Subgroups — #16797305

Order 3328.

926 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃⋊#433	C₂	1	1	yes	maximal, characteristic
2	#13131298	C₂	1	1	yes	maximal, characteristic
3	#13130634	C₂	1	1	yes	maximal, characteristic, complemented
4	#13130634	C₂	1	1	yes	maximal, characteristic, complemented
5	#13130630	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×C₄⋊#261	C₂	1	1	yes	maximal, characteristic, complemented
7	#13130576	C₂	1	1	yes	maximal, characteristic
8	#13130576	C₂	1	1	yes	maximal, characteristic
9	#13130572	C₂	1	1	yes	maximal, characteristic
10	C₈×C₂²⋊#261	C₂	1	1	yes	maximal, characteristic
11	#13130554	C₂	1	1	yes	maximal, characteristic, complemented
12	#13130549	C₂	1	1	yes	maximal, characteristic, complemented
13	#13130494	C₂	1	1	yes	maximal, characteristic, complemented
14	#97×#261	C₂	1	1	yes	maximal, characteristic, complemented
15	D₁₃×#405	C₂	1	1	yes	maximal, characteristic
16	C₂×M₁₆×D₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
18	D₁₃×#117	C₂²	1	1	yes	characteristic
19	C₄×C₂²⋊#261	C₂²	1	1	yes	characteristic
20	C₄×C₂²⋊#261	C₂²	1	1	yes	characteristic
21	D₁₃⋊(C₂²⋊C₈)	C₂²	1	1	yes	characteristic
22	D₁₃⋊(C₂²⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×#88100	C₂²	1	1	yes	characteristic
24	C₂×#88100	C₂²	1	1	yes	characteristic
25	C₂×#88100	C₂²	1	1	yes	characteristic
26	C₂×#88100	C₂²	1	1	yes	characteristic
27	C₂×C₈×#261	C₂²	1	1	yes	characteristic
28	C₂×C₈×#261	C₂²	1	1	yes	characteristic
29	C₂×C₈×#261	C₂²	1	1	yes	characteristic
30	C₂×C₈×#261	C₂²	1	1	yes	characteristic
31	#11719082	C₄	1	2	yes	—
32	#11719082	C₄	1	2	yes	—
33	#11719077	C₄	1	2	yes	complemented
34	#11719077	C₄	1	2	yes	complemented
35	#11719071	C₄	1	2	yes	—
36	#11719071	C₄	1	2	yes	—
37	#11719068	C₄	1	2	yes	complemented
38	#11719068	C₄	1	2	yes	complemented
39	C₄×C₄⋊#261	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊#261	C₂²	1	1	yes	characteristic
41	#11719057	C₂²	1	1	yes	characteristic
42	C₄²×#261	C₂²	1	1	yes	characteristic
43	D₁₃⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
44	D₁₃⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
45	#11719047	C₂²	1	1	yes	characteristic
46	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
47	C₁₃×#405	C₄	1	1	yes	characteristic, complemented
48	#11718783	C₄	1	1	yes	characteristic, complemented
49	#11718762	C₄	1	1	yes	characteristic, complemented
50	#11718658	C₄	1	1	yes	characteristic, complemented
51	#11718369	C₄	1	1	yes	characteristic, complemented
52	#11718369	C₄	1	1	yes	characteristic, complemented
53	D₁₃×#97	C₂²	1	1	yes	characteristic
54	D₁₃×#97	C₂²	1	1	yes	characteristic
55	#11718350	C₄	1	1	yes	characteristic, complemented
56	#11718350	C₄	1	1	yes	characteristic, complemented
57	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
