Subgroups — C₁₃×#19774 #15706113

Order 3328.

650 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3380	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3331	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3295	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3294	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1719	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1697	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1683	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1682	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1675	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1644	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1635	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1629	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1622	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1581	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#554	C₂²	1	1	yes	characteristic
17	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
18	C₁₃×#547	C₂²	1	1	yes	characteristic
19	D₄²×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
21	C₁₃×#499	—	2	1	no	—
22	C₁₃×#492	C₂²	1	1	yes	characteristic
23	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#486	C₂²	1	1	yes	characteristic
26	C₁₃×#486	C₂²	1	1	yes	characteristic
27	C₁₃×#483	—	2	1	no	—
28	C₁₃×#481	—	2	1	no	—
29	C₁₃×#480	—	2	1	no	—
30	C₁₃×#478	—	2	1	no	—
31	C₁₃×#478	—	2	1	no	—
32	C₁₃×#476	C₂²	1	1	yes	characteristic
33	C₁₃×#476	C₂²	1	1	yes	characteristic
34	C₁₃×#476	C₂²	1	1	yes	characteristic
35	C₁₃×#476	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#474	C₂²	1	1	yes	characteristic
37	C₁₃×#470	—	2	1	no	—
38	C₁₃×#466	—	2	1	no	—
39	C₁₃×#465	—	2	1	no	—
40	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#460	C₂²	1	1	yes	characteristic
42	C₁₃×#459	C₂²	1	1	yes	characteristic
43	C₁₃×#452	—	2	1	no	—
44	C₁₃×#450	—	2	1	no	—
45	C₁₃×#447	—	2	1	no	—
46	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
47	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×D₈	—	2	1	no	—
49	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
50	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
51	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
52	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
53	C₁₃×#417	—	2	1	no	—
54	C₂×C₁₃×#102	—	2	1	no	—
55	C₂×C₁₃×#102	—	2	1	no	—
56	C₁₃×#335	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#335	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#333	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#333	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#332	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#331	C₂²	1	1	yes	characteristic
62	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#322	C₂²	1	1	yes	characteristic, complemented
67	C₂×C₁₃×#41	—	2	1	no	—
68	C₂²×D₄×C₁₃	—	2	1	no	—
69	C₂²×D₄×C₁₃	—	2	1	no	—
70	C₂×C₁₃×Q₁₆	—	2	1	no	—
71	C₂×C₁₃×SD₁₆	—	2	1	no	—
72	C₂×C₁₃×SD₁₆	—	4	1	no	—
73	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
74	C₂×C₁₃×D₈	—	2	1	no	—
75	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
76	C₂×C₁₃×M₁₆	—	2	1	no	—
77	C₂²×C₈×C₁₃	—	2	1	no	—
78	C₂²×C₈×C₁₃	—	2	1	no	—
