Subgroups — C₁₃×#23778 #15710117

Order 3328.

768 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2092	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2088	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2087	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#2065	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#2059	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2025	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
15	C₄×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#117	—	2	1	no	—
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#390	C₂²	1	1	yes	characteristic
32	C₁₃×#390	C₂²	1	1	yes	characteristic
33	C₁₃×#389	C₂²	1	1	yes	characteristic
34	C₁₃×#389	C₂²	1	1	yes	characteristic
35	C₁₃×#389	C₂²	1	1	yes	characteristic
36	C₁₃×#389	C₂²	1	1	yes	characteristic
37	C₁₃×#388	—	2	1	no	—
38	C₁₃×#388	—	2	1	no	—
39	C₁₃×#387	—	2	1	no	—
40	C₁₃×#387	—	2	1	no	—
41	C₁₃×#382	C₂²	1	1	yes	characteristic
42	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
43	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
44	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
48	C₄³×C₁₃	C₂²	1	1	yes	characteristic
49	C₁₃×#340	C₂²	1	1	yes	characteristic
50	C₁₃×#340	C₂²	1	1	yes	characteristic
51	C₁₃×#340	C₂²	1	1	yes	characteristic
52	C₁₃×#340	C₂²	1	1	yes	characteristic
53	C₁₃×#340	C₂²	1	1	yes	characteristic
54	C₁₃×#340	C₂²	1	1	yes	characteristic
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
57	C₁₃×#336	C₂²	1	1	yes	characteristic
58	C₁₃×#336	C₂²	1	1	yes	characteristic
59	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	—	2	1	no	—
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×#125	—	2	2	no	—
66	C₁₃×#125	—	2	2	no	—
67	C₄×D₄×C₁₃	—	2	2	no	—
68	C₄×D₄×C₁₃	Q₈	1	4	yes	—
69	C₁₃×#117	—	4	4	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₄²×C₁₃	—	2	1	no	—
89	C₂×C₄²×C₁₃	—	2	1	no	—
90	C₂×C₄²×C₁₃	—	2	1	no	—
91	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₁₃×#107	—	2	2	no	—
99	C₁₃×#107	—	2	2	no	—
100	C₁₃×#106	—	2	2	no	—
101	C₁₃×#106	—	2	2	no	—
102	C₁₃×C₄⋊C₈	—	2	2	no	—
103	C₁₃×C₄⋊C₈	—	2	2	no	—
104	C₁₃×#102	—	2	2	no	—
105	C₁₃×#102	—	2	2	no	—
106	C₁₃×#102	—	2	2	no	—
107	C₁₃×#102	—	2	2	no	—
108	C₄×C₈×C₁₃	—	2	2	no	—
109	C₄×C₈×C₁₃	—	2	2	no	—
110	C₁₃×#95	—	2	1	no	—
111	C₁₃×#95	—	2	1	no	—
112	C₁₃×#95	—	2	1	no	—
113	C₁₃×#95	—	2	1	no	—
114	C₁₃×#95	—	2	1	no	—
115	C₁₃×#95	—	2	1	no	—
116	C₁₃×#95	—	2	1	no	—
117	C₁₃×#95	—	2	1	no	—
118	C₁₃×#95	—	2	1	no	—
119	#23778	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂⁴×C₁₃	—	2	1	no	—
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂×D₄×C₁₃	—	2	1	no	—
123	C₂×D₄×C₁₃	—	2	1	no	—
124	C₂×D₄×C₁₃	—	2	1	no	—
125	C₂×D₄×C₁₃	—	2	1	no	—
126	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	2	1	no	—
130	C₂²×C₄×C₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	4	2	no	—
136	C₂²×C₄×C₁₃	—	4	2	no	—
137	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
144	C₂×C₈×C₁₃	—	2	1	no	—
145	C₂×C₈×C₁₃	—	2	1	no	—
146	C₂×C₈×C₁₃	—	2	1	no	—
147	C₂×C₈×C₁₃	—	2	1	no	—
148	C₂×C₈×C₁₃	—	2	1	no	—
149	C₂×C₈×C₁₃	—	2	1	no	—
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	—	2	1	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	2	1	no	—
154	C₂×C₈×C₁₃	#41	1	2	yes	—
155	C₂×C₈×C₁₃	#41	1	2	yes	—
156	C₁₃×C₄⋊C₄	—	2	4	no	—
157	C₁₃×C₄⋊C₄	—	2	4	no	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₁₃×C₄⋊C₄	—	2	1	no	—
163	C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₁₃×C₄⋊C₄	—	2	1	no	—
166	C₁₃×C₄⋊C₄	—	2	1	no	—
167	C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₁₃×C₄⋊C₄	—	4	2	no	—
