Subgroups — #16797459

Order 3328.

838 conjugacy classes of subgroups.

The subgroup lattice has 634 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	#13130494	C₂	1	1	yes	maximal, characteristic
13	#13130492	C₂	1	1	yes	maximal, characteristic
14	#97×#261	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×#88100	C₂²	1	1	yes	characteristic
24	C₂×#88100	C₂²	1	1	yes	characteristic
25	C₂×C₈×#261	C₂²	1	1	yes	characteristic
26	C₂×C₈×#261	C₂²	1	1	yes	characteristic
27	C₂×C₈×#261	C₂²	1	1	yes	characteristic
28	C₂×C₈×#261	C₂²	1	1	yes	characteristic
29	#11719083	C₄	1	2	yes	—
30	#11719082	C₄	1	2	yes	—
31	#11719082	C₄	1	2	yes	—
32	#11719080	C₄	1	2	yes	complemented
33	#11719078	C₄	1	2	yes	complemented
34	#11719078	C₄	1	2	yes	complemented
35	C₄×C₄⋊#261	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊#261	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊#261	C₂²	1	1	yes	characteristic
38	#11719057	C₂²	1	1	yes	characteristic
39	#11719057	C₂²	1	1	yes	characteristic
40	C₄²×#261	C₂²	1	1	yes	characteristic
41	D₁₃⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
42	D₁₃⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
43	D₁₃⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
44	#11719047	C₂²	1	1	yes	characteristic
45	#11719047	C₂²	1	1	yes	characteristic
46	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
47	C₁₃×#446	C₄	1	1	yes	characteristic, complemented
48	#11718685	C₄	1	1	yes	characteristic, complemented
49	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
50	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
51	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
52	#11718492	C₄	1	1	yes	characteristic, complemented
53	#11718489	C₄	1	1	yes	characteristic, complemented
54	#11718489	C₄	1	1	yes	characteristic, complemented
55	D₁₃×#97	C₂²	1	1	yes	characteristic
56	D₁₃×#97	C₂²	1	1	yes	characteristic
57	#11718362	C₄	1	1	yes	characteristic, complemented
58	#11718362	C₄	1	1	yes	characteristic, complemented
59	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
60	#11718340	C₄	1	1	yes	characteristic, complemented
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	—	2	2	no	—
119	#88100	—	2	2	no	—
120	#88100	—	2	2	no	—
121	#88100	—	2	2	no	—
122	#88100	—	2	2	no	—
123	#88100	—	2	2	no	—
124	C₈×#261	—	2	2	no	—
125	C₈×#261	—	2	2	no	—
126	C₈×#261	—	2	2	no	—
127	C₈×#261	Q₈	1	4	yes	complemented
128	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
129	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
130	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
131	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
132	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