79	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₃×#127	C₂³	1	1	yes	characteristic
83	C₁₃×#125	—	2	1	no	—
84	C₁₃×#125	—	2	1	no	—
85	C₁₃×#123	—	4	1	no	—
86	C₁₃×C₂²⋊Q₈	—	2	1	no	—
87	C₁₃×C₂²⋊Q₈	—	2	1	no	—
88	C₁₃×C₂²⋊Q₈	—	2	1	no	—
89	C₁₃×C₂²⋊Q₈	—	4	1	no	—
90	C₁₃×C₂²⋊Q₈	—	4	1	no	—
91	C₁₃×#121	—	2	1	no	—
92	C₁₃×#121	—	2	1	no	—
93	C₁₃×#121	—	2	1	no	—
94	C₁₃×#120	—	4	1	no	—
95	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₁₃	—	2	1	no	—
97	C₄×D₄×C₁₃	—	2	1	no	—
98	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
104	C₁₃×#107	—	2	1	no	—
105	C₁₃×#107	—	2	1	no	—
106	C₁₃×#107	—	2	1	no	—
107	C₁₃×#107	D₄	1	1	yes	characteristic
108	C₁₃×#106	—	2	1	no	—
109	C₁₃×#106	—	2	1	no	—
110	C₁₃×#106	—	2	1	no	—
111	C₁₃×#106	—	2	1	no	—
112	C₁₃×#106	D₄	1	1	yes	characteristic
113	C₁₃×C₄⋊C₈	—	2	1	no	—
114	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₃×#103	—	2	1	no	—
119	C₁₃×#103	—	2	1	no	—
120	C₁₃×#103	—	2	1	no	—
121	C₁₃×#103	—	4	1	no	—
122	C₁₃×#103	D₄	1	1	yes	characteristic
123	C₁₃×#102	—	2	1	no	—
124	C₁₃×#102	—	2	1	no	—
125	C₁₃×#102	—	2	1	no	—
126	C₁₃×#102	—	2	1	no	—
127	C₁₃×#102	—	2	1	no	—
128	C₁₃×#102	—	2	1	no	—
129	C₁₃×#102	—	2	1	no	—
130	C₁₃×#102	—	2	1	no	—
131	C₁₃×#102	—	2	1	no	—
132	C₁₃×#102	—	2	1	no	—
133	C₁₃×#102	—	2	1	no	—
134	C₁₃×#102	D₄	1	1	yes	characteristic
135	C₁₃×#102	D₄	1	1	yes	characteristic
136	C₁₃×#102	D₄	1	1	yes	characteristic
137	C₁₃×C₂²⋊C₈	—	2	1	no	—
138	C₁₃×C₂²⋊C₈	—	2	1	no	—
139	C₁₃×C₂²⋊C₈	—	2	1	no	—
140	C₄×C₈×C₁₃	—	2	1	no	—
141	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	#19774	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂⁴×C₁₃	—	4	1	no	—
146	C₁₃×#41	—	4	2	no	—
147	C₁₃×#41	—	8	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	2	1	no	—
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂×D₄×C₁₃	—	2	1	no	—
153	C₂×D₄×C₁₃	—	2	1	no	—
154	C₂×D₄×C₁₃	—	2	1	no	—
155	C₂×D₄×C₁₃	—	4	1	no	—
156	C₂×D₄×C₁₃	—	4	1	no	—
157	C₂×D₄×C₁₃	—	4	2	no	—
158	C₂×D₄×C₁₃	—	4	2	no	—
159	C₂×D₄×C₁₃	—	4	1	no	—
160	C₂×D₄×C₁₃	—	8	1	no	—
161	C₂×D₄×C₁₃	—	8	1	no	—
162	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	4	1	no	—
169	C₂²×C₄×C₁₃	—	4	1	no	—
170	C₂²×C₄×C₁₃	—	4	1	no	—
171	C₁₃×Q₁₆	—	8	1	no	—
172	C₁₃×SD₁₆	—	2	2	no	—
173	C₁₃×SD₁₆	—	8	1	no	—
174	C₁₃×SD₁₆	—	8	2	no	—
175	C₁₃×D₈	—	2	2	no	—
176	C₁₃×D₈	—	8	1	no	—
177	C₁₃×M₁₆	—	8	1	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	2	1	no	—
183	C₂×C₈×C₁₃	—	8	1	no	—
184	C₂×C₈×C₁₃	—	8	1	no	—
185	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	—	4	1	no	—
197	C₁₃×C₄⋊C₄	—	4	1	no	—
198	C₁₃×C₄⋊C₄	—	4	1	no	—
199	C₁₃×C₄⋊C₄	—	4	1	no	—
200	C₁₃×C₄⋊C₄	—	4	1	no	—
201	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
202	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
203	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
204	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
205	C₁₃×C₂²⋊C₄	—	2	1	no	—
206	C₁₃×C₂²⋊C₄	—	2	1	no	—
207	C₁₃×C₂²⋊C₄	—	2	1	no	—
208	C₁₃×C₂²⋊C₄	—	4	1	no	—
209	C₁₃×C₂²⋊C₄	—	4	1	no	—
210	C₁₃×C₂²⋊C₄	—	4	1	no	—
211	C₁₃×C₂²⋊C₄	—	4	1	no	—
212	C₄²×C₁₃	—	2	1	no	—
213	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
