Subgroups — C₁₃×#24346 #15710685

Order 3328.

1064 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#478	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#440	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2538	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2057	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2025	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#2023	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1992	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1865	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1863	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	C₁₃×#557	—	2	4	no	—
18	C₁₃×#557	—	2	4	no	—
19	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#125	—	2	1	no	—
22	C₂×C₁₃×#125	—	2	1	no	—
23	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
26	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#478	—	2	4	no	—
33	C₁₃×#440	—	2	4	no	—
34	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
45	C₁₃×#396	—	2	1	no	—
46	C₁₃×#396	—	2	1	no	—
47	C₁₃×#390	C₂²	1	1	yes	characteristic
48	C₁₃×#390	C₂²	1	1	yes	characteristic
49	C₁₃×#389	C₂²	1	1	yes	characteristic
50	C₁₃×#389	C₂²	1	1	yes	characteristic
51	C₁₃×#384	C₂²	1	1	yes	characteristic
52	C₁₃×#380	—	2	1	no	—
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×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	C₂²	1	1	yes	characteristic
59	C₁₃×#336	C₂²	1	1	yes	characteristic
60	C₁₃×#336	C₂²	1	1	yes	characteristic
61	C₁₃×#336	C₂²	1	1	yes	characteristic
62	C₁₃×#336	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃	—	2	1	no	—
64	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
65	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₃	—	2	1	no	—
68	C₂×C₁₃×SD₁₆	—	2	2	no	—
69	C₂×C₁₃×SD₁₆	—	2	2	no	—
70	C₂×C₁₃×SD₁₆	Q₈	1	4	yes	complemented
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×C₄⋊Q₈	—	2	8	no	—
76	C₁₃×C₄⋊Q₈	—	2	2	no	—
77	C₁₃×C₄⋊Q₈	—	2	2	no	—
78	C₁₃×#125	—	2	8	no	—
79	C₁₃×#125	—	2	8	no	—
80	C₁₃×#125	—	2	2	no	—
81	C₁₃×#125	—	2	2	no	—
82	C₁₃×#125	—	2	2	no	—
83	C₁₃×#125	D₄	1	4	yes	—
84	C₁₃×C₂²⋊Q₈	—	4	4	no	—
85	C₄×Q₈×C₁₃	—	2	8	no	—
86	C₄×Q₈×C₁₃	—	2	2	no	—
87	C₄×Q₈×C₁₃	—	2	2	no	—
88	C₄×Q₈×C₁₃	—	2	2	no	—
89	C₄×Q₈×C₁₃	—	2	2	no	—
90	C₄×Q₈×C₁₃	—	2	2	no	—
91	C₄×Q₈×C₁₃	—	2	2	no	—
92	C₄×Q₈×C₁₃	—	2	2	no	—
93	C₄×Q₈×C₁₃	D₄	1	4	yes	—
94	C₄×D₄×C₁₃	—	2	2	no	—
95	C₄×D₄×C₁₃	—	2	2	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
109	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
110	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₄²×C₁₃	—	2	1	no	—
123	C₂×C₄²×C₁₃	—	2	1	no	—
124	C₂×C₄²×C₁₃	—	2	1	no	—
125	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
128	C₁₃×#107	—	2	2	no	—
129	C₁₃×#107	—	2	2	no	—
130	C₁₃×#106	—	2	2	no	—
131	C₁₃×C₄⋊C₈	—	2	2	no	—
132	C₁₃×#103	—	2	2	no	—
133	C₁₃×#103	—	2	2	no	—
134	C₁₃×#103	—	2	2	no	—
135	C₁₃×#102	—	2	2	no	—
136	C₁₃×#102	—	2	2	no	—
137	C₁₃×#102	—	2	2	no	—
