Subgroups — #16797729

Order 3328.

778 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃⋊#446	C₂	1	1	yes	maximal, characteristic
2	#13131295	C₂	1	1	yes	maximal, characteristic
3	#13130637	C₂	1	1	yes	maximal, characteristic
4	#13130637	C₂	1	1	yes	maximal, characteristic
5	#13130634	C₂	1	1	yes	maximal, characteristic
6	#13130634	C₂	1	1	yes	maximal, characteristic
7	#13130633	C₂	1	1	yes	maximal, characteristic
8	#13130630	C₂	1	1	yes	maximal, characteristic
9	#13130625	C₂	1	1	yes	maximal, characteristic
10	#13130625	C₂	1	1	yes	maximal, characteristic
11	#13130623	C₂	1	1	yes	maximal, characteristic
12	#13130556	C₂	1	1	yes	maximal, characteristic
13	#13130554	C₂	1	1	yes	maximal, characteristic
14	#13130552	C₂	1	1	yes	maximal, characteristic
15	D₁₃×#446	C₂	1	1	yes	maximal, characteristic
16	C₄×Q₈×D₁₃	C₂²	1	1	yes	characteristic
17	(C₂×#261)⋊Q₈	C₄	1	2	yes	—
18	#11719158	C₄	1	2	yes	complemented
19	C₂×#88100	C₂²	1	1	yes	characteristic
20	C₂×#88100	C₂²	1	1	yes	characteristic
21	C₂×#88100	C₂²	1	1	yes	characteristic
22	C₂×#88100	C₂²	1	1	yes	characteristic
23	C₂×C₈×#261	C₂²	1	1	yes	characteristic
24	C₂×C₈×#261	C₂²	1	1	yes	characteristic
25	#11719083	C₄	1	2	yes	—
26	#11719082	C₄	1	2	yes	—
27	#11719082	C₄	1	2	yes	—
28	#11719080	C₄	1	2	yes	complemented
29	#11719078	C₄	1	2	yes	complemented
30	#11719078	C₄	1	2	yes	complemented
31	C₄×C₄⋊#261	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊#261	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊#261	C₂²	1	1	yes	characteristic
34	#11719057	C₂²	1	1	yes	characteristic
35	#11719057	C₂²	1	1	yes	characteristic
36	C₄²×#261	C₂²	1	1	yes	characteristic
37	D₁₃⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
38	D₁₃⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
39	D₁₃⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
40	#11719047	C₂²	1	1	yes	characteristic
41	#11719047	C₂²	1	1	yes	characteristic
42	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
43	C₁₃×#446	C₄	1	1	yes	characteristic, complemented
44	#11718685	C₄	1	1	yes	characteristic, complemented
45	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
48	#11718492	C₄	1	1	yes	characteristic, complemented
49	#11718489	C₄	1	1	yes	characteristic, complemented
50	#11718489	C₄	1	1	yes	characteristic, complemented
51	D₁₃×#97	C₂²	1	1	yes	characteristic
52	D₁₃×#97	C₂²	1	1	yes	characteristic
53	#11718362	C₄	1	1	yes	characteristic, complemented
54	#11718362	C₄	1	1	yes	characteristic, complemented
55	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
56	#11718340	C₄	1	1	yes	characteristic, complemented
57	(C₂×#261)⋊C₈	C₂²	1	1	yes	characteristic
58	(C₂×#261)⋊C₈	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	C₂×Q₈×D₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄⋊#261	C₂×C₄	1	2	yes	—
