Subgroups — C₁₃×#22432 #15708771

Order 3328.

1582 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#417	C₂	1	2	yes	maximal, complemented
4	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1895	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1874	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1788	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	2	yes	—
13	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
14	C₁₃×#550	—	2	4	no	—
15	C₁₃×#550	C₄	1	8	yes	complemented
16	C₂×C₁₃×#127	—	2	1	no	—
17	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#121	—	2	2	no	—
19	C₂×C₁₃×#121	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	—	2	1	no	—
22	C₂×C₄×D₄×C₁₃	—	2	1	no	—
23	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
25	C₁₃×#436	—	2	4	no	—
26	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₁₃×#417	—	2	8	no	—
28	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#103	C₂²	1	2	yes	—
30	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	C₂²	1	2	yes	—
32	C₂×C₁₃×#102	C₂²	1	2	yes	—
33	C₂×C₁₃×#102	C₂²	1	2	yes	—
34	C₂×C₁₃×#102	C₂²	1	2	yes	—
35	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
36	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#389	—	2	1	no	—
38	C₁₃×#385	—	2	2	no	—
39	C₁₃×#384	C₂²	1	1	yes	characteristic
40	C₁₃×#380	C₂²	1	2	yes	—
41	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₁₃×#340	C₂²	1	1	yes	characteristic
43	C₁₃×#340	C₂²	1	1	yes	characteristic
44	C₁₃×#340	C₂²	1	2	yes	—
45	C₂×C₁₃×#41	—	2	4	no	—
46	C₂×C₁₃×#41	—	2	4	no	—
47	C₂×C₁₃×#41	—	2	4	no	—
48	C₂×C₁₃×#41	—	4	2	no	—
49	C₂×C₁₃×#41	—	4	2	no	—
50	C₂×C₁₃×#41	C₂×C₄	1	8	yes	complemented
51	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₃	—	2	2	no	—
53	C₂²×D₄×C₁₃	—	2	2	no	—
54	C₂²×D₄×C₁₃	—	2	1	no	—
55	C₂²×D₄×C₁₃	—	2	1	no	—
56	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
57	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₃	—	2	2	no	—
59	C₂³×C₄×C₁₃	—	2	2	no	—
60	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
61	C₂×C₁₃×M₁₆	—	2	4	no	—
62	C₂×C₁₃×M₁₆	—	2	4	no	—
63	C₂×C₁₃×M₁₆	—	4	2	no	—
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
66	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₁₃×#127	—	2	8	no	—
68	C₁₃×#127	—	2	2	no	—
69	C₁₃×#127	C₂×C₄	1	4	yes	complemented
70	C₁₃×#121	—	2	4	no	—
71	C₁₃×#121	—	2	16	no	—
72	C₁₃×#121	C₂×C₄	1	8	yes	complemented
73	C₄×Q₈×C₁₃	—	2	2	no	—
74	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	complemented
75	C₄×D₄×C₁₃	—	2	8	no	—
76	C₄×D₄×C₁₃	—	4	4	no	—
77	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
78	C₄×D₄×C₁₃	D₄	1	4	yes	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
85	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
92	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
93	C₂×C₄²×C₁₃	—	2	1	no	—
94	C₂×C₄²×C₁₃	—	2	1	no	—
95	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
96	C₁₃×C₄⋊C₈	—	2	2	no	—
97	C₁₃×#103	—	2	4	no	—
98	C₁₃×#103	—	2	2	no	—
99	C₁₃×#103	D₄	1	4	yes	complemented
100	C₁₃×#102	—	2	4	no	—
101	C₁₃×#102	—	2	4	no	—
