Subgroups — C₁₃×#24165 #15710504

Order 3328.

1022 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#541	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2323	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2036	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2035	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2001	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#2001	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1989	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1865	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1863	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1798	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
18	C₁₃×#541	—	2	4	no	—
19	C₁₃×#541	—	2	4	no	—
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#126	—	2	1	no	—
22	C₂×C₁₃×#126	—	2	1	no	—
23	C₂×C₁₃×#125	—	2	1	no	—
24	C₂×C₁₃×#125	—	2	1	no	—
25	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₂²⋊Q₈	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×Q₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
33	C₁₃×#479	—	2	4	no	—
34	C₁₃×#462	—	2	4	no	—
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×C₄⋊C₈	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×#103	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
49	C₁₃×#391	C₂²	1	1	yes	characteristic
50	C₁₃×#389	—	2	1	no	—
51	C₁₃×#389	C₂²	1	1	yes	characteristic
52	C₁₃×#388	—	2	1	no	—
53	C₁₃×#388	—	2	1	no	—
54	C₁₃×#387	—	2	1	no	—
55	C₁₃×#380	C₂²	1	1	yes	characteristic
56	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
57	C₁₃×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	C₂²	1	1	yes	characteristic
59	C₁₃×#340	C₂²	1	1	yes	characteristic
60	C₁₃×#340	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	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×Q₁₆	—	2	2	no	—
68	C₂×C₁₃×Q₁₆	—	2	2	no	—
69	C₂×C₁₃×Q₁₆	—	2	2	no	—
70	C₂×C₁₃×Q₁₆	—	2	2	no	—
71	C₂×C₁₃×Q₁₆	—	4	1	no	—
72	C₂×C₁₃×Q₁₆	—	4	1	no	—
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₁₃×C₄⋊Q₈	—	2	2	no	—
78	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
79	C₁₃×#126	—	2	8	no	—
80	C₁₃×#126	—	2	8	no	—
81	C₁₃×#125	—	2	8	no	—
82	C₁₃×#125	—	2	8	no	—
83	C₁₃×#125	—	2	2	no	—
84	C₁₃×#125	D₄	1	4	yes	—
85	C₁₃×C₂²⋊Q₈	—	2	2	no	—
86	C₁₃×C₂²⋊Q₈	—	2	2	no	—
87	C₁₃×C₂²⋊Q₈	—	2	2	no	—
88	C₁₃×C₂²⋊Q₈	—	2	2	no	—
89	C₁₃×C₂²⋊Q₈	—	2	2	no	—
90	C₁₃×C₂²⋊Q₈	—	2	2	no	—
91	C₄×Q₈×C₁₃	—	2	2	no	—
92	C₄×Q₈×C₁₃	—	2	2	no	—
93	C₄×Q₈×C₁₃	—	2	2	no	—
94	C₄×Q₈×C₁₃	—	2	2	no	—
95	C₄×Q₈×C₁₃	—	2	2	no	—
96	C₄×Q₈×C₁₃	—	2	2	no	—
97	C₁₃×#117	—	2	2	no	—
98	C₁₃×#117	—	2	2	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	—	2	1	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	D₄	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	D₄	1	1	yes	characteristic
122	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
123	C₂×C₄²×C₁₃	—	2	1	no	—
124	C₂×C₄²×C₁₃	—	2	1	no	—
125	C₂×C₄²×C₁₃	—	2	1	no	—
126	C₂×C₄²×C₁₃	—	2	1	no	—
127	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