69	C₂×C₄⋊#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	C₂³	1	1	yes	characteristic
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×D₁₃⋊C₈	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	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
82	Q₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
83	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
84	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
85	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
86	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
87	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
88	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
89	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
90	#88141	C₂×C₄	1	1	yes	characteristic
91	#88141	C₂×C₄	1	1	yes	characteristic
92	#88141	C₂×C₄	1	1	yes	characteristic
93	C₄²×D₁₃	C₂³	1	1	yes	characteristic
94	C₄²×D₁₃	C₂³	1	1	yes	characteristic
95	C₄²×D₁₃	C₂³	1	1	yes	characteristic
96	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
97	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
98	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
99	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
100	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
101	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
102	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
103	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
104	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
105	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
106	#88112	C₂×C₄	1	2	yes	—
107	#88112	C₂×C₄	1	2	yes	—
108	#88112	C₂×C₄	1	2	yes	—
109	#88110	C₂×C₄	1	2	yes	—
110	#88110	C₂×C₄	1	2	yes	—
111	#88110	C₂×C₄	1	2	yes	—
112	#88110	C₂×C₄	1	2	yes	—
113	C₄⋊#1057	C₂×C₄	1	2	yes	—
114	C₄⋊#1057	C₂×C₄	1	2	yes	—
115	C₄⋊#1057	C₂×C₄	1	2	yes	—
116	C₄×#1057	C₂×C₄	1	2	yes	—
117	C₄×#1057	C₂×C₄	1	2	yes	—
118	#88100	—	4	1	no	—
119	#88100	—	4	1	no	—
120	#88100	—	4	1	no	—
121	#88100	—	4	1	no	—
122	C₈×#261	—	4	1	no	—
123	C₈×#261	—	4	1	no	—
124	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
125	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
126	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
127	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
128	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
129	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
130	#88055	C₂×C₄	1	1	yes	characteristic
131	#88055	C₂×C₄	1	1	yes	characteristic
132	#88055	C₂×C₄	1	1	yes	characteristic
133	#88055	C₂×C₄	1	1	yes	characteristic
134	#88054	C₂×C₄	1	1	yes	characteristic
135	#88054	C₂×C₄	1	1	yes	characteristic
136	#88054	C₂×C₄	1	1	yes	characteristic
137	#88054	C₂×C₄	1	1	yes	characteristic
138	#88054	C₂×C₄	1	1	yes	characteristic
139	#88054	C₂×C₄	1	1	yes	characteristic
140	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
