Subgroups — C₁₃×#23479 #15709818

Order 3328.

1610 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#525	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2036	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2035	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2034	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2033	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1735	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#525	—	2	4	no	—
17	C₁₃×#525	—	2	4	no	—
18	C₂×C₁₃×#123	—	2	1	no	—
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₁₃×#121	C₂²	1	2	yes	—
21	C₂×C₁₃×#120	—	2	1	no	—
22	C₂×C₄×D₄×C₁₃	—	2	2	no	—
23	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
26	C₁₃×#427	—	2	4	no	—
27	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
28	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
29	C₁₃×#416	—	2	4	no	—
30	C₁₃×#416	—	2	4	no	—
31	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
33	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
36	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₁₃×C₂²⋊C₈	—	2	4	no	—
38	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
39	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
40	C₁₃×#381	—	2	1	no	—
41	C₁₃×#380	C₂²	1	2	yes	—
42	C₁₃×#380	C₂²	1	2	yes	—
43	C₁₃×#379	—	2	1	no	—
44	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
45	C₁₃×#340	C₂²	1	2	yes	complemented
46	C₁₃×#340	C₂²	1	2	yes	complemented
47	C₂⁵×C₁₃	D₄	1	1	yes	characteristic
48	C₂×C₁₃×#41	—	2	2	no	—
49	C₂×C₁₃×#41	—	2	2	no	—
50	C₂×C₁₃×#41	—	2	2	no	—
51	C₂×C₁₃×#41	—	2	2	no	—
52	C₂×C₁₃×#41	—	2	2	no	—
53	C₂×C₁₃×#41	D₄	1	4	yes	—
54	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×D₄×C₁₃	—	2	2	no	—
56	C₂²×D₄×C₁₃	—	2	1	no	—
57	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₃	—	2	2	no	—
59	C₂³×C₄×C₁₃	—	2	2	no	—
60	C₂³×C₄×C₁₃	—	2	2	no	—
61	C₂³×C₄×C₁₃	—	2	1	no	—
62	C₂³×C₄×C₁₃	—	2	2	no	—
63	C₂³×C₄×C₁₃	—	2	2	no	—
64	C₂³×C₄×C₁₃	—	2	2	no	—
65	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	D₄	1	2	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	—	2	2	no	—
70	C₂²×C₈×C₁₃	—	2	2	no	—
71	C₂²×C₈×C₁₃	—	2	2	no	—
72	C₂²×C₈×C₁₃	—	2	2	no	—
73	C₂²×C₈×C₁₃	—	2	2	no	—
74	C₂²×C₈×C₁₃	D₄	1	4	yes	complemented
75	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
76	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×#123	—	2	8	no	—
79	C₁₃×C₂²⋊Q₈	—	2	4	no	—
80	C₁₃×C₂²⋊Q₈	—	2	4	no	—
81	C₁₃×#121	—	2	4	no	—
82	C₁₃×#121	—	2	4	no	—
83	C₁₃×#120	—	2	8	no	—
84	C₄×D₄×C₁₃	—	2	16	no	—
85	C₁₃×#117	—	2	2	no	—
86	C₁₃×#117	—	2	2	no	—
87	C₁₃×#117	—	2	2	no	—
88	C₁₃×#117	—	2	2	no	—
89	C₁₃×#117	—	2	2	no	—
90	C₁₃×#117	D₄	1	4	yes	—
