Subgroups — C₁₃×#19831 #15706170

Order 3328.

614 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3392	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3364	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3332	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#3302	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1719	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1699	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1682	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1680	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1665	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1648	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1647	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1641	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1628	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1583	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#557	C₂²	1	1	yes	characteristic
17	C₁₃×#556	C₂²	1	1	yes	characteristic
18	C₁₃×#550	C₂²	1	1	yes	characteristic
19	C₁₃×#547	C₂²	1	1	yes	characteristic
20	C₁₃×#500	C₂²	1	1	yes	characteristic
21	C₁₃×#492	—	2	1	no	—
22	C₁₃×#492	C₂²	1	1	yes	characteristic
23	C₁₃×#488	—	2	1	no	—
24	C₁₃×#487	C₂²	1	1	yes	characteristic
25	C₁₃×#487	C₂²	1	1	yes	characteristic
26	C₁₃×#486	C₂²	1	1	yes	characteristic
27	C₁₃×#486	C₂²	1	1	yes	characteristic
28	C₁₃×#485	—	2	1	no	—
29	C₁₃×#481	—	2	1	no	—
30	C₁₃×#479	—	2	1	no	—
31	C₁₃×#475	C₂²	1	1	yes	characteristic
32	C₁₃×#474	C₂²	1	1	yes	characteristic
33	C₁₃×#474	C₂²	1	1	yes	characteristic
34	C₁₃×#469	—	2	1	no	—
35	C₁₃×#467	—	2	1	no	—
36	C₁₃×#464	—	2	1	no	—
37	C₁₃×#462	C₂²	1	1	yes	characteristic
38	C₁₃×#462	C₂²	1	1	yes	characteristic
39	C₁₃×#461	—	2	1	no	—
40	C₁₃×#461	C₂²	1	1	yes	characteristic
41	C₁₃×#460	—	2	1	no	—
42	C₁₃×#460	C₂²	1	1	yes	characteristic
43	C₁₃×#459	C₂²	1	1	yes	characteristic
44	C₁₃×#452	—	2	1	no	—
45	C₁₃×#449	—	2	1	no	—
46	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×Q₁₆	—	2	1	no	—
49	C₄×C₁₃×SD₁₆	—	2	1	no	—
50	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
52	C₁₃×#436	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
54	C₁₃×#417	—	2	1	no	—
55	C₁₃×#416	—	2	1	no	—
56	C₁₃×#335	C₂²	1	1	yes	characteristic
57	C₁₃×#334	C₂²	1	1	yes	characteristic
58	C₁₃×#332	C₂²	1	1	yes	characteristic
59	C₁₃×#332	C₂²	1	1	yes	characteristic
60	C₁₃×#332	C₂²	1	1	yes	characteristic
61	C₁₃×#331	C₂²	1	1	yes	characteristic
62	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₃×#322	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	—	2	1	no	—
68	C₂×C₁₃×#41	—	2	1	no	—
69	C₂×C₁₃×Q₁₆	—	2	1	no	—
70	C₂×C₁₃×Q₁₆	—	2	1	no	—
71	C₂×C₁₃×SD₁₆	—	2	1	no	—
72	C₂×C₁₃×SD₁₆	—	2	1	no	—
73	C₂×C₁₃×SD₁₆	—	2	1	no	—
74	C₂×C₁₃×SD₁₆	—	2	1	no	—
75	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
76	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
77	C₂×C₁₃×D₈	—	2	1	no	—
78	C₂×C₁₃×M₁₆	—	2	1	no	—
79	C₂²×C₈×C₁₃	—	2	1	no	—
80	C₁₃×C₄⋊Q₈	—	2	1	no	—
81	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₃×#127	—	2	1	no	—
85	C₁₃×#127	C₂³	1	1	yes	characteristic
86	C₁₃×#126	—	4	1	no	—
87	C₁₃×#125	—	2	1	no	—
88	C₁₃×#125	—	4	1	no	—
89	C₁₃×#124	—	2	1	no	—
90	C₁₃×#123	—	4	1	no	—
91	C₁₃×C₂²⋊Q₈	—	2	1	no	—
92	C₁₃×C₂²⋊Q₈	—	2	1	no	—
93	C₁₃×#121	—	2	1	no	—
94	C₁₃×#121	—	2	1	no	—
95	C₁₃×#121	—	4	1	no	—
96	C₄×Q₈×C₁₃	—	2	1	no	—