58	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
59	(C₂×#261)⋊C₈	C₂²	1	1	yes	characteristic
60	(C₂×#261)⋊C₈	C₂²	1	1	yes	characteristic
61	(C₂×#261)⋊C₈	C₂²	1	1	yes	characteristic
62	(C₂×#261)⋊C₈	C₂²	1	1	yes	characteristic
63	(C₂×#261)⋊C₈	C₂²	1	1	yes	characteristic
64	(C₂×#261)⋊C₈	C₂²	1	1	yes	characteristic
65	(C₂×#261)⋊C₈	C₂²	1	1	yes	characteristic
66	(C₂×#261)⋊C₈	C₂²	1	1	yes	characteristic
67	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
68	C₂×C₂²⋊#261	C₂×C₄	1	2	yes	—
69	C₂×C₂²⋊#261	C₂×C₄	1	2	yes	—
70	C₂×C₄⋊#261	C₂×C₄	1	2	yes	—
71	C₂×C₄⋊#261	C₂×C₄	1	2	yes	—
72	C₂×C₄×#261	C₂×C₄	1	2	yes	—
73	C₂×C₄×#261	C₂×C₄	1	2	yes	—
74	C₂×C₄×#261	C₂³	1	1	yes	characteristic
75	C₂×C₄×#261	C₂³	1	1	yes	characteristic
76	C₂×C₄×#261	C₂³	1	1	yes	characteristic
77	C₂×C₄×#261	C₂³	1	1	yes	characteristic
78	C₂×D₁₃⋊C₈	C₂³	1	1	yes	characteristic
79	C₂×D₁₃⋊C₈	C₂³	1	1	yes	characteristic
80	C₂×D₁₃⋊C₈	C₂³	1	1	yes	characteristic
81	C₂×D₁₃⋊C₈	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
84	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
85	#88180	C₂×C₄	1	1	yes	characteristic
86	C₂×#6099	C₂×C₄	1	1	yes	characteristic
87	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
88	M₁₆×D₁₃	—	2	2	no	—
89	M₁₆×D₁₃	—	2	2	no	—
90	C₂×#6094	C₂×C₄	1	1	yes	characteristic
91	C₂×#6094	C₂×C₄	1	1	yes	characteristic
92	C₂×C₈×D₁₃	—	2	2	no	—
93	C₂×C₈×D₁₃	—	2	2	no	—
94	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
100	#88146	C₂×C₄	1	1	yes	characteristic
101	#88146	C₂×C₄	1	1	yes	characteristic
102	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
103	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
104	C₂²⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
105	C₂²⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
106	#88131	C₂×C₄	1	1	yes	characteristic
107	#88131	C₂×C₄	1	1	yes	characteristic
108	#88126	C₂×C₄	1	1	yes	characteristic
109	#88126	C₂×C₄	1	1	yes	characteristic
110	C₄²×D₁₃	C₂³	1	1	yes	characteristic
111	C₄²×D₁₃	C₂³	1	1	yes	characteristic
112	C₂²⋊#1057	C₂×C₄	1	2	yes	—
113	C₂²⋊#1057	C₂×C₄	1	2	yes	—
114	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
115	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
116	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
117	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
118	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
119	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
120	#88112	C₂×C₄	1	2	yes	—
121	#88112	C₂×C₄	1	2	yes	—
122	#88111	C₂×C₄	1	2	yes	—
123	#88111	C₂×C₄	1	2	yes	—
124	#88110	C₂×C₄	1	2	yes	—
125	#88110	C₂×C₄	1	2	yes	—
126	C₄⋊#1057	C₂×C₄	1	2	yes	—
127	C₄⋊#1057	C₂×C₄	1	2	yes	—
128	C₄×#1057	C₂×C₄	1	2	yes	—
129	C₄×#1057	C₂×C₄	1	2	yes	—
130	#88100	—	2	2	no	—
131	#88100	—	2	2	no	—