91	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
100	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₄²×C₁₃	—	2	1	no	—
104	C₂×C₄²×C₁₃	—	2	1	no	—
105	C₂×C₄²×C₁₃	—	2	1	no	—
106	C₁₃×#107	—	2	4	no	—
107	C₁₃×#106	—	2	4	no	—
108	C₁₃×#103	—	2	4	no	—
109	C₁₃×#103	—	2	2	no	—
110	C₁₃×#103	—	2	2	no	—
111	C₁₃×#102	—	2	4	no	—
112	C₁₃×#102	—	2	2	no	—
113	C₁₃×#102	—	2	2	no	—
114	C₁₃×C₂²⋊C₈	—	2	4	no	—
115	C₁₃×C₂²⋊C₈	—	2	4	no	—
116	C₁₃×#95	—	2	2	no	—
117	C₁₃×#95	—	2	2	no	—
118	#23479	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂⁴×C₁₃	—	2	2	no	—
120	C₂⁴×C₁₃	—	2	4	no	—
121	C₂⁴×C₁₃	—	2	2	no	—
122	C₂⁴×C₁₃	—	2	2	no	—
123	C₂⁴×C₁₃	—	2	1	no	—
124	C₂⁴×C₁₃	—	4	2	no	—
125	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
126	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₁₃×#41	—	2	8	no	—
128	C₁₃×#41	—	2	8	no	—
129	C₁₃×#41	—	4	4	no	—
130	C₁₃×#41	—	4	4	no	—
131	C₂×Q₈×C₁₃	—	2	1	no	—
132	C₂×Q₈×C₁₃	—	2	1	no	—
133	C₂×Q₈×C₁₃	—	2	1	no	—
134	C₂×Q₈×C₁₃	—	2	1	no	—
135	C₂×Q₈×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
137	C₂×D₄×C₁₃	—	2	8	no	—
138	C₂×D₄×C₁₃	—	2	4	no	—
139	C₂×D₄×C₁₃	—	2	1	no	—
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	4	4	no	—
145	C₂×D₄×C₁₃	—	4	2	no	—
146	C₂×D₄×C₁₃	—	4	2	no	—
147	C₂×D₄×C₁₃	—	4	4	no	—
148	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₁₃	—	2	2	no	—
150	C₂²×C₄×C₁₃	—	2	2	no	—
151	C₂²×C₄×C₁₃	—	2	2	no	—
152	C₂²×C₄×C₁₃	—	2	2	no	—
153	C₂²×C₄×C₁₃	—	2	1	no	—
154	C₂²×C₄×C₁₃	—	2	4	no	—
155	C₂²×C₄×C₁₃	—	2	4	no	—
156	C₂²×C₄×C₁₃	—	2	4	no	—
157	C₂²×C₄×C₁₃	—	2	4	no	—
158	C₂²×C₄×C₁₃	—	2	2	no	—
159	C₂²×C₄×C₁₃	—	2	2	no	—
160	C₂²×C₄×C₁₃	—	2	2	no	—
161	C₂²×C₄×C₁₃	—	2	2	no	—
162	C₂²×C₄×C₁₃	—	2	2	no	—
163	C₂²×C₄×C₁₃	—	2	2	no	—
164	C₂²×C₄×C₁₃	—	2	2	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	4	4	no	—
168	C₂²×C₄×C₁₃	—	4	4	no	—
169	C₂²×C₄×C₁₃	—	4	2	no	—
170	C₂²×C₄×C₁₃	—	4	4	no	—
171	C₂²×C₄×C₁₃	—	4	2	no	—
172	C₂²×C₄×C₁₃	—	4	4	no	—
173	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
177	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₃	#41	1	2	yes	—
179	C₂²×C₄×C₁₃	#41	1	2	yes	—
180	C₂²×C₄×C₁₃	#41	1	2	yes	—
181	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
182	C₂×C₈×C₁₃	—	2	8	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	2	no	—
188	C₂×C₈×C₁₃	—	2	2	no	—
189	C₂×C₈×C₁₃	—	2	2	no	—
190	C₂×C₈×C₁₃	—	4	4	no	—
191	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
192	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
193	C₁₃×C₄⋊C₄	—	2	8	no	—
194	C₁₃×C₄⋊C₄	—	2	2	no	—
195	C₁₃×C₄⋊C₄	—	2	2	no	—
196	C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	—	2	2	no	—