214	#3380	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#3331	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#3295	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#3294	C₂×C₁₃	1	1	yes	characteristic
218	#1719	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1697	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1683	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1682	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1675	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1644	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1635	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1629	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1622	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1581	C₂×C₁₃	1	1	yes	characteristic, complemented
228	SD₁₆⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
229	C₂³×C₁₃	—	2	1	no	—
230	C₂³×C₁₃	—	2	1	no	—
231	C₂³×C₁₃	—	2	1	no	—
232	C₂³×C₁₃	—	4	1	no	—
233	C₂³×C₁₃	—	8	2	no	—
234	C₂³×C₁₃	—	8	2	no	—
235	C₂³×C₁₃	—	16	1	no	—
236	Q₈×C₁₃	—	2	1	no	—
237	Q₈×C₁₃	—	2	1	no	—
238	Q₈×C₁₃	—	4	1	no	—
239	Q₈×C₁₃	—	4	1	no	—
240	Q₈×C₁₃	—	8	1	no	—
241	Q₈×C₁₃	—	8	1	no	—
242	D₄×C₁₃	—	2	1	no	—
243	D₄×C₁₃	—	2	1	no	—
244	D₄×C₁₃	—	2	1	no	—
245	D₄×C₁₃	—	2	1	no	—
246	D₄×C₁₃	—	4	1	no	—
247	D₄×C₁₃	—	4	1	no	—
248	D₄×C₁₃	—	4	1	no	—
249	D₄×C₁₃	—	4	1	no	—
250	D₄×C₁₃	—	8	1	no	—
251	D₄×C₁₃	—	8	2	no	—
252	D₄×C₁₃	—	8	2	no	—
253	D₄×C₁₃	—	8	2	no	—
254	D₄×C₁₃	#135	1	2	yes	—
255	D₄×C₁₃	#137	1	2	yes	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	1	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	1	no	—
268	C₂×C₄×C₁₃	—	4	1	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	8	2	no	—
271	C₂×C₄×C₁₃	—	16	1	no	—
272	C₂×C₄×C₁₃	—	16	1	no	—
273	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
276	C₈×C₁₃	—	2	1	no	—
277	C₈×C₁₃	—	2	1	no	—
278	C₈×C₁₃	—	2	1	no	—
279	C₈×C₁₃	—	2	1	no	—
280	C₈×C₁₃	—	4	1	no	—
281	C₈×C₁₃	—	4	1	no	—
282	C₈×C₁₃	—	4	1	no	—
283	C₈×C₁₃	—	4	1	no	—
284	C₈×C₁₃	—	4	1	no	—
285	#554	C₂²×C₁₃	1	1	yes	characteristic
286	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
287	#547	C₂²×C₁₃	1	1	yes	characteristic
288	D₄²	C₂²×C₁₃	1	1	yes	characteristic
289	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
290	#499	—	2	1	no	—
291	#492	C₂²×C₁₃	1	1	yes	characteristic
292	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
293	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
294	#486	C₂²×C₁₃	1	1	yes	characteristic
295	#486	C₂²×C₁₃	1	1	yes	characteristic
296	#483	—	2	1	no	—
297	#481	—	2	1	no	—
298	#480	—	2	1	no	—
299	#478	—	2	1	no	—
300	#478	—	2	1	no	—
301	#476	C₂²×C₁₃	1	1	yes	characteristic
302	#476	C₂²×C₁₃	1	1	yes	characteristic
303	#476	C₂²×C₁₃	1	1	yes	characteristic
304	#476	C₂²×C₁₃	1	1	yes	characteristic, complemented
305	#474	C₂²×C₁₃	1	1	yes	characteristic
306	#470	—	2	1	no	—
307	#466	—	2	1	no	—
308	#465	—	2	1	no	—
309	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
310	#460	C₂²×C₁₃	1	1	yes	characteristic
311	#459	C₂²×C₁₃	1	1	yes	characteristic
312	#452	—	2	1	no	—
313	#450	—	2	1	no	—
314	#447	—	2	1	no	—
315	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
316	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
317	C₄×D₈	—	2	1	no	—