129	C₁₃×#107	—	2	2	no	—
130	C₁₃×#106	—	2	2	no	—
131	C₁₃×C₄⋊C₈	—	2	2	no	—
132	C₁₃×C₄⋊C₈	—	2	2	no	—
133	C₁₃×#103	—	2	2	no	—
134	C₁₃×#103	—	2	2	no	—
135	C₁₃×#103	—	2	2	no	—
136	C₁₃×#103	—	2	2	no	—
137	C₁₃×#103	—	2	2	no	—
138	C₁₃×#103	—	2	2	no	—
139	C₁₃×#103	—	4	1	no	—
140	C₁₃×#103	—	4	1	no	—
141	C₁₃×C₂²⋊C₈	—	4	1	no	—
142	C₁₃×C₂²⋊C₈	—	4	1	no	—
143	C₁₃×#95	—	2	1	no	—
144	C₁₃×#95	—	2	1	no	—
145	C₁₃×#95	—	2	1	no	—
146	C₁₃×#95	—	2	1	no	—
147	C₁₃×#95	—	2	1	no	—
148	#24165	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	—	2	1	no	—
152	C₂×Q₈×C₁₃	—	2	1	no	—
153	C₂×Q₈×C₁₃	—	2	1	no	—
154	C₂×Q₈×C₁₃	—	2	1	no	—
155	C₂×Q₈×C₁₃	—	2	1	no	—
156	C₂×Q₈×C₁₃	—	2	1	no	—
157	C₂×Q₈×C₁₃	—	2	1	no	—
158	C₂×Q₈×C₁₃	—	2	1	no	—
159	C₂×Q₈×C₁₃	—	2	1	no	—
160	C₂×Q₈×C₁₃	—	2	1	no	—
161	C₂×Q₈×C₁₃	—	2	1	no	—
162	C₂×Q₈×C₁₃	—	2	1	no	—
163	C₂×Q₈×C₁₃	—	2	1	no	—
164	C₂×Q₈×C₁₃	—	2	1	no	—
165	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
166	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
167	C₂×Q₈×C₁₃	#41	1	2	yes	—
168	C₂²×C₄×C₁₃	—	2	1	no	—
169	C₂²×C₄×C₁₃	—	2	1	no	—
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	2	1	no	—
172	C₂²×C₄×C₁₃	—	2	1	no	—
173	C₂²×C₄×C₁₃	—	2	1	no	—
174	C₂²×C₄×C₁₃	—	2	1	no	—
175	C₂²×C₄×C₁₃	—	2	1	no	—
176	C₂²×C₄×C₁₃	—	2	1	no	—
177	C₂²×C₄×C₁₃	—	2	1	no	—
178	C₂²×C₄×C₁₃	—	2	1	no	—
179	C₂²×C₄×C₁₃	—	2	1	no	—
180	C₂²×C₄×C₁₃	—	2	1	no	—
181	C₂²×C₄×C₁₃	—	2	1	no	—
182	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
188	C₁₃×Q₁₆	—	4	4	no	—
189	C₁₃×Q₁₆	—	4	4	no	—
190	C₂×C₈×C₁₃	—	2	1	no	—
191	C₂×C₈×C₁₃	—	2	1	no	—
192	C₂×C₈×C₁₃	—	2	1	no	—
193	C₂×C₈×C₁₃	—	2	1	no	—
194	C₂×C₈×C₁₃	—	2	1	no	—
195	C₂×C₈×C₁₃	—	2	1	no	—
196	C₂×C₈×C₁₃	—	2	1	no	—
197	C₂×C₈×C₁₃	—	2	1	no	—
198	C₂×C₈×C₁₃	—	2	1	no	—
199	C₂×C₈×C₁₃	—	2	1	no	—
200	C₂×C₈×C₁₃	—	2	1	no	—
201	C₂×C₈×C₁₃	—	2	1	no	—
202	C₁₃×C₄⋊C₄	—	2	4	no	—
203	C₁₃×C₄⋊C₄	—	2	4	no	—
204	C₁₃×C₄⋊C₄	—	2	4	no	—
205	C₁₃×C₄⋊C₄	—	2	4	no	—
206	C₁₃×C₄⋊C₄	—	2	4	no	—
207	C₁₃×C₄⋊C₄	—	2	4	no	—
208	C₁₃×C₄⋊C₄	—	2	4	no	—
209	C₁₃×C₄⋊C₄	—	2	4	no	—
210	C₁₃×C₄⋊C₄	—	2	4	no	—
211	C₁₃×C₄⋊C₄	—	2	2	no	—
212	C₁₃×C₄⋊C₄	—	2	2	no	—
213	C₁₃×C₄⋊C₄	—	2	1	no	—
214	C₁₃×C₄⋊C₄	—	2	1	no	—
215	C₁₃×C₄⋊C₄	—	2	1	no	—
216	C₁₃×C₄⋊C₄	—	2	1	no	—
217	C₁₃×C₄⋊C₄	—	2	1	no	—
218	C₁₃×C₄⋊C₄	—	2	1	no	—
219	C₁₃×C₄⋊C₄	—	2	1	no	—
220	C₁₃×C₄⋊C₄	—	4	2	no	—
221	C₁₃×C₄⋊C₄	—	8	1	no	—
222	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
223	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
224	C₁₃×C₄⋊C₄	#41	1	2	yes	—
225	C₁₃×C₂²⋊C₄	—	2	4	no	—
226	C₁₃×C₂²⋊C₄	—	2	4	no	—
227	C₁₃×C₂²⋊C₄	—	2	4	no	—
228	C₁₃×C₂²⋊C₄	—	2	2	no	—
229	C₁₃×C₂²⋊C₄	—	2	2	no	—
230	C₁₃×C₂²⋊C₄	—	8	1	no	—
231	C₄²×C₁₃	—	2	4	no	—
232	C₄²×C₁₃	—	2	4	no	—
233	C₄²×C₁₃	—	2	1	no	—
234	C₄²×C₁₃	—	2	1	no	—
235	C₄²×C₁₃	—	4	2	no	—
236	C₄²×C₁₃	—	8	1	no	—
237	C₄²×C₁₃	C₂×D₄	1	2	yes	—
238	C₄²×C₁₃	C₂×D₄	1	2	yes	—
239	C₂×#541	C₂×C₁₃	1	1	yes	characteristic
240	C₂×#479	C₂×C₁₃	1	1	yes	characteristic, complemented
