Subgroups — #16807134

Order 3328.

710 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719096	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₁₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#13131219	C₂	1	1	yes	maximal, characteristic, complemented
4	#13131218	C₂	1	1	yes	maximal, characteristic, complemented
5	#13131217	C₂	1	1	yes	maximal, characteristic, complemented
6	#13131216	C₂	1	1	yes	maximal, characteristic, complemented
7	#13131215	C₂	1	1	yes	maximal, characteristic, complemented
8	#13131214	C₂	1	1	yes	maximal, characteristic, complemented
9	#13131214	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×#6092	C₂	1	1	yes	maximal, characteristic, complemented
11	#13131172	C₂	1	1	yes	maximal, characteristic, complemented
12	#13131067	C₂	1	1	yes	maximal, characteristic, complemented
13	#13131064	C₂	1	1	yes	maximal, characteristic, complemented
14	#13131046	C₂	1	1	yes	maximal, characteristic, complemented
15	#13123527	C₂	1	1	yes	maximal, characteristic
16	C₂×#88161	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
18	#11719252	C₄	1	1	yes	characteristic
19	C₂×#88106	C₂²	1	1	yes	characteristic, complemented
20	C₂²×#6092	C₂²	1	1	yes	characteristic
21	C₂²×#6092	C₂²	1	1	yes	characteristic
22	C₂²×#6092	C₂²	1	1	yes	characteristic, complemented
23	#11719096	—	2	4	no	—
24	C₂×#88098	C₂²	1	1	yes	characteristic
25	C₂×#88098	C₂²	1	1	yes	characteristic
26	C₂×#88098	C₂²	1	1	yes	characteristic, complemented
27	C₂×D₁₃⋊C₁₆	—	2	4	no	—
28	C₂×D₁₃⋊C₁₆	C₂²	1	1	yes	characteristic
29	C₂×D₁₃⋊C₁₆	C₂²	1	1	yes	characteristic
30	C₂×D₁₃⋊C₁₆	C₂²	1	1	yes	characteristic
31	C₂×D₁₃⋊C₁₆	C₂²	1	1	yes	characteristic
32	C₂×D₁₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#435	C₄	1	1	yes	characteristic
34	#11718788	C₄	1	1	yes	characteristic
35	#11718772	C₄	1	1	yes	characteristic
36	D₄×#1055	C₂²	1	1	yes	characteristic
37	#11718500	C₄	1	1	yes	characteristic
38	#11718495	C₂²	1	1	yes	characteristic
39	#11718388	C₄	1	1	yes	characteristic
40	#11718387	C₄	1	1	yes	characteristic
41	#11718386	C₂²	1	1	yes	characteristic
42	#11718386	C₂²	1	1	yes	characteristic
43	#11718369	C₂²	1	1	yes	characteristic
44	#11718367	C₄	1	1	yes	characteristic
45	C₂²⋊#6092	C₂²	1	1	yes	characteristic
46	C₂²⋊#6092	C₂²	1	1	yes	characteristic
47	C₂²⋊#6092	C₂²	1	1	yes	characteristic, complemented
48	C₂²⋊#6092	C₂²	1	1	yes	characteristic, complemented
49	#11718260	C₂²	1	1	yes	characteristic, complemented
50	#11718260	C₂²	1	1	yes	characteristic, complemented
51	#11718259	C₂²	1	1	yes	characteristic
52	#11718259	C₂²	1	1	yes	characteristic
53	#11718259	C₂²	1	1	yes	characteristic, complemented
