Subgroups — C₁₃×#26466 #15712805

Order 3328.

810 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#477	C₂	1	2	yes	maximal
2	C₁₃×#2551	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2365	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2068	C₂	1	2	yes	maximal
5	C₁₃×#2024	C₂	1	2	yes	maximal
6	C₁₃×#1981	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1956	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1863	C₂	1	2	yes	maximal
11	C₄×C₁₃×#107	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
16	C₁₃×#477	—	2	8	no	—
17	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#107	C₂²	1	2	yes	—
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
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×#103	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#395	—	2	2	no	—
28	C₁₃×#391	C₂²	1	2	yes	—
29	C₁₃×#389	—	2	1	no	—
30	C₁₃×#389	—	2	1	no	—
31	C₁₃×#389	C₂²	1	2	yes	—
32	C₁₃×#387	—	2	2	no	—
33	C₁₃×#384	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₄×C₁₃×C₄⋊C₄	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	1	yes	characteristic
41	C₁₃×#336	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₃	—	2	2	no	—
43	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₁₃×C₄⋊Q₈	—	2	4	no	—
48	C₁₃×C₄⋊Q₈	—	2	2	no	—
49	C₁₃×C₄⋊Q₈	—	4	2	no	—
50	C₁₃×C₄⋊Q₈	—	4	4	no	—
51	C₁₃×C₄⋊Q₈	Q₈	1	4	yes	complemented
52	C₄×Q₈×C₁₃	—	2	4	no	—
53	C₄×Q₈×C₁₃	—	4	2	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
61	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
62	C₂×C₁₃×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	—	2	1	no	—
69	C₂×C₄²×C₁₃	—	2	2	no	—
70	C₂×C₄²×C₁₃	—	2	1	no	—
71	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×#107	—	2	4	no	—
74	C₁₃×#107	—	2	2	no	—
75	C₁₃×#107	D₄	1	4	yes	—
76	C₁₃×C₄⋊C₈	—	2	4	no	—
77	C₁₃×C₄⋊C₈	—	2	2	no	—
78	C₁₃×#103	—	2	4	no	—
79	C₁₃×#103	—	2	4	no	—
80	C₁₃×#103	—	2	4	no	—
81	C₁₃×#103	—	4	2	no	—
82	C₄×C₈×C₁₃	—	2	2	no	—
83	C₁₃×#95	—	2	2	no	—
84	C₁₃×#95	—	2	1	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	#26466	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	4	4	no	—
96	C₂×Q₈×C₁₃	—	4	4	no	—
97	C₂×Q₈×C₁₃	—	8	2	no	—
98	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
110	C₂×C₈×C₁₃	—	2	1	no	—
111	C₂×C₈×C₁₃	—	2	1	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	2	1	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	1	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
119	C₁₃×C₄⋊C₄	—	2	4	no	—
120	C₁₃×C₄⋊C₄	—	2	4	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	1	no	—
123	C₁₃×C₄⋊C₄	—	2	1	no	—
124	C₁₃×C₄⋊C₄	—	2	1	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	4	4	no	—
130	C₁₃×C₄⋊C₄	—	4	4	no	—
131	C₁₃×C₄⋊C₄	—	4	4	no	—
132	C₁₃×C₄⋊C₄	—	4	2	no	—
133	C₁₃×C₄⋊C₄	—	8	1	no	—
134	C₁₃×C₄⋊C₄	Q₁₆	1	4	yes	—
135	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
136	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
137	C₁₃×C₄⋊C₄	#41	1	2	yes	—
138	C₄²×C₁₃	—	2	2	no	—
139	C₄²×C₁₃	—	2	2	no	—
140	C₄²×C₁₃	—	4	4	no	—
141	C₄²×C₁₃	—	4	2	no	—
142	C₄²×C₁₃	—	4	2	no	—
143	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
144	C₄²×C₁₃	#41	1	2	yes	—
145	C₂×#477	C₂×C₁₃	1	2	yes	—
146	#2551	C₂×C₁₃	1	1	yes	characteristic
147	#2365	C₂×C₁₃	1	1	yes	characteristic
148	#2068	C₂×C₁₃	1	2	yes	—
149	#2024	C₂×C₁₃	1	2	yes	—
150	#1981	C₂×C₁₃	1	1	yes	characteristic
151	#1956	C₂×C₁₃	1	1	yes	characteristic
152	#1947	C₂×C₁₃	1	1	yes	characteristic
153	#1939	C₂×C₁₃	1	1	yes	characteristic
154	#1863	C₂×C₁₃	1	2	yes	—
155	C₄×#107	C₂×C₁₃	1	1	yes	characteristic
156	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₁₃	—	2	4	no	—
