Subgroups — C₁₃×#18711 #15705050

Order 3328.

818 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3555	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3252	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1650	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1648	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1645	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1643	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1638	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1636	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1633	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1632	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1559	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1494	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1493	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#563	—	2	2	no	—
17	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#557	—	2	1	no	—
19	C₁₃×#557	C₂²	1	1	yes	characteristic
20	C₁₃×#556	—	2	1	no	—
21	C₁₃×#556	—	2	1	no	—
22	C₁₃×#556	C₂²	1	1	yes	characteristic
23	C₁₃×#554	C₂²	1	1	yes	characteristic
24	C₁₃×#552	—	2	1	no	—
25	C₁₃×#544	—	2	1	no	—
26	C₁₃×#542	—	2	1	no	—
27	C₁₃×#541	—	2	1	no	—
28	C₁₃×#541	—	2	1	no	—
29	C₁₃×#541	—	2	2	no	—
30	C₁₃×#533	C₂²	1	1	yes	characteristic
31	C₁₃×#533	C₂²	1	1	yes	characteristic
32	C₁₃×#533	C₂²	1	1	yes	characteristic
33	C₁₃×#529	C₂²	1	1	yes	characteristic
34	C₁₃×#501	—	2	1	no	—
35	C₁₃×#500	C₂²	1	1	yes	characteristic
36	C₁₃×#494	C₂²	1	1	yes	characteristic
37	C₁₃×#491	—	2	1	no	—
38	C₁₃×#487	C₂²	1	1	yes	characteristic
39	C₁₃×#487	C₂²	1	1	yes	characteristic
40	C₁₃×#485	—	2	1	no	—
41	C₁₃×#485	—	2	1	no	—
42	C₁₃×#479	—	2	1	no	—
43	C₁₃×#477	C₂²	1	1	yes	characteristic
44	C₁₃×#477	C₂²	1	1	yes	characteristic
45	C₁₃×#477	C₂²	1	1	yes	characteristic
46	C₁₃×#476	C₂²	1	1	yes	characteristic
47	C₁₃×#475	C₂²	1	1	yes	characteristic
48	C₁₃×#475	C₂²	1	1	yes	characteristic
49	C₁₃×#470	—	2	1	no	—
50	C₁₃×#468	—	2	1	no	—
51	C₁₃×#467	—	2	2	no	—
52	C₁₃×#464	—	2	1	no	—
53	C₁₃×#462	C₂²	1	1	yes	characteristic
54	C₁₃×#461	C₂²	1	1	yes	characteristic
55	C₄×C₁₃×Q₁₆	—	2	2	no	—
56	C₁₃×#432	C₂²	1	1	yes	characteristic
57	C₁₃×#423	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
59	C₁₃×#333	C₂²	1	1	yes	characteristic
60	C₁₃×#333	C₂²	1	1	yes	characteristic
61	C₁₃×#332	C₂²	1	1	yes	characteristic
62	C₁₃×#332	C₂²	1	1	yes	characteristic
63	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
67	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
68	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
69	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
71	C₂×C₁₃×Q₁₆	—	2	2	no	—
72	C₂×C₁₃×Q₁₆	—	2	1	no	—
73	C₂×C₁₃×SD₁₆	—	2	1	no	—
74	C₂×C₁₃×M₁₆	—	2	1	no	—
75	C₂²×C₈×C₁₃	—	2	1	no	—
76	C₁₃×C₄⋊Q₈	—	2	2	no	—
77	C₁₃×C₄⋊Q₈	—	2	1	no	—
78	C₁₃×C₄⋊Q₈	—	2	2	no	—
79	C₁₃×C₄⋊Q₈	—	2	1	no	—
80	C₁₃×C₄⋊Q₈	—	2	1	no	—
81	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
