Subgroups — #16798325

Order 3328.

810 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131314	C₂	1	2	yes	maximal
2	#13130774	C₂	1	2	yes	maximal, complemented
3	#13130758	C₂	1	1	yes	maximal, characteristic, complemented
4	#13130757	C₂	1	1	yes	maximal, characteristic, complemented
5	#13130714	C₂	1	2	yes	maximal
6	#13130713	C₂	1	1	yes	maximal, characteristic
7	#13130712	C₂	1	1	yes	maximal, characteristic
8	#13130650	C₂	1	2	yes	maximal, complemented
9	C₄×#88102	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#88101	C₂	1	1	yes	maximal, characteristic, complemented
11	D₁₃×#405	C₂	1	1	yes	maximal, characteristic
12	C₂×M₁₆×D₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
14	D₁₃×#117	C₂²	1	1	yes	characteristic
15	#11719136	C₂²	1	2	yes	—
16	#11719136	C₂²	1	2	yes	—
17	C₂×#88102	C₂²	1	2	yes	—
18	C₂×#88102	C₂²	1	2	yes	—
19	C₂×#88101	C₂²	1	2	yes	—
20	C₂×#88101	C₂²	1	2	yes	—
21	#11719082	—	2	2	no	—
22	#11719082	—	2	2	no	—
23	#11719071	—	2	2	no	—
24	#11719071	—	2	2	no	—
25	#11719060	C₂²	1	2	yes	—
26	#11719059	C₂²	1	2	yes	—
27	C₄×C₄⋊#261	C₂²	1	2	yes	—
28	C₄×C₄⋊#261	C₂²	1	2	yes	—
29	C₁₃×#405	C₄	1	1	yes	characteristic, complemented
30	#11718783	C₄	1	1	yes	characteristic, complemented
31	#11718762	C₄	1	1	yes	characteristic, complemented
32	#11718658	C₄	1	1	yes	characteristic, complemented
33	#11718369	C₄	1	1	yes	characteristic, complemented
34	#11718369	C₄	1	1	yes	characteristic, complemented
35	D₁₃×#97	C₂²	1	1	yes	characteristic
36	D₁₃×#97	C₂²	1	1	yes	characteristic
37	#11718350	C₄	1	1	yes	characteristic, complemented
38	#11718350	C₄	1	1	yes	characteristic, complemented
39	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
40	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
41	#11718265	C₂²	1	1	yes	characteristic
42	#11718265	C₂²	1	1	yes	characteristic
43	#11718265	C₂²	1	2	yes	—
44	#11718265	C₂²	1	1	yes	characteristic
45	#11718265	C₂²	1	1	yes	characteristic
46	#11718265	C₂²	1	2	yes	—
47	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
48	C₂×C₂²⋊#261	—	2	2	no	—
49	C₂×C₂²⋊#261	—	2	2	no	—
50	C₂×C₄⋊#261	—	2	2	no	—
51	C₂×C₄⋊#261	—	2	2	no	—
52	C₂×C₄⋊#261	C₂³	1	2	yes	—
53	C₂×C₄⋊#261	C₂³	1	2	yes	—
54	C₂×C₄⋊#261	C₂³	1	2	yes	—
55	C₂×C₄⋊#261	C₂³	1	2	yes	—
56	C₂×C₄×#261	—	2	2	no	—
57	C₂×C₄×#261	—	2	2	no	—
58	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
60	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
61	#88180	C₂×C₄	1	1	yes	characteristic
62	C₂×#6099	C₂×C₄	1	1	yes	characteristic
63	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
64	M₁₆×D₁₃	—	2	4	no	—
65	C₂×#6094	C₂×C₄	1	1	yes	characteristic
66	C₂×#6094	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₁₃	—	2	4	no	—
68	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
71	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
73	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
74	#88146	Q₈	1	1	yes	characteristic
