Subgroups — C₁₃×#19858 #15706197

Order 3328.

580 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3400	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3394	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3364	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3342	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1714	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1694	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1680	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1666	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1665	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1653	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1652	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1640	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1628	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1582	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1579	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#559	C₂²	1	1	yes	characteristic
17	C₁₃×#557	C₂²	1	1	yes	characteristic
18	C₁₃×#556	C₂²	1	1	yes	characteristic
19	C₁₃×#556	C₂²	1	1	yes	characteristic
20	C₁₃×#500	C₂²	1	1	yes	characteristic
21	C₁₃×#498	C₂²	1	1	yes	characteristic
22	C₁₃×#497	—	2	1	no	—
23	C₁₃×#495	—	2	1	no	—
24	C₁₃×#492	C₂²	1	1	yes	characteristic
25	C₁₃×#492	C₂²	1	1	yes	characteristic
26	C₁₃×#488	—	2	1	no	—
27	C₁₃×#487	C₂²	1	1	yes	characteristic
28	C₁₃×#486	C₂²	1	1	yes	characteristic
29	C₁₃×#485	—	2	1	no	—
30	C₁₃×#485	—	2	1	no	—
31	C₁₃×#479	—	2	1	no	—
32	C₁₃×#475	C₂²	1	1	yes	characteristic
33	C₁₃×#475	C₂²	1	1	yes	characteristic
34	C₁₃×#474	C₂²	1	1	yes	characteristic
35	C₁₃×#467	—	2	1	no	—
36	C₁₃×#464	—	2	1	no	—
37	C₁₃×#464	—	2	1	no	—
38	C₁₃×#464	—	2	1	no	—
39	C₁₃×#463	—	2	1	no	—
40	C₁₃×#462	C₂²	1	1	yes	characteristic
41	C₁₃×#462	C₂²	1	1	yes	characteristic
42	C₁₃×#462	C₂²	1	1	yes	characteristic
43	C₁₃×#461	—	2	1	no	—
44	C₁₃×#460	C₂²	1	1	yes	characteristic
45	C₁₃×#459	C₂²	1	1	yes	characteristic
46	C₁₃×#446	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
49	C₁₃×#440	—	2	1	no	—
50	C₄×C₁₃×Q₁₆	—	2	1	no	—
51	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
52	C₄×C₁₃×SD₁₆	—	2	1	no	—
53	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
55	C₁₃×#427	—	2	1	no	—
56	C₁₃×#334	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×Q₈⋊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×Q₁₆	—	2	1	no	—
68	C₂×C₁₃×Q₁₆	—	2	1	no	—
69	C₂×C₁₃×Q₁₆	—	2	1	no	—
70	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
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	—	2	1	no	—
76	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
77	C₂×C₁₃×D₈	—	2	1	no	—
78	C₂²×C₈×C₁₃	—	2	1	no	—
79	C₁₃×C₄⋊Q₈	—	2	1	no	—
80	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₃×#127	C₂³	1	1	yes	characteristic
84	C₁₃×#126	—	4	1	no	—
85	C₁₃×#126	—	4	1	no	—
86	C₁₃×#125	—	2	1	no	—
87	C₁₃×#125	—	4	1	no	—
88	C₁₃×#124	—	2	1	no	—
89	C₁₃×#124	—	2	1	no	—
90	C₁₃×#124	—	2	1	no	—
91	C₁₃×#124	—	2	1	no	—
92	C₁₃×#123	—	4	1	no	—
93	C₁₃×C₂²⋊Q₈	—	2	1	no	—
94	C₁₃×C₂²⋊Q₈	—	2	1	no	—
95	C₄×Q₈×C₁₃	—	2	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×Q₈×C₁₃	C₂³	1	1	yes	characteristic
102	C₄×D₄×C₁₃	—	2	1	no	—
103	C₄×D₄×C₁₃	—	2	1	no	—