97	C₄×Q₈×C₁₃	—	2	1	no	—
98	C₄×Q₈×C₁₃	—	2	1	no	—
99	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₁₃	—	2	1	no	—
102	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
103	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₁₃×#117	—	2	1	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₁₃×#107	—	2	1	no	—
107	C₁₃×#107	—	2	1	no	—
108	C₁₃×#107	—	4	1	no	—
109	C₁₃×#106	—	2	1	no	—
110	C₁₃×#106	D₄	1	1	yes	characteristic
111	C₁₃×#106	D₄	1	1	yes	characteristic
112	C₁₃×C₄⋊C₈	—	2	1	no	—
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	—	2	1	no	—
122	C₁₃×#103	—	2	1	no	—
123	C₁₃×#103	—	2	1	no	—
124	C₁₃×#103	—	2	1	no	—
125	C₁₃×#103	—	2	1	no	—
126	C₁₃×#103	D₄	1	1	yes	characteristic
127	C₁₃×#103	D₄	1	1	yes	characteristic
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	—	4	1	no	—
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	C₄×C₈×C₁₃	—	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	#19831	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₁₃×#41	—	4	2	no	—
146	C₁₃×#41	—	4	2	no	—
147	C₁₃×#41	—	8	1	no	—
148	C₁₃×#41	—	8	1	no	—
149	C₂×Q₈×C₁₃	—	2	1	no	—
150	C₂×Q₈×C₁₃	—	2	1	no	—
151	C₂×Q₈×C₁₃	—	2	1	no	—
152	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂×D₄×C₁₃	—	2	1	no	—
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	—	4	1	no	—
158	C₂×D₄×C₁₃	—	4	1	no	—
159	C₂×D₄×C₁₃	—	4	1	no	—
160	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	4	1	no	—
165	C₂²×C₄×C₁₃	—	4	1	no	—
166	C₁₃×Q₁₆	—	4	2	no	—
167	C₁₃×Q₁₆	—	8	1	no	—
168	C₁₃×SD₁₆	—	2	2	no	—
169	C₁₃×SD₁₆	—	4	1	no	—
170	C₁₃×SD₁₆	—	4	2	no	—
171	C₁₃×SD₁₆	—	8	1	no	—
172	C₁₃×SD₁₆	—	8	1	no	—
173	C₁₃×SD₁₆	—	8	1	no	—
174	C₁₃×D₈	—	8	1	no	—
175	C₁₃×M₁₆	—	8	1	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	2	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	—	8	1	no	—
182	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
195	C₁₃×C₄⋊C₄	—	4	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	C₂×D₄	1	1	yes	characteristic
200	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
201	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
202	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
203	C₁₃×C₂²⋊C₄	—	2	1	no	—
204	C₁₃×C₂²⋊C₄	—	2	1	no	—
205	C₁₃×C₂²⋊C₄	—	4	1	no	—
206	C₁₃×C₂²⋊C₄	—	4	1	no	—
207	C₁₃×C₂²⋊C₄	—	4	1	no	—
208	C₁₃×C₂²⋊C₄	—	4	1	no	—
209	C₄²×C₁₃	—	2	1	no	—
210	C₄²×C₁₃	—	2	1	no	—
211	C₄²×C₁₃	—	4	1	no	—
212	C₄²×C₁₃	—	4	1	no	—
213	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
214	#3392	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#3364	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#3332	C₂×C₁₃	1	1	yes	characteristic
217	#3302	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1719	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1699	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1682	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1680	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1665	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1648	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1647	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1641	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1628	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1583	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	—	4	1	no	—
232	Q₈×C₁₃	—	2	1	no	—
233	Q₈×C₁₃	—	2	1	no	—