54	#11718259	C₂²	1	1	yes	characteristic, complemented
55	#11718258	C₂²	1	1	yes	characteristic, complemented
56	#11718257	C₂²	1	1	yes	characteristic, complemented
57	#11718231	C₂²	1	1	yes	characteristic, complemented
58	C₄⋊#6092	C₂²	1	1	yes	characteristic, complemented
59	C₄⋊#6092	C₂²	1	1	yes	characteristic, complemented
60	C₄×#6092	C₂²	1	1	yes	characteristic, complemented
61	C₂×#6127	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
65	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
66	#88193	C₈	1	1	yes	characteristic
67	#88191	C₈	1	1	yes	characteristic
68	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
69	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
70	C₂²×#1055	C₂³	1	1	yes	characteristic
71	C₂²×#1055	C₂³	1	1	yes	characteristic
72	#88161	—	2	2	no	—
73	#88161	—	2	2	no	—
74	C₂×#6094	C₂×C₄	1	1	yes	characteristic
75	C₂×#6094	C₂×C₄	1	1	yes	characteristic
76	C₂×#6094	C₂×C₄	1	1	yes	characteristic
77	C₂×C₈×D₁₃	—	2	2	no	—
78	C₂×C₈×D₁₃	—	2	2	no	—
79	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
81	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
82	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
83	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
84	#88150	C₈	1	1	yes	characteristic
85	#88148	C₈	1	1	yes	characteristic
86	#88138	C₈	1	1	yes	characteristic
87	#88137	C₈	1	1	yes	characteristic
88	#88136	C₈	1	1	yes	characteristic
89	#88132	C₈	1	1	yes	characteristic
90	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
91	#88126	C₂×C₄	1	1	yes	characteristic
92	#88106	—	2	2	no	—
93	C₂×#6092	—	2	2	no	—
94	C₂×#6092	—	2	2	no	—
95	C₂×#6092	—	2	2	no	—
96	C₂×#6092	C₂³	1	1	yes	characteristic
97	C₂×#6092	C₂³	1	1	yes	characteristic
98	C₂×#6092	C₂³	1	1	yes	characteristic
99	C₂×#6092	C₂³	1	1	yes	characteristic
100	C₂×#6092	C₂³	1	1	yes	characteristic
101	C₂×#6092	C₂³	1	1	yes	characteristic
102	C₂×#6092	C₂³	1	1	yes	characteristic
103	C₂×#6092	C₂³	1	1	yes	characteristic
104	#88098	—	2	2	no	—
105	#88098	—	2	2	no	—
106	#88098	—	2	2	no	—
107	D₁₃⋊C₁₆	—	2	2	no	—
108	D₁₃⋊C₁₆	—	2	2	no	—
109	D₁₃⋊C₁₆	—	2	2	no	—
110	D₁₃⋊C₁₆	—	2	2	no	—
111	D₁₃⋊C₁₆	D₄	1	4	yes	complemented
112	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
113	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
114	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
115	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
116	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
117	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
118	#88060	C₂×C₄	1	1	yes	characteristic
119	#88060	C₂×C₄	1	1	yes	characteristic
120	#88060	C₂×C₄	1	1	yes	characteristic
121	#88060	C₂×C₄	1	1	yes	characteristic