75	#88146	Q₈	1	1	yes	characteristic
76	C₄⋊C₄×D₁₃	D₄	1	1	yes	characteristic
77	C₄⋊C₄×D₁₃	D₄	1	1	yes	characteristic
78	C₂²⋊C₄×D₁₃	D₄	1	1	yes	characteristic
79	C₂²⋊C₄×D₁₃	D₄	1	1	yes	characteristic
80	#88131	Q₈	1	1	yes	characteristic
81	#88131	Q₈	1	1	yes	characteristic
82	#88126	C₂×C₄	1	1	yes	characteristic
83	#88126	C₂×C₄	1	1	yes	characteristic
84	C₄²×D₁₃	C₂³	1	1	yes	characteristic
85	C₄²×D₁₃	C₂³	1	1	yes	characteristic
86	(C₂×#261)⋊C₄	—	2	2	no	—
87	(C₂×#261)⋊C₄	—	2	2	no	—
88	(C₂×#261)⋊C₄	—	2	2	no	—
89	(C₂×#261)⋊C₄	—	2	2	no	—
90	(C₂×#261)⋊C₄	—	2	2	no	—
91	(C₂×#261)⋊C₄	—	2	2	no	—
92	#88102	—	2	4	no	—
93	#88102	—	2	4	no	—
94	#88101	—	2	4	no	—
95	#88101	—	2	4	no	—
96	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
97	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
98	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
99	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
100	#88055	C₂×C₄	1	1	yes	characteristic
101	#88055	C₂×C₄	1	1	yes	characteristic
102	#88055	C₂×C₄	1	1	yes	characteristic
103	#88055	C₂×C₄	1	1	yes	characteristic
104	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
105	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
106	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
107	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
108	#88043	C₂×C₄	1	1	yes	characteristic
109	#88043	C₂×C₄	1	1	yes	characteristic
110	C₄×#1055	C₂×C₄	1	1	yes	characteristic
111	C₄×#1055	C₂×C₄	1	1	yes	characteristic
112	#20822	—	13	1	no	maximal, Sylow
113	C₂³×D₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×#261	—	2	2	no	—
115	C₂²×#261	—	2	2	no	—
116	C₂²×#261	—	2	2	no	—
117	C₂²×#261	—	2	2	no	—
118	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
120	C₂×C₄×D₁₃	—	2	2	no	—
121	C₂×C₄×D₁₃	—	2	2	no	—
122	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
129	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
130	C₂²⋊#261	—	8	2	no	—
131	C₂²⋊#261	—	8	2	no	—
132	C₄⋊#261	—	2	2	no	—
133	C₄⋊#261	—	2	2	no	—
134	C₄⋊#261	—	2	2	no	—
135	C₄⋊#261	—	2	2	no	—
136	C₄⋊#261	—	2	2	no	—
137	C₄⋊#261	—	2	2	no	—
138	C₄⋊#261	—	2	2	no	—
139	C₄⋊#261	—	2	2	no	—
140	C₄⋊#261	—	8	2	no	—
141	C₄⋊#261	—	8	2	no	—
142	C₄×#261	—	8	2	no	—
143	C₄×#261	—	8	2	no	—
144	C₁₃×M₁₆	—	2	2	no	—
145	C₂×C₈×C₁₃	—	2	2	no	—
146	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
151	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
152	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
153	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	1	yes	characteristic
154	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
155	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
156	C₂²⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
157	C₂²⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
158	#6103	C₄⋊C₄	1	1	yes	characteristic
159	#6103	C₄⋊C₄	1	1	yes	characteristic
