁₃	—	4	1	no	—
209	C₈×C₁₃	#123	1	4	yes	—
210	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
211	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
213	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
214	#467	—	2	4	no	—
215	C₄×Q₁₆	—	2	4	no	—
216	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×#107	C₂²×C₁₃	1	2	yes	—
220	C₂×#103	C₂²×C₁₃	1	2	yes	—
221	C₂×#103	C₂²×C₁₃	1	2	yes	—
222	C₂×#103	C₂²×C₁₃	1	2	yes	—
223	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
226	#399	—	2	2	no	—
227	#398	—	2	2	no	—
228	#391	C₂²×C₁₃	1	2	yes	—
229	#389	C₂²×C₁₃	1	2	yes	—
230	#388	—	2	2	no	—
231	#387	—	2	2	no	—
232	#384	C₂²×C₁₃	1	2	yes	—
233	#380	C₂²×C₁₃	1	2	yes	—
234	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
235	#340	C₂²×C₁₃	1	2	yes	—
236	#340	C₂²×C₁₃	1	2	yes	—
237	#336	C₂²×C₁₃	1	1	yes	characteristic
238	#336	C₂²×C₁₃	1	1	yes	characteristic
239	C₂²×C₁₃	—	2	2	no	—
240	C₂²×C₁₃	—	2	2	no	—
241	C₂²×C₁₃	—	2	2	no	—
242	C₂²×C₁₃	—	4	1	no	—
243	C₂²×C₁₃	—	4	1	no	—
244	C₂²×C₁₃	—	4	1	no	—
245	C₂²×C₁₃	—	4	1	no	—
246	C₂²×C₁₃	#532	1	1	yes	characteristic
247	C₂²×C₁₃	D₄²	1	1	yes	characteristic
248	C₂²×C₁₃	#547	1	1	yes	characteristic
249	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
250	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
251	C₂²×C₁₃	#576	1	1	yes	characteristic
252	C₂²×C₁₃	#578	1	1	yes	characteristic
253	C₄×C₁₃	—	2	2	no	—
254	C₄×C₁₃	—	2	2	no	—
255	C₄×C₁₃	—	2	2	no	—
256	C₄×C₁₃	—	4	1	no	—
257	C₄×C₁₃	—	4	4	no	—
258	C₄×C₁₃	—	4	1	no	—
259	C₄×C₁₃	—	8	2	no	—
260	C₄×C₁₃	—	8	2	no	—
261	C₄×C₁₃	—	8	2	no	—
262	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
263	C₄×C₁₃	#542	1	1	yes	characteristic
264	C₄×C₁₃	#547	1	1	yes	characteristic
265	C₄×C₁₃	#553	1	1	yes	characteristic
266	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
267	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
268	C₂×Q₁₆	—	2	2	no	—
269	C₂×Q₁₆	—	2	2	no	—
270	C₂×Q₁₆	D₄×C₁₃	1	4	yes	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	—	2	2	no	—
273	C₂²×C₈	—	2	2	no	—
274	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
278	C₂²⋊Q₈	—	2	4	no	—
279	C₂²⋊Q₈	—	4	2	no	—
280	C₄×Q₈	—	2	4	no	—
281	C₄×Q₈	—	4	2	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
294	C₂×C₄²	—	2	2	no	—
295	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
296	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
297	#107	—	2	2	no	—
298	#107	—	2	2	no	—
299	#107	—	2	2	no	—
300	#107	—	4	2	no	—
301	#103	—	2	4	no	—
302	#103	—	2	4	no	—
303	#103	—	2	4	no	—
304	C₂²⋊C₈	—	2	2	no	—
305	C₄×C₈	—	2	2	no	—
306	C₄×C₈	—	2	2	no	—
307	#95	—	2	2	no	—
308	#95	—	2	2	no	—
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	#95	D₄×C₁₃	1	1	yes	characteristic
312	#95	D₄×C₁₃	1	1	yes	characteristic
313	C₂×C₁₃	—	4	2	no	—
314	C₂×C₁₃	#2422	1	1	yes	characteristic
315	C₂×C₁₃	#3170	1	1	yes	characteristic
316	C₂×C₁₃	#3175	1	1	yes	characteristic
317	C₂×C₁₃	D₄×Q₁₆	1	1	yes	characteristic
318	C₂×C₁₃	#3287	1	1	yes	characteristic
319	C₂×C₁₃	#3336	1	1	yes	characteristic
320	C₂×C₁₃	#3338	1	1	yes	characteristic
321	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
343	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
344	Q₁₆	—	2	8	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	4	4	no	—