234	Q₈×C₁₃	—	2	1	no	—
235	Q₈×C₁₃	—	4	1	no	—
236	Q₈×C₁₃	—	4	1	no	—
237	Q₈×C₁₃	—	4	1	no	—
238	Q₈×C₁₃	—	4	1	no	—
239	Q₈×C₁₃	—	4	1	no	—
240	Q₈×C₁₃	—	4	1	no	—
241	Q₈×C₁₃	#135	1	2	yes	—
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	2	no	—
251	D₄×C₁₃	—	8	1	no	—
252	D₄×C₁₃	—	8	2	no	—
253	D₄×C₁₃	—	16	1	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
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	—	4	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	—	8	2	no	—
268	C₂×C₄×C₁₃	—	8	2	no	—
269	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
272	C₈×C₁₃	—	2	1	no	—
273	C₈×C₁₃	—	2	1	no	—
274	C₈×C₁₃	—	2	1	no	—
275	C₈×C₁₃	—	2	1	no	—
276	C₈×C₁₃	—	4	1	no	—
277	C₈×C₁₃	—	4	1	no	—
278	C₈×C₁₃	—	4	1	no	—
279	C₈×C₁₃	—	4	1	no	—
280	C₈×C₁₃	—	4	1	no	—
281	#557	C₂²×C₁₃	1	1	yes	characteristic
282	#556	C₂²×C₁₃	1	1	yes	characteristic
283	#550	C₂²×C₁₃	1	1	yes	characteristic
284	#547	C₂²×C₁₃	1	1	yes	characteristic
285	#500	C₂²×C₁₃	1	1	yes	characteristic
286	#492	—	2	1	no	—
287	#492	C₂²×C₁₃	1	1	yes	characteristic
288	#488	—	2	1	no	—
289	#487	C₂²×C₁₃	1	1	yes	characteristic
290	#487	C₂²×C₁₃	1	1	yes	characteristic
291	#486	C₂²×C₁₃	1	1	yes	characteristic
292	#486	C₂²×C₁₃	1	1	yes	characteristic
293	#485	—	2	1	no	—
294	#481	—	2	1	no	—
295	#479	—	2	1	no	—
296	#475	C₂²×C₁₃	1	1	yes	characteristic
297	#474	C₂²×C₁₃	1	1	yes	characteristic
298	#474	C₂²×C₁₃	1	1	yes	characteristic
299	#469	—	2	1	no	—
300	#467	—	2	1	no	—
301	#464	—	2	1	no	—
302	#462	C₂²×C₁₃	1	1	yes	characteristic
303	#462	C₂²×C₁₃	1	1	yes	characteristic
304	#461	—	2	1	no	—
305	#461	C₂²×C₁₃	1	1	yes	characteristic
306	#460	—	2	1	no	—
307	#460	C₂²×C₁₃	1	1	yes	characteristic
308	#459	C₂²×C₁₃	1	1	yes	characteristic
309	#452	—	2	1	no	—
310	#449	—	2	1	no	—
311	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
312	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
313	C₄×Q₁₆	—	2	1	no	—
314	C₄×SD₁₆	—	2	1	no	—
315	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
316	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
317	#436	C₂²×C₁₃	1	1	yes	characteristic
318	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
319	#417	—	2	1	no	—
320	#416	—	2	1	no	—
321	#335	C₂²×C₁₃	1	1	yes	characteristic
322	#334	C₂²×C₁₃	1	1	yes	characteristic
323	#332	C₂²×C₁₃	1	1	yes	characteristic
324	#332	C₂²×C₁₃	1	1	yes	characteristic
325	#332	C₂²×C₁₃	1	1	yes	characteristic
326	#331	C₂²×C₁₃	1	1	yes	characteristic
327	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
328	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
329	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
330	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
331	#322	C₂²×C₁₃	1	1	yes	characteristic
332	C₂²×C₁₃	—	4	1	no	—
333	C₂²×C₁₃	—	4	1	no	—
334	C₂²×C₁₃	—	4	1	no	—
335	C₂²×C₁₃	—	4	1	no	—
336	C₂²×C₁₃	—	4	1	no	—
337	C₂²×C₁₃	—	4	1	no	—
338	C₂²×C₁₃	—	8	1	no	—
339	C₂²×C₁₃	—	8	1	no	—
340	C₂²×C₁₃	—	8	1	no	—
341	C₂²×C₁₃	D₄²	1	1	yes	characteristic
342	C₄×C₁₃	—	2	2	no	—
343	C₄×C₁₃	—	2	1	no	—
344	C₄×C₁₃	—	4	1	no	—
345	C₄×C₁₃	—	4	1	no	—
346	C₄×C₁₃	—	4	1	no	—
347	C₄×C₁₃	—	4	1	no	—
348	C₄×C₁₃	—	4	1	no	—
349	C₄×C₁₃	—	8	1	no	—
350	C₄×C₁₃	—	8	1	no	—
351	C₄×C₁₃	—	8	1	no	—
352	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
353	C₄×C₁₃	#575	1	1	yes	characteristic
354	C₄×C₁₃	#576	1	1	yes	characteristic
355	C₄×C₁₃	#577	1	1	yes	characteristic