158	Q₈×C₁₃	—	2	4	no	—
159	Q₈×C₁₃	—	4	2	no	—
160	Q₈×C₁₃	—	4	2	no	—
161	Q₈×C₁₃	—	8	8	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	4	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	1	no	—
187	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
188	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
189	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	—
190	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
191	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
192	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
197	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
198	C₈×C₁₃	—	2	2	no	—
199	C₈×C₁₃	—	4	2	no	—
200	C₈×C₁₃	—	4	1	no	—
201	C₂×C₄⋊Q₈	—	2	1	no	—
202	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
203	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
204	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
205	#477	—	2	8	no	—
206	C₂×#107	C₂²×C₁₃	1	2	yes	—
207	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
210	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
211	C₂×#103	C₂²×C₁₃	1	2	yes	—
212	C₂×#103	C₂²×C₁₃	1	2	yes	—
213	C₂×#103	C₂²×C₁₃	1	2	yes	—
214	C₂×#103	C₂²×C₁₃	1	2	yes	—
215	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
216	#395	—	2	2	no	—
217	#391	C₂²×C₁₃	1	2	yes	—
218	#389	—	2	1	no	—
219	#389	—	2	1	no	—
220	#389	C₂²×C₁₃	1	2	yes	—
221	#387	—	2	2	no	—
222	#384	C₂²×C₁₃	1	1	yes	characteristic
223	C₄×C₄⋊C₄	—	2	1	no	—
224	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
225	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
226	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
227	#340	C₂²×C₁₃	1	2	yes	—
228	#340	C₂²×C₁₃	1	1	yes	characteristic
229	#340	C₂²×C₁₃	1	1	yes	characteristic
230	#336	C₂²×C₁₃	1	2	yes	—
231	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
232	C₂²×C₁₃	D₄²	1	1	yes	characteristic
233	C₂²×C₁₃	#548	1	1	yes	characteristic
234	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
235	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
236	C₂²×C₁₃	#577	1	1	yes	characteristic
237	C₂²×C₁₃	#578	1	1	yes	characteristic
238	C₄×C₁₃	—	2	2	no	—
239	C₄×C₁₃	—	2	4	no	—
240	C₄×C₁₃	—	4	2	no	—
241	C₄×C₁₃	—	4	4	no	—
242	C₄×C₁₃	—	4	2	no	—
243	C₄×C₁₃	—	4	2	no	—
244	C₄×C₁₃	—	4	2	no	—
245	C₄×C₁₃	—	8	1	no	—
246	C₄×C₁₃	—	8	2	no	—
247	C₄×C₁₃	#477	1	4	yes	complemented
248	C₄×C₁₃	#532	1	1	yes	characteristic
249	C₄×C₁₃	#542	1	1	yes	characteristic
250	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
251	C₄×C₁₃	#554	1	1	yes	characteristic
252	C₂²×Q₈	—	2	2	no	—
253	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
254	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
255	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
256	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
257	C₄⋊Q₈	—	2	4	no	—
258	C₄⋊Q₈	—	2	2	no	—
259	C₄⋊Q₈	—	4	2	no	—
260	C₄⋊Q₈	—	4	4	no	—
261	C₄⋊Q₈	Q₈×C₁₃	1	4	yes	complemented
262	C₄×Q₈	—	2	4	no	—
263	C₄×Q₈	—	4	2	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
272	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	—	2	1	no	—
281	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
282	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
283	#107	—	2	4	no	—
284	#107	—	2	2	no	—
285	#107	D₄×C₁₃	1	4	yes	—
286	C₄⋊C₈	—	2	4	no	—
287	C₄⋊C₈	—	2	2	no	—
288	#103	—	2	4	no	—
289	#103	—	2	4	no	—
290	#103	—	2	4	no	—
291	#103	—	4	2	no	—
292	C₄×C₈	—	2	2	no	—
293	#95	—	2	2	no	—
294	#95	—	2	1	no	—
295	#95	—	2	1	no	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	#95	D₄×C₁₃	1	2	yes	—
299	C₂×C₁₃	#2452	1	1	yes	characteristic
