Subgroups — C₁₃×#17588 #15703927

Order 3328.

1086 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3444	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#382	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1518	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1517	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1512	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1504	C₂	1	4	yes	maximal, complemented
8	C₁₃×#533	C₄	1	1	yes	characteristic, complemented
9	C₁₃×#533	C₄	1	1	yes	characteristic, complemented
10	C₁₃×#533	C₂²	1	1	yes	characteristic
11	C₁₃×#532	C₄	1	1	yes	characteristic, complemented
12	C₁₃×#532	C₄	1	1	yes	characteristic, complemented
13	C₁₃×#532	C₂²	1	1	yes	characteristic
14	C₁₃×#529	—	2	1	no	—
15	C₁₃×#529	—	2	1	no	—
16	C₁₃×#529	—	2	1	no	—
17	C₁₃×#529	—	2	1	no	—
18	C₁₃×#529	C₄	1	2	yes	complemented
19	C₁₃×#529	C₂²	1	2	yes	—
20	C₁₃×#525	—	2	1	no	—
21	C₁₃×#525	—	2	1	no	—
22	C₁₃×#525	C₂²	1	2	yes	—
23	C₄×C₁₃×#41	—	2	1	no	—
24	C₄×C₁₃×#41	—	2	1	no	—
25	C₄×C₁₃×#41	C₄	1	2	yes	complemented
26	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
27	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#432	—	2	1	no	—
29	C₁₃×#432	C₂²	1	2	yes	—
30	C₁₃×#431	—	2	1	no	—
31	C₁₃×#431	C₂²	1	2	yes	—
32	C₁₃×#423	—	2	1	no	—
33	C₁₃×#407	C₂²	1	2	yes	—
34	C₄×C₁₃×M₁₆	—	2	1	no	—
35	C₁₃×#382	—	2	1	no	—
36	C₁₃×#382	—	2	1	no	—
37	C₁₃×#382	C₂²	1	2	yes	—
38	C₁₃×#382	C₂²	1	2	yes	—
39	C₂×C₁₃×#95	—	2	1	no	—
40	C₂×C₁₃×#95	C₂²	1	2	yes	—
41	C₁₃×#328	C₂²	1	8	yes	—
42	C₁₃×#327	C₂²	1	8	yes	—
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂×C₁₃×#41	—	2	1	no	—
45	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₁₃	—	2	2	no	—
47	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂×C₁₃×M₁₆	—	2	2	no	—
51	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
52	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
53	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
54	C₁₃×#127	C₂×C₄	1	1	yes	characteristic, complemented
55	C₁₃×#126	—	2	2	no	—
56	C₁₃×#126	—	2	2	no	—
57	C₁₃×#125	—	2	1	no	—
58	C₁₃×#125	—	2	1	no	—
59	C₁₃×#125	C₂×C₄	1	2	yes	complemented
60	C₁₃×#124	—	2	1	no	—
61	C₁₃×#124	—	2	1	no	—
62	C₁₃×#124	C₂×C₄	1	2	yes	complemented
63	C₁₃×#123	—	2	2	no	—
64	C₁₃×#123	—	2	2	no	—
65	C₁₃×#123	—	2	2	no	—
66	C₁₃×C₂²⋊Q₈	—	2	1	no	—
67	C₁₃×C₂²⋊Q₈	—	2	1	no	—
68	C₁₃×C₂²⋊Q₈	—	2	1	no	—
69	C₁₃×C₂²⋊Q₈	—	2	1	no	—
70	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
71	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
72	C₁₃×#121	—	2	1	no	—
73	C₁₃×#121	—	2	1	no	—
74	C₁₃×#121	—	2	1	no	—
75	C₁₃×#121	—	2	1	no	—
76	C₁₃×#121	C₂×C₄	1	2	yes	—
77	C₁₃×#121	C₂³	1	2	yes	—
78	C₁₃×#120	—	2	2	no	—
79	C₄×Q₈×C₁₃	—	2	1	no	—
80	C₄×Q₈×C₁₃	—	2	1	no	—
81	C₄×Q₈×C₁₃	—	2	1	no	—
82	C₄×Q₈×C₁₃	—	2	1	no	—
83	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	complemented
84	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	complemented
85	C₄×D₄×C₁₃	—	2	2	no	—
86	C₄×D₄×C₁₃	—	2	2	no	—
87	C₄×D₄×C₁₃	—	2	2	no	—
88	C₄×D₄×C₁₃	—	2	2	no	—
89	C₄×D₄×C₁₃	—	2	2	no	—
90	C₄×D₄×C₁₃	—	2	2	no	—
91	C₄×D₄×C₁₃	—	2	1	no	—
92	C₄×D₄×C₁₃	—	2	1	no	—
93	C₄×D₄×C₁₃	—	2	1	no	—
94	C₄×D₄×C₁₃	—	2	1	no	—
95	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	complemented
96	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	complemented
97	C₁₃×#117	—	2	1	no	—
98	C₁₃×#117	—	2	1	no	—
99	C₁₃×#117	—	2	2	no	—
100	C₁₃×#117	—	2	2	no	—
101	C₁₃×#117	—	2	2	no	—
102	C₁₃×#117	C₂×C₄	1	2	yes	—
103	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
105	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
106	C₂×C₄²×C₁₃	—	2	2	no	—
107	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
109	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
113	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
115	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊C₈	—	2	2	no	—