356	C₂×#41	—	2	1	no	—
357	C₂×#41	—	2	1	no	—
358	C₂×Q₁₆	—	2	1	no	—
359	C₂×Q₁₆	—	2	1	no	—
360	C₂×SD₁₆	—	2	1	no	—
361	C₂×SD₁₆	—	2	1	no	—
362	C₂×SD₁₆	—	2	1	no	—
363	C₂×SD₁₆	—	2	1	no	—
364	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
365	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
366	C₂×D₈	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂²×C₈	—	2	1	no	—
369	C₄⋊Q₈	—	2	1	no	—
370	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
371	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
372	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
373	#127	—	2	1	no	—
374	#127	C₂³×C₁₃	1	1	yes	characteristic
375	#126	—	4	1	no	—
376	#125	—	2	1	no	—
377	#125	—	4	1	no	—
378	#124	—	2	1	no	—
379	#123	—	4	1	no	—
380	C₂²⋊Q₈	—	2	1	no	—
381	C₂²⋊Q₈	—	2	1	no	—
382	#121	—	2	1	no	—
383	#121	—	2	1	no	—
384	#121	—	4	1	no	—
385	C₄×Q₈	—	2	1	no	—
386	C₄×Q₈	—	2	1	no	—
387	C₄×Q₈	—	2	1	no	—
388	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
389	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
392	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
393	#117	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	#107	—	2	1	no	—
396	#107	—	2	1	no	—
397	#107	—	4	1	no	—
398	#106	—	2	1	no	—
399	#106	D₄×C₁₃	1	1	yes	characteristic
400	#106	D₄×C₁₃	1	1	yes	characteristic
401	C₄⋊C₈	—	2	1	no	—
402	C₄⋊C₈	—	2	1	no	—
403	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
404	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
405	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
406	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
407	#103	—	2	1	no	—
408	#103	—	2	1	no	—
409	#103	—	2	1	no	—
410	#103	—	2	1	no	—
411	#103	—	2	1	no	—
412	#103	—	2	1	no	—
413	#103	—	2	1	no	—
414	#103	—	2	1	no	—
415	#103	D₄×C₁₃	1	1	yes	characteristic
416	#103	D₄×C₁₃	1	1	yes	characteristic
417	#102	—	2	1	no	—
418	#102	—	2	1	no	—
419	#102	—	2	1	no	—
420	#102	—	2	1	no	—
421	#102	—	2	1	no	—
422	#102	—	2	1	no	—
423	#102	—	4	1	no	—
424	#102	D₄×C₁₃	1	1	yes	characteristic
425	#102	D₄×C₁₃	1	1	yes	characteristic
426	C₂²⋊C₈	—	2	1	no	—
427	C₂²⋊C₈	—	2	1	no	—
428	C₄×C₈	—	2	1	no	—
429	C₄×C₈	—	2	1	no	—
430	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
431	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
432	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
433	C₂×C₁₃	—	8	1	no	—
434	C₂×C₁₃	—	8	1	no	—
435	C₂×C₁₃	—	16	1	no	—
436	C₂×C₁₃	#3268	1	1	yes	characteristic
437	C₂×C₁₃	#3282	1	1	yes	characteristic
438	C₂×C₁₃	#3289	1	1	yes	characteristic
439	#41	—	4	2	no	—
440	#41	—	4	2	no	—
441	#41	—	8	1	no	—
442	#41	—	8	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
447	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	4	1	no	—
452	C₂×D₄	—	4	1	no	—
453	C₂×D₄	—	4	1	no	—
454	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
455	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	4	1	no	—
459	C₂²×C₄	—	4	1	no	—
460	Q₁₆	—	4	2	no	—
461	Q₁₆	—	8	1	no	—
462	SD₁₆	—	2	2	no	—
463	SD₁₆	—	4	1	no	—
464	SD₁₆	—	4	2	no	—
465	SD₁₆	—	8	1	no	—
466	SD₁₆	—	8	1	no	—
467	SD₁₆	—	8	1	no	—
468	D₈	—	8	1	no	—
469	M₁₆	—	8	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	8	1	no	—
476	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
478	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
479	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	4	1	no	—
