Subgroups — C₁₃×#19855 #15706194

Order 3328.

622 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3399	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3394	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3340	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3305	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1715	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1692	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1678	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1667	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1665	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1641	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1630	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1628	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1624	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1582	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#559	C₂²	1	1	yes	characteristic
17	C₁₃×#556	C₂²	1	1	yes	characteristic
18	C₁₃×#555	C₂²	1	1	yes	characteristic
19	C₁₃×#550	C₂²	1	1	yes	characteristic
20	C₁₃×#498	C₂²	1	1	yes	characteristic
21	C₁₃×#496	—	2	1	no	—
22	C₁₃×#495	—	2	1	no	—
23	C₁₃×#493	C₂²	1	1	yes	characteristic
24	C₁₃×#492	C₂²	1	1	yes	characteristic
25	C₁₃×#492	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×#482	—	2	1	no	—
30	C₁₃×#482	—	2	1	no	—
31	C₁₃×#477	C₂²	1	1	yes	characteristic
32	C₁₃×#477	C₂²	1	1	yes	characteristic
33	C₁₃×#474	C₂²	1	1	yes	characteristic
34	C₁₃×#466	—	2	1	no	—
35	C₁₃×#465	—	2	1	no	—
36	C₁₃×#464	—	2	1	no	—
37	C₁₃×#463	—	2	1	no	—
38	C₁₃×#463	—	2	1	no	—
39	C₁₃×#462	C₂²	1	1	yes	characteristic
40	C₁₃×#460	C₂²	1	1	yes	characteristic
41	C₁₃×#459	—	2	1	no	—
42	C₁₃×#459	C₂²	1	1	yes	characteristic
43	C₁₃×#459	C₂²	1	1	yes	characteristic
44	C₁₃×#459	C₂²	1	1	yes	characteristic
45	C₁₃×#449	—	2	1	no	—
46	C₁₃×#446	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₁₃×#442	—	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	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
54	C₁₃×#427	—	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×#333	C₂²	1	1	yes	characteristic
59	C₁₃×#332	C₂²	1	1	yes	characteristic
60	C₁₃×#331	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×Q₁₆	—	2	1	no	—
69	C₂×C₁₃×SD₁₆	—	2	1	no	—
70	C₂×C₁₃×SD₁₆	—	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×SD₁₆	D₄	1	1	yes	characteristic
75	C₂×C₁₃×D₈	—	2	1	no	—
76	C₂×C₁₃×D₈	—	2	1	no	—
77	C₂×C₁₃×D₈	—	2	1	no	—
78	C₂×C₁₃×D₈	—	2	1	no	—
79	C₂×C₁₃×D₈	—	2	1	no	—
80	C₂²×C₈×C₁₃	—	2	1	no	—
81	C₂²×C₈×C₁₃	—	2	1	no	—
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×#127	C₂³	1	1	yes	characteristic
87	C₁₃×#126	—	4	1	no	—
88	C₁₃×#124	—	2	1	no	—
89	C₁₃×#124	—	2	1	no	—
90	C₁₃×#124	—	2	1	no	—
91	C₁₃×#124	—	4	1	no	—
92	C₁₃×#123	—	4	1	no	—
93	C₁₃×C₂²⋊Q₈	—	2	1	no	—
94	C₁₃×#121	—	2	1	no	—
95	C₁₃×#121	—	2	1	no	—
96	C₁₃×#121	—	2	1	no	—
97	C₁₃×#121	—	4	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	—	2	1	no	—
103	C₄×D₄×C₁₃	—	2	1	no	—
104	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₁₃×#117	—	2	1	no	—
107	C₁₃×#117	—	2	1	no	—
108	C₁₃×#117	—	2	1	no	—
109	C₁₃×#107	—	2	1	no	—
110	C₁₃×#107	—	2	1	no	—
111	C₁₃×#107	—	2	1	no	—
112	C₁₃×#106	—	2	1	no	—
113	C₁₃×#106	—	2	1	no	—