199	C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
202	C₁₃×C₂²⋊C₄	—	2	8	no	—
203	C₁₃×C₂²⋊C₄	—	2	8	no	—
204	C₁₃×C₂²⋊C₄	—	2	4	no	—
205	C₁₃×C₂²⋊C₄	—	4	4	no	—
206	C₁₃×C₂²⋊C₄	—	4	2	no	—
207	C₁₃×C₂²⋊C₄	—	4	2	no	—
208	C₁₃×C₂²⋊C₄	—	4	4	no	—
209	C₄²×C₁₃	—	2	4	no	—
210	C₄²×C₁₃	—	4	2	no	—
211	C₄²×C₁₃	—	4	2	no	—
212	C₂×#525	C₂×C₁₃	1	1	yes	characteristic
213	C₂×#427	C₂×C₁₃	1	1	yes	characteristic, complemented
214	C₂×#416	C₂×C₁₃	1	1	yes	characteristic, complemented
215	C₂×#416	C₂×C₁₃	1	1	yes	characteristic, complemented
216	C₂²×C₂²⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#2280	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#2036	C₂×C₁₃	1	2	yes	complemented
219	#2035	C₂×C₁₃	1	2	yes	complemented
220	#2034	C₂×C₁₃	1	2	yes	complemented
221	#2033	C₂×C₁₃	1	2	yes	complemented
222	#1735	C₂×C₁₃	1	1	yes	characteristic, complemented
223	C₂³×C₁₃	—	2	2	no	—
224	C₂³×C₁₃	—	2	2	no	—
225	C₂³×C₁₃	—	2	8	no	—
226	C₂³×C₁₃	—	2	2	no	—
227	C₂³×C₁₃	—	2	2	no	—
228	C₂³×C₁₃	—	2	2	no	—
229	C₂³×C₁₃	—	2	2	no	—
230	C₂³×C₁₃	—	2	2	no	—
231	C₂³×C₁₃	—	2	2	no	—
232	C₂³×C₁₃	—	2	2	no	—
233	C₂³×C₁₃	—	4	8	no	—
234	C₂³×C₁₃	—	4	8	no	—
235	C₂³×C₁₃	—	4	4	no	—
236	C₂³×C₁₃	—	4	4	no	—
237	C₂³×C₁₃	—	4	1	no	—
238	C₂³×C₁₃	—	4	1	no	—
239	C₂³×C₁₃	—	4	2	no	—
240	C₂³×C₁₃	—	4	2	no	—
241	C₂³×C₁₃	#120	1	2	yes	—
242	C₂³×C₁₃	#121	1	2	yes	—
243	C₂³×C₁₃	#123	1	2	yes	—
244	C₂³×C₁₃	#135	1	4	yes	—
245	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
246	Q₈×C₁₃	—	2	2	no	—
247	Q₈×C₁₃	—	2	2	no	—
248	Q₈×C₁₃	—	4	1	no	—
249	Q₈×C₁₃	—	4	1	no	—
250	D₄×C₁₃	—	2	2	no	—
251	D₄×C₁₃	—	2	2	no	—
252	D₄×C₁₃	—	4	16	no	—
253	D₄×C₁₃	—	4	8	no	—
254	D₄×C₁₃	—	4	1	no	—
255	D₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	4	2	no	—
264	C₂×C₄×C₁₃	—	4	2	no	—
265	C₂×C₄×C₁₃	—	4	4	no	—
266	C₂×C₄×C₁₃	—	4	2	no	—
267	C₂×C₄×C₁₃	—	4	2	no	—
268	C₂×C₄×C₁₃	—	4	2	no	—
269	C₂×C₄×C₁₃	—	4	2	no	—
270	C₂×C₄×C₁₃	—	4	8	no	—
271	C₂×C₄×C₁₃	—	4	8	no	—
272	C₂×C₄×C₁₃	—	4	2	no	—
273	C₂×C₄×C₁₃	—	4	1	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	4	2	no	—
276	C₂×C₄×C₁₃	—	4	2	no	—
277	C₂×C₄×C₁₃	—	4	2	no	—
278	C₂×C₄×C₁₃	—	4	2	no	—
279	C₂×C₄×C₁₃	#120	1	2	yes	—
280	C₂×C₄×C₁₃	#121	1	4	yes	—
281	C₂×C₄×C₁₃	#121	1	4	yes	—
282	C₂×C₄×C₁₃	#121	1	2	yes	—
283	C₂×C₄×C₁₃	#123	1	4	yes	—
284	C₂×C₄×C₁₃	#123	1	2	yes	—
285	C₂×C₄×C₁₃	#124	1	4	yes	—
286	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
292	C₈×C₁₃	—	2	2	no	—
293	C₈×C₁₃	—	2	2	no	—
294	C₈×C₁₃	—	4	2	no	—
295	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
296	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
297	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
298	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