160	#6103	C₄⋊C₄	1	1	yes	characteristic
161	#6103	C₄⋊C₄	1	1	yes	characteristic
162	C₄⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
163	C₄⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
164	#6101	C₄⋊C₄	1	1	yes	characteristic
165	#6101	C₄⋊C₄	1	1	yes	characteristic
166	#6101	C₄⋊C₄	1	1	yes	characteristic
167	#6101	C₄⋊C₄	1	1	yes	characteristic
168	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
169	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
170	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
171	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
172	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
173	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
174	#6099	—	2	2	no	—
175	C₂×#1055	—	2	2	no	—
176	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
177	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
178	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
179	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
180	#6094	—	2	2	no	—
181	#6094	—	2	2	no	—
182	C₈×D₁₃	—	2	2	no	—
183	C₈×D₁₃	—	2	2	no	—
184	C₈×D₁₃	—	2	2	no	—
185	C₈×D₁₃	—	2	2	no	—
186	C₈×D₁₃	#41	1	4	yes	—
187	C₈×D₁₃	#41	1	4	yes	—
188	C₂×#405	—	13	1	no	—
189	#2314	—	13	2	no	—
190	#1847	—	13	2	no	—
191	#1835	—	13	1	no	—
192	#1834	—	13	1	no	—
193	#1809	—	13	2	no	—
194	#1808	—	13	1	no	—
195	#1807	—	13	1	no	—
196	#1776	—	13	2	no	—
197	C₄×#107	—	13	1	no	—
198	C₄×#106	—	13	1	no	—
199	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
200	C₂²×D₁₃	—	2	2	no	—
201	C₂²×D₁₃	—	2	1	no	—
202	C₂²×D₁₃	—	2	2	no	—
203	C₂²×D₁₃	—	2	1	no	—
204	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
205	C₂²×D₁₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×#261	—	4	2	no	—
207	C₂×#261	—	4	2	no	—
208	C₂×#261	—	4	2	no	—
209	C₂×#261	—	4	2	no	—
210	C₂×#261	—	4	2	no	—
211	C₂×#261	—	4	2	no	—
212	C₂×#261	—	4	2	no	—
213	C₂×#261	—	4	2	no	—
214	C₂×#261	—	4	2	no	—
215	C₂×#261	—	4	2	no	—
216	C₂×#261	—	4	2	no	—
217	C₂×#261	—	4	2	no	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
226	C₂×Dic₁₃	—	2	2	no	—
227	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
230	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
231	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
232	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
233	C₄×D₁₃	—	2	2	no	—
234	C₄×D₁₃	—	2	1	no	—
235	C₄×D₁₃	—	2	1	no	—
236	C₄×D₁₃	—	2	2	no	—
237	C₄×D₁₃	—	2	2	no	—
238	C₄×D₁₃	—	2	1	no	—
239	C₄×D₁₃	—	2	1	no	—
240	C₄×D₁₃	—	2	1	no	—
241	C₄×D₁₃	—	2	1	no	—
242	C₄×D₁₃	—	2	2	no	—
243	C₄×D₁₃	C₂×#41	1	2	yes	—
244	C₄×D₁₃	C₂×#41	1	2	yes	—
245	C₈×C₁₃	—	2	1	no	—
246	C₈×C₁₃	—	2	1	no	—
247	C₈×C₁₃	#117	1	2	yes	—
248	C₈×C₁₃	#117	1	2	yes	—
249	#1055	—	2	1	no	—
250	#1055	—	2	1	no	—
251	#1055	#117	1	2	yes	—
252	#1055	#117	1	2	yes	—
253	C₂²×M₁₆	—	13	1	no	—
254	C₂³×C₈	—	13	1	no	—
255	C₂×#117	—	13	1	no	—
256	C₂×#107	—	13	2	no	—
257	C₂×#107	—	13	2	no	—