114	C₁₃×#106	D₄	1	1	yes	characteristic
115	C₁₃×#106	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
126	C₁₃×#103	D₄	1	1	yes	characteristic
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	—	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	C₁₃×#97	—	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	#19855	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₁₃×#41	—	4	2	no	—
146	C₁₃×#41	—	8	1	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
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	—	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	—	8	1	no	—
167	C₁₃×SD₁₆	—	2	2	no	—
168	C₁₃×SD₁₆	—	4	1	no	—
169	C₁₃×SD₁₆	—	4	2	no	—
170	C₁₃×SD₁₆	—	8	1	no	—
171	C₁₃×SD₁₆	—	8	1	no	—
172	C₁₃×SD₁₆	—	8	2	no	—
173	C₁₃×D₈	—	4	2	no	—
174	C₁₃×D₈	—	8	1	no	—
175	C₁₃×D₈	—	8	1	no	—
176	C₁₃×D₈	—	8	1	no	—
177	C₁₃×D₈	—	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	—	4	2	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	—	4	1	no	—
196	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
197	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
198	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
199	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
200	C₁₃×C₂²⋊C₄	—	2	1	no	—
201	C₁₃×C₂²⋊C₄	—	2	1	no	—
202	C₁₃×C₂²⋊C₄	—	4	1	no	—
203	C₁₃×C₂²⋊C₄	—	4	1	no	—
204	C₁₃×C₂²⋊C₄	—	4	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	C₁₃×C₂²⋊C₄	—	4	1	no	—
210	C₄²×C₁₃	—	2	1	no	—
211	C₄²×C₁₃	—	2	1	no	—
212	C₄²×C₁₃	—	4	1	no	—
213	C₄²×C₁₃	—	4	1	no	—
214	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
215	#3399	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#3394	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#3340	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#3305	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1715	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1692	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1678	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1667	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1665	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1641	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1630	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1628	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1624	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1582	C₂×C₁₃	1	1	yes	characteristic, complemented
229	SD₁₆⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
230	C₂³×C₁₃	—	2	1	no	—
231	C₂³×C₁₃	—	2	1	no	—
232	C₂³×C₁₃	—	4	1	no	—
233	C₂³×C₁₃	—	4	1	no	—
234	Q₈×C₁₃	—	2	1	no	—
235	Q₈×C₁₃	—	2	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	D₄×C₁₃	—	2	1	no	—
242	D₄×C₁₃	—	2	1	no	—
243	D₄×C₁₃	—	2	1	no	—
244	D₄×C₁₃	—	2	1	no	—
245	D₄×C₁₃	—	4	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	—	4	1	no	—
251	D₄×C₁₃	—	4	1	no	—
252	D₄×C₁₃	—	4	1	no	—
253	D₄×C₁₃	—	8	1	no	—
254	D₄×C₁₃	—	8	1	no	—
255	D₄×C₁₃	—	8	2	no	—
256	D₄×C₁₃	—	16	1	no	—
257	D₄×C₁₃	—	16	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	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	1	no	—
263	C₂×C₄×C₁₃	—	2	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	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
275	C₈×C₁₃	—	2	1	no	—