300	C₂×C₁₃	C₂×#477	1	1	yes	characteristic
301	C₂×C₁₃	#3082	1	1	yes	characteristic
302	C₂×C₁₃	#3272	1	1	yes	characteristic
303	C₂×C₁₃	D₄×Q₁₆	1	1	yes	characteristic
304	C₂×C₁₃	#3363	1	1	yes	characteristic
305	C₂×C₁₃	#3367	1	1	yes	characteristic
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	4	4	no	—
312	C₂×Q₈	—	4	4	no	—
313	C₂×Q₈	—	8	2	no	—
314	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
322	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
324	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
325	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	2	4	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	4	4	no	—
346	C₄⋊C₄	—	4	4	no	—
347	C₄⋊C₄	—	4	4	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	—	8	1	no	—
350	C₄⋊C₄	C₁₃×Q₁₆	1	4	yes	—
351	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
352	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
353	C₄⋊C₄	C₁₃×#41	1	2	yes	—
354	C₄²	—	2	2	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	4	4	no	—
357	C₄²	—	4	2	no	—
358	C₄²	—	4	2	no	—
359	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
360	C₄²	C₁₃×#41	1	2	yes	—
361	C₁₃	#26466	1	1	yes	characteristic, direct product factor, Sylow
362	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
363	Q₈	—	2	4	no	—
364	Q₈	—	2	4	no	—
365	Q₈	—	4	2	no	—
366	Q₈	—	4	2	no	—
367	Q₈	—	8	8	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
394	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
395	C₂×C₄	C₂×C₁₃×Q₁₆	1	4	yes	—
396	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
397	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
398	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
399	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
400	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
401	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
402	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
403	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
404	C₈	—	2	2	no	—
405	C₈	—	4	2	no	—
406	C₈	—	4	1	no	—
407	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
408	C₂²	D₄²×C₁₃	1	1	yes	characteristic
409	C₂²	C₁₃×#548	1	1	yes	characteristic
410	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
411	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
412	C₂²	C₁₃×#577	1	1	yes	characteristic
413	C₂²	C₁₃×#578	1	1	yes	characteristic
414	C₄	—	2	4	no	—
415	C₄	—	2	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	4	no	—
421	C₄	—	8	2	no	—
422	C₄	—	8	1	no	—
423	C₄	C₁₃×#477	1	4	yes	complemented
424	C₄	C₁₃×#532	1	1	yes	characteristic
425	C₄	C₁₃×#542	1	1	yes	characteristic
426	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
427	C₄	C₁₃×#554	1	1	yes	characteristic
428	C₂	C₁₃×#2452	1	1	yes	characteristic
429	C₂	C₂×C₁₃×#477	1	1	yes	characteristic
430	C₂	C₁₃×#3082	1	1	yes	characteristic
431	C₂	C₁₃×#3272	1	1	yes	characteristic
432	C₂	D₄×C₁₃×Q₁₆	1	1	yes	characteristic
433	C₂	C₁₃×#3363	1	1	yes	characteristic
434	C₂	C₁₃×#3367	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
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
51. C₁₃×C₄⋊Q₈	Q₈	semidirect
89. #26466	C₁₃	direct (N × H)
247. C₄×C₁₃	#477	semidirect
261. C₄⋊Q₈	Q₈×C₁₃	semidirect
361. C₁₃	#26466	direct (N × H)
423. C₄	C₁₃×#477	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#477	2
C₁₃×#2551	2
C₁₃×#2365	2
C₁₃×#2068	2
C₁₃×#2024	2
C₁₃×#1981	2
C₁₃×#1956	2
C₁₃×#1947	2
C₁₃×#1939	2
C₁₃×#1863	2
C₄×C₁₃×#107	2
#26466	13

Subgroups — C13×#26466 #15712805

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26466 #15712805