Subgroups — C₁₃×#32957 #15719296

Order 3328.

1332 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	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#477	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2857	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1863	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1852	C₂	1	2	yes	maximal
6	C₁₃×#1803	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1787	C₂	1	2	yes	maximal
9	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
12	C₂×C₄×Q₈×C₁₃	—	2	8	no	—
13	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
14	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
15	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
17	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₁₃	—	2	1	no	—
20	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#477	—	2	8	no	—
22	C₂×C₁₃×#107	C₂²	1	4	yes	—
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	4	yes	—
25	C₂×C₁₃×#103	C₂²	1	4	yes	—
26	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₁₃×#391	—	2	1	no	—
28	C₁₃×#389	—	2	1	no	—
29	C₁₃×#389	C₂²	1	2	yes	—
30	C₁₃×#384	C₂²	1	1	yes	characteristic
31	C₁₃×#380	—	2	1	no	—
32	C₁₃×#380	C₂²	1	2	yes	—
33	C₁₃×#340	C₂²	1	4	yes	—
34	C₁₃×#336	C₂²	1	2	yes	—
35	C₂²×Q₈×C₁₃	—	2	4	no	—
36	C₂²×Q₈×C₁₃	—	2	4	no	—
37	C₂²×Q₈×C₁₃	—	2	1	no	—
38	C₂²×Q₈×C₁₃	—	2	1	no	—
39	C₂²×Q₈×C₁₃	—	2	2	no	—
40	C₂²×Q₈×C₁₃	Q₈	1	4	yes	complemented
41	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₃	—	2	1	no	—
43	C₂³×C₄×C₁₃	—	2	1	no	—
44	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
48	C₁₃×C₄⋊Q₈	—	2	4	no	—
49	C₁₃×C₂²⋊Q₈	—	4	4	no	—
50	C₄×Q₈×C₁₃	—	2	8	no	—
51	C₄×Q₈×C₁₃	—	2	8	no	—
52	C₄×Q₈×C₁₃	—	2	4	no	—
53	C₄×Q₈×C₁₃	—	2	4	no	—
54	C₄×Q₈×C₁₃	—	2	4	no	—
55	C₄×Q₈×C₁₃	D₄	1	8	yes	—
56	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₄²×C₁₃	—	2	8	no	—
70	C₂×C₄²×C₁₃	—	2	2	no	—
71	C₂×C₄²×C₁₃	—	2	2	no	—
72	C₂×C₄²×C₁₃	—	2	4	no	—
73	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₁₃×#107	—	2	8	no	—
78	C₁₃×C₄⋊C₈	—	2	4	no	—
79	C₁₃×#103	—	2	8	no	—
80	C₁₃×#103	—	2	8	no	—
81	C₁₃×C₂²⋊C₈	—	2	4	no	—
82	C₁₃×#95	—	2	2	no	—
83	C₁₃×#95	—	2	2	no	—
84	#32957	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
86	C₂×Q₈×C₁₃	—	2	4	no	—
87	C₂×Q₈×C₁₃	—	2	16	no	—
88	C₂×Q₈×C₁₃	—	2	4	no	—
89	C₂×Q₈×C₁₃	—	2	16	no	—
90	C₂×Q₈×C₁₃	—	2	4	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	—	4	2	no	—
95	C₂×Q₈×C₁₃	—	4	2	no	—
96	C₂×Q₈×C₁₃	—	4	2	no	—
97	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
98	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	—
99	C₂×Q₈×C₁₃	#41	1	4	yes	—
100	C₂²×C₄×C₁₃	—	2	4	no	—
101	C₂²×C₄×C₁₃	—	2	4	no	—
102	C₂²×C₄×C₁₃	—	2	4	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	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	4	1	no	—
115	C₂²×C₄×C₁₃	—	4	2	no	—
116	C₂²×C₄×C₁₃	—	4	2	no	—
117	C₂²×C₄×C₁₃	Q₁₆	1	4	yes	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
124	C₂²×C₄×C₁₃	#41	1	2	yes	—
125	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
126	C₂×C₈×C₁₃	—	2	4	no	—
127	C₂×C₈×C₁₃	—	2	4	no	—
128	C₂×C₈×C₁₃	—	2	4	no	—
129	C₁₃×C₄⋊C₄	—	2	8	no	—
130	C₁₃×C₄⋊C₄	—	2	4	no	—