133	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
134	#88055	C₂×C₄	1	1	yes	characteristic
135	#88055	C₂×C₄	1	1	yes	characteristic
136	#88055	C₂×C₄	1	1	yes	characteristic
137	#88055	C₂×C₄	1	1	yes	characteristic
138	#88054	C₂×C₄	1	1	yes	characteristic
139	#88054	C₂×C₄	1	1	yes	characteristic
140	#88054	C₂×C₄	1	1	yes	characteristic
141	#88054	C₂×C₄	1	1	yes	characteristic
142	#88054	C₂×C₄	1	1	yes	characteristic
143	#88054	C₂×C₄	1	1	yes	characteristic
144	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
145	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
146	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
147	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
148	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
149	#88043	C₂×C₄	1	1	yes	characteristic
150	#88043	C₂×C₄	1	1	yes	characteristic
151	C₄×#1055	C₂×C₄	1	1	yes	characteristic
152	#20518	—	13	1	no	maximal, Sylow
153	C₂²×#261	C₂²×C₄	1	2	yes	—
154	C₂²×#261	C₂²×C₄	1	2	yes	—
155	C₂²×#261	C₂²×C₄	1	2	yes	—
156	C₂²×#261	C₂²×C₄	1	2	yes	—
157	C₂×Q₈×C₁₃	C₄²	1	1	yes	characteristic
158	Q₈×D₁₃	—	4	2	no	—
159	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
166	C₂×Dic₂₆	C₄²	1	1	yes	characteristic
167	C₂×Dic₂₆	C₄²	1	1	yes	characteristic
168	C₂×Dic₂₆	C₄²	1	1	yes	characteristic
169	C₂×#1057	C₂²×C₄	1	2	yes	—
170	C₂×#1057	C₂²×C₄	1	2	yes	—
171	C₂×#1057	C₂²×C₄	1	2	yes	—
172	C₂×#1057	C₂²×C₄	1	2	yes	—
173	C₄⋊#261	—	4	2	no	—
174	C₄⋊#261	—	4	2	no	—
175	C₄⋊#261	—	4	2	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	—	2	1	no	—
181	C₄×#261	—	2	1	no	—
182	C₄×#261	—	4	2	no	—
183	C₄×#261	—	4	2	no	—
184	C₄×#261	C₂×Q₈	1	2	yes	—
185	C₄×#261	#41	1	2	yes	—
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	D₁₃⋊C₈	—	2	1	no	—
191	D₁₃⋊C₈	—	2	1	no	—
192	D₁₃⋊C₈	C₂×Q₈	1	2	yes	—
193	D₁₃⋊C₈	#41	1	2	yes	—
194	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
198	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
199	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
200	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
201	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
202	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
203	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
204	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
205	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
206	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
207	#6101	C₄²	1	1	yes	characteristic
208	#6101	C₄²	1	1	yes	characteristic
209	#6101	C₄²	1	1	yes	characteristic
210	#6101	C₄²	1	1	yes	characteristic
211	#6101	C₄²	1	1	yes	characteristic
212	#6101	C₄²	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	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
