Subgroups — C₁₃×#32958 #15719297

Order 3328.

1364 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1865	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1862	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1854	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1788	C₂	1	2	yes	maximal
12	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
15	C₄×C₁₃×#41	—	2	4	no	—
16	C₄×C₁₃×#41	—	2	4	no	—
17	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃	—	2	1	no	—
20	C₂×C₄×D₄×C₁₃	—	2	1	no	—
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#117	—	2	1	no	—
24	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₁₃	—	2	1	no	—
26	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#477	—	2	4	no	—
28	C₁₃×#476	—	2	4	no	—
29	C₂×C₁₃×#107	C₂²	1	2	yes	—
30	C₂×C₁₃×#106	C₂²	1	2	yes	—
31	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#103	C₂²	1	2	yes	—
34	C₂×C₁₃×#103	C₂²	1	2	yes	—
35	C₂×C₁₃×#102	C₂²	1	2	yes	—
36	C₂×C₁₃×#102	C₂²	1	2	yes	—
37	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
38	C₁₃×#391	—	2	1	no	—
39	C₁₃×#389	—	2	1	no	—
40	C₁₃×#389	C₂²	1	2	yes	—
41	C₁₃×#384	C₂²	1	1	yes	characteristic
42	C₁₃×#380	—	2	1	no	—
43	C₁₃×#380	C₂²	1	2	yes	—
44	C₁₃×#340	C₂²	1	2	yes	—
45	C₁₃×#340	C₂²	1	2	yes	—
46	C₁₃×#336	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	—	2	2	no	—
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	Q₈	1	4	yes	complemented
53	C₂²×Q₈×C₁₃	—	2	1	no	—
54	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×D₄×C₁₃	—	2	1	no	—
56	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	—	2	1	no	—
58	C₂³×C₄×C₁₃	—	2	1	no	—
59	C₂³×C₄×C₁₃	—	2	1	no	—
60	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
64	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
65	C₁₃×C₄⋊Q₈	—	2	2	no	—
66	C₁₃×C₄⋊Q₈	—	2	2	no	—
67	C₁₃×C₂²⋊Q₈	—	4	4	no	—
68	C₄×Q₈×C₁₃	—	2	2	no	—
69	C₄×Q₈×C₁₃	—	2	2	no	—
70	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×Q₈×C₁₃	D₄	1	4	yes	—
72	C₄×D₄×C₁₃	—	2	8	no	—
73	C₄×D₄×C₁₃	—	2	8	no	—
74	C₄×D₄×C₁₃	—	2	2	no	—
75	C₄×D₄×C₁₃	—	2	2	no	—
76	C₄×D₄×C₁₃	—	2	2	no	—
77	C₄×D₄×C₁₃	D₄	1	4	yes	—
78	C₁₃×#117	—	2	8	no	—
79	C₁₃×#117	—	2	2	no	—
80	C₁₃×#117	—	2	2	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
95	C₂×C₄²×C₁₃	—	2	8	no	—
96	C₂×C₄²×C₁₃	—	2	1	no	—
97	C₂×C₄²×C₁₃	—	2	1	no	—
98	C₂×C₄²×C₁₃	—	2	1	no	—
99	C₂×C₄²×C₁₃	—	2	2	no	—
100	C₂×C₄²×C₁₃	—	2	2	no	—
101	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
105	C₁₃×#107	—	2	4	no	—
106	C₁₃×#106	—	2	4	no	—
107	C₁₃×C₄⋊C₈	—	2	2	no	—
108	C₁₃×C₄⋊C₈	—	2	2	no	—
109	C₁₃×#103	—	2	4	no	—
110	C₁₃×#103	—	2	4	no	—
111	C₁₃×#102	—	2	4	no	—
112	C₁₃×#102	—	2	4	no	—
113	C₁₃×C₂²⋊C₈	—	2	4	no	—
114	C₁₃×#95	—	2	2	no	—
115	C₁₃×#95	—	2	2	no	—
116	#32958	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂⁴×C₁₃	—	2	1	no	—
118	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₁₃×#41	—	2	8	no	—
120	C₁₃×#41	—	2	8	no	—