131	C₁₃×C₄⋊C₄	—	2	8	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	4	no	—
134	C₁₃×C₄⋊C₄	—	2	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	—	4	2	no	—
139	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
140	C₁₃×C₂²⋊C₄	—	4	4	no	—
141	C₄²×C₁₃	—	2	8	no	—
142	C₄²×C₁₃	—	2	8	no	—
143	C₄²×C₁₃	—	2	2	no	—
144	C₄²×C₁₃	—	2	2	no	—
145	C₄²×C₁₃	—	2	2	no	—
146	C₄²×C₁₃	C₂×D₄	1	4	yes	—
147	C₂²×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic
148	C₂×#477	C₂×C₁₃	1	2	yes	complemented
149	#2857	C₂×C₁₃	1	1	yes	characteristic
150	#1863	C₂×C₁₃	1	4	yes	complemented
151	#1852	C₂×C₁₃	1	2	yes	—
152	#1803	C₂×C₁₃	1	2	yes	complemented
153	#1797	C₂×C₁₃	1	1	yes	characteristic
154	#1787	C₂×C₁₃	1	2	yes	—
155	C₂³×C₁₃	—	2	1	no	—
156	C₂³×C₁₃	—	2	1	no	—
157	C₂³×C₁₃	—	2	1	no	—
158	C₂³×C₁₃	—	2	1	no	—
159	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
160	C₂³×C₁₃	C₂×Q₁₆	1	2	yes	—
161	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
162	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
163	Q₈×C₁₃	—	2	16	no	—
164	Q₈×C₁₃	—	2	4	no	—
165	Q₈×C₁₃	—	2	4	no	—
166	Q₈×C₁₃	—	2	4	no	—
167	Q₈×C₁₃	—	8	4	no	—
168	Q₈×C₁₃	C₂²⋊Q₈	1	8	yes	complemented
169	C₂×C₄×C₁₃	—	2	16	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	4	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	4	no	—
174	C₂×C₄×C₁₃	—	2	4	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	4	no	—
180	C₂×C₄×C₁₃	—	2	4	no	—
181	C₂×C₄×C₁₃	—	2	8	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	4	4	no	—
187	C₂×C₄×C₁₃	—	4	8	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	#120	1	2	yes	—
197	C₂×C₄×C₁₃	#120	1	2	yes	—
198	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
199	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
200	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
201	C₂×C₄×C₁₃	#137	1	2	yes	—
202	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
203	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
205	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
206	C₈×C₁₃	—	4	4	no	—
207	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×C₂²⋊Q₈	—	2	1	no	—
210	C₂×C₄×Q₈	—	2	8	no	—
211	C₂×C₄×Q₈	—	2	1	no	—
212	C₂×C₄×Q₈	—	2	1	no	—
213	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
214	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
215	C₂²×C₄⋊C₄	—	2	1	no	—
216	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
217	C₂²×C₄²	—	2	1	no	—
218	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
219	#477	—	2	8	no	—
220	C₂×#107	C₂²×C₁₃	1	4	yes	—
221	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
222	C₂×#103	C₂²×C₁₃	1	4	yes	—
223	C₂×#103	C₂²×C₁₃	1	4	yes	—
224	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
225	#391	—	2	1	no	—
226	#389	—	2	1	no	—
227	#389	C₂²×C₁₃	1	2	yes	—
228	#384	C₂²×C₁₃	1	1	yes	characteristic
229	#380	—	2	1	no	—
230	#380	C₂²×C₁₃	1	2	yes	—
231	#340	C₂²×C₁₃	1	4	yes	—
232	#336	C₂²×C₁₃	1	2	yes	—
233	C₂²×C₁₃	—	2	2	no	—
234	C₂²×C₁₃	—	2	2	no	—
235	C₂²×C₁₃	—	2	2	no	—
236	C₂²×C₁₃	—	2	2	no	—
237	C₂²×C₁₃	—	2	2	no	—
238	C₂²×C₁₃	—	2	2	no	—
239	C₂²×C₁₃	#477	1	4	yes	complemented
240	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