219	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
220	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
221	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
222	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
223	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
224	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
225	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
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	C₈×D₁₃	—	2	1	no	—
231	C₈×D₁₃	—	2	1	no	—
232	C₈×D₁₃	C₂×Q₈	1	2	yes	—
233	C₈×D₁₃	#41	1	2	yes	—
234	C₂×#446	—	13	1	no	—
235	C₂×#446	—	13	1	no	—
236	#2295	—	13	1	no	—
237	#1771	—	13	1	no	—
238	#1771	—	13	1	no	—
239	#1771	—	13	1	no	—
240	#1771	—	13	1	no	—
241	#1770	—	13	1	no	—
242	#1770	—	13	1	no	—
243	#1768	—	13	1	no	—
244	#1768	—	13	1	no	—
245	#1767	—	13	1	no	—
246	#1726	—	13	1	no	—
247	#1726	—	13	1	no	—
248	C₄×#97	—	13	1	no	—
249	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
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	C₂×#261	—	2	2	no	—
259	C₂×#261	—	2	2	no	—
260	C₂×#261	—	2	2	no	—
261	C₂×#261	C₄×Q₈	1	4	yes	—
262	Q₈×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
267	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
269	C₂×C₄×C₁₃	C₂³×C₄	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	C₂×C₄²	1	1	yes	characteristic
273	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
274	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
275	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
276	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
277	C₄×D₁₃	—	2	2	no	—
278	C₄×D₁₃	—	2	2	no	—
279	C₄×D₁₃	—	2	2	no	—
280	C₄×D₁₃	—	2	2	no	—
281	C₄×D₁₃	—	2	2	no	—
282	C₄×D₁₃	—	2	2	no	—
283	C₄×D₁₃	C₂²×Q₈	1	1	yes	characteristic
284	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
285	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
286	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
287	Dic₂₆	—	4	1	no	—
288	Dic₂₆	—	4	1	no	—
289	Dic₂₆	—	4	1	no	—
290	#1057	—	2	2	no	—
291	#1057	—	2	2	no	—
292	#1057	—	2	2	no	—
293	#1057	C₄×Q₈	1	4	yes	—
294	C₈×C₁₃	—	2	1	no	—
295	C₈×C₁₃	—	2	1	no	—
296	C₈×C₁₃	—	2	1	no	—
297	C₈×C₁₃	C₄×Q₈	1	2	yes	—
298	#1055	—	2	1	no	—
299	#1055	—	2	1	no	—
300	#1055	—	2	1	no	—
301	#1055	C₄×Q₈	1	2	yes	—
302	C₂×C₄×Q₈	—	13	1	no	—
303	#446	—	13	2	no	—
304	#446	—	13	2	no	—
305	#446	—	13	2	no	—
306	#446	—	13	2	no	—
307	#446	—	13	1	no	—
308	#446	—	13	1	no	—
309	#446	—	13	1	no	—
310	#446	—	13	1	no	—
311	#446	—	13	1	no	—
312	#446	—	13	1	no	—
313	#446	—	13	1	no	—
314	#446	#261	1	1	yes	characteristic, complemented
315	C₂×C₄⋊C₈	—	13	1	no	—
316	C₂×C₄⋊C₈	—	13	1	no	—
317	C₂×C₄⋊C₈	—	13	1	no	—
318	C₂×C₄⋊C₈	—	13	1	no	—