170	C₁₃×C₄⋊C₄	—	4	2	no	—
171	C₁₃×C₄⋊C₄	—	4	2	no	—
172	C₁₃×C₄⋊C₄	—	4	2	no	—
173	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
174	C₁₃×C₄⋊C₄	#41	1	2	yes	—
175	C₁₃×C₄⋊C₄	#41	1	2	yes	—
176	C₁₃×C₂²⋊C₄	—	2	4	no	—
177	C₁₃×C₂²⋊C₄	—	4	2	no	—
178	C₁₃×C₂²⋊C₄	—	4	2	no	—
179	C₁₃×C₂²⋊C₄	—	4	2	no	—
180	C₁₃×C₂²⋊C₄	—	4	2	no	—
181	C₄²×C₁₃	—	2	2	no	—
182	C₄²×C₁₃	—	2	2	no	—
183	C₄²×C₁₃	—	2	2	no	—
184	C₄²×C₁₃	—	2	1	no	—
185	C₄²×C₁₃	—	2	1	no	—
186	C₄²×C₁₃	—	2	1	no	—
187	C₄²×C₁₃	—	2	1	no	—
188	C₄²×C₁₃	—	4	1	no	—
189	C₄²×C₁₃	—	4	2	no	—
190	C₄²×C₁₃	—	4	2	no	—
191	C₄²×C₁₃	—	4	2	no	—
192	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
193	C₄²×C₁₃	#41	1	2	yes	—
194	C₄×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#2293	C₂×C₁₃	1	1	yes	characteristic
196	#2101	C₂×C₁₃	1	1	yes	characteristic, complemented
197	#2092	C₂×C₁₃	1	1	yes	characteristic
198	#2088	C₂×C₁₃	1	1	yes	characteristic, complemented
199	#2087	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#2067	C₂×C₁₃	1	1	yes	characteristic
201	#2065	C₂×C₁₃	1	1	yes	characteristic
202	#2059	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#2025	C₂×C₁₃	1	1	yes	characteristic
204	C₄×#107	C₂×C₁₃	1	1	yes	characteristic, complemented
205	C₄×#106	C₂×C₁₃	1	1	yes	characteristic, complemented
206	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
207	C₄×#102	C₂×C₁₃	1	1	yes	characteristic
208	C₄×#102	C₂×C₁₃	1	1	yes	characteristic
209	C₂³×C₁₃	—	2	2	no	—
210	C₂³×C₁₃	—	4	1	no	—
211	C₂³×C₁₃	—	4	1	no	—
212	C₂³×C₁₃	—	4	1	no	—
213	C₂³×C₁₃	—	4	1	no	—
214	C₂³×C₁₃	—	4	1	no	—
215	C₂³×C₁₃	—	4	1	no	—
216	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
217	D₄×C₁₃	—	2	2	no	—
218	D₄×C₁₃	—	2	2	no	—
219	D₄×C₁₃	—	4	1	no	—
220	D₄×C₁₃	—	4	1	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	2	1	no	—
224	C₂×C₄×C₁₃	—	2	1	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	1	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	—	2	1	no	—
237	C₂×C₄×C₁₃	—	4	1	no	—
238	C₂×C₄×C₁₃	—	4	1	no	—
239	C₂×C₄×C₁₃	—	4	1	no	—
240	C₂×C₄×C₁₃	—	4	1	no	—
241	C₂×C₄×C₁₃	—	4	1	no	—
242	C₂×C₄×C₁₃	—	4	1	no	—
243	C₂×C₄×C₁₃	—	4	8	no	—
244	C₂×C₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	4	1	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	—	4	1	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
257	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
258	C₂×C₄×C₁₃	#135	1	2	yes	—
259	C₂×C₄×C₁₃	#135	1	2	yes	—
260	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
261	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
267	C₈×C₁₃	—	2	2	no	—
268	C₈×C₁₃	—	2	2	no	—
269	C₈×C₁₃	—	4	1	no	—
270	C₈×C₁₃	—	4	1	no	—
271	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
272	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
273	C₂×#117	—	2	1	no	—
274	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
281	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
286	#390	C₂²×C₁₃	1	1	yes	characteristic
287	#390	C₂²×C₁₃	1	1	yes	characteristic
288	#389	C₂²×C₁₃	1	1	yes	characteristic
289	#389	C₂²×C₁₃	1	1	yes	characteristic
290	#389	C₂²×C₁₃	1	1	yes	characteristic
291	#389	C₂²×C₁₃	1	1	yes	characteristic
292	#388	—	2	1	no	—
293	#388	—	2	1	no	—
294	#387	—	2	1	no	—
295	#387	—	2	1	no	—
296	#382	C₂²×C₁₃	1	1	yes	characteristic
297	C₄×C₄⋊C₄	—	2	1	no	—
298	C₄×C₄⋊C₄	—	2	1	no	—
299	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
300	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
301	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
302	C₄×C₂²⋊C₄	—	2	1	no	—
303	C₄³	C₂²×C₁₃	1	1	yes	characteristic
