Subgroups — C₁₃×#26484 #15712823

Order 3328.

918 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×#500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2452	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2067	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2023	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1862	C₂	1	2	yes	maximal, complemented
11	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
15	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
16	C₁₃×#500	—	2	4	no	—
17	C₄×C₁₃×D₈	—	2	4	no	—
18	C₂×C₁₃×#107	C₂²	1	2	yes	—
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#102	C₂²	1	2	yes	—
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#396	—	2	2	no	—
30	C₁₃×#393	—	2	2	no	—
31	C₁₃×#390	C₂²	1	2	yes	—
32	C₁₃×#390	C₂²	1	2	yes	—
33	C₁₃×#389	C₂²	1	2	yes	—
34	C₁₃×#389	C₂²	1	2	yes	—
35	C₁₃×#385	—	2	2	no	—
36	C₄×C₁₃×C₄⋊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	—	2	2	no	—
42	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₃	—	2	2	no	—
44	C₂×C₁₃×D₈	—	2	2	no	—
45	C₂×C₁₃×D₈	—	2	2	no	—
46	C₂×C₁₃×D₈	Q₈	1	4	yes	complemented
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₁₃×C₄⋊Q₈	—	2	4	no	—
52	C₁₃×C₄⋊Q₈	—	4	2	no	—
53	C₁₃×C₂²⋊Q₈	—	4	8	no	—
54	C₄×D₄×C₁₃	—	2	4	no	—
55	C₄×D₄×C₁₃	—	4	2	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
60	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	4	no	—
75	C₁₃×#107	D₄	1	4	yes	—
76	C₁₃×C₄⋊C₈	—	2	2	no	—
77	C₁₃×#102	—	2	4	no	—
78	C₁₃×#102	—	2	4	no	—
79	C₁₃×#102	—	4	2	no	—
80	C₄×C₈×C₁₃	—	2	2	no	—
81	C₄×C₈×C₁₃	—	2	2	no	—
82	C₄×C₈×C₁₃	—	2	2	no	—
83	C₁₃×#95	—	2	2	no	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	D₄	1	1	yes	characteristic
86	C₁₃×#95	D₄	1	1	yes	characteristic
87	#26484	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂⁴×C₁₃	—	2	2	no	—
89	C₂×Q₈×C₁₃	—	4	4	no	—
90	C₂×Q₈×C₁₃	—	4	4	no	—
91	C₂×Q₈×C₁₃	—	8	2	no	—
92	C₂×D₄×C₁₃	—	2	2	no	—
93	C₂×D₄×C₁₃	—	2	2	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	4	4	no	—
102	C₂²×C₄×C₁₃	—	4	4	no	—
103	C₂²×C₄×C₁₃	—	8	2	no	—
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
111	C₁₃×D₈	—	2	8	no	—
112	C₂×C₈×C₁₃	—	2	1	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	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
122	C₂×C₈×C₁₃	#41	1	2	yes	—
123	C₂×C₈×C₁₃	#41	1	2	yes	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
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	—	4	4	no	—
131	C₁₃×C₄⋊C₄	—	4	4	no	—
132	C₁₃×C₄⋊C₄	—	4	4	no	—
133	C₁₃×C₄⋊C₄	D₈	1	4	yes	complemented
134	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
135	C₁₃×C₂²⋊C₄	—	4	4	no	—
136	C₁₃×C₂²⋊C₄	—	4	4	no	—
137	C₁₃×C₂²⋊C₄	—	4	4	no	—
138	C₁₃×C₂²⋊C₄	—	4	4	no	—
139	C₁₃×C₂²⋊C₄	—	8	2	no	—
140	C₄²×C₁₃	—	2	1	no	—
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	—	2	1	no	—
146	C₂×#500	C₂×C₁₃	1	1	yes	characteristic, complemented
147	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic
148	#2452	C₂×C₁₃	1	2	yes	complemented
149	#2067	C₂×C₁₃	1	2	yes	complemented
150	#2023	C₂×C₁₃	1	2	yes	complemented
151	#1970	C₂×C₁₃	1	1	yes	characteristic
152	#1970	C₂×C₁₃	1	1	yes	characteristic
153	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#1862	C₂×C₁₃	1	2	yes	complemented
156	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
157	C₂³×C₁₃	—	2	4	no	—
158	C₂³×C₁₃	—	4	2	no	—
159	C₂³×C₁₃	—	4	2	no	—
160	C₂³×C₁₃	—	4	2	no	—
161	C₂³×C₁₃	—	4	2	no	—
162	C₂³×C₁₃	—	4	2	no	—
163	C₂³×C₁₃	—	4	2	no	—
164	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₁₃	—	8	8	no	—
166	D₄×C₁₃	—	2	4	no	—
167	D₄×C₁₃	—	2	4	no	—
168	D₄×C₁₃	—	4	2	no	—
169	D₄×C₁₃	—	4	2	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	1	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	4	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	2	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	—	8	8	no	—
194	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