120	C₁₃×C₄⋊C₈	—	2	2	no	—
121	C₁₃×C₂²⋊C₈	—	2	2	no	—
122	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
123	C₁₃×#97	—	2	2	no	—
124	C₄×C₈×C₁₃	—	2	2	no	—
125	C₁₃×#95	—	2	2	no	—
126	C₁₃×#95	—	2	2	no	—
127	C₁₃×#95	—	2	2	no	—
128	C₁₃×#95	C₂³	1	4	yes	—
129	#17588	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₁₃×#41	—	4	4	no	—
132	C₁₃×#41	—	4	4	no	—
133	C₁₃×#41	—	4	2	no	—
134	C₁₃×#41	—	4	2	no	—
135	C₂×Q₈×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	—	2	1	no	—
137	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
138	C₂×D₄×C₁₃	—	2	2	no	—
139	C₂×D₄×C₁₃	—	2	2	no	—
140	C₂×D₄×C₁₃	—	2	2	no	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
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	2	no	—
148	C₂²×C₄×C₁₃	—	2	2	no	—
149	C₂²×C₄×C₁₃	—	2	4	no	—
150	C₂²×C₄×C₁₃	—	4	2	no	—
151	C₂²×C₄×C₁₃	—	4	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	C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
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×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₁₃×M₁₆	—	4	4	no	—
174	C₂×C₈×C₁₃	—	2	4	no	—
175	C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₁₃×C₄⋊C₄	—	2	1	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	—	2	2	no	—
181	C₁₃×C₄⋊C₄	—	2	2	no	—
182	C₁₃×C₄⋊C₄	—	2	2	no	—
183	C₁₃×C₄⋊C₄	—	2	2	no	—
184	C₁₃×C₄⋊C₄	—	2	2	no	—
185	C₁₃×C₄⋊C₄	—	4	4	no	—
186	C₁₃×C₄⋊C₄	—	4	4	no	—
187	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
188	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
189	C₁₃×C₂²⋊C₄	—	2	2	no	—
190	C₁₃×C₂²⋊C₄	—	2	2	no	—
191	C₁₃×C₂²⋊C₄	—	2	2	no	—
192	C₁₃×C₂²⋊C₄	—	2	2	no	—
193	C₁₃×C₂²⋊C₄	—	2	2	no	—
194	C₁₃×C₂²⋊C₄	—	2	2	no	—
195	C₁₃×C₂²⋊C₄	—	2	2	no	—
196	C₁₃×C₂²⋊C₄	—	2	2	no	—
197	C₁₃×C₂²⋊C₄	—	2	2	no	—
198	C₄²×C₁₃	—	2	2	no	—
199	C₄²×C₁₃	—	2	2	no	—
200	C₄²×C₁₃	—	2	2	no	—
201	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
202	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
203	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
204	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
205	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
206	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
207	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
208	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
209	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
210	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
211	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
212	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
213	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
217	#3444	C₂×C₁₃	1	1	yes	characteristic
218	#2920	C₂×C₁₃	1	1	yes	characteristic, complemented
219	C₂×#382	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1518	C₂×C₁₃	1	2	yes	complemented
221	#1517	C₂×C₁₃	1	2	yes	complemented
222	#1512	C₂×C₁₃	1	4	yes	complemented
223	#1504	C₂×C₁₃	1	4	yes	complemented
224	C₂³×C₁₃	—	2	1	no	—
225	C₂³×C₁₃	—	2	1	no	—
226	C₂³×C₁₃	—	2	2	no	—
227	C₂³×C₁₃	—	2	2	no	—
228	C₂³×C₁₃	—	2	2	no	—
229	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
232	Q₈×C₁₃	—	4	2	no	—
233	Q₈×C₁₃	—	4	2	no	—
234	Q₈×C₁₃	—	4	2	no	—
235	D₄×C₁₃	—	4	2	no	—
236	D₄×C₁₃	—	4	2	no	—
237	D₄×C₁₃	—	4	2	no	—
238	D₄×C₁₃	—	4	2	no	—
239	D₄×C₁₃	—	4	4	no	—
240	D₄×C₁₃	—	4	4	no	—
241	D₄×C₁₃	—	4	2	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	2	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	2	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	—	4	1	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	4	4	no	—
264	C₂×C₄×C₁₃	—	4	4	no	—
265	C₂×C₄×C₁₃	—	4	4	no	—
266	C₂×C₄×C₁₃	—	4	4	no	—
267	C₂×C₄×C₁₃	—	4	4	no	—
268	C₂×C₄×C₁₃	—	4	4	no	—
269	C₂×C₄×C₁₃	—	8	8	no	—
270	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
277	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
281	C₂×C₄×C₁₃	#137	1	2	yes	—