122	#88055	C₂×C₄	1	1	yes	characteristic
123	#88054	C₂×C₄	1	1	yes	characteristic
124	#88054	C₂×C₄	1	1	yes	characteristic
125	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
126	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
127	C₄×#1055	C₂³	1	1	yes	characteristic
128	#33432	—	13	1	no	maximal, Sylow
129	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
130	C₂×D₄×C₁₃	C₂×C₈	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
137	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
138	#6127	—	2	2	no	—
139	#6127	—	2	2	no	—
140	C₂×D₅₂	C₂×C₈	1	1	yes	characteristic
141	C₂×D₅₂	C₂×C₈	1	1	yes	characteristic
142	C₂×C₄×D₁₃	—	2	2	no	—
143	C₂×C₄×D₁₃	—	2	2	no	—
144	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
145	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
146	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×Dic₂₆	C₂×C₈	1	1	yes	characteristic
150	C₁₃×M₁₆	—	2	2	no	—
151	C₂×C₈×C₁₃	—	2	2	no	—
152	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
156	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
157	C₁₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
158	C₁₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
159	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
161	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
162	#6103	C₂×C₈	1	1	yes	characteristic
163	#6103	C₂×C₈	1	1	yes	characteristic
164	#6103	C₂×C₈	1	1	yes	characteristic
165	#6103	C₂×C₈	1	1	yes	characteristic
166	#6103	C₂×C₈	1	1	yes	characteristic
167	#6103	C₂×C₈	1	1	yes	characteristic
168	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
169	#6101	C₂×C₈	1	1	yes	characteristic
170	#6101	C₂×C₈	1	1	yes	characteristic
171	#6101	C₂×C₈	1	1	yes	characteristic
172	#6101	C₂×C₈	1	1	yes	characteristic
173	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
174	C₂×#1055	—	2	1	no	—
175	C₂×#1055	—	2	1	no	—
176	C₂×#1055	—	2	1	no	—
177	C₂×#1055	—	2	1	no	—
178	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
179	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
180	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
181	C₂×#1055	C₂⁴	1	1	yes	characteristic
182	#6094	—	2	2	no	—
183	#6094	—	2	2	no	—
184	#6094	—	2	2	no	—
185	C₈×D₁₃	—	2	2	no	—
186	C₈×D₁₃	—	2	2	no	—
187	C₈×D₁₃	—	2	1	no	—
188	C₈×D₁₃	—	2	1	no	—
189	C₈×D₁₃	—	2	1	no	—
190	C₈×D₁₃	—	2	1	no	—
191	C₈×D₁₃	C₂×D₄	1	2	yes	—
192	C₈×D₁₃	#41	1	2	yes	—
193	#6092	—	2	1	no	—
194	#6092	—	2	1	no	—
195	#6092	—	2	1	no	—
196	#6092	—	2	1	no	—
197	#6092	—	2	1	no	—
198	#6092	—	2	1	no	—
199	#6092	C₂×D₄	1	2	yes	—
200	#6092	C₂×D₄	1	2	yes	—
201	C₂×#504	—	13	1	no	—
202	C₂³×C₁₆	—	13	1	no	—
203	#2929	—	13	1	no	—