104	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₁₃×#117	—	2	1	no	—
106	C₁₃×#117	—	2	1	no	—
107	C₁₃×#107	—	2	1	no	—
108	C₁₃×#107	—	2	1	no	—
109	C₁₃×#107	—	2	1	no	—
110	C₁₃×#107	D₄	1	1	yes	characteristic
111	C₁₃×#106	—	2	1	no	—
112	C₁₃×#106	—	2	1	no	—
113	C₁₃×#106	—	4	1	no	—
114	C₁₃×#106	D₄	1	1	yes	characteristic
115	C₁₃×C₄⋊C₈	—	2	1	no	—
116	C₁₃×C₄⋊C₈	—	2	1	no	—
117	C₁₃×C₄⋊C₈	—	2	1	no	—
118	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
127	C₁₃×#103	—	2	1	no	—
128	C₁₃×#103	—	2	1	no	—
129	C₁₃×#103	D₄	1	1	yes	characteristic
130	C₁₃×#103	D₄	1	1	yes	characteristic
131	C₁₃×#103	D₄	1	1	yes	characteristic
132	C₁₃×#102	—	2	1	no	—
133	C₁₃×#102	—	2	1	no	—
134	C₁₃×#102	—	2	1	no	—
135	C₁₃×#102	—	4	1	no	—
136	C₁₃×#102	D₄	1	1	yes	characteristic
137	C₁₃×C₂²⋊C₈	—	2	1	no	—
138	C₁₃×#97	—	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	#19858	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂×Q₈×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	—	2	1	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	2	1	no	—
153	C₂×D₄×C₁₃	—	2	1	no	—
154	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	4	1	no	—
157	C₁₃×Q₁₆	—	2	2	no	—
158	C₁₃×Q₁₆	—	4	2	no	—
159	C₁₃×Q₁₆	—	8	1	no	—
160	C₁₃×Q₁₆	—	8	1	no	—
161	C₁₃×SD₁₆	—	4	1	no	—
162	C₁₃×SD₁₆	—	4	2	no	—
163	C₁₃×SD₁₆	—	4	2	no	—
164	C₁₃×SD₁₆	—	8	1	no	—
165	C₁₃×SD₁₆	—	8	1	no	—
166	C₁₃×SD₁₆	—	8	1	no	—
167	C₁₃×D₈	—	8	1	no	—
168	C₂×C₈×C₁₃	—	2	1	no	—
169	C₂×C₈×C₁₃	—	2	1	no	—
170	C₂×C₈×C₁₃	—	2	1	no	—
171	C₂×C₈×C₁₃	—	2	1	no	—
172	C₂×C₈×C₁₃	—	2	1	no	—
173	C₂×C₈×C₁₃	—	4	2	no	—
174	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₁₃×C₄⋊C₄	—	2	1	no	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	4	1	no	—
188	C₁₃×C₄⋊C₄	—	4	1	no	—
189	C₁₃×C₄⋊C₄	—	4	1	no	—
190	C₁₃×C₄⋊C₄	—	4	1	no	—
191	C₁₃×C₄⋊C₄	—	4	1	no	—
192	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
193	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
194	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
195	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
196	C₁₃×C₂²⋊C₄	—	2	1	no	—
197	C₁₃×C₂²⋊C₄	—	4	1	no	—
198	C₁₃×C₂²⋊C₄	—	4	1	no	—
199	C₁₃×C₂²⋊C₄	—	4	1	no	—
200	C₁₃×C₂²⋊C₄	—	4	1	no	—
201	C₁₃×C₂²⋊C₄	—	4	1	no	—
202	C₁₃×C₂²⋊C₄	—	4	1	no	—
203	C₁₃×C₂²⋊C₄	—	4	1	no	—
204	C₄²×C₁₃	—	2	1	no	—
205	C₄²×C₁₃	—	2	1	no	—
206	C₄²×C₁₃	—	2	1	no	—
207	C₄²×C₁₃	—	4	1	no	—
208	C₄²×C₁₃	—	4	1	no	—
209	C₄²×C₁₃	—	4	1	no	—
210	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
211	#3400	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#3394	C₂×C₁₃	1	1	yes	characteristic
213	#3364	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#3342	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1714	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1694	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1680	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1666	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1665	C₂×C₁₃	1	1	yes	characteristic
220	#1653	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1652	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1640	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1628	C₂×C₁₃	1	1	yes	characteristic
224	#1582	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1579	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₂³×C₁₃	—	2	1	no	—