282	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
283	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
284	C₈×C₁₃	—	4	4	no	—
285	#533	C₄×C₁₃	1	1	yes	characteristic, complemented
286	#533	C₄×C₁₃	1	1	yes	characteristic, complemented
287	#533	C₂²×C₁₃	1	1	yes	characteristic
288	#532	C₄×C₁₃	1	1	yes	characteristic, complemented
289	#532	C₄×C₁₃	1	1	yes	characteristic, complemented
290	#532	C₂²×C₁₃	1	1	yes	characteristic
291	#529	—	2	1	no	—
292	#529	—	2	1	no	—
293	#529	—	2	1	no	—
294	#529	—	2	1	no	—
295	#529	C₄×C₁₃	1	2	yes	complemented
296	#529	C₂²×C₁₃	1	2	yes	—
297	#525	—	2	1	no	—
298	#525	—	2	1	no	—
299	#525	C₂²×C₁₃	1	2	yes	—
300	C₄×#41	—	2	1	no	—
301	C₄×#41	—	2	1	no	—
302	C₄×#41	C₄×C₁₃	1	2	yes	complemented
303	C₂²×C₄⋊C₄	—	2	1	no	—
304	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
305	#432	—	2	1	no	—
306	#432	C₂²×C₁₃	1	2	yes	—
307	#431	—	2	1	no	—
308	#431	C₂²×C₁₃	1	2	yes	—
309	#423	—	2	1	no	—
310	#407	C₂²×C₁₃	1	2	yes	—
311	C₄×M₁₆	—	2	1	no	—
312	#382	—	2	1	no	—
313	#382	—	2	1	no	—
314	#382	C₂²×C₁₃	1	2	yes	—
315	#382	C₂²×C₁₃	1	2	yes	—
316	C₂×#95	—	2	1	no	—
317	C₂×#95	C₂²×C₁₃	1	2	yes	—
318	#328	C₂²×C₁₃	1	8	yes	—
319	#327	C₂²×C₁₃	1	8	yes	—
320	C₂²×C₁₃	—	2	4	no	—
321	C₂²×C₁₃	—	2	4	no	—
322	C₂²×C₁₃	—	2	1	no	—
323	C₂²×C₁₃	—	2	1	no	—
324	C₂²×C₁₃	—	2	1	no	—
325	C₂²×C₁₃	—	2	1	no	—
326	C₂²×C₁₃	—	2	1	no	—
327	C₂²×C₁₃	—	2	1	no	—
328	C₂²×C₁₃	—	4	2	no	—
329	C₂²×C₁₃	—	4	2	no	—
330	C₂²×C₁₃	—	4	2	no	—
331	C₂²×C₁₃	#410	1	2	yes	—
332	C₂²×C₁₃	#421	1	2	yes	—
333	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
334	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
335	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
336	C₄×C₁₃	—	2	1	no	—
337	C₄×C₁₃	—	2	1	no	—
338	C₄×C₁₃	—	2	1	no	—
339	C₄×C₁₃	—	2	1	no	—
340	C₄×C₁₃	—	2	1	no	—
341	C₄×C₁₃	—	2	1	no	—
342	C₄×C₁₃	—	2	1	no	—
343	C₄×C₁₃	—	2	1	no	—
344	C₄×C₁₃	—	2	1	no	—
345	C₄×C₁₃	—	2	1	no	—
346	C₄×C₁₃	—	4	2	no	—
347	C₄×C₁₃	—	4	2	no	—
348	C₄×C₁₃	—	4	2	no	—
349	C₄×C₁₃	—	8	4	no	—
350	C₄×C₁₃	#417	1	2	yes	—
351	C₄×C₁₃	#417	1	2	yes	—
352	C₂×#41	—	2	1	no	—
353	C₂×#41	—	2	1	no	—
354	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
355	C₂³×C₄	—	2	2	no	—
356	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
357	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
359	C₂×M₁₆	—	2	2	no	—
360	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
361	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
362	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
363	#127	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
364	#126	—	2	2	no	—
365	#126	—	2	2	no	—
366	#125	—	2	1	no	—
367	#125	—	2	1	no	—
368	#125	C₂×C₄×C₁₃	1	2	yes	complemented
369	#124	—	2	1	no	—
370	#124	—	2	1	no	—
371	#124	C₂×C₄×C₁₃	1	2	yes	complemented
372	#123	—	2	2	no	—
373	#123	—	2	2	no	—
374	#123	—	2	2	no	—
375	C₂²⋊Q₈	—	2	1	no	—
376	C₂²⋊Q₈	—	2	1	no	—
377	C₂²⋊Q₈	—	2	1	no	—
378	C₂²⋊Q₈	—	2	1	no	—
379	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
380	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
381	#121	—	2	1	no	—
382	#121	—	2	1	no	—
383	#121	—	2	1	no	—
384	#121	—	2	1	no	—
385	#121	C₂×C₄×C₁₃	1	2	yes	—
386	#121	C₂³×C₁₃	1	2	yes	—
387	#120	—	2	2	no	—
388	C₄×Q₈	—	2	1	no	—
389	C₄×Q₈	—	2	1	no	—
390	C₄×Q₈	—	2	1	no	—
391	C₄×Q₈	—	2	1	no	—
392	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	complemented
393	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	complemented
394	C₄×D₄	—	2	2	no	—
395	C₄×D₄	—	2	2	no	—
396	C₄×D₄	—	2	2	no	—
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	—	2	2	no	—
400	C₄×D₄	—	2	1	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	—	2	1	no	—
404	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	complemented
405	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	complemented
406	#117	—	2	1	no	—
407	#117	—	2	1	no	—
408	#117	—	2	2	no	—