241	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#2323	C₂×C₁₃	1	1	yes	characteristic
243	#2036	C₂×C₁₃	1	1	yes	characteristic
244	#2035	C₂×C₁₃	1	1	yes	characteristic
245	#2001	C₂×C₁₃	1	1	yes	characteristic
246	#2001	C₂×C₁₃	1	1	yes	characteristic
247	#1989	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#1981	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#1878	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#1878	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#1865	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#1863	C₂×C₁₃	1	1	yes	characteristic, complemented
253	#1798	C₂×C₁₃	1	1	yes	characteristic
254	C₂³×C₁₃	—	2	1	no	—
255	C₂³×C₁₃	—	2	1	no	—
256	C₂³×C₁₃	—	2	1	no	—
257	C₂³×C₁₃	—	2	1	no	—
258	C₂³×C₁₃	—	2	1	no	—
259	C₂³×C₁₃	—	2	1	no	—
260	C₂³×C₁₃	—	2	1	no	—
261	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
262	Q₈×C₁₃	—	2	2	no	—
263	Q₈×C₁₃	—	2	2	no	—
264	Q₈×C₁₃	—	2	2	no	—
265	Q₈×C₁₃	—	2	2	no	—
266	Q₈×C₁₃	—	2	2	no	—
267	Q₈×C₁₃	—	2	2	no	—
268	Q₈×C₁₃	—	4	1	no	—
269	Q₈×C₁₃	—	4	1	no	—
270	Q₈×C₁₃	—	4	1	no	—
271	Q₈×C₁₃	—	4	1	no	—
272	Q₈×C₁₃	—	4	1	no	—
273	Q₈×C₁₃	—	4	1	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	2	1	no	—
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	—	2	2	no	—
281	C₂×C₄×C₁₃	—	2	2	no	—
282	C₂×C₄×C₁₃	—	2	2	no	—
283	C₂×C₄×C₁₃	—	2	2	no	—
284	C₂×C₄×C₁₃	—	2	1	no	—
285	C₂×C₄×C₁₃	—	2	2	no	—
286	C₂×C₄×C₁₃	—	2	2	no	—
287	C₂×C₄×C₁₃	—	2	1	no	—
288	C₂×C₄×C₁₃	—	2	1	no	—
289	C₂×C₄×C₁₃	—	2	1	no	—
290	C₂×C₄×C₁₃	—	2	1	no	—
291	C₂×C₄×C₁₃	—	2	1	no	—
292	C₂×C₄×C₁₃	—	2	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	—	4	1	no	—
302	C₂×C₄×C₁₃	—	4	1	no	—
303	C₂×C₄×C₁₃	—	4	1	no	—
304	C₂×C₄×C₁₃	—	4	1	no	—
305	C₂×C₄×C₁₃	—	4	1	no	—
306	C₂×C₄×C₁₃	—	4	1	no	—
307	C₂×C₄×C₁₃	—	4	1	no	—
308	C₂×C₄×C₁₃	—	4	1	no	—
309	C₂×C₄×C₁₃	—	4	1	no	—
310	C₂×C₄×C₁₃	—	4	1	no	—
311	C₂×C₄×C₁₃	—	4	1	no	—
312	C₂×C₄×C₁₃	—	4	1	no	—
313	C₂×C₄×C₁₃	—	4	1	no	—
314	C₂×C₄×C₁₃	—	4	1	no	—
315	C₂×C₄×C₁₃	#120	1	2	yes	—
316	C₂×C₄×C₁₃	#120	1	2	yes	—
317	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
320	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
321	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
322	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
323	C₈×C₁₃	—	4	1	no	—
324	C₈×C₁₃	—	4	1	no	—
325	C₈×C₁₃	—	4	1	no	—
326	C₈×C₁₃	—	4	1	no	—
327	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
328	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
329	#541	—	2	4	no	—
330	#541	—	2	4	no	—
331	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
332	C₂×#126	—	2	1	no	—
333	C₂×#126	—	2	1	no	—
334	C₂×#125	—	2	1	no	—
335	C₂×#125	—	2	1	no	—
336	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
339	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
341	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
342	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
343	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
344	#479	—	2	4	no	—
345	#462	—	2	4	no	—