138	C₁₃×#97	—	2	2	no	—
139	C₁₃×#95	—	2	1	no	—
140	C₁₃×#95	—	2	1	no	—
141	#24346	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂⁴×C₁₃	—	2	1	no	—
143	C₂×Q₈×C₁₃	—	2	4	no	—
144	C₂×Q₈×C₁₃	—	2	2	no	—
145	C₂×Q₈×C₁₃	—	2	2	no	—
146	C₂×Q₈×C₁₃	—	2	1	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	4	1	no	—
150	C₂×Q₈×C₁₃	—	4	2	no	—
151	C₂×Q₈×C₁₃	—	4	2	no	—
152	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
153	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
154	C₂×Q₈×C₁₃	#41	1	2	yes	—
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	2	1	no	—
159	C₂×D₄×C₁₃	—	2	1	no	—
160	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	4	2	no	—
169	C₂²×C₄×C₁₃	—	4	2	no	—
170	C₂²×C₄×C₁₃	—	4	2	no	—
171	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₁₃×SD₁₆	—	2	8	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	2	1	no	—
183	C₂×C₈×C₁₃	—	2	1	no	—
184	C₂×C₈×C₁₃	—	2	1	no	—
185	C₂×C₈×C₁₃	—	2	1	no	—
186	C₂×C₈×C₁₃	—	2	1	no	—
187	C₂×C₈×C₁₃	—	2	1	no	—
188	C₂×C₈×C₁₃	—	2	1	no	—
189	C₂×C₈×C₁₃	—	2	1	no	—
190	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
191	C₁₃×C₄⋊C₄	—	2	4	no	—
192	C₁₃×C₄⋊C₄	—	2	4	no	—
193	C₁₃×C₄⋊C₄	—	2	4	no	—
194	C₁₃×C₄⋊C₄	—	2	4	no	—
195	C₁₃×C₄⋊C₄	—	2	4	no	—
196	C₁₃×C₄⋊C₄	—	2	4	no	—
197	C₁₃×C₄⋊C₄	—	2	4	no	—
198	C₁₃×C₄⋊C₄	—	2	4	no	—
199	C₁₃×C₄⋊C₄	—	2	2	no	—
200	C₁₃×C₄⋊C₄	—	2	2	no	—
201	C₁₃×C₄⋊C₄	—	2	2	no	—
202	C₁₃×C₄⋊C₄	—	2	1	no	—
203	C₁₃×C₄⋊C₄	—	2	1	no	—
204	C₁₃×C₄⋊C₄	—	2	1	no	—
205	C₁₃×C₄⋊C₄	—	2	1	no	—
206	C₁₃×C₄⋊C₄	—	2	1	no	—
207	C₁₃×C₄⋊C₄	—	2	1	no	—
208	C₁₃×C₄⋊C₄	—	2	1	no	—
209	C₁₃×C₄⋊C₄	—	2	1	no	—
210	C₁₃×C₄⋊C₄	—	2	1	no	—
211	C₁₃×C₄⋊C₄	—	4	2	no	—
212	C₁₃×C₄⋊C₄	—	4	2	no	—
213	C₁₃×C₄⋊C₄	—	4	2	no	—
214	C₁₃×C₄⋊C₄	—	8	1	no	—
215	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
216	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
217	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
218	C₁₃×C₂²⋊C₄	—	4	2	no	—
219	C₁₃×C₂²⋊C₄	—	4	2	no	—
220	C₁₃×C₂²⋊C₄	—	4	2	no	—
221	C₁₃×C₂²⋊C₄	—	8	1	no	—
222	C₁₃×C₂²⋊C₄	—	8	1	no	—
223	C₄²×C₁₃	—	2	4	no	—
224	C₄²×C₁₃	—	2	4	no	—
225	C₄²×C₁₃	—	2	4	no	—
226	C₄²×C₁₃	—	2	1	no	—
227	C₄²×C₁₃	—	2	1	no	—
228	C₄²×C₁₃	—	2	1	no	—
229	C₄²×C₁₃	—	2	1	no	—
230	C₄²×C₁₃	C₂×D₄	1	2	yes	—
231	C₄²×C₁₃	C₂×D₄	1	2	yes	—
232	C₂×#557	C₂×C₁₃	1	1	yes	characteristic, complemented
233	C₂×#478	C₂×C₁₃	1	1	yes	characteristic
234	C₂×#440	C₂×C₁₃	1	1	yes	characteristic
235	#2538	C₂×C₁₃	1	1	yes	characteristic
236	#2059	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#2057	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#2025	C₂×C₁₃	1	1	yes	characteristic
239	#2023	C₂×C₁₃	1	1	yes	characteristic
240	#1992	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#1985	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#1880	C₂×C₁₃	1	1	yes	characteristic
243	#1880	C₂×C₁₃	1	1	yes	characteristic
244	#1865	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#1863	C₂×C₁₃	1	1	yes	characteristic, complemented