82	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
83	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₁₃×#126	—	2	2	no	—
88	C₁₃×#126	—	2	2	no	—
89	C₁₃×#126	—	2	2	no	—
90	C₁₃×#126	—	2	2	no	—
91	C₁₃×#126	—	2	2	no	—
92	C₁₃×#126	—	2	2	no	—
93	C₁₃×#126	—	2	1	no	—
94	C₁₃×#125	—	2	2	no	—
95	C₁₃×#125	—	2	2	no	—
96	C₁₃×#125	—	2	2	no	—
97	C₁₃×#125	—	2	2	no	—
98	C₁₃×#125	—	2	1	no	—
99	C₁₃×#125	—	2	2	no	—
100	C₁₃×#125	—	2	1	no	—
101	C₁₃×#125	—	2	1	no	—
102	C₁₃×#125	—	2	1	no	—
103	C₁₃×#125	—	2	1	no	—
104	C₁₃×#125	D₄	1	1	yes	characteristic
105	C₁₃×#124	—	2	2	no	—
106	C₁₃×#124	—	2	1	no	—
107	C₁₃×#124	D₄	1	1	yes	characteristic
108	C₁₃×#123	—	2	2	no	—
109	C₁₃×#123	—	2	1	no	—
110	C₁₃×C₂²⋊Q₈	—	2	2	no	—
111	C₁₃×C₂²⋊Q₈	—	2	2	no	—
112	C₁₃×C₂²⋊Q₈	—	2	1	no	—
113	C₁₃×C₂²⋊Q₈	—	2	1	no	—
114	C₁₃×C₂²⋊Q₈	—	2	2	no	—
115	C₁₃×C₂²⋊Q₈	—	2	1	no	—
116	C₁₃×C₂²⋊Q₈	—	2	1	no	—
117	C₁₃×C₂²⋊Q₈	—	2	1	no	—
118	C₁₃×C₂²⋊Q₈	—	2	1	no	—
119	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
120	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
121	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
122	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
123	C₁₃×#121	D₄	1	1	yes	characteristic
124	C₄×Q₈×C₁₃	—	2	2	no	—
125	C₄×Q₈×C₁₃	—	2	1	no	—
126	C₄×Q₈×C₁₃	—	2	1	no	—
127	C₄×Q₈×C₁₃	—	2	1	no	—
128	C₄×Q₈×C₁₃	—	2	1	no	—
129	C₄×Q₈×C₁₃	—	2	1	no	—
130	C₄×Q₈×C₁₃	—	2	1	no	—
131	C₄×Q₈×C₁₃	—	2	1	no	—
132	C₄×Q₈×C₁₃	—	2	1	no	—
133	C₄×Q₈×C₁₃	—	2	1	no	—
134	C₄×Q₈×C₁₃	D₄	1	2	yes	—
135	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
136	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
137	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
138	C₄×D₄×C₁₃	—	2	1	no	—
139	C₄×D₄×C₁₃	—	2	1	no	—
140	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
141	C₁₃×#117	—	2	2	no	—
142	C₁₃×#117	—	2	1	no	—
143	C₁₃×#117	—	2	1	no	—
144	C₁₃×#117	—	2	1	no	—
145	C₁₃×#117	—	2	1	no	—
146	C₁₃×#117	—	2	1	no	—
147	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
148	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
149	C₁₃×#107	—	2	2	no	—
150	C₁₃×#107	—	2	1	no	—
151	C₁₃×#107	—	2	1	no	—
152	C₁₃×#107	—	2	1	no	—
153	C₁₃×#106	—	2	1	no	—
154	C₁₃×#106	—	2	1	no	—
155	C₁₃×#106	—	2	1	no	—
156	C₁₃×C₄⋊C₈	—	2	1	no	—
157	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₁₃×#103	—	2	2	no	—
162	C₁₃×#103	—	2	1	no	—
163	C₁₃×#103	—	2	1	no	—
164	C₁₃×#103	—	2	1	no	—
165	C₁₃×#103	—	2	1	no	—
166	C₁₃×#103	—	2	1	no	—
167	C₁₃×#103	—	2	2	no	—
168	C₁₃×#103	—	2	1	no	—
169	C₁₃×#103	—	2	1	no	—
170	C₁₃×#102	—	2	1	no	—
171	C₁₃×C₂²⋊C₈	—	2	1	no	—
172	C₁₃×#97	—	2	1	no	—
173	C₄×C₈×C₁₃	—	2	1	no	—
174	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
175	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
176	#18711	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂×Q₈×C₁₃	—	2	2	no	—
178	C₂×Q₈×C₁₃	—	2	1	no	—
179	C₂×Q₈×C₁₃	—	2	1	no	—
180	C₂×Q₈×C₁₃	—	2	1	no	—
181	C₂×Q₈×C₁₃	—	2	1	no	—