318	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
319	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
320	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
321	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
322	#417	—	2	1	no	—
323	C₂×#102	—	2	1	no	—
324	C₂×#102	—	2	1	no	—
325	#335	C₂²×C₁₃	1	1	yes	characteristic, complemented
326	#335	C₂²×C₁₃	1	1	yes	characteristic, complemented
327	#333	C₂²×C₁₃	1	1	yes	characteristic, complemented
328	#333	C₂²×C₁₃	1	1	yes	characteristic, complemented
329	#332	C₂²×C₁₃	1	1	yes	characteristic, complemented
330	#331	C₂²×C₁₃	1	1	yes	characteristic
331	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
332	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
333	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
334	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
335	#322	C₂²×C₁₃	1	1	yes	characteristic, complemented
336	C₂²×C₁₃	—	2	2	no	—
337	C₂²×C₁₃	—	2	2	no	—
338	C₂²×C₁₃	—	4	1	no	—
339	C₂²×C₁₃	—	4	1	no	—
340	C₂²×C₁₃	—	4	1	no	—
341	C₂²×C₁₃	—	4	1	no	—
342	C₂²×C₁₃	—	4	1	no	—
343	C₂²×C₁₃	—	4	1	no	—
344	C₂²×C₁₃	—	4	1	no	—
345	C₂²×C₁₃	—	8	1	no	—
346	C₂²×C₁₃	—	8	1	no	—
347	C₂²×C₁₃	—	8	1	no	—
348	C₂²×C₁₃	—	16	4	no	—
349	C₂²×C₁₃	D₄²	1	1	yes	characteristic
350	C₄×C₁₃	—	2	1	no	—
351	C₄×C₁₃	—	4	1	no	—
352	C₄×C₁₃	—	4	1	no	—
353	C₄×C₁₃	—	4	1	no	—
354	C₄×C₁₃	—	4	1	no	—
355	C₄×C₁₃	—	4	1	no	—
356	C₄×C₁₃	—	8	1	no	—
357	C₄×C₁₃	—	8	1	no	—
358	C₄×C₁₃	—	8	1	no	—
359	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
360	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
361	C₄×C₁₃	#576	1	1	yes	characteristic
362	C₄×C₁₃	#577	1	1	yes	characteristic
363	C₂×#41	—	2	1	no	—
364	C₂²×D₄	—	2	1	no	—
365	C₂²×D₄	—	2	1	no	—
366	C₂×Q₁₆	—	2	1	no	—
367	C₂×SD₁₆	—	2	1	no	—
368	C₂×SD₁₆	—	4	1	no	—
369	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
370	C₂×D₈	—	2	1	no	—
371	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
372	C₂×M₁₆	—	2	1	no	—
373	C₂²×C₈	—	2	1	no	—
374	C₂²×C₈	—	2	1	no	—
375	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
376	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
377	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
378	#127	C₂³×C₁₃	1	1	yes	characteristic
379	#125	—	2	1	no	—
380	#125	—	2	1	no	—
381	#123	—	4	1	no	—
382	C₂²⋊Q₈	—	2	1	no	—
383	C₂²⋊Q₈	—	2	1	no	—
384	C₂²⋊Q₈	—	2	1	no	—
385	C₂²⋊Q₈	—	4	1	no	—
386	C₂²⋊Q₈	—	4	1	no	—
387	#121	—	2	1	no	—
388	#121	—	2	1	no	—
389	#121	—	2	1	no	—
390	#120	—	4	1	no	—
391	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
395	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
396	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	#107	—	2	1	no	—
401	#107	—	2	1	no	—
402	#107	—	2	1	no	—
403	#107	D₄×C₁₃	1	1	yes	characteristic
404	#106	—	2	1	no	—
405	#106	—	2	1	no	—
406	#106	—	2	1	no	—
407	#106	—	2	1	no	—
408	#106	D₄×C₁₃	1	1	yes	characteristic
409	C₄⋊C₈	—	2	1	no	—
410	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
411	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
412	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
413	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
414	#103	—	2	1	no	—
415	#103	—	2	1	no	—
416	#103	—	2	1	no	—