258	C₂×#106	—	13	2	no	—
259	C₂×#106	—	13	2	no	—
260	#405	—	13	1	no	—
261	#405	—	13	1	no	—
262	#405	—	13	1	no	—
263	#405	—	13	1	no	—
264	#405	—	13	1	no	—
265	#405	—	13	1	no	—
266	#405	—	13	1	no	—
267	#405	#261	1	1	yes	characteristic, complemented
268	C₂×#97	—	13	1	no	—
269	C₂×#97	—	13	1	no	—
270	C₂×C₄×C₈	—	13	1	no	—
271	C₂×C₄×C₈	—	13	1	no	—
272	#388	—	26	2	no	—
273	#388	—	26	2	no	—
274	#387	—	26	2	no	—
275	#387	—	26	2	no	—
276	#384	—	13	2	no	—
277	#382	—	13	2	no	—
278	#380	—	13	2	no	—
279	#380	—	13	2	no	—
280	C₄×C₄⋊C₄	—	13	2	no	—
281	C₄×C₄⋊C₄	—	13	2	no	—
282	#340	—	13	1	no	—
283	#340	—	13	1	no	—
284	#340	—	13	1	no	—
285	#340	—	13	1	no	—
286	#340	—	13	2	no	—
287	#340	—	13	2	no	—
288	C₂²×C₁₃	—	2	1	no	—
289	C₂²×C₁₃	—	2	1	no	—
290	C₂²×C₁₃	—	2	1	no	—
291	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
292	C₂×D₁₃	—	2	1	no	—
293	C₂×D₁₃	—	2	1	no	—
294	C₂×D₁₃	—	2	1	no	—
295	C₂×D₁₃	—	4	2	no	—
296	C₂×D₁₃	—	4	2	no	—
297	C₂×D₁₃	#532	1	2	yes	—
298	C₂×D₁₃	#576	1	1	yes	characteristic
299	C₂×D₁₃	#577	1	2	yes	—
300	C₂×D₁₃	#578	1	1	yes	characteristic
301	#261	—	8	2	no	—
302	#261	—	8	2	no	—
303	#261	—	8	2	no	—
304	#261	—	8	2	no	—
305	C₄×C₁₃	—	2	1	no	—
306	C₄×C₁₃	—	2	1	no	—
307	C₄×C₁₃	—	2	1	no	—
308	C₄×C₁₃	—	2	1	no	—
309	C₄×C₁₃	—	2	1	no	—
310	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
311	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
312	Dic₁₃	—	2	1	no	—
313	Dic₁₃	—	2	1	no	—
314	Dic₁₃	—	2	1	no	—
315	Dic₁₃	—	2	1	no	—
316	Dic₁₃	—	2	1	no	—
317	Dic₁₃	#533	1	2	yes	—
318	C₂³×C₄	—	13	1	no	—
319	C₂×M₁₆	—	13	1	no	—
320	C₂×M₁₆	—	13	1	no	—
321	C₂×M₁₆	—	13	1	no	—
322	C₂×M₁₆	—	26	4	no	—
323	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
324	C₂²×C₈	—	13	1	no	—
325	C₂²×C₈	—	13	1	no	—
326	C₂²×C₈	—	13	1	no	—
327	C₂²×C₈	—	13	1	no	—
328	C₂²×C₈	—	13	1	no	—
329	C₂²×C₈	—	13	1	no	—
330	C₂²×C₈	—	13	1	no	—
331	C₂²×C₈	—	26	4	no	—
332	C₂²×C₈	C₂×#261	1	1	yes	characteristic
333	#117	—	13	1	no	—
334	#117	—	13	1	no	—
335	#117	—	13	1	no	—
336	#117	—	13	1	no	—
337	#117	—	13	1	no	—
338	#117	—	13	1	no	—
339	#117	—	13	1	no	—
340	#117	C₂×#261	1	1	yes	characteristic
341	C₂×C₄⋊C₄	—	13	1	no	—
342	C₂×C₄⋊C₄	—	13	1	no	—
343	C₂×C₄⋊C₄	—	13	2	no	—
344	C₂×C₄⋊C₄	—	13	2	no	—
345	C₂×C₄⋊C₄	—	13	2	no	—
346	C₂×C₄⋊C₄	—	13	2	no	—
347	C₂×C₄⋊C₄	—	26	2	no	—
348	C₂×C₄⋊C₄	—	26	2	no	—
349	C₂×C₂²⋊C₄	—	13	1	no	—
350	C₂×C₂²⋊C₄	—	13	1	no	—
351	C₂×C₂²⋊C₄	—	26	2	no	—
352	C₂×C₂²⋊C₄	—	26	2	no	—
353	C₂×C₄²	—	13	1	no	—
354	C₂×C₄²	—	13	1	no	—
355	C₂×C₄²	—	26	2	no	—
356	C₂×C₄²	—	26	2	no	—
357	#107	—	26	4	no	—
358	#107	—	26	4	no	—
359	#106	—	26	4	no	—
360	#106	—	26	4	no	—
361	#97	—	13	1	no	—
362	#97	—	13	1	no	—
363	#97	—	13	1	no	—
364	#97	—	13	1	no	—
365	#97	—	13	1	no	—
366	#97	—	13	1	no	—
367	#97	C₂×#261	1	1	yes	characteristic
368	#97	C₂×#261	1	1	yes	characteristic
369	C₄×C₈	—	13	1	no	—
370	C₄×C₈	—	13	1	no	—
371	C₄×C₈	—	13	1	no	—