182	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
186	C₂×D₄×C₁₃	—	2	1	no	—
187	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₃	—	2	2	no	—
189	C₂²×C₄×C₁₃	—	2	1	no	—
190	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
193	C₁₃×Q₁₆	—	4	4	no	—
194	C₁₃×Q₁₆	—	8	1	no	—
195	C₁₃×SD₁₆	—	8	1	no	—
196	C₁₃×M₁₆	—	8	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	C₂×C₈×C₁₃	—	2	1	no	—
203	C₂×C₈×C₁₃	—	4	2	no	—
204	C₁₃×C₄⋊C₄	—	2	2	no	—
205	C₁₃×C₄⋊C₄	—	2	2	no	—
206	C₁₃×C₄⋊C₄	—	2	2	no	—
207	C₁₃×C₄⋊C₄	—	2	2	no	—
208	C₁₃×C₄⋊C₄	—	2	2	no	—
209	C₁₃×C₄⋊C₄	—	2	2	no	—
210	C₁₃×C₄⋊C₄	—	2	2	no	—
211	C₁₃×C₄⋊C₄	—	2	2	no	—
212	C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
220	C₁₃×C₄⋊C₄	—	2	1	no	—
221	C₁₃×C₄⋊C₄	—	2	2	no	—
222	C₁₃×C₄⋊C₄	—	2	1	no	—
223	C₁₃×C₄⋊C₄	—	2	1	no	—
224	C₁₃×C₄⋊C₄	—	2	1	no	—
225	C₁₃×C₄⋊C₄	—	2	1	no	—
226	C₁₃×C₄⋊C₄	—	2	1	no	—
227	C₁₃×C₄⋊C₄	—	2	1	no	—
228	C₁₃×C₄⋊C₄	—	2	1	no	—
229	C₁₃×C₄⋊C₄	—	2	1	no	—
230	C₁₃×C₄⋊C₄	—	2	1	no	—
231	C₁₃×C₄⋊C₄	—	2	1	no	—
232	C₁₃×C₄⋊C₄	—	4	1	no	—
233	C₁₃×C₄⋊C₄	—	4	1	no	—
234	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
235	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
236	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
237	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
238	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
239	C₁₃×C₂²⋊C₄	—	2	2	no	—
240	C₁₃×C₂²⋊C₄	—	2	2	no	—
241	C₁₃×C₂²⋊C₄	—	2	2	no	—
242	C₁₃×C₂²⋊C₄	—	2	1	no	—
243	C₁₃×C₂²⋊C₄	—	2	2	no	—
244	C₁₃×C₂²⋊C₄	—	2	1	no	—
245	C₁₃×C₂²⋊C₄	—	2	1	no	—
246	C₁₃×C₂²⋊C₄	—	2	1	no	—
247	C₁₃×C₂²⋊C₄	—	2	1	no	—
248	C₁₃×C₂²⋊C₄	—	2	1	no	—
249	C₁₃×C₂²⋊C₄	—	2	1	no	—
250	C₁₃×C₂²⋊C₄	—	4	1	no	—
251	C₄²×C₁₃	—	2	2	no	—
252	C₄²×C₁₃	—	2	2	no	—
253	C₄²×C₁₃	—	2	2	no	—
254	C₄²×C₁₃	—	2	2	no	—
255	C₄²×C₁₃	—	2	1	no	—
256	C₄²×C₁₃	—	2	1	no	—
257	C₄²×C₁₃	—	2	1	no	—
258	C₄²×C₁₃	—	4	1	no	—
259	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
260	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
261	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
262	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
263	#3555	C₂×C₁₃	1	1	yes	characteristic
264	#3252	C₂×C₁₃	1	1	yes	characteristic
265	#3237	C₂×C₁₃	1	1	yes	characteristic, complemented
266	#3170	C₂×C₁₃	1	1	yes	characteristic, complemented
267	#1650	C₂×C₁₃	1	1	yes	characteristic, complemented
268	#1648	C₂×C₁₃	1	1	yes	characteristic, complemented
269	#1645	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#1643	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#1638	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#1636	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#1633	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#1632	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#1559	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#1494	C₂×C₁₃	1	1	yes	characteristic
277	#1493	C₂×C₁₃	1	1	yes	characteristic, complemented
278	C₂³×C₁₃	—	2	1	no	—