417	#103	—	4	1	no	—
418	#103	D₄×C₁₃	1	1	yes	characteristic
419	#102	—	2	1	no	—
420	#102	—	2	1	no	—
421	#102	—	2	1	no	—
422	#102	—	2	1	no	—
423	#102	—	2	1	no	—
424	#102	—	2	1	no	—
425	#102	—	2	1	no	—
426	#102	—	2	1	no	—
427	#102	—	2	1	no	—
428	#102	—	2	1	no	—
429	#102	—	2	1	no	—
430	#102	D₄×C₁₃	1	1	yes	characteristic
431	#102	D₄×C₁₃	1	1	yes	characteristic
432	#102	D₄×C₁₃	1	1	yes	characteristic
433	C₂²⋊C₈	—	2	1	no	—
434	C₂²⋊C₈	—	2	1	no	—
435	C₂²⋊C₈	—	2	1	no	—
436	C₄×C₈	—	2	1	no	—
437	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
438	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
439	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
440	C₂×C₁₃	—	4	2	no	—
441	C₂×C₁₃	—	4	2	no	—
442	C₂×C₁₃	—	8	1	no	—
443	C₂×C₁₃	—	16	1	no	—
444	C₂×C₁₃	#3266	1	1	yes	characteristic
445	C₂×C₁₃	#3280	1	1	yes	characteristic
446	C₂×C₁₃	#3288	1	1	yes	characteristic
447	C₂⁴	—	4	1	no	—
448	#41	—	4	2	no	—
449	#41	—	8	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	4	1	no	—
458	C₂×D₄	—	4	1	no	—
459	C₂×D₄	—	4	2	no	—
460	C₂×D₄	—	4	2	no	—
461	C₂×D₄	—	4	1	no	—
462	C₂×D₄	—	8	1	no	—
463	C₂×D₄	—	8	1	no	—
464	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
465	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
466	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	4	1	no	—
471	C₂²×C₄	—	4	1	no	—
472	C₂²×C₄	—	4	1	no	—
473	Q₁₆	—	8	1	no	—
474	SD₁₆	—	2	2	no	—
475	SD₁₆	—	8	1	no	—
476	SD₁₆	—	8	2	no	—
477	D₈	—	2	2	no	—
478	D₈	—	8	1	no	—
479	M₁₆	—	8	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	8	1	no	—
486	C₂×C₈	—	8	1	no	—
487	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
488	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
489	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
490	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
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	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	4	1	no	—
499	C₄⋊C₄	—	4	1	no	—
500	C₄⋊C₄	—	4	1	no	—
501	C₄⋊C₄	—	4	1	no	—
502	C₄⋊C₄	—	4	1	no	—
503	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
504	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
505	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
506	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	2	1	no	—
510	C₂²⋊C₄	—	4	1	no	—
511	C₂²⋊C₄	—	4	1	no	—
512	C₂²⋊C₄	—	4	1	no	—
513	C₂²⋊C₄	—	4	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
516	C₁₃	#19774	1	1	yes	characteristic, direct product factor, Sylow
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	2	1	no	—
520	C₂³	—	4	1	no	—
521	C₂³	—	8	2	no	—
522	C₂³	—	8	2	no	—
523	C₂³	—	16	1	no	—
524	Q₈	—	2	1	no	—
525	Q₈	—	2	1	no	—
526	Q₈	—	4	1	no	—
527	Q₈	—	4	1	no	—
528	Q₈	—	8	1	no	—
529	Q₈	—	8	1	no	—
530	D₄	—	2	1	no	—
531	D₄	—	2	1	no	—
532	D₄	—	2	1	no	—
533	D₄	—	2	1	no	—
534	D₄	—	4	1	no	—
535	D₄	—	4	1	no	—
536	D₄	—	4	1	no	—
537	D₄	—	4	1	no	—
538	D₄	—	8	1	no	—
539	D₄	—	8	2	no	—
540	D₄	—	8	2	no	—
541	D₄	—	8	2	no	—
542	D₄	C₁₃×#135	1	2	yes	—
543	D₄	C₁₃×#137	1	2	yes	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	8	2	no	—
559	C₂×C₄	—	16	1	no	—
560	C₂×C₄	—	16	1	no	—
561	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