409	#117	—	2	2	no	—
410	#117	—	2	2	no	—
411	#117	C₂×C₄×C₁₃	1	2	yes	—
412	C₂×C₄⋊C₄	—	2	2	no	—
413	C₂×C₄⋊C₄	—	2	2	no	—
414	C₂×C₄⋊C₄	—	4	4	no	—
415	C₂×C₄²	—	2	2	no	—
416	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
417	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
418	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
419	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
420	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
421	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
422	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
423	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
424	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
425	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
426	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
427	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
428	C₄⋊C₈	—	2	2	no	—
429	C₄⋊C₈	—	2	2	no	—
430	C₂²⋊C₈	—	2	2	no	—
431	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
432	#97	—	2	2	no	—
433	C₄×C₈	—	2	2	no	—
434	#95	—	2	2	no	—
435	#95	—	2	2	no	—
436	#95	—	2	2	no	—
437	#95	C₂³×C₁₃	1	4	yes	—
438	C₂×C₁₃	—	2	1	no	—
439	C₂×C₁₃	—	2	1	no	—
440	C₂×C₁₃	—	2	2	no	—
441	C₂×C₁₃	—	2	2	no	—
442	C₂×C₁₃	—	8	2	no	—
443	C₂×C₁₃	C₂×#410	1	1	yes	characteristic
444	C₂×C₁₃	C₂×#417	1	1	yes	characteristic
445	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
446	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
447	#41	—	4	4	no	—
448	#41	—	4	4	no	—
449	#41	—	4	2	no	—
450	#41	—	4	2	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	4	2	no	—
467	C₂²×C₄	—	4	2	no	—
468	C₂²×C₄	—	4	4	no	—
469	C₂²×C₄	—	4	4	no	—
470	C₂²×C₄	—	4	4	no	—
471	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
472	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
473	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
474	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
475	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
476	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
477	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
478	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
479	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
480	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
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	C₂⁴×C₁₃	1	1	yes	characteristic
489	M₁₆	—	4	4	no	—
490	C₂×C₈	—	2	4	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	4	4	no	—
502	C₄⋊C₄	—	4	4	no	—
503	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
504	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	2	no	—
514	C₄²	—	2	2	no	—
515	C₄²	—	2	2	no	—
516	C₄²	—	2	2	no	—
517	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
518	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
519	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
520	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
521	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
522	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
523	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
524	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
525	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
526	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
527	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
528	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
529	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
530	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
531	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
532	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
533	C₁₃	#17588	1	1	yes	characteristic, direct product factor, Sylow
534	C₂³	—	2	2	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	2	no	—
539	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
540	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