279	C₂³×C₁₃	#120	1	1	yes	characteristic
280	Q₈×C₁₃	—	2	1	no	—
281	Q₈×C₁₃	—	2	1	no	—
282	Q₈×C₁₃	—	2	1	no	—
283	Q₈×C₁₃	—	2	1	no	—
284	Q₈×C₁₃	—	2	1	no	—
285	Q₈×C₁₃	—	2	1	no	—
286	Q₈×C₁₃	—	4	2	no	—
287	Q₈×C₁₃	—	4	2	no	—
288	Q₈×C₁₃	—	4	1	no	—
289	Q₈×C₁₃	—	4	1	no	—
290	Q₈×C₁₃	—	4	1	no	—
291	Q₈×C₁₃	—	4	1	no	—
292	Q₈×C₁₃	—	8	1	no	—
293	Q₈×C₁₃	—	8	2	no	—
294	D₄×C₁₃	—	2	1	no	—
295	D₄×C₁₃	—	2	1	no	—
296	D₄×C₁₃	—	8	1	no	—
297	C₂×C₄×C₁₃	—	2	1	no	—
298	C₂×C₄×C₁₃	—	2	1	no	—
299	C₂×C₄×C₁₃	—	2	1	no	—
300	C₂×C₄×C₁₃	—	2	1	no	—
301	C₂×C₄×C₁₃	—	2	1	no	—
302	C₂×C₄×C₁₃	—	2	1	no	—
303	C₂×C₄×C₁₃	—	2	1	no	—
304	C₂×C₄×C₁₃	—	2	2	no	—
305	C₂×C₄×C₁₃	—	2	1	no	—
306	C₂×C₄×C₁₃	—	2	1	no	—
307	C₂×C₄×C₁₃	—	2	1	no	—
308	C₂×C₄×C₁₃	—	2	2	no	—
309	C₂×C₄×C₁₃	—	2	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	—	8	2	no	—
316	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
317	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
318	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
319	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
322	C₈×C₁₃	—	2	2	no	—
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	C₈×C₁₃	—	4	1	no	—
328	#563	—	2	2	no	—
329	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
330	#557	—	2	1	no	—
331	#557	C₂²×C₁₃	1	1	yes	characteristic
332	#556	—	2	1	no	—
333	#556	—	2	1	no	—
334	#556	C₂²×C₁₃	1	1	yes	characteristic
335	#554	C₂²×C₁₃	1	1	yes	characteristic
336	#552	—	2	1	no	—
337	#544	—	2	1	no	—
338	#542	—	2	1	no	—
339	#541	—	2	1	no	—
340	#541	—	2	1	no	—
341	#541	—	2	2	no	—
342	#533	C₂²×C₁₃	1	1	yes	characteristic
343	#533	C₂²×C₁₃	1	1	yes	characteristic
344	#533	C₂²×C₁₃	1	1	yes	characteristic
345	#529	C₂²×C₁₃	1	1	yes	characteristic
346	#501	—	2	1	no	—
347	#500	C₂²×C₁₃	1	1	yes	characteristic
348	#494	C₂²×C₁₃	1	1	yes	characteristic
349	#491	—	2	1	no	—
350	#487	C₂²×C₁₃	1	1	yes	characteristic
351	#487	C₂²×C₁₃	1	1	yes	characteristic
352	#485	—	2	1	no	—
353	#485	—	2	1	no	—
354	#479	—	2	1	no	—
355	#477	C₂²×C₁₃	1	1	yes	characteristic
356	#477	C₂²×C₁₃	1	1	yes	characteristic
357	#477	C₂²×C₁₃	1	1	yes	characteristic
358	#476	C₂²×C₁₃	1	1	yes	characteristic
359	#475	C₂²×C₁₃	1	1	yes	characteristic
360	#475	C₂²×C₁₃	1	1	yes	characteristic
361	#470	—	2	1	no	—
362	#468	—	2	1	no	—
363	#467	—	2	2	no	—
364	#464	—	2	1	no	—
365	#462	C₂²×C₁₃	1	1	yes	characteristic
366	#461	C₂²×C₁₃	1	1	yes	characteristic
367	C₄×Q₁₆	—	2	2	no	—
368	#432	C₂²×C₁₃	1	1	yes	characteristic
369	#423	C₂²×C₁₃	1	1	yes	characteristic
370	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
371	#333	C₂²×C₁₃	1	1	yes	characteristic
372	#333	C₂²×C₁₃	1	1	yes	characteristic
373	#332	C₂²×C₁₃	1	1	yes	characteristic
374	#332	C₂²×C₁₃	1	1	yes	characteristic
375	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
376	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
377	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
378	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