246	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
247	C₂³×C₁₃	—	2	2	no	—
248	C₂³×C₁₃	—	4	1	no	—
249	C₂³×C₁₃	—	4	1	no	—
250	C₂³×C₁₃	—	4	1	no	—
251	C₂³×C₁₃	—	4	1	no	—
252	C₂³×C₁₃	—	4	1	no	—
253	C₂³×C₁₃	—	4	1	no	—
254	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
255	Q₈×C₁₃	—	2	2	no	—
256	Q₈×C₁₃	—	2	2	no	—
257	Q₈×C₁₃	—	2	2	no	—
258	Q₈×C₁₃	—	4	4	no	—
259	Q₈×C₁₃	—	4	8	no	—
260	Q₈×C₁₃	C₂²⋊Q₈	1	4	yes	complemented
261	D₄×C₁₃	—	2	2	no	—
262	D₄×C₁₃	—	2	2	no	—
263	D₄×C₁₃	—	4	1	no	—
264	D₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	2	2	no	—
266	C₂×C₄×C₁₃	—	2	1	no	—
267	C₂×C₄×C₁₃	—	2	2	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	2	1	no	—
271	C₂×C₄×C₁₃	—	2	1	no	—
272	C₂×C₄×C₁₃	—	2	1	no	—
273	C₂×C₄×C₁₃	—	2	1	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	2	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	2	2	no	—
279	C₂×C₄×C₁₃	—	2	2	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	2	1	no	—
282	C₂×C₄×C₁₃	—	2	1	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	1	no	—
285	C₂×C₄×C₁₃	—	2	1	no	—
286	C₂×C₄×C₁₃	—	4	1	no	—
287	C₂×C₄×C₁₃	—	4	1	no	—
288	C₂×C₄×C₁₃	—	4	1	no	—
289	C₂×C₄×C₁₃	—	4	1	no	—
290	C₂×C₄×C₁₃	—	4	1	no	—
291	C₂×C₄×C₁₃	—	4	1	no	—
292	C₂×C₄×C₁₃	—	4	1	no	—
293	C₂×C₄×C₁₃	—	4	1	no	—
294	C₂×C₄×C₁₃	—	4	1	no	—
295	C₂×C₄×C₁₃	—	4	1	no	—
296	C₂×C₄×C₁₃	—	4	1	no	—
297	C₂×C₄×C₁₃	—	4	1	no	—
298	C₂×C₄×C₁₃	—	4	1	no	—
299	C₂×C₄×C₁₃	—	4	1	no	—
300	C₂×C₄×C₁₃	—	4	1	no	—
301	C₂×C₄×C₁₃	—	8	4	no	—
302	C₂×C₄×C₁₃	#120	1	2	yes	—
303	C₂×C₄×C₁₃	#120	1	2	yes	—
304	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
305	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
308	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
309	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
310	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
311	C₈×C₁₃	—	2	2	no	—
312	C₈×C₁₃	—	4	1	no	—
313	C₈×C₁₃	—	4	1	no	—
314	C₈×C₁₃	—	4	1	no	—
315	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
316	#557	—	2	4	no	—
317	#557	—	2	4	no	—
318	C₂×C₄⋊Q₈	—	2	1	no	—
319	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×#125	—	2	1	no	—
321	C₂×#125	—	2	1	no	—
322	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×C₂²⋊Q₈	—	2	1	no	—
325	C₂×C₄×Q₈	—	2	1	no	—
326	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
329	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
331	#478	—	2	4	no	—
332	#440	—	2	4	no	—
333	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
339	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
341	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
342	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
343	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
344	#396	—	2	1	no	—
345	#396	—	2	1	no	—
346	#390	C₂²×C₁₃	1	1	yes	characteristic
347	#390	C₂²×C₁₃	1	1	yes	characteristic
348	#389	C₂²×C₁₃	1	1	yes	characteristic
349	#389	C₂²×C₁₃	1	1	yes	characteristic