132	#88100	—	2	2	no	—
133	#88100	—	2	2	no	—
134	C₈×#261	—	2	2	no	—
135	C₈×#261	—	2	2	no	—
136	C₈×#261	—	2	2	no	—
137	C₈×#261	—	2	2	no	—
138	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
139	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
140	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
141	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
142	#88055	C₂×C₄	1	1	yes	characteristic
143	#88055	C₂×C₄	1	1	yes	characteristic
144	#88055	C₂×C₄	1	1	yes	characteristic
145	#88055	C₂×C₄	1	1	yes	characteristic
146	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
147	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
148	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
149	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
150	#88043	C₂×C₄	1	1	yes	characteristic
151	#88043	C₂×C₄	1	1	yes	characteristic
152	C₄×#1055	C₂×C₄	1	1	yes	characteristic
153	C₄×#1055	C₂×C₄	1	1	yes	characteristic
154	#20478	—	13	1	no	maximal, Sylow
155	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
156	C₂²×#261	C₂²×C₄	1	2	yes	—
157	C₂²×#261	C₂²×C₄	1	2	yes	—
158	C₂²×#261	C₂²×C₄	1	2	yes	—
159	C₂²×#261	C₂²×C₄	1	2	yes	—
160	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₄×D₁₃	—	2	1	no	—
163	C₂×C₄×D₁₃	—	2	1	no	—
164	C₂×C₄×D₁₃	—	2	1	no	—
165	C₂×C₄×D₁₃	—	2	1	no	—
166	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
174	C₂²⋊#261	—	2	4	no	—
175	C₂²⋊#261	—	4	2	no	—
176	C₂×#1057	C₂²×C₄	1	2	yes	—
177	C₂×#1057	C₂²×C₄	1	2	yes	—
178	C₂×#1057	C₂²×C₄	1	2	yes	—
179	C₂×#1057	C₂²×C₄	1	2	yes	—
180	C₄⋊#261	—	2	4	no	—
181	C₄⋊#261	—	4	2	no	—
182	C₄×#261	—	2	4	no	—
183	C₄×#261	—	2	1	no	—
184	C₄×#261	—	2	1	no	—
185	C₄×#261	—	2	1	no	—
186	C₄×#261	—	2	1	no	—
187	C₄×#261	—	2	1	no	—
188	C₄×#261	—	2	1	no	—
189	C₄×#261	—	2	1	no	—
190	C₄×#261	—	2	1	no	—
191	C₄×#261	—	4	2	no	—
192	D₁₃⋊C₈	—	2	1	no	—
193	D₁₃⋊C₈	—	2	1	no	—
194	D₁₃⋊C₈	—	2	1	no	—
195	D₁₃⋊C₈	—	2	1	no	—
196	D₁₃⋊C₈	—	2	1	no	—
197	D₁₃⋊C₈	—	2	1	no	—
198	D₁₃⋊C₈	—	2	1	no	—
199	D₁₃⋊C₈	—	2	1	no	—
200	C₁₃×M₁₆	—	2	2	no	—
201	C₂×C₈×C₁₃	—	2	2	no	—
202	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
206	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
207	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
208	C₁₃×C₂²⋊C₄	C₄²	1	1	yes	characteristic
209	C₁₃×C₂²⋊C₄	C₄²	1	1	yes	characteristic
210	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
211	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
212	C₂²⋊Dic₁₃	C₄²	1	1	yes	characteristic
213	C₂²⋊Dic₁₃	C₄²	1	1	yes	characteristic
214	#6103	C₄²	1	1	yes	characteristic
215	#6103	C₄²	1	1	yes	characteristic
216	#6103	C₄²	1	1	yes	characteristic
217	#6103	C₄²	1	1	yes	characteristic
218	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
219	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