372	C₄×C₈	—	13	1	no	—
373	C₄×C₈	—	13	1	no	—
374	C₄×C₈	—	13	1	no	—
375	C₄×C₈	C₂×#261	1	1	yes	characteristic
376	C₄×C₈	C₂×#261	1	1	yes	characteristic
377	#95	—	26	2	no	—
378	#95	—	26	2	no	—
379	#95	—	26	2	no	—
380	#95	—	26	2	no	—
381	#95	—	26	2	no	—
382	#95	—	26	2	no	—
383	C₂×C₁₃	—	4	1	no	—
384	C₂×C₁₃	#2285	1	1	yes	characteristic
385	C₂×C₁₃	#2912	1	1	yes	characteristic
386	C₂×C₁₃	#2913	1	1	yes	characteristic
387	D₁₃	—	4	1	no	—
388	D₁₃	#3178	1	2	yes	—
389	D₁₃	#3179	1	2	yes	—
390	C₂⁴	—	13	1	no	—
391	C₂²×C₄	—	13	1	no	—
392	C₂²×C₄	—	13	1	no	—
393	C₂²×C₄	—	13	1	no	—
394	C₂²×C₄	—	13	1	no	—
395	C₂²×C₄	—	13	1	no	—
396	C₂²×C₄	—	13	1	no	—
397	C₂²×C₄	—	13	1	no	—
398	C₂²×C₄	—	13	1	no	—
399	C₂²×C₄	—	13	1	no	—
400	C₂²×C₄	—	26	2	no	—
401	C₂²×C₄	—	26	2	no	—
402	C₂²×C₄	—	26	2	no	—
403	C₂²×C₄	—	26	2	no	—
404	C₂²×C₄	—	26	2	no	—
405	C₂²×C₄	—	26	2	no	—
406	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
407	M₁₆	—	2	2	no	—
408	M₁₆	—	26	2	no	—
409	M₁₆	—	26	2	no	—
410	M₁₆	—	26	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	13	1	no	—
413	C₂×C₈	—	13	1	no	—
414	C₂×C₈	—	13	4	no	—
415	C₂×C₈	—	13	4	no	—
416	C₂×C₈	—	13	1	no	—
417	C₂×C₈	—	13	1	no	—
418	C₂×C₈	—	26	2	no	—
419	C₂×C₈	—	26	2	no	—
420	C₂×C₈	—	26	2	no	—
421	C₂×C₈	—	26	2	no	—
422	C₂×C₈	—	26	2	no	—
423	C₂×C₈	C₂²×#261	1	1	yes	characteristic
424	C₂×C₈	C₂²×#261	1	1	yes	characteristic
425	C₂×C₈	C₂²×#261	1	1	yes	characteristic
426	C₂×C₈	C₂²×#261	1	1	yes	characteristic
427	C₄⋊C₄	—	13	1	no	—
428	C₄⋊C₄	—	13	1	no	—
429	C₄⋊C₄	—	13	1	no	—
430	C₄⋊C₄	—	13	1	no	—
431	C₄⋊C₄	—	13	1	no	—
432	C₄⋊C₄	—	13	1	no	—
433	C₄⋊C₄	—	26	2	no	—
434	C₄⋊C₄	—	26	2	no	—
435	C₄⋊C₄	—	26	2	no	—
436	C₄⋊C₄	—	26	2	no	—
437	C₄⋊C₄	—	26	2	no	—
438	C₄⋊C₄	—	26	2	no	—
439	C₄⋊C₄	—	26	2	no	—
440	C₄⋊C₄	—	26	2	no	—
441	C₄⋊C₄	—	104	2	no	—
442	C₄⋊C₄	—	104	2	no	—
443	C₄⋊C₄	C₄⋊#261	1	1	yes	characteristic
444	C₄⋊C₄	C₄⋊#261	1	1	yes	characteristic
445	C₂²⋊C₄	—	13	1	no	—
446	C₂²⋊C₄	—	13	1	no	—
447	C₂²⋊C₄	—	13	1	no	—
448	C₂²⋊C₄	—	13	1	no	—
449	C₂²⋊C₄	—	13	1	no	—
450	C₂²⋊C₄	—	13	1	no	—
451	C₂²⋊C₄	—	104	2	no	—
452	C₂²⋊C₄	—	104	2	no	—
453	C₂²⋊C₄	C₄⋊#261	1	1	yes	characteristic
454	C₂²⋊C₄	C₄⋊#261	1	1	yes	characteristic
455	C₄²	—	13	1	no	—
456	C₄²	—	13	1	no	—
457	C₄²	—	13	1	no	—
458	C₄²	—	13	1	no	—
459	C₄²	—	13	1	no	—
460	C₄²	—	13	1	no	—
461	C₄²	—	104	2	no	—
462	C₄²	—	104	2	no	—
463	C₄²	C₂²×#261	1	1	yes	characteristic
464	C₄²	C₂²×#261	1	1	yes	characteristic
465	C₁₃	#20822	1	1	yes	characteristic, complemented, Sylow
466	C₂³	—	13	1	no	—
467	C₂³	—	13	1	no	—
468	C₂³	—	26	1	no	—
469	C₂³	—	26	2	no	—
470	C₂³	—	26	2	no	—
471	C₂³	—	26	1	no	—
472	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	13	1	no	—
476	C₂×C₄	—	13	2	no	—
477	C₂×C₄	—	13	2	no	—
478	C₂×C₄	—	13	1	no	—
479	C₂×C₄	—	13	1	no	—
480	C₂×C₄	—	13	1	no	—
481	C₂×C₄	—	13	1	no	—
482	C₂×C₄	—	13	1	no	—
483	C₂×C₄	—	26	2	no	—
484	C₂×C₄	—	26	1	no	—
485	C₂×C₄	—	26	2	no	—