350	#384	C₂²×C₁₃	1	1	yes	characteristic
351	#380	—	2	1	no	—
352	#340	C₂²×C₁₃	1	1	yes	characteristic
353	#340	C₂²×C₁₃	1	1	yes	characteristic
354	#340	C₂²×C₁₃	1	1	yes	characteristic
355	#340	C₂²×C₁₃	1	1	yes	characteristic
356	#340	C₂²×C₁₃	1	1	yes	characteristic
357	#340	C₂²×C₁₃	1	1	yes	characteristic
358	#336	C₂²×C₁₃	1	1	yes	characteristic
359	#336	C₂²×C₁₃	1	1	yes	characteristic
360	#336	C₂²×C₁₃	1	1	yes	characteristic
361	#336	C₂²×C₁₃	1	1	yes	characteristic
362	C₂²×C₁₃	—	4	2	no	—
363	C₂²×C₁₃	—	4	2	no	—
364	C₂²×C₁₃	—	4	2	no	—
365	C₂²×C₁₃	—	8	1	no	—
366	C₂²×C₁₃	—	8	1	no	—
367	C₂²×C₁₃	—	8	1	no	—
368	C₂²×C₁₃	—	8	1	no	—
369	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
370	C₂²×C₁₃	#548	1	1	yes	characteristic
371	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
372	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
373	C₂²×C₁₃	#575	1	1	yes	characteristic
374	C₂²×C₁₃	#577	1	1	yes	characteristic
375	C₂²×C₁₃	#578	1	1	yes	characteristic
376	C₄×C₁₃	—	2	4	no	—
377	C₄×C₁₃	—	2	2	no	—
378	C₄×C₁₃	—	2	2	no	—
379	C₄×C₁₃	—	2	2	no	—
380	C₄×C₁₃	—	4	1	no	—
381	C₄×C₁₃	—	4	2	no	—
382	C₄×C₁₃	—	4	2	no	—
383	C₄×C₁₃	—	4	1	no	—
384	C₄×C₁₃	—	4	1	no	—
385	C₄×C₁₃	—	4	2	no	—
386	C₄×C₁₃	—	8	1	no	—
387	C₄×C₁₃	—	8	1	no	—
388	C₄×C₁₃	—	8	1	no	—
389	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
390	C₄×C₁₃	#536	1	1	yes	characteristic
391	C₄×C₁₃	#548	1	1	yes	characteristic
392	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
393	C₂²×Q₈	—	2	1	no	—
394	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
395	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
396	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
397	C₂³×C₄	—	2	1	no	—
398	C₂×SD₁₆	—	2	2	no	—
399	C₂×SD₁₆	—	2	2	no	—
400	C₂×SD₁₆	Q₈×C₁₃	1	4	yes	complemented
401	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
402	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
403	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
404	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
405	C₄⋊Q₈	—	2	8	no	—
406	C₄⋊Q₈	—	2	2	no	—
407	C₄⋊Q₈	—	2	2	no	—
408	#125	—	2	8	no	—
409	#125	—	2	8	no	—
410	#125	—	2	2	no	—
411	#125	—	2	2	no	—
412	#125	—	2	2	no	—
413	#125	D₄×C₁₃	1	4	yes	—
414	C₂²⋊Q₈	—	4	4	no	—
415	C₄×Q₈	—	2	8	no	—
416	C₄×Q₈	—	2	2	no	—
417	C₄×Q₈	—	2	2	no	—
418	C₄×Q₈	—	2	2	no	—
419	C₄×Q₈	—	2	2	no	—
420	C₄×Q₈	—	2	2	no	—
421	C₄×Q₈	—	2	2	no	—
422	C₄×Q₈	—	2	2	no	—
423	C₄×Q₈	D₄×C₁₃	1	4	yes	—
424	C₄×D₄	—	2	2	no	—
425	C₄×D₄	—	2	2	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	—	2	1	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	2	1	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	—	2	1	no	—
438	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
439	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
440	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₄²	—	2	1	no	—
453	C₂×C₄²	—	2	1	no	—
454	C₂×C₄²	—	2	1	no	—
455	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