241	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
242	C₂²×C₁₃	#525	1	1	yes	characteristic
243	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
244	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
245	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
246	C₂²×C₁₃	#575	1	1	yes	characteristic
247	C₄×C₁₃	—	2	8	no	—
248	C₄×C₁₃	—	2	2	no	—
249	C₄×C₁₃	—	2	2	no	—
250	C₄×C₁₃	—	2	2	no	—
251	C₄×C₁₃	—	4	1	no	—
252	C₄×C₁₃	—	4	4	no	—
253	C₄×C₁₃	—	8	2	no	—
254	C₄×C₁₃	—	8	2	no	—
255	C₄×C₁₃	#451	1	4	yes	—
256	C₄×C₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
257	C₄×C₁₃	#525	1	2	yes	—
258	C₂²×Q₈	—	2	4	no	—
259	C₂²×Q₈	—	2	4	no	—
260	C₂²×Q₈	—	2	1	no	—
261	C₂²×Q₈	—	2	1	no	—
262	C₂²×Q₈	—	2	2	no	—
263	C₂²×Q₈	Q₈×C₁₃	1	4	yes	complemented
264	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
265	C₂³×C₄	—	2	1	no	—
266	C₂³×C₄	—	2	1	no	—
267	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
268	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
269	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
271	C₄⋊Q₈	—	2	4	no	—
272	C₂²⋊Q₈	—	4	4	no	—
273	C₄×Q₈	—	2	8	no	—
274	C₄×Q₈	—	2	8	no	—
275	C₄×Q₈	—	2	4	no	—
276	C₄×Q₈	—	2	4	no	—
277	C₄×Q₈	—	2	4	no	—
278	C₄×Q₈	D₄×C₁₃	1	8	yes	—
279	C₂×C₄⋊C₄	—	2	8	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	4	no	—
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	1	no	—
288	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₄²	—	2	8	no	—
293	C₂×C₄²	—	2	2	no	—
294	C₂×C₄²	—	2	2	no	—
295	C₂×C₄²	—	2	4	no	—
296	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
297	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
299	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
300	#107	—	2	8	no	—
301	C₄⋊C₈	—	2	4	no	—
302	#103	—	2	8	no	—
303	#103	—	2	8	no	—
304	C₂²⋊C₈	—	2	4	no	—
305	#95	—	2	2	no	—
306	#95	—	2	2	no	—
307	C₂×C₁₃	—	2	4	no	—
308	C₂×C₁₃	#2848	1	1	yes	characteristic
309	C₂×C₁₃	C₂×#451	1	1	yes	characteristic
310	C₂×C₁₃	#3006	1	1	yes	characteristic
311	C₂×C₁₃	C₂×#477	1	1	yes	characteristic
312	C₂×C₁₃	#3078	1	1	yes	characteristic
313	C₂×C₁₃	#3104	1	1	yes	characteristic
314	C₂×C₁₃	#3112	1	1	yes	characteristic
315	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
316	C₂×Q₈	—	2	4	no	—
317	C₂×Q₈	—	2	16	no	—
318	C₂×Q₈	—	2	4	no	—
319	C₂×Q₈	—	2	16	no	—
320	C₂×Q₈	—	2	4	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	4	2	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×Q₈	—	4	2	no	—
327	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
328	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	—
329	C₂×Q₈	C₁₃×#41	1	4	yes	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	C₁₃×Q₁₆	1	4	yes	—
348	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
353	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
354	C₂²×C₄	C₁₃×#41	1	2	yes	—
355	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
356	C₂×C₈	—	2	4	no	—
357	C₂×C₈	—	2	4	no	—
358	C₂×C₈	—	2	4	no	—
359	C₄⋊C₄	—	2	8	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	8	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	—	4	4	no	—