319	C₂×C₄⋊C₈	—	13	1	no	—
320	C₂×C₄⋊C₈	—	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×#97	—	13	1	no	—
326	C₂×#97	—	13	1	no	—
327	C₂×#97	—	13	1	no	—
328	C₂×#97	—	13	1	no	—
329	C₂×#97	—	13	1	no	—
330	C₂×#97	—	13	1	no	—
331	C₂×C₄×C₈	—	13	1	no	—
332	C₂×C₄×C₈	—	13	1	no	—
333	C₂×C₄×C₈	—	13	1	no	—
334	C₂×C₄×C₈	—	13	1	no	—
335	C₂×C₄×C₈	—	13	1	no	—
336	C₂×C₄×C₈	—	13	1	no	—
337	#391	—	13	2	no	—
338	#389	—	13	2	no	—
339	#387	—	13	2	no	—
340	#387	—	13	2	no	—
341	C₄×C₄⋊C₄	—	13	1	no	—
342	C₄×C₄⋊C₄	—	13	1	no	—
343	C₄×C₄⋊C₄	—	13	1	no	—
344	#376	—	13	1	no	—
345	#376	—	13	1	no	—
346	C₄³	—	13	1	no	—
347	#336	—	13	1	no	—
348	#336	—	13	1	no	—
349	#336	—	13	1	no	—
350	#336	—	13	1	no	—
351	#336	—	13	1	no	—
352	#336	—	13	1	no	—
353	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
354	C₂×D₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
355	C₂×D₁₃	C₄×#41	1	1	yes	characteristic
356	C₂×D₁₃	#568	1	2	yes	—
357	C₂×D₁₃	#568	1	2	yes	—
358	#261	—	2	4	no	—
359	#261	—	4	2	no	—
360	#261	—	4	2	no	—
361	#261	—	4	2	no	—
362	C₄×C₁₃	—	2	1	no	—
363	C₄×C₁₃	—	2	1	no	—
364	C₄×C₁₃	—	2	1	no	—
365	C₄×C₁₃	—	2	1	no	—
366	C₄×C₁₃	—	2	1	no	—
367	C₄×C₁₃	—	2	1	no	—
368	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
369	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
370	Dic₁₃	—	2	1	no	—
371	Dic₁₃	—	2	1	no	—
372	Dic₁₃	—	2	1	no	—
373	Dic₁₃	—	2	1	no	—
374	Dic₁₃	—	2	1	no	—
375	Dic₁₃	—	2	1	no	—
376	Dic₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
377	Dic₁₃	C₄×#41	1	1	yes	characteristic
378	C₂²×Q₈	—	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	C₂²×C₈	—	13	1	no	—
384	C₂²×C₈	—	13	1	no	—
385	C₂²×C₈	—	13	1	no	—
386	C₂²×C₈	—	13	1	no	—
387	C₄×Q₈	—	13	1	no	—
388	C₄×Q₈	—	13	1	no	—
389	C₄×Q₈	—	13	1	no	—
390	C₄×Q₈	—	13	1	no	—
391	C₄×Q₈	—	13	1	no	—
392	C₄×Q₈	—	13	1	no	—
393	C₄×Q₈	—	13	1	no	—
394	C₄×Q₈	C₂×#261	1	1	yes	characteristic
395	C₂×C₄⋊C₄	—	13	1	no	—
396	C₂×C₄⋊C₄	—	13	1	no	—
397	C₂×C₄⋊C₄	—	13	1	no	—
398	C₂×C₄⋊C₄	—	13	2	no	—
399	C₂×C₄⋊C₄	—	13	2	no	—
400	C₂×C₄⋊C₄	—	13	2	no	—
401	C₂×C₄²	—	13	1	no	—
402	C₂×C₄²	—	13	1	no	—
403	C₂×C₄²	—	13	1	no	—
404	C₂×C₄²	—	13	1	no	—
405	C₂×C₄²	—	13	1	no	—
406	C₂×C₄²	—	13	1	no	—
407	C₂×C₄²	—	13	1	no	—
408	C₂×C₄²	—	13	2	no	—
409	C₂×C₄²	—	13	2	no	—
410	C₄⋊C₈	—	13	2	no	—
411	C₄⋊C₈	—	13	2	no	—
412	C₄⋊C₈	—	13	2	no	—
413	C₄⋊C₈	—	13	2	no	—
414	C₄⋊C₈	—	13	2	no	—
415	C₄⋊C₈	—	13	2	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	—	13	1	no	—
422	C₄⋊C₈	—	13	1	no	—
423	C₄⋊C₈	—	13	1	no	—
424	C₄⋊C₈	—	13	1	no	—
425	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
426	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
427	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
428	#97	—	13	2	no	—