141	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
142	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
143	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
144	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
145	#88043	C₂×C₄	1	1	yes	characteristic
146	#88043	C₂×C₄	1	1	yes	characteristic
147	C₄×#1055	C₂×C₄	1	1	yes	characteristic
148	#20576	—	13	1	no	maximal, Sylow
149	C₂²×#261	C₂²×C₄	1	2	yes	—
150	C₂²×#261	C₂²×C₄	1	2	yes	—
151	C₂²×#261	C₂²×C₄	1	2	yes	—
152	C₂²×#261	C₂²×C₄	1	2	yes	—
153	C₂×Q₈×C₁₃	C₄²	1	1	yes	characteristic
154	Q₈×D₁₃	—	4	2	no	—
155	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
162	C₂×Dic₂₆	C₄²	1	1	yes	characteristic
163	C₂×Dic₂₆	C₄²	1	1	yes	characteristic
164	C₂×Dic₂₆	C₄²	1	1	yes	characteristic
165	C₂×#1057	C₂²×C₄	1	2	yes	—
166	C₂×#1057	C₂²×C₄	1	2	yes	—
167	C₂×#1057	C₂²×C₄	1	2	yes	—
168	C₂×#1057	C₂²×C₄	1	2	yes	—
169	C₄⋊#261	—	4	2	no	—
170	C₄⋊#261	—	4	2	no	—
171	C₄⋊#261	—	4	2	no	—
172	C₄×#261	—	2	1	no	—
173	C₄×#261	—	2	1	no	—
174	C₄×#261	—	2	1	no	—
175	C₄×#261	—	2	1	no	—
176	C₄×#261	—	2	1	no	—
177	C₄×#261	—	2	1	no	—
178	C₄×#261	—	2	1	no	—
179	C₄×#261	—	2	1	no	—
180	C₄×#261	—	4	2	no	—
181	C₄×#261	—	4	2	no	—
182	D₁₃⋊C₈	—	2	1	no	—
183	D₁₃⋊C₈	—	2	1	no	—
184	D₁₃⋊C₈	—	2	1	no	—
185	D₁₃⋊C₈	—	2	1	no	—
186	D₁₃⋊C₈	—	2	1	no	—
187	D₁₃⋊C₈	—	2	1	no	—
188	D₁₃⋊C₈	—	2	1	no	—
189	D₁₃⋊C₈	—	2	1	no	—
190	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
194	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
195	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
196	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
197	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
198	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
199	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
200	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
201	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
202	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
203	#6101	C₄²	1	1	yes	characteristic
204	#6101	C₄²	1	1	yes	characteristic
205	#6101	C₄²	1	1	yes	characteristic
206	#6101	C₄²	1	1	yes	characteristic
207	#6101	C₄²	1	1	yes	characteristic
208	#6101	C₄²	1	1	yes	characteristic
209	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
210	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
211	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
212	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
213	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
214	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
215	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
216	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
217	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
218	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
219	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