367	C₄⋊C₄	—	4	2	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
370	C₂²⋊C₄	—	4	4	no	—
371	C₄²	—	2	8	no	—
372	C₄²	—	2	8	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	C₂×D₄×C₁₃	1	4	yes	—
377	C₁₃	#32957	1	1	yes	characteristic, direct product factor, Sylow
378	C₂³	—	2	1	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	1	no	—
381	C₂³	—	2	1	no	—
382	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
383	C₂³	C₂×C₁₃×Q₁₆	1	2	yes	—
384	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
385	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
386	Q₈	—	2	16	no	—
387	Q₈	—	2	4	no	—
388	Q₈	—	2	4	no	—
389	Q₈	—	2	4	no	—
390	Q₈	—	8	4	no	—
391	Q₈	C₁₃×C₂²⋊Q₈	1	8	yes	complemented
392	C₂×C₄	—	2	16	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	8	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	8	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	C₁₃×#120	1	2	yes	—
420	C₂×C₄	C₁₃×#120	1	2	yes	—
421	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
422	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
423	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
424	C₂×C₄	C₁₃×#137	1	2	yes	—
425	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
426	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
427	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
428	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
429	C₈	—	4	4	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	C₁₃×#477	1	4	yes	complemented
437	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
438	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
439	C₂²	C₁₃×#525	1	1	yes	characteristic
440	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
441	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
442	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
443	C₂²	C₁₃×#575	1	1	yes	characteristic
444	C₄	—	2	2	no	—
445	C₄	—	2	8	no	—
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	4	1	no	—
449	C₄	—	4	4	no	—
450	C₄	—	8	2	no	—
451	C₄	—	8	2	no	—
452	C₄	C₁₃×#451	1	4	yes	—
453	C₄	C₂×C₁₃×C₂²⋊Q₈	1	2	yes	—
454	C₄	C₁₃×#525	1	2	yes	—
455	C₂	—	2	4	no	—
456	C₂	C₁₃×#2848	1	1	yes	characteristic
457	C₂	C₂×C₁₃×#451	1	1	yes	characteristic
458	C₂	C₁₃×#3006	1	1	yes	characteristic
459	C₂	C₂×C₁₃×#477	1	1	yes	characteristic
460	C₂	C₁₃×#3078	1	1	yes	characteristic
461	C₂	C₁₃×#3104	1	1	yes	characteristic
462	C₂	C₁₃×#3112	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 ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#477	C₂	semidirect
4. C₁₃×#1863	C₂	semidirect
6. C₁₃×#1803	C₂	semidirect
40. C₂²×Q₈×C₁₃	Q₈	semidirect
84. #32957	C₁₃	direct (N × H)
148. C₂×#477	C₂×C₁₃	semidirect
150. #1863	C₂×C₁₃	semidirect
152. #1803	C₂×C₁₃	semidirect
168. Q₈×C₁₃	C₂²⋊Q₈	semidirect
239. C₂²×C₁₃	#477	semidirect
263. C₂²×Q₈	Q₈×C₁₃	semidirect
377. C₁₃	#32957	direct (N × H)
391. Q₈	C₁₃×C₂²⋊Q₈	semidirect
436. C₂²	C₁₃×#477	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×Q₈×C₁₃	2
C₂×C₁₃×#477	2
C₁₃×#2857	2
C₁₃×#1863	2
C₁₃×#1852	2
C₁₃×#1803	2
C₁₃×#1797	2
C₁₃×#1787	2
#32957	13

Subgroups — C13×#32957 #15719296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32957 #15719296