220	#6101	C₄²	1	1	yes	characteristic
221	#6101	C₄²	1	1	yes	characteristic
222	#6101	C₄²	1	1	yes	characteristic
223	#6101	C₄²	1	1	yes	characteristic
224	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
225	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
226	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
227	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
228	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
229	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
230	#6099	—	2	2	no	—
231	C₂×#1055	—	2	2	no	—
232	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
233	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
234	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
235	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
236	#6094	—	2	2	no	—
237	#6094	—	2	2	no	—
238	C₈×D₁₃	—	2	1	no	—
239	C₈×D₁₃	—	2	1	no	—
240	C₈×D₁₃	—	2	1	no	—
241	C₈×D₁₃	—	2	1	no	—
242	C₈×D₁₃	—	2	2	no	—
243	C₈×D₁₃	—	2	2	no	—
244	C₈×D₁₃	#41	1	2	yes	—
245	C₈×D₁₃	#41	1	2	yes	—
246	C₈×D₁₃	#41	1	2	yes	—
247	C₈×D₁₃	#41	1	2	yes	—
248	C₂×#433	—	13	1	no	—
249	C₂×#405	—	13	1	no	—
250	#2298	—	13	1	no	—
251	#1771	—	13	1	no	—
252	#1771	—	13	1	no	—
253	#1770	—	13	1	no	—
254	C₈×C₄⋊C₄	—	13	1	no	—
255	#1753	—	13	1	no	—
256	#1753	—	13	1	no	—
257	#1752	—	13	1	no	—
258	C₈×C₂²⋊C₄	—	13	1	no	—
259	#1746	—	13	1	no	—
260	#1744	—	13	1	no	—
261	#1726	—	13	1	no	—
262	C₄×#97	—	13	1	no	—
263	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
264	C₂²×D₁₃	—	2	1	no	—
265	C₂²×D₁₃	—	2	1	no	—
266	C₂²×D₁₃	—	2	2	no	—
267	C₂²×D₁₃	—	2	2	no	—
268	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
269	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
270	C₂×#261	—	2	2	no	—
271	C₂×#261	—	2	2	no	—
272	C₂×#261	—	2	2	no	—
273	C₂×#261	—	2	2	no	—
274	C₂×#261	—	2	2	no	—
275	C₂×#261	—	2	2	no	—
276	C₂×#261	—	2	2	no	—
277	C₂×#261	—	2	2	no	—
278	C₂×#261	—	2	2	no	—
279	C₂×#261	—	2	2	no	—
280	C₂×#261	—	2	2	no	—
281	C₂×#261	#131	1	4	yes	—
282	C₂×C₄×C₁₃	—	2	1	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
285	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
286	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
287	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
288	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
289	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
290	C₂×Dic₁₃	—	2	1	no	—
291	C₂×Dic₁₃	—	2	1	no	—
292	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
293	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
294	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
295	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
296	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
297	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