204	#2168	—	13	1	no	—
205	#2168	—	13	1	no	—
206	#2168	—	13	1	no	—
207	#2168	—	13	1	no	—
208	D₄×C₁₆	—	13	1	no	—
209	D₄×C₁₆	—	13	1	no	—
210	D₄×C₁₆	—	13	1	no	—
211	D₄×C₁₆	—	13	1	no	—
212	#2151	—	13	1	no	—
213	#2113	—	13	1	no	—
214	#2112	—	13	1	no	—
215	#2108	—	13	1	no	—
216	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
217	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
218	C₂²×D₁₃	—	2	2	no	—
219	C₂²×D₁₃	—	2	2	no	—
220	C₂²×D₁₃	—	2	2	no	—
221	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
222	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
223	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
224	D₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
234	C₂²⋊D₁₃	—	2	2	no	—
235	C₂²⋊D₁₃	—	2	2	no	—
236	C₂²⋊D₁₃	—	2	2	no	—
237	C₂²⋊D₁₃	—	2	2	no	—
238	C₂×Dic₁₃	—	2	2	no	—
239	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
240	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
241	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
242	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
243	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
244	D₅₂	—	2	2	no	—
245	D₅₂	—	2	2	no	—
246	C₄×D₁₃	—	2	2	no	—
247	C₄×D₁₃	—	2	1	no	—
248	C₄×D₁₃	—	2	1	no	—
249	C₄×D₁₃	—	2	1	no	—
250	C₄×D₁₃	—	2	1	no	—
251	C₄×D₁₃	—	2	2	no	—
252	C₄×D₁₃	C₄×D₄	1	2	yes	—
253	C₄×D₁₃	#131	1	2	yes	—
254	Dic₂₆	—	2	2	no	—
255	C₈×C₁₃	—	2	1	no	—
256	C₈×C₁₃	—	2	1	no	—
257	C₈×C₁₃	—	2	1	no	—
258	C₈×C₁₃	C₄×D₄	1	2	yes	—
259	#1055	—	2	1	no	—
260	#1055	—	2	1	no	—
261	#1055	—	2	1	no	—
262	#1055	C₂²×D₄	1	1	yes	characteristic
263	#1055	C₂×#41	1	1	yes	characteristic
264	C₂×#131	—	13	1	no	—
265	C₂³×C₈	—	13	1	no	—
266	#525	—	13	1	no	—
267	#504	—	26	4	no	—
268	C₂×M₃₂	—	13	1	no	—
269	C₂×M₃₂	—	13	1	no	—
270	C₂×M₃₂	—	13	1	no	—
271	C₂×M₃₂	—	13	1	no	—
272	C₂²×C₁₆	—	13	1	no	—
273	C₂²×C₁₆	—	13	1	no	—
274	C₂²×C₁₆	—	13	1	no	—
275	C₂²×C₁₆	—	13	1	no	—
276	C₂²×C₁₆	—	13	1	no	—
277	C₂²×C₁₆	—	13	1	no	—
278	C₂²×C₁₆	—	13	1	no	—
279	C₂²×C₁₆	—	13	1	no	—
280	C₂²×C₁₆	—	26	4	no	—
281	#435	—	13	1	no	—
282	#435	—	13	1	no	—
283	#435	—	13	1	no	—
284	#435	#261	1	1	yes	characteristic
285	C₈×D₄	—	13	1	no	—
286	C₈×D₄	—	13	1	no	—
287	C₈×D₄	—	13	1	no	—
288	C₈×D₄	—	13	1	no	—
289	#424	—	13	1	no	—
290	#408	—	13	1	no	—
291	#407	—	13	1	no	—
292	#405	—	13	1	no	—
293	C₄⋊C₁₆	—	13	1	no	—
294	C₄⋊C₁₆	—	13	1	no	—
295	C₄⋊C₁₆	—	13	1	no	—
296	C₄⋊C₁₆	—	13	1	no	—
297	C₂²⋊C₁₆	—	13	1	no	—
298	C₂²⋊C₁₆	—	13	1	no	—
299	C₂²⋊C₁₆	—	13	1	no	—
300	C₂²⋊C₁₆	—	13	1	no	—
301	C₂²⋊C₁₆	—	13	1	no	—
302	C₂²⋊C₁₆	—	13	1	no	—
303	C₂²⋊C₁₆	—	13	1	no	—
304	C₂²⋊C₁₆	—	13	1	no	—
305	#346	—	13	1	no	—
306	#346	—	13	1	no	—
307	C₄×C₁₆	—	13	1	no	—
308	C₄×C₁₆	—	13	1	no	—