121	C₁₃×#41	—	2	8	no	—
122	C₁₃×#41	—	2	8	no	—
123	C₂×Q₈×C₁₃	—	2	1	no	—
124	C₂×Q₈×C₁₃	—	2	1	no	—
125	C₂×Q₈×C₁₃	—	2	1	no	—
126	C₂×Q₈×C₁₃	—	4	2	no	—
127	C₂×Q₈×C₁₃	—	4	2	no	—
128	C₂×Q₈×C₁₃	—	4	2	no	—
129	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
130	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
131	C₂×Q₈×C₁₃	#41	1	2	yes	—
132	C₂×D₄×C₁₃	—	2	4	no	—
133	C₂×D₄×C₁₃	—	2	4	no	—
134	C₂×D₄×C₁₃	—	2	4	no	—
135	C₂×D₄×C₁₃	—	2	1	no	—
136	C₂×D₄×C₁₃	—	2	1	no	—
137	C₂×D₄×C₁₃	—	2	1	no	—
138	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
139	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
140	C₂×D₄×C₁₃	#41	1	2	yes	—
141	C₂²×C₄×C₁₃	—	2	4	no	—
142	C₂²×C₄×C₁₃	—	2	4	no	—
143	C₂²×C₄×C₁₃	—	2	1	no	—
144	C₂²×C₄×C₁₃	—	2	4	no	—
145	C₂²×C₄×C₁₃	—	2	1	no	—
146	C₂²×C₄×C₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂²×C₄×C₁₃	—	2	4	no	—
150	C₂²×C₄×C₁₃	—	2	1	no	—
151	C₂²×C₄×C₁₃	—	2	1	no	—
152	C₂²×C₄×C₁₃	—	2	2	no	—
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	—	2	4	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	2	no	—
159	C₂²×C₄×C₁₃	—	2	2	no	—
160	C₂²×C₄×C₁₃	—	4	1	no	—
161	C₂²×C₄×C₁₃	—	4	2	no	—
162	C₂²×C₄×C₁₃	—	4	2	no	—
163	C₂²×C₄×C₁₃	—	4	2	no	—
164	C₂²×C₄×C₁₃	—	4	2	no	—
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
171	C₂²×C₄×C₁₃	#41	1	2	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₂×C₈×C₁₃	—	2	2	no	—
174	C₂×C₈×C₁₃	—	2	2	no	—
175	C₂×C₈×C₁₃	—	2	2	no	—
176	C₂×C₈×C₁₃	—	2	2	no	—
177	C₂×C₈×C₁₃	—	2	2	no	—
178	C₂×C₈×C₁₃	—	2	2	no	—
179	C₁₃×C₄⋊C₄	—	2	4	no	—
180	C₁₃×C₄⋊C₄	—	2	4	no	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₁₃×C₄⋊C₄	—	2	2	no	—
184	C₁₃×C₄⋊C₄	—	2	2	no	—
185	C₁₃×C₄⋊C₄	—	2	2	no	—
186	C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₁₃×C₄⋊C₄	—	4	2	no	—
188	C₁₃×C₄⋊C₄	—	4	2	no	—
189	C₁₃×C₄⋊C₄	—	4	2	no	—
190	C₁₃×C₄⋊C₄	—	4	4	no	—
191	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
192	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
193	C₁₃×C₂²⋊C₄	—	2	4	no	—
194	C₁₃×C₂²⋊C₄	—	2	4	no	—
195	C₁₃×C₂²⋊C₄	—	2	4	no	—
196	C₁₃×C₂²⋊C₄	—	4	4	no	—
197	C₄²×C₁₃	—	2	4	no	—
198	C₄²×C₁₃	—	2	4	no	—
199	C₄²×C₁₃	—	2	2	no	—
200	C₄²×C₁₃	—	2	4	no	—
201	C₄²×C₁₃	—	2	2	no	—
202	C₄²×C₁₃	—	2	1	no	—
203	C₄²×C₁₃	—	2	1	no	—
204	C₄²×C₁₃	C₂×D₄	1	2	yes	—
205	C₄²×C₁₃	C₂×D₄	1	2	yes	—
206	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic
207	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
208	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#2857	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#1865	C₂×C₁₃	1	2	yes	complemented
211	#1862	C₂×C₁₃	1	2	yes	complemented
212	#1854	C₂×C₁₃	1	2	yes	complemented
213	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#1802	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1797	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1788	C₂×C₁₃	1	2	yes	—
217	C₂³×C₁₃	—	2	1	no	—