298	C₄×D₁₃	—	2	1	no	—
299	C₄×D₁₃	—	2	1	no	—
300	C₄×D₁₃	—	2	2	no	—
301	C₄×D₁₃	—	2	2	no	—
302	C₄×D₁₃	—	2	2	no	—
303	C₄×D₁₃	—	2	2	no	—
304	C₄×D₁₃	—	2	1	no	—
305	C₄×D₁₃	—	2	1	no	—
306	C₄×D₁₃	—	2	1	no	—
307	C₄×D₁₃	—	2	1	no	—
308	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
309	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
310	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
311	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
312	#1057	—	2	2	no	—
313	#1057	—	2	2	no	—
314	#1057	—	2	2	no	—
315	#1057	—	2	2	no	—
316	C₈×C₁₃	—	2	1	no	—
317	C₈×C₁₃	—	2	1	no	—
318	C₈×C₁₃	#117	1	2	yes	—
319	C₈×C₁₃	#117	1	2	yes	—
320	#1055	—	2	1	no	—
321	#1055	—	2	1	no	—
322	#1055	#117	1	2	yes	—
323	#1055	#117	1	2	yes	—
324	C₂²×M₁₆	—	13	1	no	—
325	C₂³×C₈	—	13	1	no	—
326	C₂×#117	—	13	1	no	—
327	#433	—	13	2	no	—
328	#433	—	13	2	no	—
329	#433	—	13	2	no	—
330	#433	—	13	2	no	—
331	C₂×C₄⋊C₈	—	13	1	no	—
332	C₂×C₄⋊C₈	—	13	1	no	—
333	C₂×C₂²⋊C₈	—	13	1	no	—
334	C₂×C₂²⋊C₈	—	13	1	no	—
335	#405	—	13	1	no	—
336	#405	—	13	1	no	—
337	#405	—	13	1	no	—
338	#405	—	13	1	no	—
339	#405	—	13	1	no	—
340	#405	—	13	1	no	—
341	#405	—	13	1	no	—
342	#405	#261	1	1	yes	characteristic, complemented
343	C₂×#97	—	13	1	no	—
344	C₂×#97	—	13	1	no	—
345	C₂×#97	—	13	1	no	—
346	C₂×#97	—	13	1	no	—
347	C₂×#97	—	13	1	no	—
348	C₂×#97	—	13	1	no	—
349	C₂×#97	—	13	1	no	—
350	C₂×C₄×C₈	—	13	1	no	—
351	C₂×C₄×C₈	—	13	1	no	—
352	C₂×C₄×C₈	—	13	1	no	—
353	C₂×C₄×C₈	—	13	1	no	—
354	C₂×C₄×C₈	—	13	1	no	—
355	C₂×C₄×C₈	—	13	1	no	—
356	C₂×C₄×C₈	—	13	1	no	—
357	#388	—	13	2	no	—
358	#388	—	13	2	no	—
359	#387	—	13	2	no	—
360	#387	—	13	2	no	—
361	C₄×C₄⋊C₄	—	13	1	no	—
362	C₄×C₄⋊C₄	—	13	1	no	—
363	C₄×C₂²⋊C₄	—	13	1	no	—
364	C₄×C₂²⋊C₄	—	13	1	no	—
365	#376	—	13	1	no	—
366	C₄³	—	13	1	no	—
367	#336	—	13	1	no	—
368	#336	—	13	1	no	—
369	#336	—	13	1	no	—
370	#336	—	13	1	no	—
371	#336	—	13	1	no	—
372	#336	—	13	1	no	—
373	#336	—	13	1	no	—
374	#336	—	13	1	no	—
375	C₂²×C₁₃	—	2	1	no	—
376	C₂²×C₁₃	—	2	1	no	—
377	C₂²×C₁₃	—	2	1	no	—
378	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
379	C₂×D₁₃	—	2	1	no	—
380	C₂×D₁₃	—	2	1	no	—
381	C₂×D₁₃	—	2	1	no	—
382	C₂×D₁₃	—	4	2	no	—
383	C₂×D₁₃	—	4	2	no	—
384	C₂×D₁₃	C₄×#41	1	1	yes	characteristic
385	C₂×D₁₃	C₄×#41	1	1	yes	characteristic
386	C₂×D₁₃	C₂×#131	1	2	yes	—
387	C₂×D₁₃	#568	1	2	yes	—
388	#261	—	2	4	no	—
389	#261	—	4	2	no	—
390	#261	—	4	2	no	—
391	#261	—	4	2	no	—
392	C₄×C₁₃	—	2	1	no	—
393	C₄×C₁₃	—	2	1	no	—
394	C₄×C₁₃	—	2	1	no	—
395	C₄×C₁₃	—	2	1	no	—
396	C₄×C₁₃	—	2	1	no	—
397	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
398	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
399	Dic₁₃	—	2	1	no	—
400	Dic₁₃	—	2	1	no	—
401	Dic₁₃	—	2	1	no	—
402	Dic₁₃	—	2	1	no	—
403	Dic₁₃	—	2	1	no	—