102	C₁₃×#102	—	4	2	no	—
103	C₁₃×#102	—	4	2	no	—
104	C₁₃×C₂²⋊C₈	—	2	4	no	—
105	C₄×C₈×C₁₃	—	2	2	no	—
106	C₁₃×#95	—	2	1	no	—
107	C₁₃×#95	—	2	2	no	—
108	#22432	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂⁴×C₁₃	—	2	2	no	—
110	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
111	C₁₃×#41	—	2	16	no	—
112	C₁₃×#41	—	4	8	no	—
113	C₁₃×#41	—	4	8	no	—
114	C₁₃×#41	—	4	8	no	—
115	C₂×Q₈×C₁₃	—	2	1	no	—
116	C₂×Q₈×C₁₃	—	2	1	no	—
117	C₂×Q₈×C₁₃	—	2	1	no	—
118	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
119	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
120	C₂×Q₈×C₁₃	#41	1	2	yes	—
121	C₂×D₄×C₁₃	—	2	8	no	—
122	C₂×D₄×C₁₃	—	2	8	no	—
123	C₂×D₄×C₁₃	—	2	4	no	—
124	C₂×D₄×C₁₃	—	2	4	no	—
125	C₂×D₄×C₁₃	—	2	2	no	—
126	C₂×D₄×C₁₃	—	2	2	no	—
127	C₂×D₄×C₁₃	—	2	2	no	—
128	C₂×D₄×C₁₃	—	2	2	no	—
129	C₂×D₄×C₁₃	—	2	2	no	—
130	C₂×D₄×C₁₃	—	2	2	no	—
131	C₂×D₄×C₁₃	—	2	2	no	—
132	C₂×D₄×C₁₃	—	4	4	no	—
133	C₂×D₄×C₁₃	—	4	4	no	—
134	C₂×D₄×C₁₃	—	4	2	no	—
135	C₂×D₄×C₁₃	—	4	2	no	—
136	C₂×D₄×C₁₃	—	8	1	no	—
137	C₂×D₄×C₁₃	—	8	1	no	—
138	C₂×D₄×C₁₃	—	8	2	no	—
139	C₂×D₄×C₁₃	—	8	2	no	—
140	C₂×D₄×C₁₃	C₂²⋊C₄	1	4	yes	—
141	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	—	2	2	no	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	—	2	2	no	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂²×C₄×C₁₃	—	2	8	no	—
150	C₂²×C₄×C₁₃	—	2	1	no	—
151	C₂²×C₄×C₁₃	—	2	2	no	—
152	C₂²×C₄×C₁₃	—	4	4	no	—
153	C₂²×C₄×C₁₃	—	4	4	no	—
154	C₂²×C₄×C₁₃	—	4	4	no	—
155	C₂²×C₄×C₁₃	—	4	4	no	—
156	C₂²×C₄×C₁₃	—	8	2	no	—
157	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₁₃×M₁₆	—	4	8	no	—
164	C₂×C₈×C₁₃	—	2	1	no	—
165	C₂×C₈×C₁₃	—	2	1	no	—
166	C₂×C₈×C₁₃	—	2	1	no	—
167	C₂×C₈×C₁₃	—	2	2	no	—
168	C₂×C₈×C₁₃	—	2	2	no	—
169	C₂×C₈×C₁₃	—	2	1	no	—
170	C₂×C₈×C₁₃	—	2	1	no	—
171	C₂×C₈×C₁₃	—	2	2	no	—
172	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
173	C₁₃×C₄⋊C₄	—	2	4	no	—
174	C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₁₃×C₄⋊C₄	—	2	2	no	—
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	2	no	—
180	C₁₃×C₄⋊C₄	—	4	4	no	—
181	C₁₃×C₄⋊C₄	—	4	2	no	—
182	C₁₃×C₄⋊C₄	—	8	1	no	—
183	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
184	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
185	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
186	C₁₃×C₂²⋊C₄	—	2	8	no	—
187	C₁₃×C₂²⋊C₄	—	4	4	no	—
188	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	8	yes	—
189	C₄²×C₁₃	—	2	4	no	—
190	C₄²×C₁₃	—	4	2	no	—
191	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
192	C₄²×C₁₃	C₂×D₄	1	2	yes	—
193	C₂×#550	C₂×C₁₃	1	1	yes	characteristic
194	C₂×#436	C₂×C₁₃	1	1	yes	characteristic, complemented
195	C₂×#417	C₂×C₁₃	1	2	yes	complemented
196	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
197	#1982	C₂×C₁₃	1	1	yes	characteristic, complemented
198	#1957	C₂×C₁₃	1	1	yes	characteristic, complemented
199	#1895	C₂×C₁₃	1	2	yes	complemented
200	#1874	C₂×C₁₃	1	2	yes	complemented
201	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
202	#1788	C₂×C₁₃	1	2	yes	complemented