220	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
221	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
222	C₈×D₁₃	—	2	1	no	—
223	C₈×D₁₃	—	2	1	no	—
224	C₈×D₁₃	—	2	1	no	—
225	C₈×D₁₃	—	2	1	no	—
226	C₈×D₁₃	—	2	1	no	—
227	C₈×D₁₃	—	2	1	no	—
228	C₈×D₁₃	—	2	1	no	—
229	C₈×D₁₃	—	2	1	no	—
230	C₂×#446	—	13	1	no	—
231	C₂×#446	—	13	1	no	—
232	#2295	—	13	1	no	—
233	#1771	—	13	1	no	—
234	#1771	—	13	1	no	—
235	#1771	—	13	1	no	—
236	#1771	—	13	1	no	—
237	#1770	—	13	1	no	—
238	#1770	—	13	1	no	—
239	#1768	—	13	1	no	—
240	#1768	—	13	1	no	—
241	#1767	—	13	1	no	—
242	#1746	—	13	1	no	—
243	#1746	—	13	1	no	—
244	#1745	—	13	1	no	—
245	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
246	C₂×#261	—	2	2	no	—
247	C₂×#261	—	2	2	no	—
248	C₂×#261	—	2	2	no	—
249	C₂×#261	—	2	2	no	—
250	C₂×#261	—	2	2	no	—
251	C₂×#261	—	2	2	no	—
252	C₂×#261	—	2	2	no	—
253	C₂×#261	—	2	2	no	—
254	C₂×#261	—	2	2	no	—
255	C₂×#261	—	2	2	no	—
256	C₂×#261	—	2	2	no	—
257	C₂×#261	—	2	2	no	—
258	Q₈×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
260	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
261	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
266	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
267	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
268	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
269	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
270	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
271	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
272	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
273	C₄×D₁₃	—	2	2	no	—
274	C₄×D₁₃	—	2	2	no	—
275	C₄×D₁₃	—	2	2	no	—
276	C₄×D₁₃	—	2	2	no	—
277	C₄×D₁₃	—	2	2	no	—
278	C₄×D₁₃	—	2	2	no	—
279	C₄×D₁₃	H(5,𝔽₂)	1	1	yes	characteristic
280	C₄×D₁₃	2₋¹⁺⁴	1	1	yes	characteristic
281	C₄×D₁₃	2₋¹⁺⁴	1	1	yes	characteristic
282	C₄×D₁₃	2₋¹⁺⁴	1	1	yes	characteristic
283	Dic₂₆	—	4	1	no	—
284	Dic₂₆	—	4	1	no	—
285	Dic₂₆	—	4	1	no	—
286	#1057	—	2	2	no	—
287	#1057	—	2	2	no	—
288	#1057	—	2	2	no	—
289	#1057	—	2	2	no	—
290	C₈×C₁₃	—	2	1	no	—
291	C₈×C₁₃	—	2	1	no	—
292	C₈×C₁₃	—	2	1	no	—
293	C₈×C₁₃	—	2	1	no	—
294	#1055	—	2	1	no	—
295	#1055	—	2	1	no	—
296	#1055	—	2	1	no	—
297	#1055	—	2	1	no	—
298	C₂×C₄×Q₈	—	13	1	no	—
299	#446	—	13	2	no	—
300	#446	—	13	2	no	—
301	#446	—	13	2	no	—
302	#446	—	13	2	no	—
303	#446	—	13	1	no	—
304	#446	—	13	1	no	—
305	#446	—	13	1	no	—
306	#446	—	13	1	no	—
307	#446	—	13	1	no	—
308	#446	—	13	1	no	—
309	#446	—	13	1	no	—
310	#446	#261	1	1	yes	characteristic, complemented
311	C₂×C₄⋊C₈	—	13	1	no	—
312	C₂×C₄⋊C₈	—	13	1	no	—
313	C₂×C₄⋊C₈	—	13	1	no	—
314	C₂×C₄⋊C₈	—	13	1	no	—
315	C₂×C₄⋊C₈	—	13	1	no	—
316	C₂×C₄⋊C₈	—	13	1	no	—
317	C₂×#97	—	13	1	no	—
318	C₂×#97	—	13	1	no	—
319	C₂×#97	—	13	1	no	—
320	C₂×#97	—	13	1	no	—
321	C₂×#97	—	13	1	no	—
322	C₂×#97	—	13	1	no	—
323	C₂×#97	—	13	1	no	—