404	Dic₁₃	C₄×#41	1	1	yes	characteristic
405	Dic₁₃	C₄×#41	1	1	yes	characteristic
406	C₂³×C₄	—	13	1	no	—
407	C₂×M₁₆	—	13	1	no	—
408	C₂×M₁₆	—	13	1	no	—
409	C₂×M₁₆	—	13	1	no	—
410	C₂×M₁₆	—	26	2	no	—
411	C₂×M₁₆	—	26	2	no	—
412	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
413	C₂²×C₈	—	13	1	no	—
414	C₂²×C₈	—	13	1	no	—
415	C₂²×C₈	—	13	1	no	—
416	C₂²×C₈	—	13	1	no	—
417	C₂²×C₈	—	13	1	no	—
418	C₂²×C₈	—	13	1	no	—
419	C₂²×C₈	—	13	1	no	—
420	C₂²×C₈	—	13	1	no	—
421	C₂²×C₈	—	13	1	no	—
422	C₂²×C₈	—	13	1	no	—
423	C₂²×C₈	—	13	1	no	—
424	C₂²×C₈	—	26	2	no	—
425	C₂²×C₈	—	26	2	no	—
426	C₂²×C₈	C₂×#261	1	1	yes	characteristic
427	#117	—	13	1	no	—
428	#117	—	13	1	no	—
429	#117	—	13	1	no	—
430	#117	—	13	1	no	—
431	#117	—	13	1	no	—
432	#117	—	13	1	no	—
433	#117	—	13	1	no	—
434	#117	C₂×#261	1	1	yes	characteristic
435	C₂×C₄⋊C₄	—	13	1	no	—
436	C₂×C₄⋊C₄	—	13	1	no	—
437	C₂×C₄⋊C₄	—	13	2	no	—
438	C₂×C₄⋊C₄	—	13	2	no	—
439	C₂×C₂²⋊C₄	—	13	1	no	—
440	C₂×C₂²⋊C₄	—	13	1	no	—
441	C₂×C₂²⋊C₄	—	13	2	no	—
442	C₂×C₂²⋊C₄	—	13	2	no	—
443	C₂×C₄²	—	13	1	no	—
444	C₂×C₄²	—	13	1	no	—
445	C₂×C₄²	—	13	1	no	—
446	C₂×C₄²	—	13	1	no	—
447	C₂×C₄²	—	13	1	no	—
448	C₂×C₄²	—	13	1	no	—
449	C₂×C₄²	—	13	2	no	—
450	C₂×C₄²	—	13	2	no	—
451	C₄⋊C₈	—	13	2	no	—
452	C₄⋊C₈	—	13	2	no	—
453	C₄⋊C₈	—	13	2	no	—
454	C₄⋊C₈	—	13	2	no	—
455	C₂²⋊C₈	—	13	2	no	—
456	C₂²⋊C₈	—	13	2	no	—
457	C₂²⋊C₈	—	13	2	no	—
458	C₂²⋊C₈	—	13	2	no	—
459	#97	—	13	2	no	—
460	#97	—	13	2	no	—
461	#97	—	13	1	no	—
462	#97	—	13	1	no	—
463	#97	—	13	1	no	—
464	#97	—	13	1	no	—
465	#97	—	13	1	no	—
466	#97	—	13	1	no	—
467	#97	—	26	2	no	—
468	#97	—	26	2	no	—
469	#97	—	26	2	no	—
470	#97	—	26	2	no	—
471	#97	C₂×#261	1	1	yes	characteristic
472	#97	C₂×#261	1	1	yes	characteristic
473	C₄×C₈	—	13	2	no	—
474	C₄×C₈	—	13	2	no	—
475	C₄×C₈	—	13	1	no	—
476	C₄×C₈	—	13	1	no	—
477	C₄×C₈	—	13	1	no	—
478	C₄×C₈	—	13	1	no	—
479	C₄×C₈	—	13	1	no	—
480	C₄×C₈	—	13	1	no	—
481	C₄×C₈	—	26	2	no	—
482	C₄×C₈	—	26	2	no	—
483	C₄×C₈	—	26	2	no	—
484	C₄×C₈	—	26	2	no	—
485	C₄×C₈	C₂×#261	1	1	yes	characteristic
486	C₄×C₈	C₂×#261	1	1	yes	characteristic
487	#95	—	13	2	no	—
488	#95	—	13	2	no	—
489	#95	—	13	2	no	—
490	#95	—	13	2	no	—
491	#95	—	13	2	no	—
492	#95	—	13	2	no	—
493	C₂×C₁₃	—	4	1	no	—
494	C₂×C₁₃	C₄×#117	1	1	yes	characteristic
495	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
496	C₂×C₁₃	#2875	1	1	yes	characteristic
497	D₁₃	—	4	1	no	—
498	D₁₃	#2968	1	2	yes	—
499	D₁₃	#2969	1	2	yes	—
500	C₂⁴	—	13	1	no	—
501	C₂²×C₄	—	13	1	no	—
502	C₂²×C₄	—	13	2	no	—
503	C₂²×C₄	—	13	1	no	—
504	C₂²×C₄	—	13	1	no	—
505	C₂²×C₄	—	13	1	no	—
506	C₂²×C₄	—	13	1	no	—
507	C₂²×C₄	—	13	1	no	—
508	C₂²×C₄	—	13	1	no	—
509	C₂²×C₄	—	13	1	no	—
510	C₂²×C₄	—	13	1	no	—
511	C₂²×C₄	—	13	2	no	—
512	C₂²×C₄	—	13	2	no	—
513	C₂²×C₄	—	13	2	no	—
514	C₂²×C₄	—	26	1	no	—