299	#525	—	2	4	no	—
300	#525	—	2	4	no	—
301	C₂×#123	—	2	1	no	—
302	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
303	C₂×#121	C₂²×C₁₃	1	2	yes	—
304	C₂×#120	—	2	1	no	—
305	C₂×C₄×D₄	—	2	2	no	—
306	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
309	#427	—	2	4	no	—
310	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
311	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
312	#416	—	2	4	no	—
313	#416	—	2	4	no	—
314	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
315	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
316	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
317	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
318	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
319	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
320	C₂×C₂²⋊C₈	—	2	4	no	—
321	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
322	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
323	#381	—	2	1	no	—
324	#380	C₂²×C₁₃	1	2	yes	—
325	#380	C₂²×C₁₃	1	2	yes	—
326	#379	—	2	1	no	—
327	C₄×C₂²⋊C₄	—	2	2	no	—
328	#340	C₂²×C₁₃	1	2	yes	complemented
329	#340	C₂²×C₁₃	1	2	yes	complemented
330	C₂²×C₁₃	—	2	4	no	—
331	C₂²×C₁₃	—	2	4	no	—
332	C₂²×C₁₃	—	2	2	no	—
333	C₂²×C₁₃	—	2	2	no	—
334	C₂²×C₁₃	—	2	4	no	—
335	C₂²×C₁₃	—	2	4	no	—
336	C₂²×C₁₃	—	2	4	no	—
337	C₂²×C₁₃	—	4	16	no	—
338	C₂²×C₁₃	—	4	2	no	—
339	C₂²×C₁₃	—	4	2	no	—
340	C₂²×C₁₃	—	4	2	no	—
341	C₂²×C₁₃	—	4	2	no	—
342	C₂²×C₁₃	—	4	2	no	—
343	C₂²×C₁₃	—	4	4	no	—
344	C₂²×C₁₃	—	8	2	no	—
345	C₂²×C₁₃	—	8	1	no	—
346	C₂²×C₁₃	—	8	1	no	—
347	C₂²×C₁₃	#394	1	4	yes	—
348	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
349	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
350	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
351	C₂²×C₁₃	C₂×#135	1	2	yes	—
352	C₂²×C₁₃	#575	1	2	yes	—
353	C₄×C₁₃	—	4	2	no	—
354	C₄×C₁₃	—	4	2	no	—
355	C₄×C₁₃	—	4	4	no	—
356	C₄×C₁₃	—	8	2	no	—
357	C₄×C₁₃	—	8	1	no	—
358	C₄×C₁₃	—	8	1	no	—
359	C₄×C₁₃	#394	1	4	yes	—
360	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
361	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
362	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
363	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
364	C₂⁵	D₄×C₁₃	1	1	yes	characteristic
365	C₂×#41	—	2	2	no	—
366	C₂×#41	—	2	2	no	—
367	C₂×#41	—	2	2	no	—
368	C₂×#41	—	2	2	no	—
369	C₂×#41	—	2	2	no	—
370	C₂×#41	D₄×C₁₃	1	4	yes	—
371	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
372	C₂²×D₄	—	2	2	no	—
373	C₂²×D₄	—	2	1	no	—
374	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
375	C₂³×C₄	—	2	1	no	—
376	C₂³×C₄	—	2	2	no	—
377	C₂³×C₄	—	2	2	no	—
378	C₂³×C₄	—	2	2	no	—