324	C₂×#97	—	13	1	no	—
325	C₂×C₄×C₈	—	13	1	no	—
326	C₂×C₄×C₈	—	13	1	no	—
327	C₂×C₄×C₈	—	13	1	no	—
328	C₂×C₄×C₈	—	13	1	no	—
329	#391	—	13	2	no	—
330	#389	—	13	2	no	—
331	#387	—	13	2	no	—
332	#387	—	13	2	no	—
333	C₄×C₄⋊C₄	—	13	1	no	—
334	C₄×C₄⋊C₄	—	13	1	no	—
335	C₄×C₄⋊C₄	—	13	1	no	—
336	#376	—	13	1	no	—
337	#376	—	13	1	no	—
338	C₄³	—	13	1	no	—
339	#336	—	13	1	no	—
340	#336	—	13	1	no	—
341	#336	—	13	1	no	—
342	#336	—	13	1	no	—
343	#336	—	13	1	no	—
344	#336	—	13	1	no	—
345	#336	—	13	1	no	—
346	#336	—	13	1	no	—
347	#336	—	13	1	no	—
348	#336	—	13	1	no	—
349	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
350	C₂×D₁₃	#519	1	1	yes	characteristic
351	C₂×D₁₃	#520	1	1	yes	characteristic
352	C₂×D₁₃	#568	1	2	yes	—
353	C₂×D₁₃	#568	1	2	yes	—
354	#261	—	4	2	no	—
355	#261	—	4	2	no	—
356	#261	—	4	2	no	—
357	#261	—	4	2	no	—
358	C₄×C₁₃	—	2	1	no	—
359	C₄×C₁₃	—	2	1	no	—
360	C₄×C₁₃	—	2	1	no	—
361	C₄×C₁₃	—	2	1	no	—
362	C₄×C₁₃	—	2	1	no	—
363	C₄×C₁₃	—	2	1	no	—
364	C₄×C₁₃	#519	1	1	yes	characteristic
365	C₄×C₁₃	#520	1	1	yes	characteristic
366	Dic₁₃	—	2	1	no	—
367	Dic₁₃	—	2	1	no	—
368	Dic₁₃	—	2	1	no	—
369	Dic₁₃	—	2	1	no	—
370	Dic₁₃	—	2	1	no	—
371	Dic₁₃	—	2	1	no	—
372	Dic₁₃	#519	1	1	yes	characteristic
373	Dic₁₃	#520	1	1	yes	characteristic
374	C₂²×Q₈	—	13	1	no	—
375	C₂²×C₈	—	13	1	no	—
376	C₂²×C₈	—	13	1	no	—
377	C₂²×C₈	—	13	1	no	—
378	C₂²×C₈	—	13	1	no	—
379	C₂²×C₈	—	13	1	no	—
380	C₂²×C₈	—	13	1	no	—
381	C₂²×C₈	—	13	1	no	—
382	C₂²×C₈	—	13	1	no	—
383	C₄×Q₈	—	13	1	no	—
384	C₄×Q₈	—	13	1	no	—
385	C₄×Q₈	—	13	1	no	—
386	C₄×Q₈	—	13	1	no	—
387	C₄×Q₈	—	13	1	no	—
388	C₄×Q₈	—	13	1	no	—
389	C₄×Q₈	—	13	1	no	—
390	C₄×Q₈	C₂×#261	1	1	yes	characteristic
391	C₂×C₄⋊C₄	—	13	1	no	—
392	C₂×C₄⋊C₄	—	13	1	no	—
393	C₂×C₄⋊C₄	—	13	1	no	—
394	C₂×C₄⋊C₄	—	13	2	no	—
395	C₂×C₄⋊C₄	—	13	2	no	—
396	C₂×C₄⋊C₄	—	13	2	no	—
397	C₂×C₄²	—	13	1	no	—
398	C₂×C₄²	—	13	1	no	—
399	C₂×C₄²	—	13	1	no	—
400	C₂×C₄²	—	13	1	no	—
401	C₂×C₄²	—	13	1	no	—
402	C₂×C₄²	—	13	1	no	—
403	C₂×C₄²	—	13	1	no	—
404	C₂×C₄²	—	13	2	no	—
405	C₂×C₄²	—	13	2	no	—
406	C₄⋊C₈	—	13	2	no	—
407	C₄⋊C₈	—	13	2	no	—
408	C₄⋊C₈	—	13	2	no	—
409	C₄⋊C₈	—	13	2	no	—
410	C₄⋊C₈	—	13	2	no	—
411	C₄⋊C₈	—	13	2	no	—
412	C₄⋊C₈	—	13	1	no	—
413	C₄⋊C₈	—	13	1	no	—
414	C₄⋊C₈	—	13	1	no	—
415	C₄⋊C₈	—	13	1	no	—
416	C₄⋊C₈	—	13	1	no	—
417	C₄⋊C₈	—	13	1	no	—
418	C₄⋊C₈	—	13	1	no	—
419	C₄⋊C₈	—	13	1	no	—
420	C₄⋊C₈	—	13	1	no	—
421	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
422	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
423	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
424	#97	—	13	2	no	—
425	#97	—	13	2	no	—
426	#97	—	13	2	no	—
427	#97	—	13	2	no	—
428	#97	—	13	1	no	—
429	#97	—	13	1	no	—
430	#97	—	13	1	no	—
431	#97	—	13	1	no	—
432	#97	—	13	1	no	—
433	#97	—	13	1	no	—
434	#97	—	52	1	no	—
435	#97	—	52	1	no	—
436	#97	—	52	1	no	—
437	#97	—	52	1	no	—