515	C₂²×C₄	—	26	1	no	—
516	C₂²×C₄	—	26	1	no	—
517	C₂²×C₄	—	26	1	no	—
518	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
519	M₁₆	—	2	2	no	—
520	M₁₆	—	26	2	no	—
521	M₁₆	—	26	2	no	—
522	M₁₆	—	26	2	no	—
523	C₂×C₈	—	2	2	no	—
524	C₂×C₈	—	13	1	no	—
525	C₂×C₈	—	13	1	no	—
526	C₂×C₈	—	13	2	no	—
527	C₂×C₈	—	13	2	no	—
528	C₂×C₈	—	13	2	no	—
529	C₂×C₈	—	13	2	no	—
530	C₂×C₈	—	13	2	no	—
531	C₂×C₈	—	13	2	no	—
532	C₂×C₈	—	13	2	no	—
533	C₂×C₈	—	13	2	no	—
534	C₂×C₈	—	13	1	no	—
535	C₂×C₈	—	13	1	no	—
536	C₂×C₈	—	26	2	no	—
537	C₂×C₈	—	26	1	no	—
538	C₂×C₈	—	26	1	no	—
539	C₂×C₈	—	26	1	no	—
540	C₂×C₈	—	26	1	no	—
541	C₂×C₈	—	26	2	no	—
542	C₂×C₈	—	26	1	no	—
543	C₂×C₈	—	26	1	no	—
544	C₂×C₈	—	26	1	no	—
545	C₂×C₈	—	26	1	no	—
546	C₂×C₈	—	26	1	no	—
547	C₂×C₈	—	26	1	no	—
548	C₂×C₈	—	26	1	no	—
549	C₂×C₈	—	26	1	no	—
550	C₂×C₈	—	26	2	no	—
551	C₂×C₈	C₂²×#261	1	1	yes	characteristic
552	C₂×C₈	C₂²×#261	1	1	yes	characteristic
553	C₂×C₈	C₂²×#261	1	1	yes	characteristic
554	C₂×C₈	C₂²×#261	1	1	yes	characteristic
555	C₄⋊C₄	—	13	1	no	—
556	C₄⋊C₄	—	13	1	no	—
557	C₄⋊C₄	—	13	1	no	—
558	C₄⋊C₄	—	13	1	no	—
559	C₄⋊C₄	—	13	1	no	—
560	C₄⋊C₄	—	13	1	no	—
561	C₄⋊C₄	—	26	4	no	—
562	C₄⋊C₄	—	52	2	no	—
563	C₄⋊C₄	C₄×#261	1	1	yes	characteristic
564	C₄⋊C₄	C₄×#261	1	1	yes	characteristic
565	C₂²⋊C₄	—	13	1	no	—
566	C₂²⋊C₄	—	13	1	no	—
567	C₂²⋊C₄	—	13	1	no	—
568	C₂²⋊C₄	—	13	1	no	—
569	C₂²⋊C₄	—	13	1	no	—
570	C₂²⋊C₄	—	13	1	no	—
571	C₂²⋊C₄	—	26	4	no	—
572	C₂²⋊C₄	—	52	2	no	—
573	C₂²⋊C₄	C₄×#261	1	1	yes	characteristic
574	C₂²⋊C₄	C₄×#261	1	1	yes	characteristic
575	C₄²	—	13	1	no	—
576	C₄²	—	13	1	no	—
577	C₄²	—	13	1	no	—
578	C₄²	—	13	1	no	—
579	C₄²	—	13	1	no	—
580	C₄²	—	13	1	no	—
581	C₄²	—	26	1	no	—
582	C₄²	—	26	1	no	—
583	C₄²	—	26	1	no	—
584	C₄²	—	26	1	no	—
585	C₄²	—	26	1	no	—
586	C₄²	—	26	1	no	—
587	C₄²	—	26	1	no	—
588	C₄²	—	26	1	no	—
589	C₄²	—	26	4	no	—
590	C₄²	—	52	2	no	—
591	C₄²	C₂²×#261	1	1	yes	characteristic
592	C₄²	C₂²×#261	1	1	yes	characteristic
593	C₁₃	#20478	1	1	yes	characteristic, complemented, Sylow
594	C₂³	—	13	1	no	—
595	C₂³	—	13	1	no	—
596	C₂³	—	26	2	no	—
597	C₂³	—	26	2	no	—
598	C₂³	—	26	1	no	—
599	C₂³	—	26	1	no	—
600	C₂³	C₂×C₄×#261	1	1	yes	characteristic
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	13	1	no	—
604	C₂×C₄	—	13	1	no	—
605	C₂×C₄	—	13	1	no	—
606	C₂×C₄	—	13	1	no	—
607	C₂×C₄	—	13	1	no	—
608	C₂×C₄	—	13	4	no	—
609	C₂×C₄	—	13	1	no	—
610	C₂×C₄	—	13	1	no	—
611	C₂×C₄	—	13	1	no	—
612	C₂×C₄	—	13	1	no	—
613	C₂×C₄	—	13	1	no	—
614	C₂×C₄	—	26	1	no	—
615	C₂×C₄	—	26	1	no	—
616	C₂×C₄	—	26	2	no	—
617	C₂×C₄	—	26	2	no	—
618	C₂×C₄	—	26	2	no	—
619	C₂×C₄	—	26	2	no	—
620	C₂×C₄	—	26	1	no	—
621	C₂×C₄	—	26	1	no	—
622	C₂×C₄	—	26	1	no	—
623	C₂×C₄	—	26	1	no	—
624	C₂×C₄	—	26	2	no	—
625	C₂×C₄	—	26	2	no	—
626	C₂×C₄	—	26	1	no	—
