Subgroups — C₁₃×#26040 #15712379

Order 3328.

914 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#474	C₂	1	2	yes	maximal
2	C₁₃×#2551	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2086	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2057	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1862	C₂	1	2	yes	maximal
9	C₁₃×#1845	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
17	C₁₃×#474	—	2	8	no	—
18	C₂×C₁₃×#107	C₂²	1	2	yes	—
19	C₂×C₁₃×#107	C₂²	1	2	yes	—
20	C₂×C₁₃×#107	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#102	C₂²	1	2	yes	—
24	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#395	—	2	2	no	—
28	C₁₃×#389	—	2	1	no	—
29	C₁₃×#389	C₂²	1	2	yes	—
30	C₁₃×#389	C₂²	1	2	yes	—
31	C₁₃×#385	—	2	2	no	—
32	C₁₃×#384	C₂²	1	1	yes	characteristic
33	C₁₃×#384	C₂²	1	1	yes	characteristic
34	C₁₃×#380	—	2	1	no	—
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	1	yes	characteristic
38	C₁₃×#340	C₂²	1	1	yes	characteristic
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#336	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₃	—	2	2	no	—
43	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	—	2	1	no	—
45	C₂³×C₄×C₁₃	—	2	2	no	—
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₁₃×C₄⋊Q₈	—	2	4	no	—
50	C₁₃×C₄⋊Q₈	—	4	2	no	—
51	C₁₃×C₄⋊Q₈	—	4	4	no	—
52	C₄×D₄×C₁₃	—	2	4	no	—
53	C₄×D₄×C₁₃	—	2	2	no	—
54	C₄×D₄×C₁₃	—	4	2	no	—
55	C₄×D₄×C₁₃	Q₈	1	4	yes	complemented
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
64	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
65	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₄²×C₁₃	—	2	1	no	—
74	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#107	—	2	4	no	—
77	C₁₃×#107	—	2	4	no	—
78	C₁₃×#107	—	4	2	no	—
79	C₁₃×C₄⋊C₈	—	2	4	no	—
80	C₁₃×C₄⋊C₈	—	2	2	no	—
81	C₁₃×#102	—	2	4	no	—
82	C₁₃×#102	D₄	1	4	yes	—
83	C₁₃×#102	Q₈	1	4	yes	complemented
84	C₄×C₈×C₁₃	—	2	2	no	—
85	C₁₃×#95	—	2	1	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	—	2	2	no	—
88	C₁₃×#95	D₄	1	2	yes	—
89	#26040	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	—	2	1	no	—
91	C₂×Q₈×C₁₃	—	4	4	no	—
92	C₂×Q₈×C₁₃	—	4	4	no	—
93	C₂×Q₈×C₁₃	—	8	2	no	—
94	C₂×D₄×C₁₃	—	2	1	no	—
95	C₂×D₄×C₁₃	—	2	1	no	—
96	C₂×D₄×C₁₃	—	2	1	no	—
97	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
98	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
99	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
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	4	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	4	4	no	—
107	C₂²×C₄×C₁₃	—	4	2	no	—
108	C₂²×C₄×C₁₃	—	4	2	no	—
109	C₂²×C₄×C₁₃	—	4	4	no	—
110	C₂²×C₄×C₁₃	—	8	2	no	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	2	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₁₃×C₄⋊C₄	—	2	1	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	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	4	4	no	—
134	C₁₃×C₄⋊C₄	—	4	4	no	—
135	C₁₃×C₄⋊C₄	—	4	2	no	—
136	C₁₃×C₄⋊C₄	—	4	4	no	—
137	C₁₃×C₄⋊C₄	—	4	2	no	—
138	C₁₃×C₄⋊C₄	—	8	1	no	—
139	C₁₃×C₄⋊C₄	—	8	1	no	—
140	C₁₃×C₄⋊C₄	D₈	1	4	yes	—
141	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
142	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
143	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
144	C₁₃×C₂²⋊C₄	—	2	4	no	—
145	C₁₃×C₂²⋊C₄	—	4	4	no	—
146	C₄²×C₁₃	—	2	2	no	—
147	C₄²×C₁₃	—	2	2	no	—
148	C₄²×C₁₃	—	4	2	no	—
149	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
150	C₄²×C₁₃	#41	1	2	yes	—
151	C₂×#474	C₂×C₁₃	1	2	yes	—
152	#2551	C₂×C₁₃	1	1	yes	characteristic, complemented
153	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
154	#2086	C₂×C₁₃	1	2	yes	complemented
155	#2057	C₂×C₁₃	1	2	yes	complemented
156	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#1862	C₂×C₁₃	1	2	yes	—
159	#1845	C₂×C₁₃	1	1	yes	characteristic, complemented
160	#1802	C₂×C₁₃	1	1	yes	characteristic
161	C₄×#102	C₂×C₁₃	1	1	yes	characteristic
162	C₂³×C₁₃	—	2	2	no	—
163	C₂³×C₁₃	—	2	2	no	—
164	C₂³×C₁₃	—	2	2	no	—
165	C₂³×C₁₃	—	4	1	no	—
166	C₂³×C₁₃	—	4	1	no	—
167	C₂³×C₁₃	—	4	1	no	—
168	C₂³×C₁₃	—	4	1	no	—
169	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
170	Q₈×C₁₃	—	8	8	no	—
171	D₄×C₁₃	—	2	2	no	—
172	D₄×C₁₃	—	2	2	no	—
173	D₄×C₁₃	—	2	2	no	—