309	C₂²×C₁₃	—	2	1	no	—
310	C₂²×C₁₃	—	2	1	no	—
311	C₂²×C₁₃	—	2	1	no	—
312	C₂²×C₁₃	—	2	1	no	—
313	C₂²×C₁₃	—	2	1	no	—
314	C₂²×C₁₃	#504	1	2	yes	complemented
315	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
316	C₂×D₁₃	—	2	8	no	—
317	C₂×D₁₃	—	2	1	no	—
318	C₂×D₁₃	—	2	1	no	—
319	C₂×D₁₃	—	2	1	no	—
320	C₂×D₁₃	—	2	1	no	—
321	C₂×D₁₃	—	2	1	no	—
322	C₂×D₁₃	—	2	1	no	—
323	C₂×D₁₃	—	2	1	no	—
324	C₂×D₁₃	C₈×D₄	1	2	yes	—
325	C₂×D₁₃	#504	1	2	yes	complemented
326	C₄×C₁₃	—	2	1	no	—
327	C₄×C₁₃	—	2	1	no	—
328	C₄×C₁₃	—	2	1	no	—
329	C₄×C₁₃	—	2	1	no	—
330	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
331	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
332	Dic₁₃	—	2	1	no	—
333	Dic₁₃	—	2	1	no	—
334	Dic₁₃	—	2	1	no	—
335	Dic₁₃	—	2	1	no	—
336	Dic₁₃	C₈×D₄	1	2	yes	—
337	C₂×#41	—	13	1	no	—
338	C₂³×C₄	—	13	1	no	—
339	#131	—	26	2	no	—
340	#131	—	26	2	no	—
341	C₂×M₁₆	—	13	1	no	—
342	C₂×M₁₆	—	13	1	no	—
343	C₂×M₁₆	—	13	1	no	—
344	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
345	C₂²×C₈	—	13	1	no	—
346	C₂²×C₈	—	13	1	no	—
347	C₂²×C₈	—	13	1	no	—
348	C₂²×C₈	—	13	1	no	—
349	C₂²×C₈	—	13	1	no	—
350	C₂²×C₈	—	13	1	no	—
351	C₂²×C₈	—	13	1	no	—
352	C₂²×C₈	—	26	2	no	—
353	C₂²×C₈	—	26	2	no	—
354	C₂²×C₈	C₂×#261	1	1	yes	characteristic
355	#123	—	13	1	no	—
356	#123	—	13	1	no	—
357	C₂²⋊Q₈	—	13	1	no	—
358	C₂²⋊Q₈	—	13	1	no	—
359	#121	—	13	1	no	—
360	#121	—	13	1	no	—
361	#120	—	13	1	no	—
362	#120	—	13	1	no	—
363	C₄×D₄	—	13	1	no	—
364	C₄×D₄	—	13	1	no	—
365	C₄×D₄	—	13	1	no	—
366	C₄×D₄	C₂×#261	1	1	yes	characteristic
367	#117	—	13	1	no	—
368	M₃₂	—	26	2	no	—
369	M₃₂	—	26	2	no	—
370	M₃₂	—	26	2	no	—
371	M₃₂	—	26	2	no	—
372	C₂×C₁₆	—	13	4	no	—
373	C₂×C₁₆	—	13	1	no	—
374	C₂×C₁₆	—	13	1	no	—
375	C₂×C₁₆	—	13	1	no	—
376	C₂×C₁₆	—	13	1	no	—
377	C₂×C₁₆	—	13	1	no	—
378	C₂×C₁₆	—	13	1	no	—
379	C₂×C₁₆	—	13	1	no	—
380	C₂×C₁₆	—	13	1	no	—
381	C₂×C₁₆	—	26	2	no	—
382	C₂×C₁₆	—	26	2	no	—
383	C₂×C₁₆	—	26	2	no	—
384	C₂×C₁₆	—	26	2	no	—
385	C₂×C₁₆	—	26	2	no	—
386	C₂×C₁₆	—	26	2	no	—
387	C₂×C₁₆	—	26	2	no	—
388	C₄⋊C₈	—	13	1	no	—
389	C₄⋊C₈	—	13	1	no	—
390	C₄⋊C₈	—	13	1	no	—
391	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
392	C₂²⋊C₈	—	13	1	no	—
393	C₂²⋊C₈	—	13	1	no	—
394	C₂²⋊C₈	—	13	1	no	—
395	C₂²⋊C₈	—	13	1	no	—
396	C₂²⋊C₈	—	13	1	no	—
397	C₂²⋊C₈	—	13	1	no	—
398	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
399	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
400	#97	—	13	1	no	—
401	#97	C₂×#261	1	1	yes	characteristic
402	C₄×C₈	—	13	1	no	—
403	C₄×C₈	—	13	1	no	—
404	C₂×C₁₃	—	2	2	no	—
405	C₂×C₁₃	—	4	1	no	—
406	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
407	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