203	C₄×#103	C₂×C₁₃	1	1	yes	characteristic, complemented
204	C₂³×C₁₃	—	2	2	no	—
205	C₂³×C₁₃	—	2	2	no	—
206	C₂³×C₁₃	—	2	2	no	—
207	C₂³×C₁₃	—	2	2	no	—
208	C₂³×C₁₃	—	2	2	no	—
209	C₂³×C₁₃	—	2	2	no	—
210	C₂³×C₁₃	—	2	4	no	—
211	C₂³×C₁₃	—	4	2	no	—
212	C₂³×C₁₃	—	4	2	no	—
213	C₂³×C₁₃	—	4	2	no	—
214	C₂³×C₁₃	—	4	2	no	—
215	C₂³×C₁₃	—	4	2	no	—
216	C₂³×C₁₃	—	4	2	no	—
217	C₂³×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
218	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
219	Q₈×C₁₃	—	2	2	no	—
220	Q₈×C₁₃	—	2	2	no	—
221	Q₈×C₁₃	—	2	2	no	—
222	Q₈×C₁₃	C₄×D₄	1	4	yes	complemented
223	D₄×C₁₃	—	2	4	no	—
224	D₄×C₁₃	—	2	4	no	—
225	D₄×C₁₃	—	2	8	no	—
226	D₄×C₁₃	—	4	16	no	—
227	D₄×C₁₃	—	4	2	no	—
228	D₄×C₁₃	—	4	2	no	—
229	D₄×C₁₃	—	4	8	no	—
230	D₄×C₁₃	—	8	4	no	—
231	D₄×C₁₃	—	8	8	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	2	1	no	—
239	C₂×C₄×C₁₃	—	2	4	no	—
240	C₂×C₄×C₁₃	—	2	4	no	—
241	C₂×C₄×C₁₃	—	2	4	no	—
242	C₂×C₄×C₁₃	—	2	4	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	4	16	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	—	4	1	no	—
250	C₂×C₄×C₁₃	—	4	2	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	2	no	—
254	C₂×C₄×C₁₃	—	4	2	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	8	8	no	—
257	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
258	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
259	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
260	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
261	C₂×C₄×C₁₃	#137	1	2	yes	—
262	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
266	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
267	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
268	C₈×C₁₃	—	2	2	no	—
269	C₈×C₁₃	—	4	2	no	—
270	C₈×C₁₃	—	4	1	no	—
271	C₂²×#41	C₂²×C₁₃	1	2	yes	—
272	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
273	#550	—	2	4	no	—
274	#550	C₄×C₁₃	1	8	yes	complemented
275	C₂×#127	—	2	1	no	—
276	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×#121	—	2	2	no	—
278	C₂×#121	C₂²×C₁₃	1	2	yes	—
279	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×C₄×D₄	—	2	1	no	—
281	C₂×C₄×D₄	—	2	1	no	—
282	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
283	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
284	#436	—	2	4	no	—
285	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
286	#417	—	2	8	no	—
287	C₂×#103	C₂²×C₁₃	1	2	yes	—
288	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×#102	C₂²×C₁₃	1	2	yes	—
291	C₂×#102	C₂²×C₁₃	1	2	yes	—
292	C₂×#102	C₂²×C₁₃	1	2	yes	—
293	C₂×#102	C₂²×C₁₃	1	2	yes	—
294	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
295	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
296	#389	—	2	1	no	—
297	#385	—	2	2	no	—
298	#384	C₂²×C₁₃	1	1	yes	characteristic
299	#380	C₂²×C₁₃	1	2	yes	—
300	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
301	#340	C₂²×C₁₃	1	2	yes	—
302	#340	C₂²×C₁₃	1	1	yes	characteristic
303	#340	C₂²×C₁₃	1	1	yes	characteristic
304	C₂²×C₁₃	—	2	4	no	—
305	C₂²×C₁₃	—	2	4	no	—
306	C₂²×C₁₃	—	2	4	no	—