276	C₈×C₁₃	—	2	1	no	—
277	C₈×C₁₃	—	2	1	no	—
278	C₈×C₁₃	—	4	1	no	—
279	C₈×C₁₃	—	4	1	no	—
280	C₈×C₁₃	—	4	1	no	—
281	C₈×C₁₃	—	4	1	no	—
282	C₈×C₁₃	—	4	1	no	—
283	C₈×C₁₃	#135	1	2	yes	—
284	#559	C₂²×C₁₃	1	1	yes	characteristic
285	#556	C₂²×C₁₃	1	1	yes	characteristic
286	#555	C₂²×C₁₃	1	1	yes	characteristic
287	#550	C₂²×C₁₃	1	1	yes	characteristic
288	#498	C₂²×C₁₃	1	1	yes	characteristic
289	#496	—	2	1	no	—
290	#495	—	2	1	no	—
291	#493	C₂²×C₁₃	1	1	yes	characteristic
292	#492	C₂²×C₁₃	1	1	yes	characteristic
293	#492	C₂²×C₁₃	1	1	yes	characteristic
294	#486	C₂²×C₁₃	1	1	yes	characteristic
295	#486	C₂²×C₁₃	1	1	yes	characteristic
296	#485	—	2	1	no	—
297	#482	—	2	1	no	—
298	#482	—	2	1	no	—
299	#477	C₂²×C₁₃	1	1	yes	characteristic
300	#477	C₂²×C₁₃	1	1	yes	characteristic
301	#474	C₂²×C₁₃	1	1	yes	characteristic
302	#466	—	2	1	no	—
303	#465	—	2	1	no	—
304	#464	—	2	1	no	—
305	#463	—	2	1	no	—
306	#463	—	2	1	no	—
307	#462	C₂²×C₁₃	1	1	yes	characteristic
308	#460	C₂²×C₁₃	1	1	yes	characteristic
309	#459	—	2	1	no	—
310	#459	C₂²×C₁₃	1	1	yes	characteristic
311	#459	C₂²×C₁₃	1	1	yes	characteristic
312	#459	C₂²×C₁₃	1	1	yes	characteristic
313	#449	—	2	1	no	—
314	#446	C₂²×C₁₃	1	1	yes	characteristic
315	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
316	#442	—	2	1	no	—
317	C₄×SD₁₆	—	2	1	no	—
318	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
319	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
320	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
321	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
322	#427	—	2	1	no	—
323	#416	—	2	1	no	—
324	#335	C₂²×C₁₃	1	1	yes	characteristic
325	#334	C₂²×C₁₃	1	1	yes	characteristic
326	#333	C₂²×C₁₃	1	1	yes	characteristic
327	#332	C₂²×C₁₃	1	1	yes	characteristic
328	#331	C₂²×C₁₃	1	1	yes	characteristic
329	#331	C₂²×C₁₃	1	1	yes	characteristic
330	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
331	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
332	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
333	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
334	#322	C₂²×C₁₃	1	1	yes	characteristic
335	C₂²×C₁₃	—	4	1	no	—
336	C₂²×C₁₃	—	4	1	no	—
337	C₂²×C₁₃	—	4	1	no	—
338	C₂²×C₁₃	—	4	1	no	—
339	C₂²×C₁₃	—	4	1	no	—
340	C₂²×C₁₃	—	4	1	no	—
341	C₂²×C₁₃	—	8	1	no	—
342	C₂²×C₁₃	—	8	1	no	—
343	C₂²×C₁₃	—	8	1	no	—
344	C₂²×C₁₃	—	8	1	no	—
345	C₂²×C₁₃	—	8	1	no	—
346	C₂²×C₁₃	—	8	1	no	—
347	C₂²×C₁₃	D₄²	1	1	yes	characteristic
348	C₄×C₁₃	—	2	1	no	—
349	C₄×C₁₃	—	4	1	no	—
350	C₄×C₁₃	—	4	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	—	8	1	no	—
356	C₄×C₁₃	—	8	1	no	—
357	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
358	C₄×C₁₃	#575	1	1	yes	characteristic
359	C₄×C₁₃	#576	1	1	yes	characteristic
360	C₄×C₁₃	#577	1	1	yes	characteristic
361	C₂×#41	—	2	1	no	—
362	C₂×Q₁₆	—	2	1	no	—
363	C₂×SD₁₆	—	2	1	no	—
364	C₂×SD₁₆	—	2	1	no	—
365	C₂×SD₁₆	—	2	1	no	—
366	C₂×SD₁₆	—	4	1	no	—
367	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
368	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
369	C₂×D₈	—	2	1	no	—
370	C₂×D₈	—	2	1	no	—
371	C₂×D₈	—	2	1	no	—
372	C₂×D₈	—	2	1	no	—
373	C₂×D₈	—	2	1	no	—
374	C₂²×C₈	—	2	1	no	—
375	C₂²×C₈	—	2	1	no	—
376	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