379	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
380	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
381	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
382	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
383	C₂²×C₁₃	—	2	1	no	—
384	C₂²×C₁₃	—	2	1	no	—
385	C₂²×C₁₃	—	2	1	no	—
386	C₂²×C₁₃	—	4	1	no	—
387	C₂²×C₁₃	—	4	1	no	—
388	C₂²×C₁₃	—	4	1	no	—
389	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
390	C₄×C₁₃	—	2	1	no	—
391	C₄×C₁₃	—	2	1	no	—
392	C₄×C₁₃	—	2	1	no	—
393	C₄×C₁₃	—	2	1	no	—
394	C₄×C₁₃	—	4	1	no	—
395	C₄×C₁₃	—	4	1	no	—
396	C₄×C₁₃	—	4	1	no	—
397	C₄×C₁₃	—	4	1	no	—
398	C₄×C₁₃	—	4	2	no	—
399	C₄×C₁₃	—	4	1	no	—
400	C₄×C₁₃	—	4	2	no	—
401	C₄×C₁₃	—	4	1	no	—
402	C₄×C₁₃	—	4	1	no	—
403	C₄×C₁₃	—	8	1	no	—
404	C₄×C₁₃	—	8	1	no	—
405	C₄×C₁₃	#577	1	1	yes	characteristic
406	C₄×C₁₃	#578	1	1	yes	characteristic
407	C₄×C₁₃	#578	1	1	yes	characteristic
408	C₄×C₁₃	#578	1	1	yes	characteristic
409	C₂×Q₁₆	—	2	2	no	—
410	C₂×Q₁₆	—	2	1	no	—
411	C₂×SD₁₆	—	2	1	no	—
412	C₂×M₁₆	—	2	1	no	—
413	C₂²×C₈	—	2	1	no	—
414	C₄⋊Q₈	—	2	2	no	—
415	C₄⋊Q₈	—	2	1	no	—
416	C₄⋊Q₈	—	2	2	no	—
417	C₄⋊Q₈	—	2	1	no	—
418	C₄⋊Q₈	—	2	1	no	—
419	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
420	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
421	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
422	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
423	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
424	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
425	#126	—	2	2	no	—
426	#126	—	2	2	no	—
427	#126	—	2	2	no	—
428	#126	—	2	2	no	—
429	#126	—	2	2	no	—
430	#126	—	2	2	no	—
431	#126	—	2	1	no	—
432	#125	—	2	2	no	—
433	#125	—	2	2	no	—
434	#125	—	2	2	no	—
435	#125	—	2	2	no	—
436	#125	—	2	1	no	—
437	#125	—	2	2	no	—
438	#125	—	2	1	no	—
439	#125	—	2	1	no	—
440	#125	—	2	1	no	—
441	#125	—	2	1	no	—
442	#125	D₄×C₁₃	1	1	yes	characteristic
443	#124	—	2	2	no	—
444	#124	—	2	1	no	—
445	#124	D₄×C₁₃	1	1	yes	characteristic
446	#123	—	2	2	no	—
447	#123	—	2	1	no	—
448	C₂²⋊Q₈	—	2	2	no	—
449	C₂²⋊Q₈	—	2	2	no	—
450	C₂²⋊Q₈	—	2	1	no	—
451	C₂²⋊Q₈	—	2	1	no	—
452	C₂²⋊Q₈	—	2	2	no	—
453	C₂²⋊Q₈	—	2	1	no	—
454	C₂²⋊Q₈	—	2	1	no	—
455	C₂²⋊Q₈	—	2	1	no	—
456	C₂²⋊Q₈	—	2	1	no	—
457	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
458	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
459	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
460	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
461	#121	D₄×C₁₃	1	1	yes	characteristic
462	C₄×Q₈	—	2	2	no	—
463	C₄×Q₈	—	2	1	no	—
464	C₄×Q₈	—	2	1	no	—
465	C₄×Q₈	—	2	1	no	—
466	C₄×Q₈	—	2	1	no	—
467	C₄×Q₈	—	2	1	no	—
468	C₄×Q₈	—	2	1	no	—
469	C₄×Q₈	—	2	1	no	—
470	C₄×Q₈	—	2	1	no	—
471	C₄×Q₈	—	2	1	no	—
472	C₄×Q₈	D₄×C₁₃	1	2	yes	—
473	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
474	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
475	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