218	C₂³×C₁₃	—	2	2	no	—
219	C₂³×C₁₃	—	2	2	no	—
220	C₂³×C₁₃	—	2	1	no	—
221	C₂³×C₁₃	—	2	2	no	—
222	C₂³×C₁₃	—	2	1	no	—
223	C₂³×C₁₃	—	2	1	no	—
224	C₂³×C₁₃	—	2	1	no	—
225	C₂³×C₁₃	—	2	1	no	—
226	C₂³×C₁₃	—	4	1	no	—
227	C₂³×C₁₃	—	4	1	no	—
228	C₂³×C₁₃	—	4	1	no	—
229	C₂³×C₁₃	—	4	1	no	—
230	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
231	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
232	Q₈×C₁₃	—	2	2	no	—
233	Q₈×C₁₃	—	2	2	no	—
234	Q₈×C₁₃	—	2	2	no	—
235	Q₈×C₁₃	—	8	4	no	—
236	Q₈×C₁₃	C₂²⋊Q₈	1	4	yes	complemented
237	D₄×C₁₃	—	2	16	no	—
238	D₄×C₁₃	—	2	2	no	—
239	D₄×C₁₃	—	2	2	no	—
240	D₄×C₁₃	—	2	2	no	—
241	D₄×C₁₃	C₂²⋊Q₈	1	4	yes	complemented
242	C₂×C₄×C₁₃	—	2	16	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	1	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	2	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	4	4	no	—
262	C₂×C₄×C₁₃	—	4	8	no	—
263	C₂×C₄×C₁₃	—	4	1	no	—
264	C₂×C₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	1	no	—
267	C₂×C₄×C₁₃	—	4	4	no	—
268	C₂×C₄×C₁₃	—	4	8	no	—
269	C₂×C₄×C₁₃	—	4	2	no	—
270	C₂×C₄×C₁₃	—	4	2	no	—
271	C₂×C₄×C₁₃	—	4	2	no	—
272	C₂×C₄×C₁₃	—	4	2	no	—
273	C₂×C₄×C₁₃	—	4	2	no	—
274	C₂×C₄×C₁₃	—	4	2	no	—
275	C₂×C₄×C₁₃	#120	1	2	yes	—
276	C₂×C₄×C₁₃	#120	1	2	yes	—
277	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
278	C₂×C₄×C₁₃	#135	1	2	yes	—
279	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
280	C₂×C₄×C₁₃	#137	1	2	yes	—
281	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
284	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
285	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
286	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
287	C₈×C₁₃	—	4	2	no	—
288	C₈×C₁₃	—	4	2	no	—
289	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×C₂²⋊Q₈	—	2	1	no	—
292	C₄×#41	—	2	4	no	—
293	C₄×#41	—	2	4	no	—
294	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×C₄×D₄	—	2	1	no	—
297	C₂×C₄×D₄	—	2	1	no	—
298	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×#117	—	2	1	no	—
301	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
302	C₂²×C₄²	—	2	1	no	—
303	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
304	#477	—	2	4	no	—
305	#476	—	2	4	no	—
306	C₂×#107	C₂²×C₁₃	1	2	yes	—
307	C₂×#106	C₂²×C₁₃	1	2	yes	—
308	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×#103	C₂²×C₁₃	1	2	yes	—
311	C₂×#103	C₂²×C₁₃	1	2	yes	—
312	C₂×#102	C₂²×C₁₃	1	2	yes	—
313	C₂×#102	C₂²×C₁₃	1	2	yes	—
314	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
315	#391	—	2	1	no	—
316	#389	—	2	1	no	—
317	#389	C₂²×C₁₃	1	2	yes	—
318	#384	C₂²×C₁₃	1	1	yes	characteristic
319	#380	—	2	1	no	—
320	#380	C₂²×C₁₃	1	2	yes	—
321	#340	C₂²×C₁₃	1	2	yes	—
322	#340	C₂²×C₁₃	1	2	yes	—
323	#336	C₂²×C₁₃	1	2	yes	—
324	C₂²×C₁₃	—	2	2	no	—
325	C₂²×C₁₃	—	2	2	no	—
326	C₂²×C₁₃	—	2	2	no	—
327	C₂²×C₁₃	—	2	4	no	—
328	C₂²×C₁₃	—	4	2	no	—
329	C₂²×C₁₃	—	4	2	no	—
330	C₂²×C₁₃	—	4	1	no	—