377	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
378	#127	—	2	1	no	—
379	#127	C₂³×C₁₃	1	1	yes	characteristic
380	#127	C₂³×C₁₃	1	1	yes	characteristic
381	#126	—	4	1	no	—
382	#124	—	2	1	no	—
383	#124	—	2	1	no	—
384	#124	—	2	1	no	—
385	#124	—	4	1	no	—
386	#123	—	4	1	no	—
387	C₂²⋊Q₈	—	2	1	no	—
388	#121	—	2	1	no	—
389	#121	—	2	1	no	—
390	#121	—	2	1	no	—
391	#121	—	4	1	no	—
392	C₄×Q₈	—	2	1	no	—
393	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
394	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
399	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
400	#117	—	2	1	no	—
401	#117	—	2	1	no	—
402	#117	—	2	1	no	—
403	#107	—	2	1	no	—
404	#107	—	2	1	no	—
405	#107	—	2	1	no	—
406	#106	—	2	1	no	—
407	#106	—	2	1	no	—
408	#106	D₄×C₁₃	1	1	yes	characteristic
409	#106	D₄×C₁₃	1	1	yes	characteristic
410	C₄⋊C₈	—	2	1	no	—
411	C₄⋊C₈	—	2	1	no	—
412	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
413	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
414	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
415	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
416	#103	—	2	1	no	—
417	#103	—	2	1	no	—
418	#103	—	2	1	no	—
419	#103	D₄×C₁₃	1	1	yes	characteristic
420	#103	D₄×C₁₃	1	1	yes	characteristic
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	—	4	1	no	—
429	#102	D₄×C₁₃	1	1	yes	characteristic
430	#102	D₄×C₁₃	1	1	yes	characteristic
431	C₂²⋊C₈	—	2	1	no	—
432	C₂²⋊C₈	—	2	1	no	—
433	#97	—	2	1	no	—
434	C₄×C₈	—	2	1	no	—
435	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
436	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
437	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
438	C₂×C₁₃	—	8	1	no	—
439	C₂×C₁₃	—	8	1	no	—
440	C₂×C₁₃	—	16	1	no	—
441	C₂×C₁₃	—	16	1	no	—
442	C₂×C₁₃	#3268	1	1	yes	characteristic
443	C₂×C₁₃	#3284	1	1	yes	characteristic
444	C₂×C₁₃	#3288	1	1	yes	characteristic
445	#41	—	4	2	no	—
446	#41	—	8	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
450	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
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	1	no	—
460	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
461	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	4	1	no	—
465	C₂²×C₄	—	4	1	no	—
466	Q₁₆	—	8	1	no	—
467	SD₁₆	—	2	2	no	—
468	SD₁₆	—	4	1	no	—
469	SD₁₆	—	4	2	no	—
470	SD₁₆	—	8	1	no	—
471	SD₁₆	—	8	1	no	—
472	SD₁₆	—	8	2	no	—
473	D₈	—	4	2	no	—
474	D₈	—	8	1	no	—
475	D₈	—	8	1	no	—
476	D₈	—	8	1	no	—
477	D₈	—	8	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	4	2	no	—
484	C₂×C₈	—	8	1	no	—
485	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
486	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
488	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	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	—	4	1	no	—
496	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
497	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
498	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
499	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	4	1	no	—
503	C₂²⋊C₄	—	4	1	no	—
504	C₂²⋊C₄	—	4	1	no	—
505	C₂²⋊C₄	—	4	1	no	—
506	C₂²⋊C₄	—	4	1	no	—
507	C₂²⋊C₄	—	4	1	no	—
508	C₂²⋊C₄	—	4	1	no	—
509	C₂²⋊C₄	—	4	1	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	4	1	no	—