456	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
457	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
458	#107	—	2	2	no	—
459	#107	—	2	2	no	—
460	#106	—	2	2	no	—
461	C₄⋊C₈	—	2	2	no	—
462	#103	—	2	2	no	—
463	#103	—	2	2	no	—
464	#103	—	2	2	no	—
465	#102	—	2	2	no	—
466	#102	—	2	2	no	—
467	#102	—	2	2	no	—
468	#97	—	2	2	no	—
469	#95	—	2	1	no	—
470	#95	—	2	1	no	—
471	C₂×C₁₃	—	8	2	no	—
472	C₂×C₁₃	#2409	1	1	yes	characteristic
473	C₂×C₁₃	#3006	1	1	yes	characteristic
474	C₂×C₁₃	#3013	1	1	yes	characteristic
475	C₂×C₁₃	#3368	1	1	yes	characteristic
476	C₂×C₁₃	#3377	1	1	yes	characteristic
477	C₂×C₁₃	#3386	1	1	yes	characteristic
478	C₂×C₁₃	#3388	1	1	yes	characteristic
479	C₂⁴	—	2	1	no	—
480	C₂×Q₈	—	2	4	no	—
481	C₂×Q₈	—	2	2	no	—
482	C₂×Q₈	—	2	2	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	4	1	no	—
487	C₂×Q₈	—	4	2	no	—
488	C₂×Q₈	—	4	2	no	—
489	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
490	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
491	C₂×Q₈	C₁₃×#41	1	2	yes	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	4	2	no	—
506	C₂²×C₄	—	4	2	no	—
507	C₂²×C₄	—	4	2	no	—
508	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
509	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
510	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
511	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
512	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
513	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
514	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
515	SD₁₆	—	2	8	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
528	C₄⋊C₄	—	2	4	no	—
529	C₄⋊C₄	—	2	4	no	—
530	C₄⋊C₄	—	2	4	no	—
531	C₄⋊C₄	—	2	4	no	—
532	C₄⋊C₄	—	2	4	no	—
533	C₄⋊C₄	—	2	4	no	—
534	C₄⋊C₄	—	2	4	no	—
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	2	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	4	2	no	—
549	C₄⋊C₄	—	4	2	no	—
550	C₄⋊C₄	—	4	2	no	—
551	C₄⋊C₄	—	8	1	no	—
552	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
553	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
554	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
555	C₂²⋊C₄	—	4	2	no	—
556	C₂²⋊C₄	—	4	2	no	—
557	C₂²⋊C₄	—	4	2	no	—
558	C₂²⋊C₄	—	8	1	no	—
559	C₂²⋊C₄	—	8	1	no	—
560	C₄²	—	2	4	no	—
561	C₄²	—	2	4	no	—
562	C₄²	—	2	4	no	—
563	C₄²	—	2	1	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	2	1	no	—
566	C₄²	—	2	1	no	—
567	C₄²	C₂×D₄×C₁₃	1	2	yes	—
568	C₄²	C₂×D₄×C₁₃	1	2	yes	—
569	C₁₃	#24346	1	1	yes	characteristic, direct product factor, Sylow
570	C₂³	—	2	2	no	—
571	C₂³	—	4	1	no	—
572	C₂³	—	4	1	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	1	no	—
575	C₂³	—	4	1	no	—
576	C₂³	—	4	1	no	—
577	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
578	Q₈	—	2	2	no	—
579	Q₈	—	2	2	no	—
580	Q₈	—	2	2	no	—
581	Q₈	—	4	4	no	—
582	Q₈	—	4	8	no	—
583	Q₈	C₁₃×C₂²⋊Q₈	1	4	yes	complemented
584	D₄	—	2	2	no	—
585	D₄	—	2	2	no	—