346	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
349	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
351	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
352	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
353	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
354	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
355	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
356	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
357	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
358	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
359	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
360	#391	C₂²×C₁₃	1	1	yes	characteristic
361	#389	—	2	1	no	—
362	#389	C₂²×C₁₃	1	1	yes	characteristic
363	#388	—	2	1	no	—
364	#388	—	2	1	no	—
365	#387	—	2	1	no	—
366	#380	C₂²×C₁₃	1	1	yes	characteristic
367	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
368	#340	C₂²×C₁₃	1	1	yes	characteristic
369	#340	C₂²×C₁₃	1	1	yes	characteristic
370	#340	C₂²×C₁₃	1	1	yes	characteristic
371	#340	C₂²×C₁₃	1	1	yes	characteristic
372	#336	C₂²×C₁₃	1	1	yes	characteristic
373	#336	C₂²×C₁₃	1	1	yes	characteristic
374	C₂²×C₁₃	—	4	1	no	—
375	C₂²×C₁₃	—	4	1	no	—
376	C₂²×C₁₃	—	4	1	no	—
377	C₂²×C₁₃	—	4	1	no	—
378	C₂²×C₁₃	—	4	1	no	—
379	C₂²×C₁₃	—	4	1	no	—
380	C₂²×C₁₃	—	4	1	no	—
381	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
382	C₂²×C₁₃	#525	1	1	yes	characteristic
383	C₂²×C₁₃	#537	1	1	yes	characteristic
384	C₂²×C₁₃	#577	1	1	yes	characteristic
385	C₂²×C₁₃	#578	1	1	yes	characteristic
386	C₂²×C₁₃	#578	1	1	yes	characteristic
387	C₂²×C₁₃	#578	1	1	yes	characteristic
388	C₄×C₁₃	—	2	2	no	—
389	C₄×C₁₃	—	2	2	no	—
390	C₄×C₁₃	—	4	2	no	—
391	C₄×C₁₃	—	4	1	no	—
392	C₄×C₁₃	—	4	2	no	—
393	C₄×C₁₃	—	4	2	no	—
394	C₄×C₁₃	—	4	2	no	—
395	C₄×C₁₃	—	4	1	no	—
396	C₄×C₁₃	—	4	2	no	—
397	C₄×C₁₃	—	4	1	no	—
398	C₄×C₁₃	—	4	2	no	—
399	C₄×C₁₃	—	8	1	no	—
400	C₄×C₁₃	—	8	1	no	—
401	C₄×C₁₃	#546	1	1	yes	characteristic
402	C₄×C₁₃	#547	1	1	yes	characteristic
403	C₄×C₁₃	#548	1	1	yes	characteristic
404	C₄×C₁₃	#550	1	1	yes	characteristic
405	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
406	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
407	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
408	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
409	C₂×Q₁₆	—	2	2	no	—
410	C₂×Q₁₆	—	2	2	no	—
411	C₂×Q₁₆	—	2	2	no	—
412	C₂×Q₁₆	—	2	2	no	—
413	C₂×Q₁₆	—	4	1	no	—
414	C₂×Q₁₆	—	4	1	no	—
415	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
416	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
417	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
418	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
419	C₄⋊Q₈	—	2	2	no	—
420	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
421	#126	—	2	8	no	—
422	#126	—	2	8	no	—
423	#125	—	2	8	no	—
424	#125	—	2	8	no	—
425	#125	—	2	2	no	—
426	#125	D₄×C₁₃	1	4	yes	—
427	C₂²⋊Q₈	—	2	2	no	—
428	C₂²⋊Q₈	—	2	2	no	—
429	C₂²⋊Q₈	—	2	2	no	—
430	C₂²⋊Q₈	—	2	2	no	—
431	C₂²⋊Q₈	—	2	2	no	—