195	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
196	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
197	C₂×C₄×C₁₃	#135	1	2	yes	—
198	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
203	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
204	C₈×C₁₃	—	2	2	no	—
205	C₈×C₁₃	—	4	1	no	—
206	C₈×C₁₃	—	4	1	no	—
207	C₈×C₁₃	C₂²⋊Q₈	1	4	yes	complemented
208	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
210	C₂×C₂²⋊Q₈	—	2	2	no	—
211	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
212	#500	—	2	4	no	—
213	C₄×D₈	—	2	4	no	—
214	C₂×#107	C₂²×C₁₃	1	2	yes	—
215	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×#102	C₂²×C₁₃	1	2	yes	—
220	C₂×#102	C₂²×C₁₃	1	2	yes	—
221	C₂×#102	C₂²×C₁₃	1	2	yes	—
222	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
223	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
225	#396	—	2	2	no	—
226	#393	—	2	2	no	—
227	#390	C₂²×C₁₃	1	2	yes	—
228	#390	C₂²×C₁₃	1	2	yes	—
229	#389	C₂²×C₁₃	1	2	yes	—
230	#389	C₂²×C₁₃	1	2	yes	—
231	#385	—	2	2	no	—
232	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
233	#340	C₂²×C₁₃	1	2	yes	—
234	#340	C₂²×C₁₃	1	2	yes	—
235	#336	C₂²×C₁₃	1	1	yes	characteristic
236	#336	C₂²×C₁₃	1	1	yes	characteristic
237	C₂²×C₁₃	—	4	4	no	—
238	C₂²×C₁₃	—	4	4	no	—
239	C₂²×C₁₃	—	4	4	no	—
240	C₂²×C₁₃	—	8	2	no	—
241	C₂²×C₁₃	—	8	2	no	—
242	C₂²×C₁₃	—	8	2	no	—
243	C₂²×C₁₃	—	8	2	no	—
244	C₂²×C₁₃	#532	1	1	yes	characteristic
245	C₂²×C₁₃	D₄²	1	1	yes	characteristic
246	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
247	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
248	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
249	C₂²×C₁₃	#576	1	1	yes	characteristic
250	C₂²×C₁₃	#578	1	1	yes	characteristic
251	C₄×C₁₃	—	2	2	no	—
252	C₄×C₁₃	—	2	2	no	—
253	C₄×C₁₃	—	2	2	no	—
254	C₄×C₁₃	—	2	2	no	—
255	C₄×C₁₃	—	4	1	no	—
256	C₄×C₁₃	—	4	4	no	—
257	C₄×C₁₃	—	4	1	no	—
258	C₄×C₁₃	—	8	2	no	—
259	C₄×C₁₃	—	8	2	no	—
260	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
261	C₄×C₁₃	#542	1	1	yes	characteristic
262	C₄×C₁₃	#548	1	1	yes	characteristic
263	C₄×C₁₃	#554	1	1	yes	characteristic
264	C₂²×Q₈	—	2	2	no	—
265	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
266	C₂³×C₄	—	2	2	no	—
267	C₂×D₈	—	2	2	no	—
268	C₂×D₈	—	2	2	no	—
269	C₂×D₈	Q₈×C₁₃	1	4	yes	complemented
270	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
271	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
272	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
274	C₄⋊Q₈	—	2	4	no	—
275	C₄⋊Q₈	—	4	2	no	—
276	C₂²⋊Q₈	—	4	8	no	—
277	C₄×D₄	—	2	4	no	—
278	C₄×D₄	—	4	2	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
283	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₂²⋊C₄	—	2	2	no	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
293	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
294	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
295	#107	—	2	2	no	—
296	#107	—	2	2	no	—
297	#107	—	2	4	no	—
298	#107	D₄×C₁₃	1	4	yes	—
299	C₄⋊C₈	—	2	2	no	—
300	#102	—	2	4	no	—
301	#102	—	2	4	no	—
302	#102	—	4	2	no	—
303	C₄×C₈	—	2	2	no	—
304	C₄×C₈	—	2	2	no	—
305	C₄×C₈	—	2	2	no	—
306	#95	—	2	2	no	—
307	#95	—	2	2	no	—
308	#95	D₄×C₁₃	1	1	yes	characteristic
309	#95	D₄×C₁₃	1	1	yes	characteristic
310	C₂×C₁₃	—	8	4	no	—
311	C₂×C₁₃	#2452	1	1	yes	characteristic
312	C₂×C₁₃	#3169	1	1	yes	characteristic
313	C₂×C₁₃	#3175	1	1	yes	characteristic
314	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
315	C₂×C₁₃	#3285	1	1	yes	characteristic
316	C₂×C₁₃	Q₈×D₈	1	1	yes	characteristic
317	C₂×C₁₃	#3380	1	1	yes	characteristic
318	C₂⁴	—	2	2	no	—
319	C₂×Q₈	—	4	4	no	—
320	C₂×Q₈	—	4	4	no	—
321	C₂×Q₈	—	8	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	4	4	no	—
332	C₂²×C₄	—	4	4	no	—
333	C₂²×C₄	—	8	2	no	—
334	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
341	D₈	—	2	8	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	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	C₂×D₄×C₁₃	1	2	yes	—