304	#340	C₂²×C₁₃	1	1	yes	characteristic
305	#340	C₂²×C₁₃	1	1	yes	characteristic
306	#340	C₂²×C₁₃	1	1	yes	characteristic
307	#340	C₂²×C₁₃	1	1	yes	characteristic
308	#340	C₂²×C₁₃	1	1	yes	characteristic
309	#340	C₂²×C₁₃	1	1	yes	characteristic
310	#340	C₂²×C₁₃	1	1	yes	characteristic
311	#340	C₂²×C₁₃	1	1	yes	characteristic
312	#336	C₂²×C₁₃	1	1	yes	characteristic
313	#336	C₂²×C₁₃	1	1	yes	characteristic
314	C₂²×C₁₃	—	4	2	no	—
315	C₂²×C₁₃	—	4	2	no	—
316	C₂²×C₁₃	—	4	2	no	—
317	C₂²×C₁₃	—	8	1	no	—
318	C₂²×C₁₃	—	8	1	no	—
319	C₂²×C₁₃	—	8	1	no	—
320	C₂²×C₁₃	—	8	1	no	—
321	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
322	C₂²×C₁₃	#525	1	1	yes	characteristic
323	C₂²×C₁₃	#532	1	1	yes	characteristic
324	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
325	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
326	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
327	C₂²×C₁₃	#575	1	1	yes	characteristic
328	C₄×C₁₃	—	2	2	no	—
329	C₄×C₁₃	—	2	2	no	—
330	C₄×C₁₃	—	4	2	no	—
331	C₄×C₁₃	—	4	1	no	—
332	C₄×C₁₃	—	4	2	no	—
333	C₄×C₁₃	—	4	1	no	—
334	C₄×C₁₃	—	4	2	no	—
335	C₄×C₁₃	—	4	1	no	—
336	C₄×C₁₃	—	8	1	no	—
337	C₄×C₁₃	—	8	1	no	—
338	C₄×C₁₃	—	8	1	no	—
339	C₄×C₁₃	—	8	1	no	—
340	C₄×C₁₃	#478	1	4	yes	—
341	C₄×C₁₃	#529	1	1	yes	characteristic
342	C₄×C₁₃	#529	1	1	yes	characteristic
343	C₄×C₁₃	#533	1	1	yes	characteristic
344	C₄×C₁₃	#533	1	1	yes	characteristic
345	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
346	C₂³×C₄	—	2	1	no	—
347	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
348	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
349	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
350	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
351	#125	—	2	2	no	—
352	#125	—	2	2	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	Q₈×C₁₃	1	4	yes	—
355	#117	—	4	4	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	1	no	—
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	—	2	1	no	—
377	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
378	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
379	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
380	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
382	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
383	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
384	#107	—	2	2	no	—
385	#107	—	2	2	no	—
386	#106	—	2	2	no	—
387	#106	—	2	2	no	—
388	C₄⋊C₈	—	2	2	no	—
389	C₄⋊C₈	—	2	2	no	—
390	#102	—	2	2	no	—
391	#102	—	2	2	no	—
392	#102	—	2	2	no	—
393	#102	—	2	2	no	—
394	C₄×C₈	—	2	2	no	—
395	C₄×C₈	—	2	2	no	—
396	#95	—	2	1	no	—
397	#95	—	2	1	no	—
398	#95	—	2	1	no	—
399	#95	—	2	1	no	—
400	#95	—	2	1	no	—
401	#95	—	2	1	no	—
402	#95	—	2	1	no	—
403	#95	—	2	1	no	—
404	#95	—	2	1	no	—
405	C₂×C₁₃	—	8	2	no	—
406	C₂×C₁₃	#2396	1	1	yes	characteristic
407	C₂×C₁₃	C₂×#478	1	1	yes	characteristic
408	C₂×C₁₃	#3076	1	1	yes	characteristic
409	C₂×C₁₃	#3102	1	1	yes	characteristic
410	C₂×C₁₃	#3106	1	1	yes	characteristic
411	C₂×C₁₃	#3168	1	1	yes	characteristic
412	C₂×C₁₃	#3171	1	1	yes	characteristic
413	C₂⁴	—	2	1	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	4	2	no	—
429	C₂²×C₄	—	4	2	no	—
430	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
436	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	C₁₃×#41	1	2	yes	—
448	C₂×C₈	C₁₃×#41	1	2	yes	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	4	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	4	2	no	—
463	C₄⋊C₄	—	4	2	no	—
464	C₄⋊C₄	—	4	2	no	—
465	C₄⋊C₄	—	4	2	no	—
466	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