432	C₂²⋊Q₈	—	2	2	no	—
433	C₄×Q₈	—	2	2	no	—
434	C₄×Q₈	—	2	2	no	—
435	C₄×Q₈	—	2	2	no	—
436	C₄×Q₈	—	2	2	no	—
437	C₄×Q₈	—	2	2	no	—
438	C₄×Q₈	—	2	2	no	—
439	#117	—	2	2	no	—
440	#117	—	2	2	no	—
441	C₂×C₄⋊C₄	—	2	1	no	—
442	C₂×C₄⋊C₄	—	2	1	no	—
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	—	2	1	no	—
445	C₂×C₄⋊C₄	—	2	1	no	—
446	C₂×C₄⋊C₄	—	2	1	no	—
447	C₂×C₄⋊C₄	—	2	1	no	—
448	C₂×C₄⋊C₄	—	2	1	no	—
449	C₂×C₄⋊C₄	—	2	1	no	—
450	C₂×C₄⋊C₄	—	2	1	no	—
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
453	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
459	C₂×C₂²⋊C₄	—	2	1	no	—
460	C₂×C₂²⋊C₄	—	2	1	no	—
461	C₂×C₂²⋊C₄	—	2	1	no	—
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
464	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
465	C₂×C₄²	—	2	1	no	—
466	C₂×C₄²	—	2	1	no	—
467	C₂×C₄²	—	2	1	no	—
468	C₂×C₄²	—	2	1	no	—
469	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
470	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
471	#107	—	2	2	no	—
472	#106	—	2	2	no	—
473	C₄⋊C₈	—	2	2	no	—
474	C₄⋊C₈	—	2	2	no	—
475	#103	—	2	2	no	—
476	#103	—	2	2	no	—
477	#103	—	2	2	no	—
478	#103	—	2	2	no	—
479	#103	—	2	2	no	—
480	#103	—	2	2	no	—
481	#103	—	4	1	no	—
482	#103	—	4	1	no	—
483	C₂²⋊C₈	—	4	1	no	—
484	C₂²⋊C₈	—	4	1	no	—
485	#95	—	2	1	no	—
486	#95	—	2	1	no	—
487	#95	—	2	1	no	—
488	#95	—	2	1	no	—
489	#95	—	2	1	no	—
490	C₂×C₁₃	—	8	1	no	—
491	C₂×C₁₃	#2407	1	1	yes	characteristic
492	C₂×C₁₃	#3011	1	1	yes	characteristic
493	C₂×C₁₃	#3013	1	1	yes	characteristic
494	C₂×C₁₃	#3120	1	1	yes	characteristic
495	C₂×C₁₃	#3127	1	1	yes	characteristic
496	C₂×C₁₃	#3258	1	1	yes	characteristic
497	C₂×C₁₃	#3261	1	1	yes	characteristic
498	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
515	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
516	C₂×Q₈	C₁₃×#41	1	2	yes	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
532	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
533	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
534	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
535	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
536	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
537	Q₁₆	—	4	4	no	—
538	Q₁₆	—	4	4	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₄⋊C₄	—	2	4	no	—
552	C₄⋊C₄	—	2	4	no	—
553	C₄⋊C₄	—	2	4	no	—
554	C₄⋊C₄	—	2	4	no	—
555	C₄⋊C₄	—	2	4	no	—
556	C₄⋊C₄	—	2	4	no	—
557	C₄⋊C₄	—	2	4	no	—
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	4	no	—
560	C₄⋊C₄	—	2	2	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	4	2	no	—
570	C₄⋊C₄	—	8	1	no	—
571	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
572	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
573	C₄⋊C₄	C₁₃×#41	1	2	yes	—
574	C₂²⋊C₄	—	2	4	no	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	2	no	—
578	C₂²⋊C₄	—	2	2	no	—
579	C₂²⋊C₄	—	8	1	no	—
580	C₄²	—	2	4	no	—
581	C₄²	—	2	4	no	—
582	C₄²	—	2	1	no	—
583	C₄²	—	2	1	no	—
584	C₄²	—	4	2	no	—
585	C₄²	—	8	1	no	—
586	C₄²	C₂×D₄×C₁₃	1	2	yes	—