476	C₄×D₄	—	2	1	no	—
477	C₄×D₄	—	2	1	no	—
478	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
479	#117	—	2	2	no	—
480	#117	—	2	1	no	—
481	#117	—	2	1	no	—
482	#117	—	2	1	no	—
483	#117	—	2	1	no	—
484	#117	—	2	1	no	—
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
487	#107	—	2	2	no	—
488	#107	—	2	1	no	—
489	#107	—	2	1	no	—
490	#107	—	2	1	no	—
491	#106	—	2	1	no	—
492	#106	—	2	1	no	—
493	#106	—	2	1	no	—
494	C₄⋊C₈	—	2	1	no	—
495	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
496	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
497	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
498	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
499	#103	—	2	2	no	—
500	#103	—	2	1	no	—
501	#103	—	2	1	no	—
502	#103	—	2	1	no	—
503	#103	—	2	1	no	—
504	#103	—	2	1	no	—
505	#103	—	2	2	no	—
506	#103	—	2	1	no	—
507	#103	—	2	1	no	—
508	#102	—	2	1	no	—
509	C₂²⋊C₈	—	2	1	no	—
510	#97	—	2	1	no	—
511	C₄×C₈	—	2	1	no	—
512	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
513	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
514	C₂×C₁₃	—	4	1	no	—
515	C₂×C₁₃	—	8	1	no	—
516	C₂×C₁₃	#3011	1	1	yes	characteristic
517	C₂×C₁₃	#3013	1	1	yes	characteristic
518	C₂×C₁₃	#3018	1	1	yes	characteristic
519	C₂×Q₈	—	2	2	no	—
520	C₂×Q₈	—	2	1	no	—
521	C₂×Q₈	—	2	1	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
525	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
526	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
527	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	1	no	—
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	Q₁₆	—	4	4	no	—
536	Q₁₆	—	8	1	no	—
537	SD₁₆	—	8	1	no	—
538	M₁₆	—	8	1	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	—	4	2	no	—
546	C₄⋊C₄	—	2	2	no	—
547	C₄⋊C₄	—	2	2	no	—
548	C₄⋊C₄	—	2	2	no	—
549	C₄⋊C₄	—	2	2	no	—
550	C₄⋊C₄	—	2	2	no	—
551	C₄⋊C₄	—	2	2	no	—
552	C₄⋊C₄	—	2	2	no	—
553	C₄⋊C₄	—	2	2	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	2	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	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	4	1	no	—
575	C₄⋊C₄	—	4	1	no	—
576	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
577	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
578	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
579	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
580	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
581	C₂²⋊C₄	—	2	2	no	—
582	C₂²⋊C₄	—	2	2	no	—
583	C₂²⋊C₄	—	2	2	no	—
584	C₂²⋊C₄	—	2	1	no	—
585	C₂²⋊C₄	—	2	2	no	—
586	C₂²⋊C₄	—	2	1	no	—
587	C₂²⋊C₄	—	2	1	no	—
588	C₂²⋊C₄	—	2	1	no	—
589	C₂²⋊C₄	—	2	1	no	—
590	C₂²⋊C₄	—	2	1	no	—
591	C₂²⋊C₄	—	2	1	no	—
592	C₂²⋊C₄	—	4	1	no	—
593	C₄²	—	2	2	no	—
594	C₄²	—	2	2	no	—
595	C₄²	—	2	2	no	—
596	C₄²	—	2	2	no	—
597	C₄²	—	2	1	no	—
598	C₄²	—	2	1	no	—
599	C₄²	—	2	1	no	—
600	C₄²	—	4	1	no	—
601	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
602	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