627	C₂×C₄	—	26	1	no	—
628	C₂×C₄	—	26	2	no	—
629	C₂×C₄	—	26	2	no	—
630	C₂×C₄	—	26	2	no	—
631	C₂×C₄	—	26	2	no	—
632	C₂×C₄	—	26	2	no	—
633	C₂×C₄	—	26	2	no	—
634	C₂×C₄	—	26	2	no	—
635	C₂×C₄	—	26	2	no	—
636	C₂×C₄	—	26	2	no	—
637	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
638	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
639	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
640	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
641	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
642	C₂×C₄	C₂³×#261	1	1	yes	characteristic
643	C₈	—	2	1	no	—
644	C₈	—	2	1	no	—
645	C₈	—	13	2	no	—
646	C₈	—	13	2	no	—
647	C₈	—	26	2	no	—
648	C₈	—	26	2	no	—
649	C₈	—	26	2	no	—
650	C₈	—	26	2	no	—
651	C₈	—	26	1	no	—
652	C₈	—	26	1	no	—
653	C₈	#88237	1	2	yes	—
654	C₈	#88237	1	2	yes	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	13	1	no	—
659	C₂²	—	13	1	no	—
660	C₂²	—	13	2	no	—
661	C₂²	—	13	2	no	—
662	C₂²	—	26	1	no	—
663	C₂²	—	26	1	no	—
664	C₂²	—	26	1	no	—
665	C₂²	—	52	2	no	—
666	C₂²	—	52	2	no	—
667	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
668	C₄	—	2	1	no	—
669	C₄	—	2	1	no	—
670	C₄	—	2	1	no	—
671	C₄	—	2	1	no	—
672	C₄	—	2	1	no	—
673	C₄	—	13	1	no	—
674	C₄	—	13	1	no	—
675	C₄	—	26	4	no	—
676	C₄	—	26	1	no	—
677	C₄	—	26	1	no	—
678	C₄	—	26	1	no	—
679	C₄	—	26	1	no	—
680	C₄	—	26	1	no	—
681	C₄	—	52	2	no	—
682	C₄	—	52	2	no	—
683	C₄	—	52	2	no	—
684	C₄	C₂×#88237	1	1	yes	characteristic
685	C₄	C₂×#88237	1	1	yes	characteristic
686	C₂	—	4	1	no	—
687	C₂	—	13	2	no	—
688	C₂	—	13	2	no	—
689	C₂	—	52	1	no	—
690	C₂	C₄×#88237	1	1	yes	characteristic
691	C₂	#131×#261	1	1	yes	characteristic
692	C₂	#13131406	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#405	C₄
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#405	#261
hypocenter	C₁₃	#20478
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #405

Complements

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

N	H ≅ G/N	type
3. #13130634	C₂	semidirect
4. #13130634	C₂	semidirect
5. #13130630	C₂	semidirect
6. C₈×C₄⋊#261	C₂	semidirect
11. #13130554	C₂	semidirect
12. #13130549	C₂	semidirect
13. #13130494	C₂	semidirect
14. #97×#261	C₂	semidirect
33. #11719077	C₄	semidirect
34. #11719077	C₄	semidirect
37. #11719068	C₄	semidirect
38. #11719068	C₄	semidirect
47. C₁₃×#405	C₄	semidirect
48. #11718783	C₄	semidirect
49. #11718762	C₄	semidirect
50. #11718658	C₄	semidirect
51. #11718369	C₄	semidirect
52. #11718369	C₄	semidirect
55. #11718350	C₄	semidirect
56. #11718350	C₄	semidirect
342. #405	#261	semidirect
593. C₁₃	#20478	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₁₃⋊#433	2
#13131298	2
#13130634	2
#13130630	2
C₈×C₄⋊#261	2
#13130576	2
#13130572	2
C₈×C₂²⋊#261	2
#13130554	2
#13130549	2
#13130494	2
#97×#261	2
D₁₃×#405	2
#20478	13