351	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
352	C₂×C₈	C₁₃×#41	1	2	yes	—
353	C₂×C₈	C₁₃×#41	1	2	yes	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	4	4	no	—
361	C₄⋊C₄	—	4	4	no	—
362	C₄⋊C₄	—	4	4	no	—
363	C₄⋊C₄	C₁₃×D₈	1	4	yes	complemented
364	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
365	C₂²⋊C₄	—	4	4	no	—
366	C₂²⋊C₄	—	4	4	no	—
367	C₂²⋊C₄	—	4	4	no	—
368	C₂²⋊C₄	—	4	4	no	—
369	C₂²⋊C₄	—	8	2	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₁₃	#26484	1	1	yes	characteristic, direct product factor, Sylow
377	C₂³	—	2	4	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	4	2	no	—
383	C₂³	—	4	2	no	—
384	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
385	Q₈	—	8	8	no	—
386	D₄	—	2	4	no	—
387	D₄	—	2	4	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	C₂×C₄	—	2	1	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	1	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	8	8	no	—
414	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
415	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
416	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
417	C₂×C₄	C₁₃×#135	1	2	yes	—
418	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
419	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
420	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
421	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
422	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
423	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
424	C₈	—	2	2	no	—
425	C₈	—	4	1	no	—
426	C₈	—	4	1	no	—
427	C₈	C₁₃×C₂²⋊Q₈	1	4	yes	complemented
428	C₂²	—	4	4	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	4	no	—
431	C₂²	—	8	2	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	8	2	no	—
434	C₂²	—	8	2	no	—
435	C₂²	C₁₃×#532	1	1	yes	characteristic
436	C₂²	D₄²×C₁₃	1	1	yes	characteristic
437	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
438	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
439	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
440	C₂²	C₁₃×#576	1	1	yes	characteristic
441	C₂²	C₁₃×#578	1	1	yes	characteristic
442	C₄	—	2	2	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	2	no	—
446	C₄	—	4	4	no	—
447	C₄	—	4	1	no	—
448	C₄	—	4	1	no	—
449	C₄	—	8	2	no	—
450	C₄	—	8	2	no	—
451	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
452	C₄	C₁₃×#542	1	1	yes	characteristic
453	C₄	C₁₃×#548	1	1	yes	characteristic
454	C₄	C₁₃×#554	1	1	yes	characteristic
455	C₂	—	8	4	no	—
456	C₂	C₁₃×#2452	1	1	yes	characteristic
457	C₂	C₁₃×#3169	1	1	yes	characteristic
458	C₂	C₁₃×#3175	1	1	yes	characteristic
459	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
460	C₂	C₁₃×#3285	1	1	yes	characteristic
461	C₂	Q₈×C₁₃×D₈	1	1	yes	characteristic
462	C₂	C₁₃×#3380	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
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
1. C₂×C₁₃×#500	C₂	semidirect
3. C₁₃×#2452	C₂	semidirect
4. C₁₃×#2067	C₂	semidirect
5. C₁₃×#2023	C₂	semidirect
8. C₁₃×#1942	C₂	semidirect
9. C₁₃×#1942	C₂	semidirect
10. C₁₃×#1862	C₂	semidirect
11. C₈×C₁₃×C₄⋊C₄	C₂	semidirect
46. C₂×C₁₃×D₈	Q₈	semidirect
87. #26484	C₁₃	direct (N × H)
133. C₁₃×C₄⋊C₄	D₈	semidirect
146. C₂×#500	C₂×C₁₃	semidirect
148. #2452	C₂×C₁₃	semidirect
149. #2067	C₂×C₁₃	semidirect
150. #2023	C₂×C₁₃	semidirect
153. #1942	C₂×C₁₃	semidirect
154. #1942	C₂×C₁₃	semidirect
155. #1862	C₂×C₁₃	semidirect
156. C₈×C₄⋊C₄	C₂×C₁₃	semidirect
207. C₈×C₁₃	C₂²⋊Q₈	semidirect
269. C₂×D₈	Q₈×C₁₃	semidirect
363. C₄⋊C₄	C₁₃×D₈	semidirect
376. C₁₃	#26484	direct (N × H)
427. C₈	C₁₃×C₂²⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#500	2
C₂×C₄×C₁₃×D₈	2
C₁₃×#2452	2
C₁₃×#2067	2
C₁₃×#2023	2
C₁₃×#1970	2
C₁₃×#1942	2
C₁₃×#1862	2
C₈×C₁₃×C₄⋊C₄	2
#26484	13

Subgroups — C13×#26484 #15712823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26484 #15712823