603	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
604	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
605	C₁₃	#18711	1	1	yes	characteristic, direct product factor, Sylow
606	C₂³	—	2	1	no	—
607	C₂³	C₁₃×#120	1	1	yes	characteristic
608	Q₈	—	2	1	no	—
609	Q₈	—	2	1	no	—
610	Q₈	—	2	1	no	—
611	Q₈	—	2	1	no	—
612	Q₈	—	2	1	no	—
613	Q₈	—	2	1	no	—
614	Q₈	—	4	2	no	—
615	Q₈	—	4	2	no	—
616	Q₈	—	4	1	no	—
617	Q₈	—	4	1	no	—
618	Q₈	—	4	1	no	—
619	Q₈	—	4	1	no	—
620	Q₈	—	8	1	no	—
621	Q₈	—	8	2	no	—
622	D₄	—	2	1	no	—
623	D₄	—	2	1	no	—
624	D₄	—	8	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	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	—	8	2	no	—
644	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
645	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
646	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
647	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
648	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
649	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
650	C₈	—	2	2	no	—
651	C₈	—	4	1	no	—
652	C₈	—	4	1	no	—
653	C₈	—	4	1	no	—
654	C₈	—	4	1	no	—
655	C₈	—	4	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	1	no	—
661	C₂²	—	4	1	no	—
662	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	1	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	1	no	—
671	C₄	—	4	2	no	—
672	C₄	—	4	1	no	—
673	C₄	—	4	2	no	—
674	C₄	—	4	1	no	—
675	C₄	—	4	1	no	—
676	C₄	—	8	1	no	—
677	C₄	—	8	1	no	—
678	C₄	C₁₃×#577	1	1	yes	characteristic
679	C₄	C₁₃×#578	1	1	yes	characteristic
680	C₄	C₁₃×#578	1	1	yes	characteristic
681	C₄	C₁₃×#578	1	1	yes	characteristic
682	C₂	—	4	1	no	—
683	C₂	—	8	1	no	—
684	C₂	C₁₃×#3011	1	1	yes	characteristic
685	C₂	C₁₃×#3013	1	1	yes	characteristic
686	C₂	C₁₃×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#121	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#3237	C₂	semidirect
4. C₁₃×#3170	C₂	semidirect
5. C₁₃×#1650	C₂	semidirect
6. C₁₃×#1648	C₂	semidirect
7. C₁₃×#1645	C₂	semidirect
8. C₁₃×#1643	C₂	semidirect
9. C₁₃×#1638	C₂	semidirect
10. C₁₃×#1636	C₂	semidirect
11. C₁₃×#1633	C₂	semidirect
12. C₁₃×#1632	C₂	semidirect
13. C₁₃×#1559	C₂	semidirect
15. C₁₃×#1493	C₂	semidirect
176. #18711	C₁₃	direct (N × H)
265. #3237	C₂×C₁₃	semidirect
266. #3170	C₂×C₁₃	semidirect
267. #1650	C₂×C₁₃	semidirect
268. #1648	C₂×C₁₃	semidirect
269. #1645	C₂×C₁₃	semidirect
270. #1643	C₂×C₁₃	semidirect
271. #1638	C₂×C₁₃	semidirect
272. #1636	C₂×C₁₃	semidirect
273. #1633	C₂×C₁₃	semidirect
274. #1632	C₂×C₁₃	semidirect
275. #1559	C₂×C₁₃	semidirect
277. #1493	C₂×C₁₃	semidirect
605. C₁₃	#18711	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×#3555	2
C₁₃×#3252	2
C₁₃×#3237	2
C₁₃×#3170	2
C₁₃×#1650	2
C₁₃×#1648	2
C₁₃×#1645	2
C₁₃×#1643	2
C₁₃×#1638	2
C₁₃×#1636	2
C₁₃×#1633	2
C₁₃×#1632	2
C₁₃×#1559	2
C₁₃×#1494	2
C₁₃×#1493	2
#18711	13

Subgroups — C13×#18711 #15705050

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18711 #15705050