467	C₄⋊C₄	C₁₃×#41	1	2	yes	—
468	C₄⋊C₄	C₁₃×#41	1	2	yes	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	4	2	no	—
471	C₂²⋊C₄	—	4	2	no	—
472	C₂²⋊C₄	—	4	2	no	—
473	C₂²⋊C₄	—	4	2	no	—
474	C₄²	—	2	2	no	—
475	C₄²	—	2	2	no	—
476	C₄²	—	2	2	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	4	1	no	—
482	C₄²	—	4	2	no	—
483	C₄²	—	4	2	no	—
484	C₄²	—	4	2	no	—
485	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
486	C₄²	C₁₃×#41	1	2	yes	—
487	C₁₃	#23778	1	1	yes	characteristic, direct product factor, Sylow
488	C₂³	—	2	2	no	—
489	C₂³	—	4	1	no	—
490	C₂³	—	4	1	no	—
491	C₂³	—	4	1	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	1	no	—
495	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
496	D₄	—	2	2	no	—
497	D₄	—	2	2	no	—
498	D₄	—	4	1	no	—
499	D₄	—	4	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	8	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
536	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
537	C₂×C₄	C₁₃×#135	1	2	yes	—
538	C₂×C₄	C₁₃×#135	1	2	yes	—
539	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
540	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
541	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
542	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
543	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
544	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
545	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
546	C₈	—	2	2	no	—
547	C₈	—	2	2	no	—
548	C₈	—	4	1	no	—
549	C₈	—	4	1	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	8	1	no	—
554	C₂²	—	8	1	no	—
555	C₂²	—	8	1	no	—
556	C₂²	—	8	1	no	—
557	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
558	C₂²	C₁₃×#525	1	1	yes	characteristic
559	C₂²	C₁₃×#532	1	1	yes	characteristic
560	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
561	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
562	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
563	C₂²	C₁₃×#575	1	1	yes	characteristic
564	C₄	—	2	2	no	—
565	C₄	—	2	2	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	2	no	—
571	C₄	—	4	1	no	—
572	C₄	—	8	1	no	—
573	C₄	—	8	1	no	—
574	C₄	—	8	1	no	—
575	C₄	—	8	1	no	—
576	C₄	C₁₃×#478	1	4	yes	—
577	C₄	C₁₃×#529	1	1	yes	characteristic
578	C₄	C₁₃×#529	1	1	yes	characteristic
579	C₄	C₁₃×#533	1	1	yes	characteristic
580	C₄	C₁₃×#533	1	1	yes	characteristic
581	C₂	—	8	2	no	—
582	C₂	C₁₃×#2396	1	1	yes	characteristic
583	C₂	C₂×C₁₃×#478	1	1	yes	characteristic
584	C₂	C₁₃×#3076	1	1	yes	characteristic
585	C₂	C₁₃×#3102	1	1	yes	characteristic
586	C₂	C₁₃×#3106	1	1	yes	characteristic
587	C₂	C₁₃×#3168	1	1	yes	characteristic
588	C₂	C₁₃×#3171	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄×C₁₃×#125	C₂	semidirect
3. C₁₃×#2101	C₂	semidirect
5. C₁₃×#2088	C₂	semidirect
6. C₁₃×#2087	C₂	semidirect
9. C₁₃×#2059	C₂	semidirect
11. C₄×C₁₃×#107	C₂	semidirect
12. C₄×C₁₃×#106	C₂	semidirect
13. C₄×C₁₃×C₄⋊C₈	C₂	semidirect
119. #23778	C₁₃	direct (N × H)
194. C₄×#125	C₂×C₁₃	semidirect
196. #2101	C₂×C₁₃	semidirect
198. #2088	C₂×C₁₃	semidirect
199. #2087	C₂×C₁₃	semidirect
202. #2059	C₂×C₁₃	semidirect
204. C₄×#107	C₂×C₁₃	semidirect
205. C₄×#106	C₂×C₁₃	semidirect
206. C₄×C₄⋊C₈	C₂×C₁₃	semidirect
487. C₁₃	#23778	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₃×#125	2
C₁₃×#2293	2
C₁₃×#2101	2
C₁₃×#2092	2
C₁₃×#2088	2
C₁₃×#2087	2
C₁₃×#2067	2
C₁₃×#2065	2
C₁₃×#2059	2
C₁₃×#2025	2
C₄×C₁₃×#107	2
C₄×C₁₃×#106	2
C₄×C₁₃×C₄⋊C₈	2
C₄×C₁₃×#102	2
#23778	13

Subgroups — C13×#23778 #15710117

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23778 #15710117