227	C₂³×C₁₃	—	4	1	no	—
228	Q₈×C₁₃	—	2	1	no	—
229	Q₈×C₁₃	—	2	1	no	—
230	Q₈×C₁₃	—	2	1	no	—
231	Q₈×C₁₃	—	2	1	no	—
232	Q₈×C₁₃	—	2	1	no	—
233	Q₈×C₁₃	—	2	1	no	—
234	Q₈×C₁₃	—	4	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	D₄×C₁₃	—	2	1	no	—
241	D₄×C₁₃	—	2	1	no	—
242	D₄×C₁₃	—	4	1	no	—
243	D₄×C₁₃	—	4	1	no	—
244	D₄×C₁₃	—	4	1	no	—
245	D₄×C₁₃	—	4	1	no	—
246	D₄×C₁₃	—	8	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	1	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	4	1	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	—	16	1	no	—
260	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
263	C₈×C₁₃	—	2	1	no	—
264	C₈×C₁₃	—	2	1	no	—
265	C₈×C₁₃	—	2	1	no	—
266	C₈×C₁₃	—	4	1	no	—
267	C₈×C₁₃	—	4	1	no	—
268	C₈×C₁₃	—	4	1	no	—
269	C₈×C₁₃	—	4	1	no	—
270	C₈×C₁₃	—	4	1	no	—
271	C₈×C₁₃	#135	1	2	yes	—
272	#559	C₂²×C₁₃	1	1	yes	characteristic
273	#557	C₂²×C₁₃	1	1	yes	characteristic
274	#556	C₂²×C₁₃	1	1	yes	characteristic
275	#556	C₂²×C₁₃	1	1	yes	characteristic
276	#500	C₂²×C₁₃	1	1	yes	characteristic
277	#498	C₂²×C₁₃	1	1	yes	characteristic
278	#497	—	2	1	no	—
279	#495	—	2	1	no	—
280	#492	C₂²×C₁₃	1	1	yes	characteristic
281	#492	C₂²×C₁₃	1	1	yes	characteristic
282	#488	—	2	1	no	—
283	#487	C₂²×C₁₃	1	1	yes	characteristic
284	#486	C₂²×C₁₃	1	1	yes	characteristic
285	#485	—	2	1	no	—
286	#485	—	2	1	no	—
287	#479	—	2	1	no	—
288	#475	C₂²×C₁₃	1	1	yes	characteristic
289	#475	C₂²×C₁₃	1	1	yes	characteristic
290	#474	C₂²×C₁₃	1	1	yes	characteristic
291	#467	—	2	1	no	—
292	#464	—	2	1	no	—
293	#464	—	2	1	no	—
294	#464	—	2	1	no	—
295	#463	—	2	1	no	—
296	#462	C₂²×C₁₃	1	1	yes	characteristic
297	#462	C₂²×C₁₃	1	1	yes	characteristic
298	#462	C₂²×C₁₃	1	1	yes	characteristic
299	#461	—	2	1	no	—
300	#460	C₂²×C₁₃	1	1	yes	characteristic
301	#459	C₂²×C₁₃	1	1	yes	characteristic
302	#446	C₂²×C₁₃	1	1	yes	characteristic
303	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
304	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
305	#440	—	2	1	no	—
306	C₄×Q₁₆	—	2	1	no	—
307	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
308	C₄×SD₁₆	—	2	1	no	—
309	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
310	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
311	#427	—	2	1	no	—
312	#334	C₂²×C₁₃	1	1	yes	characteristic
313	#334	C₂²×C₁₃	1	1	yes	characteristic
314	#332	C₂²×C₁₃	1	1	yes	characteristic
315	#332	C₂²×C₁₃	1	1	yes	characteristic
316	#332	C₂²×C₁₃	1	1	yes	characteristic
317	#331	C₂²×C₁₃	1	1	yes	characteristic
318	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
319	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
320	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
321	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
322	#322	C₂²×C₁₃	1	1	yes	characteristic
323	C₂²×C₁₃	—	4	1	no	—
324	C₂²×C₁₃	—	4	1	no	—
325	C₂²×C₁₃	—	4	1	no	—
326	C₂²×C₁₃	—	8	1	no	—
327	C₂²×C₁₃	—	8	1	no	—
328	C₂²×C₁₃	—	8	1	no	—
329	C₂²×C₁₃	D₄²	1	1	yes	characteristic
330	C₄×C₁₃	—	2	1	no	—
331	C₄×C₁₃	—	4	1	no	—
332	C₄×C₁₃	—	4	1	no	—
333	C₄×C₁₃	—	4	1	no	—
334	C₄×C₁₃	—	4	1	no	—
335	C₄×C₁₃	—	4	1	no	—
336	C₄×C₁₃	—	4	1	no	—
337	C₄×C₁₃	—	4	1	no	—
338	C₄×C₁₃	—	8	1	no	—
339	C₄×C₁₃	—	8	1	no	—
340	C₄×C₁₃	—	8	1	no	—