587	C₄²	C₂×D₄×C₁₃	1	2	yes	—
588	C₁₃	#24165	1	1	yes	characteristic, direct product factor, Sylow
589	C₂³	—	2	1	no	—
590	C₂³	—	2	1	no	—
591	C₂³	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
597	Q₈	—	2	2	no	—
598	Q₈	—	2	2	no	—
599	Q₈	—	2	2	no	—
600	Q₈	—	2	2	no	—
601	Q₈	—	2	2	no	—
602	Q₈	—	2	2	no	—
603	Q₈	—	4	1	no	—
604	Q₈	—	4	1	no	—
605	Q₈	—	4	1	no	—
606	Q₈	—	4	1	no	—
607	Q₈	—	4	1	no	—
608	Q₈	—	4	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	C₁₃×#120	1	2	yes	—
651	C₂×C₄	C₁₃×#120	1	2	yes	—
652	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
653	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
654	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
655	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
656	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
657	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
658	C₈	—	4	1	no	—
659	C₈	—	4	1	no	—
660	C₈	—	4	1	no	—
661	C₈	—	4	1	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	4	1	no	—
664	C₂²	—	4	1	no	—
665	C₂²	—	4	1	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
670	C₂²	C₁₃×#525	1	1	yes	characteristic
671	C₂²	C₁₃×#537	1	1	yes	characteristic
672	C₂²	C₁₃×#577	1	1	yes	characteristic
673	C₂²	C₁₃×#578	1	1	yes	characteristic
674	C₂²	C₁₃×#578	1	1	yes	characteristic
675	C₂²	C₁₃×#578	1	1	yes	characteristic
676	C₄	—	2	2	no	—
677	C₄	—	2	2	no	—
678	C₄	—	4	1	no	—
679	C₄	—	4	2	no	—
680	C₄	—	4	1	no	—
681	C₄	—	4	2	no	—
682	C₄	—	4	2	no	—
683	C₄	—	4	1	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	2	no	—
686	C₄	—	4	2	no	—
687	C₄	—	8	1	no	—
688	C₄	—	8	1	no	—
689	C₄	C₁₃×#546	1	1	yes	characteristic
690	C₄	C₁₃×#547	1	1	yes	characteristic
691	C₄	C₁₃×#548	1	1	yes	characteristic
692	C₄	C₁₃×#550	1	1	yes	characteristic
693	C₂	—	8	1	no	—
694	C₂	C₁₃×#2407	1	1	yes	characteristic
695	C₂	C₁₃×#3011	1	1	yes	characteristic
696	C₂	C₁₃×#3013	1	1	yes	characteristic
697	C₂	C₁₃×#3120	1	1	yes	characteristic
698	C₂	C₁₃×#3127	1	1	yes	characteristic
699	C₂	C₁₃×#3258	1	1	yes	characteristic
700	C₂	C₁₃×#3261	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 ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#479	C₂	semidirect
3. C₂×C₁₃×#462	C₂	semidirect
9. C₁₃×#1989	C₂	semidirect
10. C₁₃×#1981	C₂	semidirect
11. C₁₃×#1878	C₂	semidirect
12. C₁₃×#1878	C₂	semidirect
13. C₁₃×#1865	C₂	semidirect
14. C₁₃×#1863	C₂	semidirect
148. #24165	C₁₃	direct (N × H)
240. C₂×#479	C₂×C₁₃	semidirect
241. C₂×#462	C₂×C₁₃	semidirect
247. #1989	C₂×C₁₃	semidirect
248. #1981	C₂×C₁₃	semidirect
249. #1878	C₂×C₁₃	semidirect
250. #1878	C₂×C₁₃	semidirect
251. #1865	C₂×C₁₃	semidirect
252. #1863	C₂×C₁₃	semidirect
588. C₁₃	#24165	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#541	2
C₂×C₁₃×#479	2
C₂×C₁₃×#462	2
C₁₃×#2323	2
C₁₃×#2036	2
C₁₃×#2035	2
C₁₃×#2001	2
C₁₃×#1989	2
C₁₃×#1981	2
C₁₃×#1878	2
C₁₃×#1865	2
C₁₃×#1863	2
C₁₃×#1798	2
#24165	13

Subgroups — C13×#24165 #15710504

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24165 #15710504