174	D₄×C₁₃	C₄⋊Q₈	1	4	yes	complemented
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
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	2	no	—
184	C₂×C₄×C₁₃	—	2	2	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	1	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	8	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	—	8	8	no	—
199	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
200	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
201	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
202	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
203	C₂×C₄×C₁₃	#137	1	2	yes	—
204	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
209	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
210	C₈×C₁₃	—	2	2	no	—
211	C₈×C₁₃	—	2	2	no	—
212	C₈×C₁₃	—	4	2	no	—
213	C₂×C₄⋊Q₈	—	2	1	no	—
214	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
215	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
216	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
217	C₂²×C₄⋊C₄	—	2	1	no	—
218	#474	—	2	8	no	—
219	C₂×#107	C₂²×C₁₃	1	2	yes	—
220	C₂×#107	C₂²×C₁₃	1	2	yes	—
221	C₂×#107	C₂²×C₁₃	1	2	yes	—
222	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
223	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
224	C₂×#102	C₂²×C₁₃	1	2	yes	—
225	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
226	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
227	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
228	#395	—	2	2	no	—
229	#389	—	2	1	no	—
230	#389	C₂²×C₁₃	1	2	yes	—
231	#389	C₂²×C₁₃	1	2	yes	—
232	#385	—	2	2	no	—
233	#384	C₂²×C₁₃	1	1	yes	characteristic
234	#384	C₂²×C₁₃	1	1	yes	characteristic
235	#380	—	2	1	no	—
236	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
237	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
238	#340	C₂²×C₁₃	1	1	yes	characteristic
239	#340	C₂²×C₁₃	1	2	yes	—
240	#340	C₂²×C₁₃	1	1	yes	characteristic
241	#340	C₂²×C₁₃	1	2	yes	—
242	#336	C₂²×C₁₃	1	2	yes	—
243	C₂²×C₁₃	—	2	4	no	—
244	C₂²×C₁₃	—	4	2	no	—
245	C₂²×C₁₃	—	4	2	no	—
246	C₂²×C₁₃	—	4	2	no	—
247	C₂²×C₁₃	—	4	2	no	—
248	C₂²×C₁₃	—	4	2	no	—
249	C₂²×C₁₃	—	4	2	no	—
250	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
251	C₂²×C₁₃	D₄²	1	1	yes	characteristic
252	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
253	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
254	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
255	C₂²×C₁₃	#576	1	1	yes	characteristic
256	C₂²×C₁₃	#578	1	1	yes	characteristic
257	C₄×C₁₃	—	2	2	no	—
258	C₄×C₁₃	—	2	4	no	—
259	C₄×C₁₃	—	4	2	no	—
260	C₄×C₁₃	—	4	2	no	—
261	C₄×C₁₃	—	4	2	no	—
262	C₄×C₁₃	—	4	2	no	—
263	C₄×C₁₃	—	8	2	no	—
264	C₄×C₁₃	—	8	2	no	—
265	C₄×C₁₃	#474	1	4	yes	complemented
266	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
267	C₄×C₁₃	#544	1	1	yes	characteristic
268	C₄×C₁₃	#547	1	1	yes	characteristic
269	C₄×C₁₃	#554	1	1	yes	characteristic
270	C₂²×Q₈	—	2	2	no	—
271	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
272	C₂³×C₄	—	2	1	no	—
273	C₂³×C₄	—	2	2	no	—
274	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
275	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
277	C₄⋊Q₈	—	2	4	no	—
278	C₄⋊Q₈	—	4	2	no	—
279	C₄⋊Q₈	—	4	4	no	—
280	C₄×D₄	—	2	4	no	—
281	C₄×D₄	—	2	2	no	—
282	C₄×D₄	—	4	2	no	—
283	C₄×D₄	Q₈×C₁₃	1	4	yes	complemented
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	4	4	no	—
292	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
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×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
303	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
304	#107	—	2	4	no	—
305	#107	—	2	4	no	—
306	#107	—	4	2	no	—
307	C₄⋊C₈	—	2	4	no	—
308	C₄⋊C₈	—	2	2	no	—
309	#102	—	2	4	no	—
310	#102	D₄×C₁₃	1	4	yes	—
311	#102	Q₈×C₁₃	1	4	yes	complemented
312	C₄×C₈	—	2	2	no	—
313	#95	—	2	1	no	—
314	#95	—	2	2	no	—
315	#95	—	2	2	no	—
316	#95	D₄×C₁₃	1	2	yes	—
317	C₂×C₁₃	—	4	4	no	—
318	C₂×C₁₃	#2440	1	1	yes	characteristic
319	C₂×C₁₃	C₂×#474	1	1	yes	characteristic
320	C₂×C₁₃	#3083	1	1	yes	characteristic
321	C₂×C₁₃	#3276	1	1	yes	characteristic
322	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
323	C₂×C₁₃	Q₈×D₈	1	1	yes	characteristic