341	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
342	C₄×C₁₃	#575	1	1	yes	characteristic
343	C₄×C₁₃	#577	1	1	yes	characteristic
344	C₄×C₁₃	#577	1	1	yes	characteristic
345	C₂×Q₁₆	—	2	1	no	—
346	C₂×Q₁₆	—	2	1	no	—
347	C₂×Q₁₆	—	2	1	no	—
348	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
349	C₂×SD₁₆	—	2	1	no	—
350	C₂×SD₁₆	—	2	1	no	—
351	C₂×SD₁₆	—	2	1	no	—
352	C₂×SD₁₆	—	2	1	no	—
353	C₂×SD₁₆	—	2	1	no	—
354	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
355	C₂×D₈	—	2	1	no	—
356	C₂²×C₈	—	2	1	no	—
357	C₄⋊Q₈	—	2	1	no	—
358	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
359	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
360	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
361	#127	C₂³×C₁₃	1	1	yes	characteristic
362	#126	—	4	1	no	—
363	#126	—	4	1	no	—
364	#125	—	2	1	no	—
365	#125	—	4	1	no	—
366	#124	—	2	1	no	—
367	#124	—	2	1	no	—
368	#124	—	2	1	no	—
369	#124	—	2	1	no	—
370	#123	—	4	1	no	—
371	C₂²⋊Q₈	—	2	1	no	—
372	C₂²⋊Q₈	—	2	1	no	—
373	C₄×Q₈	—	2	1	no	—
374	C₄×Q₈	—	2	1	no	—
375	C₄×Q₈	—	2	1	no	—
376	C₄×Q₈	—	2	1	no	—
377	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
378	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
379	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
383	#117	—	2	1	no	—
384	#117	—	2	1	no	—
385	#107	—	2	1	no	—
386	#107	—	2	1	no	—
387	#107	—	2	1	no	—
388	#107	D₄×C₁₃	1	1	yes	characteristic
389	#106	—	2	1	no	—
390	#106	—	2	1	no	—
391	#106	—	4	1	no	—
392	#106	D₄×C₁₃	1	1	yes	characteristic
393	C₄⋊C₈	—	2	1	no	—
394	C₄⋊C₈	—	2	1	no	—
395	C₄⋊C₈	—	2	1	no	—
396	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
397	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
398	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
399	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
400	#103	—	2	1	no	—
401	#103	—	2	1	no	—
402	#103	—	2	1	no	—
403	#103	—	2	1	no	—
404	#103	—	2	1	no	—
405	#103	—	2	1	no	—
406	#103	—	2	1	no	—
407	#103	D₄×C₁₃	1	1	yes	characteristic
408	#103	D₄×C₁₃	1	1	yes	characteristic
409	#103	D₄×C₁₃	1	1	yes	characteristic
410	#102	—	2	1	no	—
411	#102	—	2	1	no	—
412	#102	—	2	1	no	—
413	#102	—	4	1	no	—
414	#102	D₄×C₁₃	1	1	yes	characteristic
415	C₂²⋊C₈	—	2	1	no	—
416	#97	—	2	1	no	—
417	C₄×C₈	—	2	1	no	—
418	C₄×C₈	—	2	1	no	—
419	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
420	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
421	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
422	C₂×C₁₃	—	8	1	no	—
423	C₂×C₁₃	—	16	1	no	—
424	C₂×C₁₃	#3271	1	1	yes	characteristic
425	C₂×C₁₃	#3284	1	1	yes	characteristic
426	C₂×C₁₃	#3289	1	1	yes	characteristic
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
431	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
432	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	4	1	no	—
439	Q₁₆	—	2	2	no	—
440	Q₁₆	—	4	2	no	—
441	Q₁₆	—	8	1	no	—
442	Q₁₆	—	8	1	no	—
443	SD₁₆	—	4	1	no	—
444	SD₁₆	—	4	2	no	—
445	SD₁₆	—	4	2	no	—
446	SD₁₆	—	8	1	no	—
447	SD₁₆	—	8	1	no	—
448	SD₁₆	—	8	1	no	—
449	D₈	—	8	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	4	2	no	—
456	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
457	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
458	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