429	#97	—	13	2	no	—
430	#97	—	13	2	no	—
431	#97	—	13	2	no	—
432	#97	—	13	1	no	—
433	#97	—	13	1	no	—
434	#97	—	13	1	no	—
435	#97	—	13	1	no	—
436	#97	—	13	1	no	—
437	#97	—	13	1	no	—
438	#97	—	26	2	no	—
439	#97	—	26	2	no	—
440	#97	—	26	2	no	—
441	#97	—	26	2	no	—
442	#97	—	26	2	no	—
443	#97	—	26	2	no	—
444	#97	C₂×#261	1	1	yes	characteristic
445	#97	C₂×#261	1	1	yes	characteristic
446	C₄×C₈	—	13	4	no	—
447	C₄×C₈	—	13	2	no	—
448	C₄×C₈	—	13	2	no	—
449	C₄×C₈	—	13	1	no	—
450	C₄×C₈	—	13	1	no	—
451	C₄×C₈	—	13	1	no	—
452	C₄×C₈	—	26	2	no	—
453	C₄×C₈	—	26	2	no	—
454	C₄×C₈	—	26	2	no	—
455	C₄×C₈	C₂×#261	1	1	yes	characteristic
456	#95	—	13	2	no	—
457	#95	—	13	2	no	—
458	#95	—	13	2	no	—
459	#95	—	13	2	no	—
460	#95	—	13	2	no	—
461	#95	—	13	2	no	—
462	#95	—	13	2	no	—
463	C₂×C₁₃	C₄²×Q₈	1	1	yes	characteristic
464	C₂×C₁₃	#2873	1	1	yes	characteristic
465	C₂×C₁₃	#2875	1	1	yes	characteristic
466	D₁₃	#2961	1	2	yes	—
467	D₁₃	#2967	1	2	yes	—
468	C₂×Q₈	—	13	1	no	—
469	C₂×Q₈	—	13	1	no	—
470	C₂×Q₈	—	13	1	no	—
471	C₂×Q₈	—	52	2	no	—
472	C₂×Q₈	C₄×#261	1	1	yes	characteristic
473	C₂²×C₄	—	13	1	no	—
474	C₂²×C₄	—	13	2	no	—
475	C₂²×C₄	—	13	1	no	—
476	C₂²×C₄	—	13	1	no	—
477	C₂²×C₄	—	13	1	no	—
478	C₂²×C₄	—	13	1	no	—
479	C₂²×C₄	—	13	1	no	—
480	C₂²×C₄	—	13	1	no	—
481	C₂²×C₄	—	13	2	no	—
482	C₂²×C₄	—	13	2	no	—
483	C₂²×C₄	—	13	2	no	—
484	C₂×C₈	—	13	2	no	—
485	C₂×C₈	—	13	2	no	—
486	C₂×C₈	—	13	2	no	—
487	C₂×C₈	—	13	1	no	—
488	C₂×C₈	—	13	2	no	—
489	C₂×C₈	—	13	2	no	—
490	C₂×C₈	—	13	2	no	—
491	C₂×C₈	—	13	2	no	—
492	C₂×C₈	—	13	2	no	—
493	C₂×C₈	—	13	1	no	—
494	C₂×C₈	—	13	1	no	—
495	C₂×C₈	—	13	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	—	26	1	no	—
501	C₂×C₈	—	26	1	no	—
502	C₂×C₈	—	26	1	no	—
503	C₂×C₈	—	26	1	no	—
504	C₂×C₈	—	26	1	no	—
505	C₂×C₈	—	26	1	no	—
506	C₂×C₈	—	26	1	no	—
507	C₂×C₈	—	26	1	no	—
508	C₂×C₈	C₂²×#261	1	1	yes	characteristic
509	C₂×C₈	C₂²×#261	1	1	yes	characteristic
510	C₂×C₈	C₂²×#261	1	1	yes	characteristic
511	C₂×C₈	C₂²×#261	1	1	yes	characteristic
512	C₄⋊C₄	—	13	1	no	—
513	C₄⋊C₄	—	13	1	no	—
514	C₄⋊C₄	—	13	1	no	—
515	C₄⋊C₄	—	13	1	no	—
516	C₄⋊C₄	—	13	1	no	—
517	C₄⋊C₄	—	13	1	no	—
518	C₄⋊C₄	—	13	1	no	—
519	C₄⋊C₄	—	13	1	no	—
520	C₄⋊C₄	—	13	1	no	—
521	C₄⋊C₄	—	52	2	no	—
522	C₄⋊C₄	—	52	2	no	—
523	C₄⋊C₄	—	52	2	no	—
524	C₄⋊C₄	C₄×#261	1	1	yes	characteristic
525	C₄⋊C₄	C₄×#261	1	1	yes	characteristic
526	C₄⋊C₄	C₄×#261	1	1	yes	characteristic
527	C₄²	—	13	2	no	—
528	C₄²	—	13	2	no	—
529	C₄²	—	13	1	no	—
530	C₄²	—	13	1	no	—
531	C₄²	—	13	1	no	—
532	C₄²	—	13	1	no	—
533	C₄²	—	13	1	no	—
534	C₄²	—	13	1	no	—
535	C₄²	—	13	1	no	—
536	C₄²	—	13	1	no	—
537	C₄²	—	13	1	no	—
538	C₄²	—	26	1	no	—
539	C₄²	—	26	1	no	—
540	C₄²	—	26	1	no	—
541	C₄²	—	26	1	no	—