408	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
409	D₁₃	—	2	2	no	—
410	D₁₃	—	2	2	no	—
411	D₁₃	—	4	1	no	—
412	C₂⁴	—	13	1	no	—
413	#41	—	26	2	no	—
414	#41	—	26	2	no	—
415	C₂×Q₈	—	13	1	no	—
416	C₂×D₄	—	13	1	no	—
417	C₂×D₄	—	13	1	no	—
418	C₂×D₄	—	13	1	no	—
419	C₂×D₄	—	13	1	no	—
420	C₂×D₄	—	13	1	no	—
421	C₂×D₄	—	13	1	no	—
422	C₂×D₄	D₁₃⋊C₈	1	1	yes	characteristic
423	C₂²×C₄	—	13	1	no	—
424	C₂²×C₄	—	13	1	no	—
425	C₂²×C₄	—	13	1	no	—
426	C₂²×C₄	—	13	1	no	—
427	C₂²×C₄	—	13	1	no	—
428	C₂²×C₄	—	13	1	no	—
429	C₂²×C₄	—	26	2	no	—
430	C₂²×C₄	—	26	2	no	—
431	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
432	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
433	M₁₆	—	2	2	no	—
434	M₁₆	—	26	2	no	—
435	M₁₆	—	26	2	no	—
436	M₁₆	—	26	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	13	1	no	—
439	C₂×C₈	—	13	2	no	—
440	C₂×C₈	—	13	2	no	—
441	C₂×C₈	—	13	1	no	—
442	C₂×C₈	—	13	1	no	—
443	C₂×C₈	—	13	1	no	—
444	C₂×C₈	—	26	1	no	—
445	C₂×C₈	—	26	1	no	—
446	C₂×C₈	—	26	1	no	—
447	C₂×C₈	—	26	1	no	—
448	C₂×C₈	—	26	2	no	—
449	C₂×C₈	—	26	1	no	—
450	C₂×C₈	—	26	1	no	—
451	C₂×C₈	—	26	1	no	—
452	C₂×C₈	—	26	1	no	—
453	C₂×C₈	—	26	2	no	—
454	C₂×C₈	C₂²×#261	1	1	yes	characteristic
455	C₂×C₈	C₂²×#261	1	1	yes	characteristic
456	C₂×C₈	C₂²×#261	1	1	yes	characteristic
457	C₂×C₈	C₂²×#261	1	1	yes	characteristic
458	C₄⋊C₄	—	13	1	no	—
459	C₄⋊C₄	—	13	1	no	—
460	C₄⋊C₄	—	13	1	no	—
461	C₄⋊C₄	—	13	1	no	—
462	C₄⋊C₄	—	13	1	no	—
463	C₄⋊C₄	D₁₃⋊C₈	1	1	yes	characteristic
464	C₂²⋊C₄	—	13	1	no	—
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	D₁₃⋊C₈	1	1	yes	characteristic
473	C₂²⋊C₄	D₁₃⋊C₈	1	1	yes	characteristic
474	C₄²	—	13	1	no	—
475	C₄²	C₂²×#261	1	1	yes	characteristic
476	C₁₆	—	13	2	no	—
477	C₁₆	—	13	2	no	—
478	C₁₆	—	26	1	no	—
479	C₁₆	—	26	1	no	—
480	C₁₆	—	26	1	no	—
481	C₁₆	—	26	1	no	—
482	C₁₆	—	26	1	no	—
483	C₁₆	—	26	1	no	—
484	C₁₃	#33432	1	1	yes	characteristic, complemented, Sylow
485	C₂³	—	13	1	no	—
486	C₂³	—	13	1	no	—
487	C₂³	—	13	1	no	—
488	C₂³	—	26	2	no	—
489	C₂³	—	26	2	no	—
490	C₂³	—	26	2	no	—
491	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
492	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
493	Q₈	—	26	2	no	—
494	D₄	—	2	2	no	—
495	D₄	—	26	2	no	—
496	D₄	—	26	2	no	—
497	D₄	—	26	2	no	—
498	D₄	—	26	2	no	—
499	D₄	—	26	2	no	—
500	D₄	—	26	2	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	13	1	no	—
506	C₂×C₄	—	13	2	no	—
507	C₂×C₄	—	13	2	no	—
508	C₂×C₄	—	13	1	no	—
509	C₂×C₄	—	13	1	no	—
510	C₂×C₄	—	13	1	no	—
511	C₂×C₄	—	13	1	no	—
512	C₂×C₄	—	26	2	no	—
513	C₂×C₄	—	26	2	no	—
514	C₂×C₄	—	26	2	no	—
515	C₂×C₄	—	26	1	no	—
516	C₂×C₄	—	26	1	no	—
517	C₂×C₄	—	26	1	no	—