379	C₂³×C₄	—	2	2	no	—
380	C₂³×C₄	—	2	2	no	—
381	C₂³×C₄	—	2	2	no	—
382	C₂³×C₄	D₄×C₁₃	1	2	yes	—
383	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
384	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
385	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
386	C₂²×C₈	—	2	2	no	—
387	C₂²×C₈	—	2	2	no	—
388	C₂²×C₈	—	2	2	no	—
389	C₂²×C₈	—	2	2	no	—
390	C₂²×C₈	—	2	2	no	—
391	C₂²×C₈	D₄×C₁₃	1	4	yes	complemented
392	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
393	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
394	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
395	#123	—	2	8	no	—
396	C₂²⋊Q₈	—	2	4	no	—
397	C₂²⋊Q₈	—	2	4	no	—
398	#121	—	2	4	no	—
399	#121	—	2	4	no	—
400	#120	—	2	8	no	—
401	C₄×D₄	—	2	16	no	—
402	#117	—	2	2	no	—
403	#117	—	2	2	no	—
404	#117	—	2	2	no	—
405	#117	—	2	2	no	—
406	#117	—	2	2	no	—
407	#117	D₄×C₁₃	1	4	yes	—
408	C₂×C₄⋊C₄	—	2	2	no	—
409	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	2	no	—
415	C₂×C₂²⋊C₄	—	2	2	no	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	2	no	—
419	C₂×C₂²⋊C₄	—	2	2	no	—
420	C₂×C₄²	—	2	1	no	—
421	C₂×C₄²	—	2	1	no	—
422	C₂×C₄²	—	2	1	no	—
423	#107	—	2	4	no	—
424	#106	—	2	4	no	—
425	#103	—	2	4	no	—
426	#103	—	2	2	no	—
427	#103	—	2	2	no	—
428	#102	—	2	4	no	—
429	#102	—	2	2	no	—
430	#102	—	2	2	no	—
431	C₂²⋊C₈	—	2	4	no	—
432	C₂²⋊C₈	—	2	4	no	—
433	#95	—	2	2	no	—
434	#95	—	2	2	no	—
435	C₂×C₁₃	—	2	4	no	—
436	C₂×C₁₃	—	4	4	no	—
437	C₂×C₁₃	—	8	2	no	—
438	C₂×C₁₃	C₂×#394	1	1	yes	characteristic
439	C₂×C₁₃	#3002	1	2	yes	—
440	C₂×C₁₃	#3050	1	1	yes	characteristic
441	C₂×C₁₃	#3054	1	1	yes	characteristic
442	C₂×C₁₃	#3091	1	2	yes	—
443	C₂⁴	—	2	2	no	—
444	C₂⁴	—	2	4	no	—
445	C₂⁴	—	2	2	no	—
446	C₂⁴	—	2	2	no	—
447	C₂⁴	—	2	1	no	—
448	C₂⁴	—	4	2	no	—
449	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
450	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
451	#41	—	2	8	no	—
452	#41	—	2	8	no	—
453	#41	—	4	4	no	—
454	#41	—	4	4	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
461	C₂×D₄	—	2	8	no	—
462	C₂×D₄	—	2	4	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	4	4	no	—
469	C₂×D₄	—	4	2	no	—
470	C₂×D₄	—	4	2	no	—
471	C₂×D₄	—	4	4	no	—
472	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	4	4	no	—
492	C₂²×C₄	—	4	4	no	—
493	C₂²×C₄	—	4	2	no	—
494	C₂²×C₄	—	4	4	no	—
495	C₂²×C₄	—	4	2	no	—
496	C₂²×C₄	—	4	4	no	—
497	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
498	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
499	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
500	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
501	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