331	C₂²×C₁₃	—	4	2	no	—
332	C₂²×C₁₃	—	4	1	no	—
333	C₂²×C₁₃	—	4	2	no	—
334	C₂²×C₁₃	—	4	1	no	—
335	C₂²×C₁₃	—	4	2	no	—
336	C₂²×C₁₃	—	4	1	no	—
337	C₂²×C₁₃	—	4	2	no	—
338	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
339	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
340	C₂²×C₁₃	#525	1	1	yes	characteristic
341	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
342	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
343	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
344	C₂²×C₁₃	#575	1	1	yes	characteristic
345	C₄×C₁₃	—	2	2	no	—
346	C₄×C₁₃	—	2	4	no	—
347	C₄×C₁₃	—	2	2	no	—
348	C₄×C₁₃	—	2	2	no	—
349	C₄×C₁₃	—	4	1	no	—
350	C₄×C₁₃	—	4	2	no	—
351	C₄×C₁₃	—	4	2	no	—
352	C₄×C₁₃	—	8	2	no	—
353	C₄×C₁₃	—	8	2	no	—
354	C₄×C₁₃	#452	1	4	yes	—
355	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
356	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
357	C₄×C₁₃	#525	1	1	yes	characteristic
358	C₄×C₁₃	#525	1	1	yes	characteristic
359	C₂×#41	—	2	2	no	—
360	C₂×#41	—	2	2	no	—
361	C₂×#41	—	2	2	no	—
362	C₂×#41	—	2	2	no	—
363	C₂×#41	—	2	2	no	—
364	C₂×#41	Q₈×C₁₃	1	4	yes	complemented
365	C₂²×Q₈	—	2	1	no	—
366	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
367	C₂²×D₄	—	2	1	no	—
368	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
369	C₂³×C₄	—	2	1	no	—
370	C₂³×C₄	—	2	1	no	—
371	C₂³×C₄	—	2	1	no	—
372	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
373	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
374	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
375	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
376	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
377	C₄⋊Q₈	—	2	2	no	—
378	C₄⋊Q₈	—	2	2	no	—
379	C₂²⋊Q₈	—	4	4	no	—
380	C₄×Q₈	—	2	2	no	—
381	C₄×Q₈	—	2	2	no	—
382	C₄×Q₈	—	2	2	no	—
383	C₄×Q₈	D₄×C₁₃	1	4	yes	—
384	C₄×D₄	—	2	8	no	—
385	C₄×D₄	—	2	8	no	—
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	—	2	2	no	—
389	C₄×D₄	D₄×C₁₃	1	4	yes	—
390	#117	—	2	8	no	—
391	#117	—	2	2	no	—
392	#117	—	2	2	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	2	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
401	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	2	no	—
407	C₂×C₄²	—	2	8	no	—
408	C₂×C₄²	—	2	1	no	—
409	C₂×C₄²	—	2	1	no	—
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	—	2	2	no	—
412	C₂×C₄²	—	2	2	no	—
413	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
414	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
415	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
416	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
417	#107	—	2	4	no	—
418	#106	—	2	4	no	—
419	C₄⋊C₈	—	2	2	no	—
420	C₄⋊C₈	—	2	2	no	—
421	#103	—	2	4	no	—
422	#103	—	2	4	no	—
423	#102	—	2	4	no	—
424	#102	—	2	4	no	—
425	C₂²⋊C₈	—	2	4	no	—
426	#95	—	2	2	no	—
427	#95	—	2	2	no	—
428	C₂×C₁₃	—	4	2	no	—
429	C₂×C₁₃	—	4	4	no	—
430	C₂×C₁₃	#2848	1	1	yes	characteristic