354	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
355	C₂×C₈	C₁₃×#41	1	2	yes	—
356	C₂×C₈	C₁₃×#41	1	2	yes	—
357	C₂×C₈	C₁₃×#41	1	2	yes	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	4	4	no	—
365	C₄⋊C₄	—	4	4	no	—
366	C₄⋊C₄	—	4	4	no	—
367	C₄⋊C₄	—	8	2	no	—
368	C₄⋊C₄	—	8	2	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	4	4	no	—
371	C₂²⋊C₄	—	8	2	no	—
372	C₂²⋊C₄	C₁₃×Q₁₆	1	4	yes	complemented
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	4	4	no	—
378	C₁₃	#25035	1	1	yes	characteristic, direct product factor, Sylow
379	C₂³	—	2	1	no	—
380	C₂³	—	2	1	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	C₂×C₁₃×Q₁₆	1	2	yes	—
386	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
387	Q₈	—	2	4	no	—
388	Q₈	—	2	4	no	—
389	Q₈	—	4	2	no	—
390	Q₈	—	4	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	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	C₂×C₁₃×Q₁₆	1	2	yes	—
420	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
421	C₂×C₄	C₁₃×#135	1	2	yes	—
422	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
423	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
424	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
425	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
426	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
428	C₈	—	2	2	no	—
429	C₈	—	4	1	no	—
430	C₈	—	4	1	no	—
431	C₈	C₁₃×#123	1	4	yes	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	C₁₃×#532	1	1	yes	characteristic
440	C₂²	D₄²×C₁₃	1	1	yes	characteristic
441	C₂²	C₁₃×#547	1	1	yes	characteristic
442	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
443	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
444	C₂²	C₁₃×#576	1	1	yes	characteristic
445	C₂²	C₁₃×#578	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	4	1	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	4	no	—
452	C₄	—	8	2	no	—
453	C₄	—	8	2	no	—
454	C₄	—	8	2	no	—
455	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
456	C₄	C₁₃×#542	1	1	yes	characteristic
457	C₄	C₁₃×#547	1	1	yes	characteristic
458	C₄	C₁₃×#553	1	1	yes	characteristic
459	C₂	—	4	2	no	—
460	C₂	C₁₃×#2422	1	1	yes	characteristic
461	C₂	C₁₃×#3170	1	1	yes	characteristic
462	C₂	C₁₃×#3175	1	1	yes	characteristic
463	C₂	D₄×C₁₃×Q₁₆	1	1	yes	characteristic
464	C₂	C₁₃×#3287	1	1	yes	characteristic
465	C₂	C₁₃×#3336	1	1	yes	characteristic
466	C₂	C₁₃×#3338	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
4. C₁₃×#2072	C₂	semidirect
6. C₁₃×#1969	C₂	semidirect
7. C₁₃×#1942	C₂	semidirect
8. C₁₃×#1863	C₂	semidirect
9. C₁₃×#1845	C₂	semidirect
88. #25035	C₁₃	direct (N × H)
140. C₁₃×C₂²⋊C₄	Q₁₆	semidirect
147. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
149. #2072	C₂×C₁₃	semidirect
151. #1969	C₂×C₁₃	semidirect
152. #1942	C₂×C₁₃	semidirect
153. #1863	C₂×C₁₃	semidirect
154. #1845	C₂×C₁₃	semidirect
372. C₂²⋊C₄	C₁₃×Q₁₆	semidirect
378. C₁₃	#25035	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#467	2
C₂×C₄×C₁₃×Q₁₆	2
C₁₃×#2423	2
C₁₃×#2072	2
C₁₃×#2036	2
C₁₃×#1969	2
C₁₃×#1942	2
C₁₃×#1863	2
C₁₃×#1845	2
C₁₃×#1808	2
C₈×C₁₃×C₂²⋊C₄	2
#25035	13

Subgroups — C13×#25035 #15711374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25035 #15711374