502	C₂²×C₄	C₁₃×#41	1	2	yes	—
503	C₂²×C₄	C₁₃×#41	1	2	yes	—
504	C₂²×C₄	C₁₃×#41	1	2	yes	—
505	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
506	C₂×C₈	—	2	8	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	2	no	—
512	C₂×C₈	—	2	2	no	—
513	C₂×C₈	—	2	2	no	—
514	C₂×C₈	—	4	4	no	—
515	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
516	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
517	C₄⋊C₄	—	2	8	no	—
518	C₄⋊C₄	—	2	2	no	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	2	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
526	C₂²⋊C₄	—	2	8	no	—
527	C₂²⋊C₄	—	2	8	no	—
528	C₂²⋊C₄	—	2	4	no	—
529	C₂²⋊C₄	—	4	4	no	—
530	C₂²⋊C₄	—	4	2	no	—
531	C₂²⋊C₄	—	4	2	no	—
532	C₂²⋊C₄	—	4	4	no	—
533	C₄²	—	2	4	no	—
534	C₄²	—	4	2	no	—
535	C₄²	—	4	2	no	—
536	C₁₃	#23479	1	1	yes	characteristic, direct product factor, Sylow
537	C₂³	—	2	2	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	2	8	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	4	8	no	—
548	C₂³	—	4	8	no	—
549	C₂³	—	4	4	no	—
550	C₂³	—	4	4	no	—
551	C₂³	—	4	1	no	—
552	C₂³	—	4	1	no	—
553	C₂³	—	4	2	no	—
554	C₂³	—	4	2	no	—
555	C₂³	C₁₃×#120	1	2	yes	—
556	C₂³	C₁₃×#121	1	2	yes	—
557	C₂³	C₁₃×#123	1	2	yes	—
558	C₂³	C₁₃×#135	1	4	yes	—
559	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
560	Q₈	—	2	2	no	—
561	Q₈	—	2	2	no	—
562	Q₈	—	4	1	no	—
563	Q₈	—	4	1	no	—
564	D₄	—	2	2	no	—
565	D₄	—	2	2	no	—
566	D₄	—	4	16	no	—
567	D₄	—	4	8	no	—
568	D₄	—	4	1	no	—
569	D₄	—	4	1	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	4	4	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	2	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	8	no	—
581	C₂×C₄	—	4	8	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	C₁₃×#120	1	2	yes	—
594	C₂×C₄	C₁₃×#121	1	2	yes	—
595	C₂×C₄	C₁₃×#121	1	4	yes	—
596	C₂×C₄	C₁₃×#121	1	4	yes	—
597	C₂×C₄	C₁₃×#123	1	2	yes	—
598	C₂×C₄	C₁₃×#123	1	4	yes	—
599	C₂×C₄	C₁₃×#124	1	4	yes	—
600	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
601	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
602	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
603	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
604	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
605	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
606	C₈	—	2	2	no	—
607	C₈	—	2	2	no	—
608	C₈	—	4	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	4	no	—
612	C₂²	—	2	4	no	—
613	C₂²	—	2	4	no	—
614	C₂²	—	2	4	no	—
615	C₂²	—	2	4	no	—
616	C₂²	—	4	16	no	—
617	C₂²	—	4	2	no	—
618	C₂²	—	4	2	no	—
619	C₂²	—	4	2	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	4	no	—
623	C₂²	—	8	1	no	—
624	C₂²	—	8	1	no	—
625	C₂²	—	8	2	no	—