431	C₂×C₁₃	C₂×#452	1	1	yes	characteristic
432	C₂×C₁₃	#3006	1	1	yes	characteristic
433	C₂×C₁₃	#3076	1	1	yes	characteristic
434	C₂×C₁₃	#3079	1	1	yes	characteristic
435	C₂×C₁₃	#3106	1	1	yes	characteristic
436	C₂×C₁₃	#3116	1	1	yes	characteristic
437	C₂⁴	—	2	1	no	—
438	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
439	#41	—	2	8	no	—
440	#41	—	2	8	no	—
441	#41	—	2	8	no	—
442	#41	—	2	8	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	4	2	no	—
447	C₂×Q₈	—	4	2	no	—
448	C₂×Q₈	—	4	2	no	—
449	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
450	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
451	C₂×Q₈	C₁₃×#41	1	2	yes	—
452	C₂×D₄	—	2	4	no	—
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
459	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
460	C₂×D₄	C₁₃×#41	1	2	yes	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	4	1	no	—
481	C₂²×C₄	—	4	2	no	—
482	C₂²×C₄	—	4	2	no	—
483	C₂²×C₄	—	4	2	no	—
484	C₂²×C₄	—	4	2	no	—
485	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
488	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
489	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
490	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
491	C₂²×C₄	C₁₃×#41	1	2	yes	—
492	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	2	2	no	—
496	C₂×C₈	—	2	2	no	—
497	C₂×C₈	—	2	2	no	—
498	C₂×C₈	—	2	2	no	—
499	C₄⋊C₄	—	2	4	no	—
500	C₄⋊C₄	—	2	4	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	4	2	no	—
508	C₄⋊C₄	—	4	2	no	—
509	C₄⋊C₄	—	4	2	no	—
510	C₄⋊C₄	—	4	4	no	—
511	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
512	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
513	C₂²⋊C₄	—	2	4	no	—
514	C₂²⋊C₄	—	2	4	no	—
515	C₂²⋊C₄	—	2	4	no	—
516	C₂²⋊C₄	—	4	4	no	—
517	C₄²	—	2	4	no	—
518	C₄²	—	2	4	no	—
519	C₄²	—	2	2	no	—
520	C₄²	—	2	4	no	—
521	C₄²	—	2	2	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	2	1	no	—
524	C₄²	C₂×D₄×C₁₃	1	2	yes	—
525	C₄²	C₂×D₄×C₁₃	1	2	yes	—
526	C₁₃	#32958	1	1	yes	characteristic, direct product factor, Sylow
527	C₂³	—	2	1	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	2	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	2	1	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	4	1	no	—
538	C₂³	—	4	1	no	—
539	C₂³	—	4	1	no	—
540	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
541	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
542	Q₈	—	2	2	no	—
543	Q₈	—	2	2	no	—
544	Q₈	—	2	2	no	—
545	Q₈	—	8	4	no	—
546	Q₈	C₁₃×C₂²⋊Q₈	1	4	yes	complemented
547	D₄	—	2	16	no	—
548	D₄	—	2	2	no	—
549	D₄	—	2	2	no	—
550	D₄	—	2	2	no	—
551	D₄	C₁₃×C₂²⋊Q₈	1	4	yes	complemented
552	C₂×C₄	—	2	16	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	4	4	no	—
572	C₂×C₄	—	4	8	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	4	no	—
578	C₂×C₄	—	4	8	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	C₁₃×#120	1	2	yes	—
586	C₂×C₄	C₁₃×#120	1	2	yes	—