307	C₂²×C₁₃	—	4	2	no	—
308	C₂²×C₁₃	—	4	2	no	—
309	C₂²×C₁₃	—	4	2	no	—
310	C₂²×C₁₃	—	4	2	no	—
311	C₂²×C₁₃	—	4	4	no	—
312	C₂²×C₁₃	—	4	4	no	—
313	C₂²×C₁₃	—	4	4	no	—
314	C₂²×C₁₃	—	8	2	no	—
315	C₂²×C₁₃	—	8	2	no	—
316	C₂²×C₁₃	—	8	2	no	—
317	C₂²×C₁₃	—	8	2	no	—
318	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
319	C₂²×C₁₃	D₄²	1	1	yes	characteristic
320	C₂²×C₁₃	#546	1	1	yes	characteristic
321	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
322	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
323	C₂²×C₁₃	#576	1	1	yes	characteristic
324	C₂²×C₁₃	#577	1	1	yes	characteristic
325	C₄×C₁₃	—	2	4	no	—
326	C₄×C₁₃	—	2	4	no	—
327	C₄×C₁₃	—	2	2	no	—
328	C₄×C₁₃	—	4	2	no	—
329	C₄×C₁₃	—	4	2	no	—
330	C₄×C₁₃	—	8	1	no	—
331	C₄×C₁₃	—	8	2	no	—
332	C₄×C₁₃	#417	1	4	yes	complemented
333	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
334	C₄×C₁₃	#518	1	1	yes	characteristic
335	C₄×C₁₃	D₄²	1	1	yes	characteristic
336	C₄×C₁₃	#546	1	1	yes	characteristic
337	C₂×#41	—	2	4	no	—
338	C₂×#41	—	2	4	no	—
339	C₂×#41	—	2	4	no	—
340	C₂×#41	—	4	2	no	—
341	C₂×#41	—	4	2	no	—
342	C₂×#41	C₂×C₄×C₁₃	1	8	yes	complemented
343	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
344	C₂²×D₄	—	2	2	no	—
345	C₂²×D₄	—	2	2	no	—
346	C₂²×D₄	—	2	1	no	—
347	C₂²×D₄	—	2	1	no	—
348	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
349	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
350	C₂³×C₄	—	2	2	no	—
351	C₂³×C₄	—	2	2	no	—
352	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
353	C₂×M₁₆	—	2	4	no	—
354	C₂×M₁₆	—	2	4	no	—
355	C₂×M₁₆	—	4	2	no	—
356	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
357	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
358	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
359	#127	—	2	8	no	—
360	#127	—	2	2	no	—
361	#127	C₂×C₄×C₁₃	1	4	yes	complemented
362	#121	—	2	4	no	—
363	#121	—	2	16	no	—
364	#121	C₂×C₄×C₁₃	1	8	yes	complemented
365	C₄×Q₈	—	2	2	no	—
366	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	complemented
367	C₄×D₄	—	2	8	no	—
368	C₄×D₄	—	4	4	no	—
369	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
370	C₄×D₄	D₄×C₁₃	1	4	yes	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	—	2	4	no	—
373	C₂×C₄⋊C₄	—	2	2	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	4	2	no	—
377	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
379	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
382	C₂×C₂²⋊C₄	—	2	2	no	—
383	C₂×C₂²⋊C₄	—	2	2	no	—
384	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
385	C₂×C₄²	—	2	1	no	—
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
388	C₄⋊C₈	—	2	2	no	—
389	#103	—	2	4	no	—
390	#103	—	2	2	no	—
391	#103	D₄×C₁₃	1	4	yes	complemented
392	#102	—	2	4	no	—
393	#102	—	2	4	no	—
394	#102	—	4	2	no	—
395	#102	—	4	2	no	—
396	C₂²⋊C₈	—	2	4	no	—
397	C₄×C₈	—	2	2	no	—
398	#95	—	2	1	no	—
399	#95	—	2	2	no	—
400	C₂×C₁₃	—	4	4	no	—
401	C₂×C₁₃	—	8	4	no	—
402	C₂×C₁₃	D₄×C₂²⋊C₄	1	1	yes	characteristic
403	C₂×C₁₃	C₂×#417	1	1	yes	characteristic
404	C₂×C₁₃	#2897	1	1	yes	characteristic
405	C₂×C₁₃	#3274	1	1	yes	characteristic