489	C₄⋊C₄	—	4	1	no	—
490	C₄⋊C₄	—	4	1	no	—
491	C₄⋊C₄	—	4	1	no	—
492	C₄⋊C₄	—	4	1	no	—
493	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
494	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
495	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
496	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	4	1	no	—
500	C₂²⋊C₄	—	4	1	no	—
501	C₂²⋊C₄	—	4	1	no	—
502	C₂²⋊C₄	—	4	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	4	1	no	—
506	C₄²	—	4	1	no	—
507	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
508	C₁₃	#19831	1	1	yes	characteristic, direct product factor, Sylow
509	C₂³	—	2	1	no	—
510	C₂³	—	2	1	no	—
511	C₂³	—	4	1	no	—
512	Q₈	—	2	1	no	—
513	Q₈	—	2	1	no	—
514	Q₈	—	2	1	no	—
515	Q₈	—	4	1	no	—
516	Q₈	—	4	1	no	—
517	Q₈	—	4	1	no	—
518	Q₈	—	4	1	no	—
519	Q₈	—	4	1	no	—
520	Q₈	—	4	1	no	—
521	Q₈	C₁₃×#135	1	2	yes	—
522	D₄	—	2	1	no	—
523	D₄	—	2	1	no	—
524	D₄	—	2	1	no	—
525	D₄	—	2	1	no	—
526	D₄	—	4	1	no	—
527	D₄	—	4	1	no	—
528	D₄	—	4	1	no	—
529	D₄	—	4	1	no	—
530	D₄	—	8	2	no	—
531	D₄	—	8	1	no	—
532	D₄	—	8	2	no	—
533	D₄	—	16	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	8	2	no	—
548	C₂×C₄	—	8	2	no	—
549	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
550	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
551	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
552	C₈	—	2	1	no	—
553	C₈	—	2	1	no	—
554	C₈	—	2	1	no	—
555	C₈	—	2	1	no	—
556	C₈	—	4	1	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	8	1	no	—
568	C₂²	—	8	1	no	—
569	C₂²	—	8	1	no	—
570	C₂²	D₄²×C₁₃	1	1	yes	characteristic
571	C₄	—	2	2	no	—
572	C₄	—	2	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	8	1	no	—
579	C₄	—	8	1	no	—
580	C₄	—	8	1	no	—
581	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
582	C₄	C₁₃×#575	1	1	yes	characteristic
583	C₄	C₁₃×#576	1	1	yes	characteristic
584	C₄	C₁₃×#577	1	1	yes	characteristic
585	C₂	—	8	1	no	—
586	C₂	—	8	1	no	—
587	C₂	—	16	1	no	—
588	C₂	C₁₃×#3268	1	1	yes	characteristic
589	C₂	C₁₃×#3282	1	1	yes	characteristic
590	C₂	C₁₃×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3332	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×#3392	C₂	semidirect
2. C₁₃×#3364	C₂	semidirect
4. C₁₃×#3302	C₂	semidirect
5. C₁₃×#1719	C₂	semidirect
6. C₁₃×#1699	C₂	semidirect
7. C₁₃×#1682	C₂	semidirect
8. C₁₃×#1680	C₂	semidirect
9. C₁₃×#1665	C₂	semidirect
10. C₁₃×#1648	C₂	semidirect
11. C₁₃×#1647	C₂	semidirect
12. C₁₃×#1641	C₂	semidirect
13. C₁₃×#1628	C₂	semidirect
14. C₁₃×#1583	C₂	semidirect
15. C₁₃×SD₁₆⋊C₈	C₂	semidirect
144. #19831	C₁₃	direct (N × H)
214. #3392	C₂×C₁₃	semidirect
215. #3364	C₂×C₁₃	semidirect
217. #3302	C₂×C₁₃	semidirect
218. #1719	C₂×C₁₃	semidirect
219. #1699	C₂×C₁₃	semidirect
220. #1682	C₂×C₁₃	semidirect
221. #1680	C₂×C₁₃	semidirect
222. #1665	C₂×C₁₃	semidirect
223. #1648	C₂×C₁₃	semidirect
224. #1647	C₂×C₁₃	semidirect
225. #1641	C₂×C₁₃	semidirect
226. #1628	C₂×C₁₃	semidirect
227. #1583	C₂×C₁₃	semidirect
228. SD₁₆⋊C₈	C₂×C₁₃	semidirect
508. C₁₃	#19831	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×#3392	2
C₁₃×#3364	2
C₁₃×#3332	2
C₁₃×#3302	2
C₁₃×#1719	2
C₁₃×#1699	2
C₁₃×#1682	2
C₁₃×#1680	2
C₁₃×#1665	2
C₁₃×#1648	2
C₁₃×#1647	2
C₁₃×#1641	2
C₁₃×#1628	2
C₁₃×#1583	2
C₁₃×SD₁₆⋊C₈	2
#19831	13

Subgroups — C13×#19831 #15706170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19831 #15706170