324	C₂×C₁₃	#3385	1	1	yes	characteristic
325	C₂⁴	—	2	1	no	—
326	C₂×Q₈	—	4	4	no	—
327	C₂×Q₈	—	4	4	no	—
328	C₂×Q₈	—	8	2	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
333	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
334	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	4	4	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	4	4	no	—
345	C₂²×C₄	—	8	2	no	—
346	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
359	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	4	4	no	—
369	C₄⋊C₄	—	4	4	no	—
370	C₄⋊C₄	—	4	2	no	—
371	C₄⋊C₄	—	4	4	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	8	1	no	—
374	C₄⋊C₄	—	8	1	no	—
375	C₄⋊C₄	C₁₃×D₈	1	4	yes	—
376	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
377	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
378	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
379	C₂²⋊C₄	—	2	4	no	—
380	C₂²⋊C₄	—	4	4	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	4	2	no	—
384	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
385	C₄²	C₁₃×#41	1	2	yes	—
386	C₁₃	#26040	1	1	yes	characteristic, direct product factor, Sylow
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	1	no	—
394	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
395	Q₈	—	8	8	no	—
396	D₄	—	2	2	no	—
397	D₄	—	2	2	no	—
398	D₄	—	2	2	no	—
399	D₄	C₁₃×C₄⋊Q₈	1	4	yes	complemented
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	8	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	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	8	8	no	—
424	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
425	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
426	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
427	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
428	C₂×C₄	C₁₃×#137	1	2	yes	—
429	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
430	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
431	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
432	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
433	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
434	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
435	C₈	—	2	2	no	—
436	C₈	—	2	2	no	—
437	C₈	—	4	2	no	—
438	C₂²	—	2	4	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
446	C₂²	D₄²×C₁₃	1	1	yes	characteristic
447	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
448	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
449	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
450	C₂²	C₁₃×#576	1	1	yes	characteristic
451	C₂²	C₁₃×#578	1	1	yes	characteristic
452	C₄	—	2	4	no	—
453	C₄	—	2	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	8	2	no	—
459	C₄	—	8	2	no	—
460	C₄	C₁₃×#474	1	4	yes	complemented
461	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
462	C₄	C₁₃×#544	1	1	yes	characteristic
463	C₄	C₁₃×#547	1	1	yes	characteristic
464	C₄	C₁₃×#554	1	1	yes	characteristic
465	C₂	—	4	4	no	—
466	C₂	C₁₃×#2440	1	1	yes	characteristic
467	C₂	C₂×C₁₃×#474	1	1	yes	characteristic
468	C₂	C₁₃×#3083	1	1	yes	characteristic
469	C₂	C₁₃×#3276	1	1	yes	characteristic
470	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
471	C₂	Q₈×C₁₃×D₈	1	1	yes	characteristic
472	C₂	C₁₃×#3385	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2551	C₂	semidirect
4. C₁₃×#2086	C₂	semidirect
5. C₁₃×#2057	C₂	semidirect
6. C₁₃×#1947	C₂	semidirect
7. C₁₃×#1939	C₂	semidirect
9. C₁₃×#1845	C₂	semidirect
55. C₄×D₄×C₁₃	Q₈	semidirect
83. C₁₃×#102	Q₈	semidirect
89. #26040	C₁₃	direct (N × H)
152. #2551	C₂×C₁₃	semidirect
154. #2086	C₂×C₁₃	semidirect
155. #2057	C₂×C₁₃	semidirect
156. #1947	C₂×C₁₃	semidirect
157. #1939	C₂×C₁₃	semidirect
159. #1845	C₂×C₁₃	semidirect
174. D₄×C₁₃	C₄⋊Q₈	semidirect
265. C₄×C₁₃	#474	semidirect
283. C₄×D₄	Q₈×C₁₃	semidirect
311. #102	Q₈×C₁₃	semidirect
386. C₁₃	#26040	direct (N × H)
399. D₄	C₁₃×C₄⋊Q₈	semidirect
460. C₄	C₁₃×#474	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#474	2
C₁₃×#2551	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2086	2
C₁₃×#2057	2
C₁₃×#1947	2
C₁₃×#1939	2
C₁₃×#1862	2
C₁₃×#1845	2
C₁₃×#1802	2
C₄×C₁₃×#102	2
#26040	13

Subgroups — C13×#26040 #15712379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26040 #15712379