587	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
588	C₂×C₄	C₁₃×#135	1	2	yes	—
589	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
590	C₂×C₄	C₁₃×#137	1	2	yes	—
591	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
592	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
593	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
594	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
595	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
596	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
597	C₈	—	4	2	no	—
598	C₈	—	4	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	4	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	4	2	no	—
613	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
614	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
615	C₂²	C₁₃×#525	1	1	yes	characteristic
616	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
617	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
618	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
619	C₂²	C₁₃×#575	1	1	yes	characteristic
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	4	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	2	no	—
627	C₄	—	8	2	no	—
628	C₄	—	8	2	no	—
629	C₄	C₁₃×#452	1	4	yes	—
630	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
631	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
632	C₄	C₁₃×#525	1	1	yes	characteristic
633	C₄	C₁₃×#525	1	1	yes	characteristic
634	C₂	—	4	2	no	—
635	C₂	—	4	4	no	—
636	C₂	C₁₃×#2848	1	1	yes	characteristic
637	C₂	C₂×C₁₃×#452	1	1	yes	characteristic
638	C₂	C₁₃×#3006	1	1	yes	characteristic
639	C₂	C₁₃×#3076	1	1	yes	characteristic
640	C₂	C₁₃×#3079	1	1	yes	characteristic
641	C₂	C₁₃×#3106	1	1	yes	characteristic
642	C₂	C₁₃×#3116	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
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
3. C₂×C₁₃×#476	C₂	semidirect
4. C₁₃×#2857	C₂	semidirect
5. C₁₃×#1865	C₂	semidirect
6. C₁₃×#1862	C₂	semidirect
7. C₁₃×#1854	C₂	semidirect
8. C₁₃×#1803	C₂	semidirect
9. C₁₃×#1802	C₂	semidirect
10. C₁₃×#1797	C₂	semidirect
52. C₂×C₁₃×#41	Q₈	semidirect
116. #32958	C₁₃	direct (N × H)
207. C₂×#477	C₂×C₁₃	semidirect
208. C₂×#476	C₂×C₁₃	semidirect
209. #2857	C₂×C₁₃	semidirect
210. #1865	C₂×C₁₃	semidirect
211. #1862	C₂×C₁₃	semidirect
212. #1854	C₂×C₁₃	semidirect
213. #1803	C₂×C₁₃	semidirect
214. #1802	C₂×C₁₃	semidirect
215. #1797	C₂×C₁₃	semidirect
236. Q₈×C₁₃	C₂²⋊Q₈	semidirect
241. D₄×C₁₃	C₂²⋊Q₈	semidirect
364. C₂×#41	Q₈×C₁₃	semidirect
526. C₁₃	#32958	direct (N × H)
546. Q₈	C₁₃×C₂²⋊Q₈	semidirect
551. D₄	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×C₄×C₁₃×#41	2
C₂×C₁₃×#477	2
C₂×C₁₃×#476	2
C₁₃×#2857	2
C₁₃×#1865	2
C₁₃×#1862	2
C₁₃×#1854	2
C₁₃×#1803	2
C₁₃×#1802	2
C₁₃×#1797	2
C₁₃×#1788	2
#32958	13

Subgroups — C13×#32958 #15719297

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32958 #15719297