586	D₄	—	4	1	no	—
587	D₄	—	4	1	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	8	4	no	—
625	C₂×C₄	C₁₃×#120	1	2	yes	—
626	C₂×C₄	C₁₃×#120	1	2	yes	—
627	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
628	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
629	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
630	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
631	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
632	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
633	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
634	C₈	—	2	2	no	—
635	C₈	—	4	1	no	—
636	C₈	—	4	1	no	—
637	C₈	—	4	1	no	—
638	C₂²	—	4	2	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	8	1	no	—
642	C₂²	—	8	1	no	—
643	C₂²	—	8	1	no	—
644	C₂²	—	8	1	no	—
645	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
646	C₂²	C₁₃×#548	1	1	yes	characteristic
647	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
648	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
649	C₂²	C₁₃×#575	1	1	yes	characteristic
650	C₂²	C₁₃×#577	1	1	yes	characteristic
651	C₂²	C₁₃×#578	1	1	yes	characteristic
652	C₄	—	2	2	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	4	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	2	no	—
658	C₄	—	4	2	no	—
659	C₄	—	4	1	no	—
660	C₄	—	4	1	no	—
661	C₄	—	4	2	no	—
662	C₄	—	8	1	no	—
663	C₄	—	8	1	no	—
664	C₄	—	8	1	no	—
665	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
666	C₄	C₁₃×#536	1	1	yes	characteristic
667	C₄	C₁₃×#548	1	1	yes	characteristic
668	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
669	C₂	—	8	2	no	—
670	C₂	C₁₃×#2409	1	1	yes	characteristic
671	C₂	C₁₃×#3006	1	1	yes	characteristic
672	C₂	C₁₃×#3013	1	1	yes	characteristic
673	C₂	C₁₃×#3368	1	1	yes	characteristic
674	C₂	C₁₃×#3377	1	1	yes	characteristic
675	C₂	C₁₃×#3386	1	1	yes	characteristic
676	C₂	C₁₃×#3388	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 ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#557	C₂	semidirect
5. C₁₃×#2059	C₂	semidirect
6. C₁₃×#2057	C₂	semidirect
9. C₁₃×#1992	C₂	semidirect
10. C₁₃×#1985	C₂	semidirect
13. C₁₃×#1865	C₂	semidirect
14. C₁₃×#1863	C₂	semidirect
15. C₁₃×#1803	C₂	semidirect
70. C₂×C₁₃×SD₁₆	Q₈	semidirect
141. #24346	C₁₃	direct (N × H)
232. C₂×#557	C₂×C₁₃	semidirect
236. #2059	C₂×C₁₃	semidirect
237. #2057	C₂×C₁₃	semidirect
240. #1992	C₂×C₁₃	semidirect
241. #1985	C₂×C₁₃	semidirect
244. #1865	C₂×C₁₃	semidirect
245. #1863	C₂×C₁₃	semidirect
246. #1803	C₂×C₁₃	semidirect
260. Q₈×C₁₃	C₂²⋊Q₈	semidirect
400. C₂×SD₁₆	Q₈×C₁₃	semidirect
569. C₁₃	#24346	direct (N × H)
583. Q₈	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×#557	2
C₂×C₁₃×#478	2
C₂×C₁₃×#440	2
C₁₃×#2538	2
C₁₃×#2059	2
C₁₃×#2057	2
C₁₃×#2025	2
C₁₃×#2023	2
C₁₃×#1992	2
C₁₃×#1985	2
C₁₃×#1880	2
C₁₃×#1865	2
C₁₃×#1863	2
C₁₃×#1803	2
#24346	13

Subgroups — C13×#24346 #15710685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24346 #15710685