518	C₂×C₄	—	26	1	no	—
519	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
520	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
521	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
522	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
523	C₂×C₄	C₂³×#261	1	1	yes	characteristic
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	13	1	no	—
528	C₈	—	13	1	no	—
529	C₈	—	26	1	no	—
530	C₈	—	26	1	no	—
531	C₈	—	26	1	no	—
532	C₈	D₄×#261	1	2	yes	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	13	2	no	—
539	C₂²	—	13	2	no	—
540	C₂²	—	26	8	no	—
541	C₂²	—	26	1	no	—
542	C₂²	—	26	1	no	—
543	C₂²	—	26	1	no	—
544	C₂²	—	26	1	no	—
545	C₂²	—	26	1	no	—
546	C₂²	—	26	1	no	—
547	C₂²	—	26	1	no	—
548	C₂²	#11719096	1	2	yes	complemented
549	C₂²	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	13	2	no	—
555	C₄	—	26	1	no	—
556	C₄	—	26	1	no	—
557	C₄	—	26	1	no	—
558	C₄	—	26	1	no	—
559	C₄	C₂×D₄×#261	1	1	yes	characteristic
560	C₄	D₁₃⋊#131	1	1	yes	characteristic
561	C₂	—	2	2	no	—
562	C₂	—	4	1	no	—
563	C₂	—	26	2	no	—
564	C₂	—	26	2	no	—
565	C₂	—	52	1	no	—
566	C₂	D₄×D₁₃⋊C₈	1	1	yes	characteristic
567	C₂	D₁₃⋊#504	1	1	yes	characteristic
568	C₂	C₂×#11719096	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂³×C₈
Fitting	C₁₃×#435	C₄
prime radical	#11719252	C₄
cosocle	C₂×#1055	C₂⁴
hypercenter	#435	#261
hypocenter	C₁₃	#33432
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
1. C₂×#11719096	C₂	semidirect
2. C₂²×D₁₃⋊C₁₆	C₂	semidirect
3. #13131219	C₂	semidirect
4. #13131218	C₂	semidirect
5. #13131217	C₂	semidirect
6. #13131216	C₂	semidirect
7. #13131215	C₂	semidirect
8. #13131214	C₂	semidirect
9. #13131214	C₂	semidirect
10. D₄×#6092	C₂	semidirect
11. #13131172	C₂	semidirect
12. #13131067	C₂	semidirect
13. #13131064	C₂	semidirect
14. #13131046	C₂	semidirect
19. C₂×#88106	C₂²	semidirect
22. C₂²×#6092	C₂²	semidirect
26. C₂×#88098	C₂²	semidirect
32. C₂×D₁₃⋊C₁₆	C₂²	semidirect
47. C₂²⋊#6092	C₂²	semidirect
48. C₂²⋊#6092	C₂²	semidirect
49. #11718260	C₂²	semidirect
50. #11718260	C₂²	semidirect
53. #11718259	C₂²	semidirect
54. #11718259	C₂²	semidirect
55. #11718258	C₂²	semidirect
56. #11718257	C₂²	semidirect
57. #11718231	C₂²	semidirect
58. C₄⋊#6092	C₂²	semidirect
59. C₄⋊#6092	C₂²	semidirect
60. C₄×#6092	C₂²	semidirect
111. D₁₃⋊C₁₆	D₄	semidirect
314. C₂²×C₁₃	#504	semidirect
325. C₂×D₁₃	#504	semidirect
484. C₁₃	#33432	semidirect
548. C₂²	#11719096	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11719096	2
C₂²×D₁₃⋊C₁₆	2
#13131219	2
#13131218	2
#13131217	2
#13131216	2
#13131215	2
#13131214	2
D₄×#6092	2
#13131172	2
#13131067	2
#13131064	2
#13131046	2
#13123527	2
#33432	13