438	#97	C₂×#261	1	1	yes	characteristic
439	#97	C₂×#261	1	1	yes	characteristic
440	C₄×C₈	—	13	2	no	—
441	C₄×C₈	—	13	2	no	—
442	C₄×C₈	—	13	1	no	—
443	C₄×C₈	—	13	1	no	—
444	C₄×C₈	—	13	1	no	—
445	C₄×C₈	—	52	1	no	—
446	C₄×C₈	—	52	1	no	—
447	C₄×C₈	C₂×#261	1	1	yes	characteristic
448	#95	—	13	2	no	—
449	#95	—	13	2	no	—
450	#95	—	13	2	no	—
451	#95	—	13	2	no	—
452	#95	—	13	2	no	—
453	#95	—	13	2	no	—
454	#95	—	13	2	no	—
455	C₂×C₁₃	#2276	1	1	yes	characteristic
456	C₂×C₁₃	#2873	1	1	yes	characteristic
457	C₂×C₁₃	#2875	1	1	yes	characteristic
458	D₁₃	#2987	1	2	yes	—
459	D₁₃	#2995	1	2	yes	—
460	C₂×Q₈	—	13	1	no	—
461	C₂×Q₈	—	13	1	no	—
462	C₂×Q₈	—	13	1	no	—
463	C₂×Q₈	—	52	2	no	—
464	C₂×Q₈	C₄×#261	1	1	yes	characteristic
465	C₂²×C₄	—	13	1	no	—
466	C₂²×C₄	—	13	1	no	—
467	C₂²×C₄	—	13	1	no	—
468	C₂²×C₄	—	13	1	no	—
469	C₂²×C₄	—	13	1	no	—
470	C₂²×C₄	—	13	1	no	—
471	C₂²×C₄	—	13	1	no	—
472	C₂²×C₄	—	13	2	no	—
473	C₂²×C₄	—	13	2	no	—
474	C₂²×C₄	—	13	2	no	—
475	C₂²×C₄	—	13	2	no	—
476	C₂×C₈	—	13	2	no	—
477	C₂×C₈	—	13	2	no	—
478	C₂×C₈	—	13	2	no	—
479	C₂×C₈	—	13	2	no	—
480	C₂×C₈	—	13	1	no	—
481	C₂×C₈	—	13	1	no	—
482	C₂×C₈	—	13	1	no	—
483	C₂×C₈	—	13	1	no	—
484	C₂×C₈	—	26	1	no	—
485	C₂×C₈	—	26	1	no	—
486	C₂×C₈	—	26	1	no	—
487	C₂×C₈	—	26	1	no	—
488	C₂×C₈	—	26	1	no	—
489	C₂×C₈	—	26	1	no	—
490	C₂×C₈	—	26	1	no	—
491	C₂×C₈	—	26	1	no	—
492	C₂×C₈	—	26	1	no	—
493	C₂×C₈	—	26	1	no	—
494	C₂×C₈	—	26	1	no	—
495	C₂×C₈	—	26	1	no	—
496	C₂×C₈	—	26	1	no	—
497	C₂×C₈	—	26	1	no	—
498	C₂×C₈	—	26	1	no	—
499	C₂×C₈	—	26	1	no	—
500	C₂×C₈	C₂²×#261	1	1	yes	characteristic
501	C₂×C₈	C₂²×#261	1	1	yes	characteristic
502	C₂×C₈	C₂²×#261	1	1	yes	characteristic
503	C₂×C₈	C₂²×#261	1	1	yes	characteristic
504	C₄⋊C₄	—	13	1	no	—
505	C₄⋊C₄	—	13	1	no	—
506	C₄⋊C₄	—	13	1	no	—
507	C₄⋊C₄	—	13	1	no	—
508	C₄⋊C₄	—	13	1	no	—
509	C₄⋊C₄	—	13	1	no	—
510	C₄⋊C₄	—	13	1	no	—
511	C₄⋊C₄	—	13	1	no	—
512	C₄⋊C₄	—	13	1	no	—
513	C₄⋊C₄	—	52	2	no	—
514	C₄⋊C₄	—	52	2	no	—
515	C₄⋊C₄	—	52	2	no	—
516	C₄⋊C₄	C₄×#261	1	1	yes	characteristic
517	C₄⋊C₄	C₄×#261	1	1	yes	characteristic
518	C₄⋊C₄	C₄×#261	1	1	yes	characteristic
519	C₄²	—	13	1	no	—
520	C₄²	—	13	1	no	—
521	C₄²	—	13	1	no	—
522	C₄²	—	13	1	no	—
523	C₄²	—	13	1	no	—
524	C₄²	—	13	1	no	—
525	C₄²	—	13	1	no	—
526	C₄²	—	13	1	no	—
527	C₄²	—	13	1	no	—
528	C₄²	—	26	1	no	—
529	C₄²	—	26	1	no	—
530	C₄²	—	26	1	no	—
531	C₄²	—	26	1	no	—
532	C₄²	—	26	1	no	—
533	C₄²	—	26	1	no	—
534	C₄²	—	26	1	no	—
535	C₄²	—	26	1	no	—
536	C₄²	—	52	2	no	—
537	C₄²	—	52	2	no	—
538	C₄²	C₂²×#261	1	1	yes	characteristic
539	C₄²	C₂²×#261	1	1	yes	characteristic
540	C₄²	C₂²×#261	1	1	yes	characteristic
541	C₁₃	#20576	1	1	yes	characteristic, complemented, Sylow
542	C₂³	—	13	1	no	—
543	Q₈	—	4	1	no	—
544	Q₈	—	52	1	no	—
545	Q₈	—	52	1	no	—
546	Q₈	—	52	1	no	—
547	C₂×C₄	—	13	1	no	—
548	C₂×C₄	—	13	1	no	—
549	C₂×C₄	—	13	1	no	—
550	C₂×C₄	—	13	1	no	—