541	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
542	Q₈	—	4	2	no	—
543	Q₈	—	4	2	no	—
544	Q₈	—	4	2	no	—
545	D₄	—	4	2	no	—
546	D₄	—	4	2	no	—
547	D₄	—	4	4	no	—
548	D₄	—	4	4	no	—
549	D₄	—	4	2	no	—
550	D₄	—	4	2	no	—
551	D₄	—	4	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	4	no	—
574	C₂×C₄	—	4	4	no	—
575	C₂×C₄	—	4	4	no	—
576	C₂×C₄	—	4	4	no	—
577	C₂×C₄	—	4	4	no	—
578	C₂×C₄	—	4	4	no	—
579	C₂×C₄	—	8	8	no	—
580	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
581	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
582	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
583	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
584	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
585	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
586	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
587	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
588	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
589	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
590	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
591	C₂×C₄	C₁₃×#137	1	2	yes	—
592	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
593	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
594	C₈	—	4	4	no	—
595	C₂²	—	2	4	no	—
596	C₂²	—	2	4	no	—
597	C₂²	—	2	1	no	—
598	C₂²	—	2	1	no	—
599	C₂²	—	2	1	no	—
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	2	no	—
606	C₂²	C₁₃×#410	1	2	yes	—
607	C₂²	C₁₃×#421	1	2	yes	—
608	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
609	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
610	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
611	C₄	—	2	1	no	—
612	C₄	—	2	1	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	2	no	—
623	C₄	—	4	2	no	—
624	C₄	—	8	4	no	—
625	C₄	C₁₃×#417	1	2	yes	—
626	C₄	C₁₃×#417	1	2	yes	—
627	C₂	—	2	1	no	—
628	C₂	—	2	2	no	—
629	C₂	—	2	2	no	—
630	C₂	—	2	1	no	—
631	C₂	—	8	2	no	—
632	C₂	C₂×C₁₃×#410	1	1	yes	characteristic
633	C₂	C₂×C₁₃×#417	1	1	yes	characteristic
634	C₂	C₂×C₁₃×#421	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2920	C₂	semidirect
3. C₂×C₁₃×#382	C₂	semidirect
4. C₁₃×#1518	C₂	semidirect
5. C₁₃×#1517	C₂	semidirect
6. C₁₃×#1512	C₂	semidirect
7. C₁₃×#1504	C₂	semidirect
8. C₁₃×#533	C₄	semidirect
9. C₁₃×#533	C₄	semidirect
11. C₁₃×#532	C₄	semidirect
12. C₁₃×#532	C₄	semidirect
18. C₁₃×#529	C₄	semidirect
25. C₄×C₁₃×#41	C₄	semidirect
51. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
52. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
53. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
54. C₁₃×#127	C₂×C₄	semidirect
59. C₁₃×#125	C₂×C₄	semidirect
62. C₁₃×#124	C₂×C₄	semidirect
83. C₄×Q₈×C₁₃	C₂×C₄	semidirect
84. C₄×Q₈×C₁₃	C₂×C₄	semidirect
95. C₄×D₄×C₁₃	C₂×C₄	semidirect
96. C₄×D₄×C₁₃	C₂×C₄	semidirect
129. #17588	C₁₃	direct (N × H)
218. #2920	C₂×C₁₃	semidirect
219. C₂×#382	C₂×C₁₃	semidirect
220. #1518	C₂×C₁₃	semidirect
221. #1517	C₂×C₁₃	semidirect
222. #1512	C₂×C₁₃	semidirect
223. #1504	C₂×C₁₃	semidirect
285. #533	C₄×C₁₃	semidirect
286. #533	C₄×C₁₃	semidirect
288. #532	C₄×C₁₃	semidirect
289. #532	C₄×C₁₃	semidirect
295. #529	C₄×C₁₃	semidirect
302. C₄×#41	C₄×C₁₃	semidirect
360. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
361. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
362. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
363. #127	C₂×C₄×C₁₃	semidirect
368. #125	C₂×C₄×C₁₃	semidirect
371. #124	C₂×C₄×C₁₃	semidirect
392. C₄×Q₈	C₂×C₄×C₁₃	semidirect
393. C₄×Q₈	C₂×C₄×C₁₃	semidirect
404. C₄×D₄	C₂×C₄×C₁₃	semidirect
405. C₄×D₄	C₂×C₄×C₁₃	semidirect
533. C₁₃	#17588	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3444	2
C₁₃×#2920	2
C₂×C₁₃×#382	2
C₁₃×#1518	2
C₁₃×#1517	2
C₁₃×#1512	2
C₁₃×#1504	2
#17588	13

Subgroups — C13×#17588 #15703927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17588 #15703927