406	C₂×C₁₃	#3278	1	1	yes	characteristic
407	C₂×C₁₃	#3332	1	1	yes	characteristic
408	C₂×C₁₃	#3333	1	1	yes	characteristic
409	C₂⁴	—	2	2	no	—
410	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
411	#41	—	2	16	no	—
412	#41	—	4	8	no	—
413	#41	—	4	8	no	—
414	#41	—	4	8	no	—
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
419	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
420	C₂×Q₈	C₁₃×#41	1	2	yes	—
421	C₂×D₄	—	2	8	no	—
422	C₂×D₄	—	2	8	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	4	4	no	—
433	C₂×D₄	—	4	4	no	—
434	C₂×D₄	—	4	2	no	—
435	C₂×D₄	—	4	2	no	—
436	C₂×D₄	—	8	1	no	—
437	C₂×D₄	—	8	1	no	—
438	C₂×D₄	—	8	2	no	—
439	C₂×D₄	—	8	2	no	—
440	C₂×D₄	C₁₃×C₂²⋊C₄	1	4	yes	—
441	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	8	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	4	4	no	—
453	C₂²×C₄	—	4	4	no	—
454	C₂²×C₄	—	4	4	no	—
455	C₂²×C₄	—	4	4	no	—
456	C₂²×C₄	—	8	2	no	—
457	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
458	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
460	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
461	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
462	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
463	M₁₆	—	4	8	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	4	4	no	—
481	C₄⋊C₄	—	4	2	no	—
482	C₄⋊C₄	—	8	1	no	—
483	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
484	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
485	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
486	C₂²⋊C₄	—	2	8	no	—
487	C₂²⋊C₄	—	4	4	no	—
488	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	8	yes	—
489	C₄²	—	2	4	no	—
490	C₄²	—	4	2	no	—
491	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
492	C₄²	C₂×D₄×C₁₃	1	2	yes	—
493	C₁₃	#22432	1	1	yes	characteristic, direct product factor, Sylow
494	C₂³	—	2	2	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	2	4	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	4	2	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	4	2	no	—
507	C₂³	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
508	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
509	Q₈	—	2	2	no	—
510	Q₈	—	2	2	no	—
511	Q₈	—	2	2	no	—
512	Q₈	C₄×D₄×C₁₃	1	4	yes	complemented
513	D₄	—	2	8	no	—
514	D₄	—	2	4	no	—
515	D₄	—	2	4	no	—
516	D₄	—	4	16	no	—
517	D₄	—	4	8	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	2	no	—
520	D₄	—	8	4	no	—
521	D₄	—	8	8	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	4	16	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	8	8	no	—
547	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
548	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
549	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
550	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
551	C₂×C₄	C₁₃×#137	1	2	yes	—
552	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
553	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
554	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