551	C₂×C₄	—	13	1	no	—
552	C₂×C₄	—	13	1	no	—
553	C₂×C₄	—	13	1	no	—
554	C₂×C₄	—	13	1	no	—
555	C₂×C₄	—	13	1	no	—
556	C₂×C₄	—	13	1	no	—
557	C₂×C₄	—	13	1	no	—
558	C₂×C₄	—	26	2	no	—
559	C₂×C₄	—	26	2	no	—
560	C₂×C₄	—	26	2	no	—
561	C₂×C₄	—	26	2	no	—
562	C₂×C₄	—	26	2	no	—
563	C₂×C₄	—	26	2	no	—
564	C₂×C₄	—	26	2	no	—
565	C₂×C₄	—	26	2	no	—
566	C₂×C₄	—	26	2	no	—
567	C₂×C₄	—	26	2	no	—
568	C₂×C₄	—	26	2	no	—
569	C₂×C₄	—	26	2	no	—
570	C₂×C₄	—	26	2	no	—
571	C₂×C₄	—	26	2	no	—
572	C₂×C₄	—	26	2	no	—
573	C₂×C₄	—	26	2	no	—
574	C₂×C₄	—	26	2	no	—
575	C₂×C₄	—	26	2	no	—
576	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
577	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
578	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
579	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
580	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
581	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
582	C₂×C₄	C₂³×#261	1	1	yes	characteristic
583	C₈	—	2	1	no	—
584	C₈	—	2	1	no	—
585	C₈	—	2	1	no	—
586	C₈	—	2	1	no	—
587	C₈	—	26	2	no	—
588	C₈	—	26	2	no	—
589	C₈	—	26	2	no	—
590	C₈	—	26	2	no	—
591	C₈	—	26	1	no	—
592	C₈	—	26	1	no	—
593	C₈	—	26	1	no	—
594	C₈	—	26	1	no	—
595	C₂²	—	13	1	no	—
596	C₂²	—	13	1	no	—
597	C₂²	—	13	2	no	—
598	C₂²	—	13	2	no	—
599	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
600	C₄	—	2	1	no	—
601	C₄	—	2	1	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	13	1	no	—
607	C₄	—	13	1	no	—
608	C₄	—	26	1	no	—
609	C₄	—	26	1	no	—
610	C₄	—	26	1	no	—
611	C₄	—	26	1	no	—
612	C₄	—	26	1	no	—
613	C₄	—	26	1	no	—
614	C₄	—	52	2	no	—
615	C₄	—	52	2	no	—
616	C₄	—	52	2	no	—
617	C₄	—	52	2	no	—
618	C₄	#11719627	1	1	yes	characteristic
619	C₄	#11719631	1	1	yes	characteristic
620	C₂	—	13	2	no	—
621	C₂	—	13	2	no	—
622	C₂	#13131276	1	1	yes	characteristic
623	C₂	#13131399	1	1	yes	characteristic
624	C₂	#13131406	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#446	C₄
prime radical	C₂²×D₁₃	C₂³×C₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#446	#261
hypocenter	C₁₃	#20576
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #446

Complements

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

N	H ≅ G/N	type
18. #11719158	C₄	semidirect
28. #11719080	C₄	semidirect
29. #11719078	C₄	semidirect
30. #11719078	C₄	semidirect
43. C₁₃×#446	C₄	semidirect
44. #11718685	C₄	semidirect
48. #11718492	C₄	semidirect
49. #11718489	C₄	semidirect
50. #11718489	C₄	semidirect
53. #11718362	C₄	semidirect
54. #11718362	C₄	semidirect
56. #11718340	C₄	semidirect
310. #446	#261	semidirect
541. C₁₃	#20576	semidirect

Maximal subgroups

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

subgroup	index
D₁₃⋊#446	2
#13131295	2
#13130637	2
#13130634	2
#13130633	2
#13130630	2
#13130625	2
#13130623	2
#13130556	2
#13130554	2
#13130552	2
D₁₃×#446	2
#20576	13