513	C₄²	—	4	1	no	—
514	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
515	C₁₃	#19855	1	1	yes	characteristic, direct product factor, Sylow
516	C₂³	—	2	1	no	—
517	C₂³	—	2	1	no	—
518	C₂³	—	4	1	no	—
519	C₂³	—	4	1	no	—
520	Q₈	—	2	1	no	—
521	Q₈	—	2	1	no	—
522	Q₈	—	2	1	no	—
523	Q₈	—	2	1	no	—
524	Q₈	—	4	1	no	—
525	Q₈	—	4	1	no	—
526	Q₈	—	8	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	2	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	2	1	no	—
531	D₄	—	4	1	no	—
532	D₄	—	4	1	no	—
533	D₄	—	4	1	no	—
534	D₄	—	4	1	no	—
535	D₄	—	4	1	no	—
536	D₄	—	4	1	no	—
537	D₄	—	4	1	no	—
538	D₄	—	4	1	no	—
539	D₄	—	8	1	no	—
540	D₄	—	8	1	no	—
541	D₄	—	8	2	no	—
542	D₄	—	16	1	no	—
543	D₄	—	16	1	no	—
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	—	2	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	—	8	2	no	—
557	C₂×C₄	—	16	1	no	—
558	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
559	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
560	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
561	C₈	—	2	1	no	—
562	C₈	—	2	1	no	—
563	C₈	—	2	1	no	—
564	C₈	—	4	1	no	—
565	C₈	—	4	1	no	—
566	C₈	—	4	1	no	—
567	C₈	—	4	1	no	—
568	C₈	—	4	1	no	—
569	C₈	C₁₃×#135	1	2	yes	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	8	1	no	—
577	C₂²	—	8	1	no	—
578	C₂²	—	8	1	no	—
579	C₂²	—	8	1	no	—
580	C₂²	—	8	1	no	—
581	C₂²	—	8	1	no	—
582	C₂²	D₄²×C₁₃	1	1	yes	characteristic
583	C₄	—	2	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	8	1	no	—
591	C₄	—	8	1	no	—
592	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
593	C₄	C₁₃×#575	1	1	yes	characteristic
594	C₄	C₁₃×#576	1	1	yes	characteristic
595	C₄	C₁₃×#577	1	1	yes	characteristic
596	C₂	—	8	1	no	—
597	C₂	—	8	1	no	—
598	C₂	—	16	1	no	—
599	C₂	—	16	1	no	—
600	C₂	C₁₃×#3268	1	1	yes	characteristic
601	C₂	C₁₃×#3284	1	1	yes	characteristic
602	C₂	C₁₃×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
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×#3399	C₂	semidirect
2. C₁₃×#3394	C₂	semidirect
3. C₁₃×#3340	C₂	semidirect
4. C₁₃×#3305	C₂	semidirect
5. C₁₃×#1715	C₂	semidirect
6. C₁₃×#1692	C₂	semidirect
7. C₁₃×#1678	C₂	semidirect
8. C₁₃×#1667	C₂	semidirect
9. C₁₃×#1665	C₂	semidirect
10. C₁₃×#1641	C₂	semidirect
11. C₁₃×#1630	C₂	semidirect
12. C₁₃×#1628	C₂	semidirect
13. C₁₃×#1624	C₂	semidirect
14. C₁₃×#1582	C₂	semidirect
15. C₁₃×SD₁₆⋊C₈	C₂	semidirect
144. #19855	C₁₃	direct (N × H)
215. #3399	C₂×C₁₃	semidirect
216. #3394	C₂×C₁₃	semidirect
217. #3340	C₂×C₁₃	semidirect
218. #3305	C₂×C₁₃	semidirect
219. #1715	C₂×C₁₃	semidirect
220. #1692	C₂×C₁₃	semidirect
221. #1678	C₂×C₁₃	semidirect
222. #1667	C₂×C₁₃	semidirect
223. #1665	C₂×C₁₃	semidirect
224. #1641	C₂×C₁₃	semidirect
225. #1630	C₂×C₁₃	semidirect
226. #1628	C₂×C₁₃	semidirect
227. #1624	C₂×C₁₃	semidirect
228. #1582	C₂×C₁₃	semidirect
229. SD₁₆⋊C₈	C₂×C₁₃	semidirect
515. C₁₃	#19855	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×#3399	2
C₁₃×#3394	2
C₁₃×#3340	2
C₁₃×#3305	2
C₁₃×#1715	2
C₁₃×#1692	2
C₁₃×#1678	2
C₁₃×#1667	2
C₁₃×#1665	2
C₁₃×#1641	2
C₁₃×#1630	2
C₁₃×#1628	2
C₁₃×#1624	2
C₁₃×#1582	2
C₁₃×SD₁₆⋊C₈	2
#19855	13

Subgroups — C13×#19855 #15706194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19855 #15706194