555	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
556	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
557	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
558	C₈	—	2	2	no	—
559	C₈	—	4	2	no	—
560	C₈	—	4	1	no	—
561	C₂²	—	2	4	no	—
562	C₂²	—	2	4	no	—
563	C₂²	—	2	4	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	4	no	—
569	C₂²	—	4	4	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	8	2	no	—
572	C₂²	—	8	2	no	—
573	C₂²	—	8	2	no	—
574	C₂²	—	8	2	no	—
575	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
576	C₂²	D₄²×C₁₃	1	1	yes	characteristic
577	C₂²	C₁₃×#546	1	1	yes	characteristic
578	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
579	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
580	C₂²	C₁₃×#576	1	1	yes	characteristic
581	C₂²	C₁₃×#577	1	1	yes	characteristic
582	C₄	—	2	4	no	—
583	C₄	—	2	4	no	—
584	C₄	—	2	2	no	—
585	C₄	—	4	2	no	—
586	C₄	—	4	2	no	—
587	C₄	—	8	2	no	—
588	C₄	—	8	1	no	—
589	C₄	C₁₃×#417	1	4	yes	complemented
590	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
591	C₄	C₁₃×#518	1	1	yes	characteristic
592	C₄	D₄²×C₁₃	1	1	yes	characteristic
593	C₄	C₁₃×#546	1	1	yes	characteristic
594	C₂	—	4	4	no	—
595	C₂	—	8	4	no	—
596	C₂	D₄×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
597	C₂	C₂×C₁₃×#417	1	1	yes	characteristic
598	C₂	C₁₃×#2897	1	1	yes	characteristic
599	C₂	C₁₃×#3274	1	1	yes	characteristic
600	C₂	C₁₃×#3278	1	1	yes	characteristic
601	C₂	C₁₃×#3332	1	1	yes	characteristic
602	C₂	C₁₃×#3333	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#550	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#436	C₂	semidirect
3. C₂×C₁₃×#417	C₂	semidirect
4. D₄×C₁₃×C₄⋊C₄	C₂	semidirect
5. C₁₃×#1982	C₂	semidirect
6. C₁₃×#1957	C₂	semidirect
7. C₁₃×#1895	C₂	semidirect
8. C₁₃×#1874	C₂	semidirect
9. C₁₃×#1803	C₂	semidirect
10. C₁₃×#1788	C₂	semidirect
11. C₄×C₁₃×#103	C₂	semidirect
15. C₁₃×#550	C₄	semidirect
50. C₂×C₁₃×#41	C₂×C₄	semidirect
69. C₁₃×#127	C₂×C₄	semidirect
72. C₁₃×#121	C₂×C₄	semidirect
74. C₄×Q₈×C₁₃	C₂×C₄	semidirect
99. C₁₃×#103	D₄	semidirect
108. #22432	C₁₃	direct (N × H)
194. C₂×#436	C₂×C₁₃	semidirect
195. C₂×#417	C₂×C₁₃	semidirect
196. D₄×C₄⋊C₄	C₂×C₁₃	semidirect
197. #1982	C₂×C₁₃	semidirect
198. #1957	C₂×C₁₃	semidirect
199. #1895	C₂×C₁₃	semidirect
200. #1874	C₂×C₁₃	semidirect
201. #1803	C₂×C₁₃	semidirect
202. #1788	C₂×C₁₃	semidirect
203. C₄×#103	C₂×C₁₃	semidirect
222. Q₈×C₁₃	C₄×D₄	semidirect
274. #550	C₄×C₁₃	semidirect
332. C₄×C₁₃	#417	semidirect
342. C₂×#41	C₂×C₄×C₁₃	semidirect
361. #127	C₂×C₄×C₁₃	semidirect
364. #121	C₂×C₄×C₁₃	semidirect
366. C₄×Q₈	C₂×C₄×C₁₃	semidirect
391. #103	D₄×C₁₃	semidirect
493. C₁₃	#22432	direct (N × H)
512. Q₈	C₄×D₄×C₁₃	semidirect
589. C₄	C₁₃×#417	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#550	2
C₂×C₁₃×#436	2
C₂×C₁₃×#417	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#1982	2
C₁₃×#1957	2
C₁₃×#1895	2
C₁₃×#1874	2
C₁₃×#1803	2
C₁₃×#1788	2
C₄×C₁₃×#103	2
#22432	13

Subgroups — C13×#22432 #15708771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22432 #15708771