626	C₂²	C₁₃×#394	1	4	yes	—
627	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
628	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
629	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
630	C₂²	C₂×C₁₃×#135	1	2	yes	—
631	C₂²	C₁₃×#575	1	2	yes	—
632	C₄	—	4	2	no	—
633	C₄	—	4	2	no	—
634	C₄	—	4	4	no	—
635	C₄	—	8	1	no	—
636	C₄	—	8	1	no	—
637	C₄	—	8	2	no	—
638	C₄	C₁₃×#394	1	4	yes	—
639	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
640	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
641	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
642	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
643	C₂	—	2	4	no	—
644	C₂	—	4	4	no	—
645	C₂	—	8	2	no	—
646	C₂	C₂×C₁₃×#394	1	1	yes	characteristic
647	C₂	C₁₃×#3002	1	2	yes	—
648	C₂	C₁₃×#3050	1	1	yes	characteristic
649	C₂	C₁₃×#3054	1	1	yes	characteristic
650	C₂	C₁₃×#3091	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂×C₁₃×#525	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₂⁴×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#427	C₂	semidirect
3. C₂×C₁₃×#416	C₂	semidirect
4. C₂×C₁₃×#416	C₂	semidirect
5. C₂²×C₁₃×C₂²⋊C₈	C₂	semidirect
6. C₁₃×#2280	C₂	semidirect
7. C₁₃×#2036	C₂	semidirect
8. C₁₃×#2035	C₂	semidirect
9. C₁₃×#2034	C₂	semidirect
10. C₁₃×#2033	C₂	semidirect
11. C₁₃×#1735	C₂	semidirect
27. C₂×C₁₃×#107	C₂²	semidirect
28. C₂×C₁₃×#106	C₂²	semidirect
31. C₂×C₁₃×#103	C₂²	semidirect
32. C₂×C₁₃×#103	C₂²	semidirect
33. C₂×C₁₃×#103	C₂²	semidirect
34. C₂×C₁₃×#102	C₂²	semidirect
35. C₂×C₁₃×#102	C₂²	semidirect
36. C₂×C₁₃×#102	C₂²	semidirect
45. C₁₃×#340	C₂²	semidirect
46. C₁₃×#340	C₂²	semidirect
74. C₂²×C₈×C₁₃	D₄	semidirect
118. #23479	C₁₃	direct (N × H)
213. C₂×#427	C₂×C₁₃	semidirect
214. C₂×#416	C₂×C₁₃	semidirect
215. C₂×#416	C₂×C₁₃	semidirect
216. C₂²×C₂²⋊C₈	C₂×C₁₃	semidirect
217. #2280	C₂×C₁₃	semidirect
218. #2036	C₂×C₁₃	semidirect
219. #2035	C₂×C₁₃	semidirect
220. #2034	C₂×C₁₃	semidirect
221. #2033	C₂×C₁₃	semidirect
222. #1735	C₂×C₁₃	semidirect
310. C₂×#107	C₂²×C₁₃	semidirect
311. C₂×#106	C₂²×C₁₃	semidirect
314. C₂×#103	C₂²×C₁₃	semidirect
315. C₂×#103	C₂²×C₁₃	semidirect
316. C₂×#103	C₂²×C₁₃	semidirect
317. C₂×#102	C₂²×C₁₃	semidirect
318. C₂×#102	C₂²×C₁₃	semidirect
319. C₂×#102	C₂²×C₁₃	semidirect
328. #340	C₂²×C₁₃	semidirect
329. #340	C₂²×C₁₃	semidirect
391. C₂²×C₈	D₄×C₁₃	semidirect
536. C₁₃	#23479	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×#525	2
C₂×C₁₃×#427	2
C₂×C₁₃×#416	2
C₂²×C₁₃×C₂²⋊C₈	2
C₁₃×#2280	2
C₁₃×#2036	2
C₁₃×#2035	2
C₁₃×#2034	2
C₁₃×#2033	2
C₁₃×#1735	2
#23479	13

Subgroups — C13×#23479 #15709818

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23479 #15709818