486	C₂×C₄	—	26	1	no	—
487	C₂×C₄	—	26	2	no	—
488	C₂×C₄	—	26	1	no	—
489	C₂×C₄	—	26	1	no	—
490	C₂×C₄	—	26	2	no	—
491	C₂×C₄	—	26	2	no	—
492	C₂×C₄	—	26	1	no	—
493	C₂×C₄	—	26	1	no	—
494	C₂×C₄	—	52	2	no	—
495	C₂×C₄	—	52	2	no	—
496	C₂×C₄	—	52	2	no	—
497	C₂×C₄	—	52	2	no	—
498	C₂×C₄	—	52	2	no	—
499	C₂×C₄	—	52	2	no	—
500	C₂×C₄	—	52	2	no	—
501	C₂×C₄	—	52	2	no	—
502	C₂×C₄	—	52	2	no	—
503	C₂×C₄	—	52	2	no	—
504	C₂×C₄	—	52	2	no	—
505	C₂×C₄	—	52	2	no	—
506	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
507	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
508	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
509	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
510	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
511	C₂×C₄	C₂³×#261	1	1	yes	characteristic
512	C₈	—	2	1	no	—
513	C₈	—	2	1	no	—
514	C₈	—	13	2	no	—
515	C₈	—	13	2	no	—
516	C₈	—	26	1	no	—
517	C₈	—	26	1	no	—
518	C₈	#88237	1	2	yes	—
519	C₈	#88237	1	2	yes	—
520	C₂²	—	2	1	no	—
521	C₂²	—	2	1	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	13	2	no	—
524	C₂²	—	13	2	no	—
525	C₂²	—	13	1	no	—
526	C₂²	—	13	1	no	—
527	C₂²	—	26	1	no	—
528	C₂²	—	26	1	no	—
529	C₂²	—	26	1	no	—
530	C₂²	—	52	2	no	—
531	C₂²	—	52	2	no	—
532	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
533	C₄	—	2	1	no	—
534	C₄	—	2	1	no	—
535	C₄	—	2	1	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	1	no	—
538	C₄	—	13	2	no	—
539	C₄	—	26	1	no	—
540	C₄	—	26	1	no	—
541	C₄	—	26	1	no	—
542	C₄	—	26	1	no	—
543	C₄	—	26	1	no	—
544	C₄	—	104	2	no	—
545	C₄	—	104	2	no	—
546	C₄	—	104	2	no	—
547	C₄	—	104	2	no	—
548	C₄	C₂×#88237	1	1	yes	characteristic
549	C₄	C₂×#88237	1	1	yes	characteristic
550	C₂	—	4	1	no	—
551	C₂	—	13	2	no	—
552	C₂	—	13	2	no	—
553	C₂	—	52	1	no	—
554	C₂	#13131285	1	1	yes	characteristic
555	C₂	#13131490	1	1	yes	characteristic
556	C₂	#13131491	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#261
Fitting	C₁₃×#405	C₄
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₂×D₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#405	#261
hypocenter	C₁₃	#20822
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

Complements

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

N	H ≅ G/N	type
2. #13130774	C₂	semidirect
3. #13130758	C₂	semidirect
4. #13130757	C₂	semidirect
8. #13130650	C₂	semidirect
9. C₄×#88102	C₂	semidirect
10. C₄×#88101	C₂	semidirect
29. C₁₃×#405	C₄	semidirect
30. #11718783	C₄	semidirect
31. #11718762	C₄	semidirect
32. #11718658	C₄	semidirect
33. #11718369	C₄	semidirect
34. #11718369	C₄	semidirect
37. #11718350	C₄	semidirect
38. #11718350	C₄	semidirect
267. #405	#261	semidirect
465. C₁₃	#20822	semidirect

Maximal subgroups

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

subgroup	index
#13131314	2
#13130774	2
#13130758	2
#13130757	2
#13130714	2
#13130713	2
#13130712	2
#13130650	2
C₄×#88102	2
C₄×#88101	2
D₁₃×#405	2
#20822	13