459	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	4	1	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₄⋊C₄	—	4	1	no	—
473	C₄⋊C₄	—	4	1	no	—
474	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
475	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	4	1	no	—
480	C₂²⋊C₄	—	4	1	no	—
481	C₂²⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	4	1	no	—
483	C₂²⋊C₄	—	4	1	no	—
484	C₂²⋊C₄	—	4	1	no	—
485	C₂²⋊C₄	—	4	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	4	1	no	—
490	C₄²	—	4	1	no	—
491	C₄²	—	4	1	no	—
492	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
493	C₁₃	#19858	1	1	yes	characteristic, direct product factor, Sylow
494	C₂³	—	2	1	no	—
495	C₂³	—	4	1	no	—
496	Q₈	—	2	1	no	—
497	Q₈	—	2	1	no	—
498	Q₈	—	2	1	no	—
499	Q₈	—	2	1	no	—
500	Q₈	—	2	1	no	—
501	Q₈	—	2	1	no	—
502	Q₈	—	4	1	no	—
503	Q₈	—	4	1	no	—
504	Q₈	—	4	1	no	—
505	Q₈	—	4	1	no	—
506	Q₈	—	4	1	no	—
507	Q₈	—	4	1	no	—
508	D₄	—	2	1	no	—
509	D₄	—	2	1	no	—
510	D₄	—	4	1	no	—
511	D₄	—	4	1	no	—
512	D₄	—	4	1	no	—
513	D₄	—	4	1	no	—
514	D₄	—	8	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	16	1	no	—
528	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
529	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
530	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	2	1	no	—
534	C₈	—	4	1	no	—
535	C₈	—	4	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	4	1	no	—
538	C₈	—	4	1	no	—
539	C₈	C₁₃×#135	1	2	yes	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	8	1	no	—
544	C₂²	—	8	1	no	—
545	C₂²	—	8	1	no	—
546	C₂²	D₄²×C₁₃	1	1	yes	characteristic
547	C₄	—	2	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	1	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	1	no	—
557	C₄	—	8	1	no	—
558	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
559	C₄	C₁₃×#575	1	1	yes	characteristic
560	C₄	C₁₃×#577	1	1	yes	characteristic
561	C₄	C₁₃×#577	1	1	yes	characteristic
562	C₂	—	8	1	no	—
563	C₂	—	16	1	no	—
564	C₂	C₁₃×#3271	1	1	yes	characteristic
565	C₂	C₁₃×#3284	1	1	yes	characteristic
566	C₂	C₁₃×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#459	C₂²
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×#3400	C₂	semidirect
3. C₁₃×#3364	C₂	semidirect
4. C₁₃×#3342	C₂	semidirect
5. C₁₃×#1714	C₂	semidirect
6. C₁₃×#1694	C₂	semidirect
7. C₁₃×#1680	C₂	semidirect
8. C₁₃×#1666	C₂	semidirect
10. C₁₃×#1653	C₂	semidirect
11. C₁₃×#1652	C₂	semidirect
12. C₁₃×#1640	C₂	semidirect
14. C₁₃×#1582	C₂	semidirect
15. C₁₃×#1579	C₂	semidirect
144. #19858	C₁₃	direct (N × H)
211. #3400	C₂×C₁₃	semidirect
213. #3364	C₂×C₁₃	semidirect
214. #3342	C₂×C₁₃	semidirect
215. #1714	C₂×C₁₃	semidirect
216. #1694	C₂×C₁₃	semidirect
217. #1680	C₂×C₁₃	semidirect
218. #1666	C₂×C₁₃	semidirect
220. #1653	C₂×C₁₃	semidirect
221. #1652	C₂×C₁₃	semidirect
222. #1640	C₂×C₁₃	semidirect
224. #1582	C₂×C₁₃	semidirect
225. #1579	C₂×C₁₃	semidirect
493. C₁₃	#19858	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×#3400	2
C₁₃×#3394	2
C₁₃×#3364	2
C₁₃×#3342	2
C₁₃×#1714	2
C₁₃×#1694	2
C₁₃×#1680	2
C₁₃×#1666	2
C₁₃×#1665	2
C₁₃×#1653	2
C₁₃×#1652	2
C₁₃×#1640	2
C₁₃×#1628	2
C₁₃×#1582	2
C₁₃×#1579	2
#19858	13

Subgroups — C13×#19858 #15706197

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19858 #15706197