562	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
563	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
564	C₈	—	2	1	no	—
565	C₈	—	2	1	no	—
566	C₈	—	2	1	no	—
567	C₈	—	2	1	no	—
568	C₈	—	4	1	no	—
569	C₈	—	4	1	no	—
570	C₈	—	4	1	no	—
571	C₈	—	4	1	no	—
572	C₈	—	4	1	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	8	1	no	—
583	C₂²	—	8	1	no	—
584	C₂²	—	8	1	no	—
585	C₂²	—	16	4	no	—
586	C₂²	D₄²×C₁₃	1	1	yes	characteristic
587	C₄	—	2	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	1	no	—
593	C₄	—	8	1	no	—
594	C₄	—	8	1	no	—
595	C₄	—	8	1	no	—
596	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
597	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
598	C₄	C₁₃×#576	1	1	yes	characteristic
599	C₄	C₁₃×#577	1	1	yes	characteristic
600	C₂	—	4	2	no	—
601	C₂	—	4	2	no	—
602	C₂	—	8	1	no	—
603	C₂	—	16	1	no	—
604	C₂	C₁₃×#3266	1	1	yes	characteristic
605	C₂	C₁₃×#3280	1	1	yes	characteristic
606	C₂	C₁₃×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3294	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3380	C₂	semidirect
2. C₁₃×#3331	C₂	semidirect
3. C₁₃×#3295	C₂	semidirect
5. C₁₃×#1719	C₂	semidirect
6. C₁₃×#1697	C₂	semidirect
7. C₁₃×#1683	C₂	semidirect
8. C₁₃×#1682	C₂	semidirect
9. C₁₃×#1675	C₂	semidirect
10. C₁₃×#1644	C₂	semidirect
11. C₁₃×#1635	C₂	semidirect
12. C₁₃×#1629	C₂	semidirect
13. C₁₃×#1622	C₂	semidirect
14. C₁₃×#1581	C₂	semidirect
15. C₁₃×SD₁₆⋊C₈	C₂	semidirect
17. C₁₃×#554	C₂²	semidirect
20. C₁₃×#500	C₂²	semidirect
23. C₁₃×#487	C₂²	semidirect
24. C₁₃×#487	C₂²	semidirect
35. C₁₃×#476	C₂²	semidirect
40. C₁₃×#462	C₂²	semidirect
46. C₈×Q₈×C₁₃	C₂²	semidirect
50. C₁₃×#436	C₂²	semidirect
56. C₁₃×#335	C₂²	semidirect
57. C₁₃×#335	C₂²	semidirect
58. C₁₃×#333	C₂²	semidirect
59. C₁₃×#333	C₂²	semidirect
60. C₁₃×#332	C₂²	semidirect
62. C₁₃×Q₈⋊C₈	C₂²	semidirect
65. C₁₃×D₄⋊C₈	C₂²	semidirect
66. C₁₃×#322	C₂²	semidirect
144. #19774	C₁₃	direct (N × H)
214. #3380	C₂×C₁₃	semidirect
215. #3331	C₂×C₁₃	semidirect
216. #3295	C₂×C₁₃	semidirect
218. #1719	C₂×C₁₃	semidirect
219. #1697	C₂×C₁₃	semidirect
220. #1683	C₂×C₁₃	semidirect
221. #1682	C₂×C₁₃	semidirect
222. #1675	C₂×C₁₃	semidirect
223. #1644	C₂×C₁₃	semidirect
224. #1635	C₂×C₁₃	semidirect
225. #1629	C₂×C₁₃	semidirect
226. #1622	C₂×C₁₃	semidirect
227. #1581	C₂×C₁₃	semidirect
228. SD₁₆⋊C₈	C₂×C₁₃	semidirect
286. #554	C₂²×C₁₃	semidirect
289. #500	C₂²×C₁₃	semidirect
292. #487	C₂²×C₁₃	semidirect
293. #487	C₂²×C₁₃	semidirect
304. #476	C₂²×C₁₃	semidirect
309. #462	C₂²×C₁₃	semidirect
315. C₈×Q₈	C₂²×C₁₃	semidirect
319. #436	C₂²×C₁₃	semidirect
325. #335	C₂²×C₁₃	semidirect
326. #335	C₂²×C₁₃	semidirect
327. #333	C₂²×C₁₃	semidirect
328. #333	C₂²×C₁₃	semidirect
329. #332	C₂²×C₁₃	semidirect
331. Q₈⋊C₈	C₂²×C₁₃	semidirect
334. D₄⋊C₈	C₂²×C₁₃	semidirect
335. #322	C₂²×C₁₃	semidirect
516. C₁₃	#19774	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×#3380	2
C₁₃×#3331	2
C₁₃×#3295	2
C₁₃×#3294	2
C₁₃×#1719	2
C₁₃×#1697	2
C₁₃×#1683	2
C₁₃×#1682	2
C₁₃×#1675	2
C₁₃×#1644	2
C₁₃×#1635	2
C₁₃×#1629	2
C₁₃×#1622	2
C₁₃×#1581	2
C₁₃×SD₁₆⋊C₈	2
#19774	13

Subgroups — C13×#19774 #15706113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19774 #15706113