542	C₄²	—	26	1	no	—
543	C₄²	—	26	1	no	—
544	C₄²	—	52	2	no	—
545	C₄²	—	52	2	no	—
546	C₄²	C₂²×#261	1	1	yes	characteristic
547	C₄²	C₂²×#261	1	1	yes	characteristic
548	C₄²	C₂²×#261	1	1	yes	characteristic
549	C₁₃	#20518	1	1	yes	characteristic, complemented, Sylow
550	C₂³	—	13	1	no	—
551	Q₈	—	4	1	no	—
552	Q₈	—	52	1	no	—
553	Q₈	—	52	1	no	—
554	Q₈	—	52	1	no	—
555	C₂×C₄	—	13	1	no	—
556	C₂×C₄	—	13	1	no	—
557	C₂×C₄	—	13	1	no	—
558	C₂×C₄	—	13	1	no	—
559	C₂×C₄	—	13	1	no	—
560	C₂×C₄	—	13	4	no	—
561	C₂×C₄	—	13	1	no	—
562	C₂×C₄	—	13	1	no	—
563	C₂×C₄	—	13	1	no	—
564	C₂×C₄	—	13	1	no	—
565	C₂×C₄	—	13	1	no	—
566	C₂×C₄	—	13	1	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	—	26	2	no	—
577	C₂×C₄	—	26	2	no	—
578	C₂×C₄	—	26	2	no	—
579	C₂×C₄	—	26	2	no	—
580	C₂×C₄	—	26	2	no	—
581	C₂×C₄	—	26	2	no	—
582	C₂×C₄	—	26	2	no	—
583	C₂×C₄	—	26	2	no	—
584	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
585	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
586	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
587	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
588	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
589	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
590	C₂×C₄	C₂³×#261	1	1	yes	characteristic
591	C₈	—	2	1	no	—
592	C₈	—	2	1	no	—
593	C₈	—	2	1	no	—
594	C₈	—	13	4	no	—
595	C₈	—	13	2	no	—
596	C₈	—	26	2	no	—
597	C₈	—	26	2	no	—
598	C₈	—	26	2	no	—
599	C₈	—	26	1	no	—
600	C₈	—	26	1	no	—
601	C₈	—	26	1	no	—
602	C₈	Q₈×#261	1	2	yes	—
603	C₂²	—	13	1	no	—
604	C₂²	—	13	1	no	—
605	C₂²	—	13	2	no	—
606	C₂²	—	13	2	no	—
607	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	2	1	no	—
613	C₄	—	2	1	no	—
614	C₄	—	13	1	no	—
615	C₄	—	13	1	no	—
616	C₄	—	26	4	no	—
617	C₄	—	26	1	no	—
618	C₄	—	26	1	no	—
619	C₄	—	26	1	no	—
620	C₄	—	26	1	no	—
621	C₄	—	26	1	no	—
622	C₄	—	26	1	no	—
623	C₄	—	52	2	no	—
624	C₄	—	52	2	no	—
625	C₄	—	52	2	no	—
626	C₄	C₂×Q₈×#261	1	1	yes	characteristic
627	C₄	#41×#261	1	1	yes	characteristic
628	C₂	—	13	2	no	—
629	C₂	—	13	2	no	—
630	C₂	C₄×Q₈×#261	1	1	yes	characteristic
631	C₂	#13131399	1	1	yes	characteristic
632	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	#20518
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
32. #11719080	C₄	semidirect
33. #11719078	C₄	semidirect
34. #11719078	C₄	semidirect
47. C₁₃×#446	C₄	semidirect
48. #11718685	C₄	semidirect
52. #11718492	C₄	semidirect
53. #11718489	C₄	semidirect
54. #11718489	C₄	semidirect
57. #11718362	C₄	semidirect
58. #11718362	C₄	semidirect
60. #11718340	C₄	semidirect
127. C₈×#261	Q₈	semidirect
314. #446	#261	semidirect
549. C₁₃	#20518	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
#13130494	2
#13130492	2
#97×#261	2
D₁₃×#446	2
#20518	13