Subgroups — #15770830

Order 3328.

958 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718589	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718596	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718143	C₂	1	2	yes	maximal
4	C₂×#11718143	C₂	1	2	yes	maximal
5	C₂×C₁₃×#336	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
7	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊Dic₁₃	—	2	1	no	—
9	C₂²×C₄⋊Dic₁₃	—	2	1	no	—
10	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	—
12	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
13	C₂²×#6101	—	2	1	no	—
14	C₂×#88071	—	2	1	no	—
15	#11718596	—	2	4	no	—
16	#11718589	—	2	2	no	—
17	#11718589	C₄	1	4	yes	complemented
18	C₁₃×#336	—	2	2	no	—
19	#11718143	—	2	4	no	—
20	#11718143	—	2	4	no	—
21	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	C₂³×Dic₁₃	—	2	1	no	—
25	C₂³×Dic₁₃	—	2	1	no	—
26	C₂³×Dic₁₃	—	2	2	no	—
27	C₂²×C₈×C₁₃	—	2	2	no	—
28	C₂²×C₈×C₁₃	—	2	2	no	—
29	C₂²×C₈×C₁₃	—	2	2	no	—
30	C₂²×C₈×C₁₃	—	2	2	no	—
31	C₂²×C₈×C₁₃	—	2	2	no	—
32	C₂²×C₈×C₁₃	—	2	2	no	—
33	C₂²×C₈×C₁₃	Q₈	1	4	yes	—
34	C₂×C₄²×C₁₃	—	2	2	no	—
35	C₂×C₄²×C₁₃	—	2	2	no	—
36	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
37	C₂×C₄²×C₁₃	D₄	1	2	yes	—
38	C₂×C₄⋊Dic₁₃	—	2	1	no	—
39	C₂×C₄⋊Dic₁₃	—	2	1	no	—
40	C₂×C₄⋊Dic₁₃	—	2	1	no	—
41	C₂×C₄⋊Dic₁₃	—	2	2	no	—
42	C₂×C₄⋊Dic₁₃	—	2	2	no	—
43	C₂×C₄⋊Dic₁₃	—	2	2	no	—
44	C₂×C₄⋊Dic₁₃	—	2	2	no	—
45	C₂×C₄⋊Dic₁₃	—	2	2	no	—
46	C₂×C₄⋊Dic₁₃	—	2	2	no	—
47	C₂×C₄⋊Dic₁₃	—	2	4	no	—
48	C₂×C₄⋊Dic₁₃	—	2	4	no	—
49	C₂×C₄⋊Dic₁₃	—	2	1	no	—
50	C₂×C₄⋊Dic₁₃	—	2	2	no	—
51	C₂×C₄⋊Dic₁₃	—	4	2	no	—
52	C₂×C₄⋊Dic₁₃	—	4	2	no	—
53	C₂×C₄⋊Dic₁₃	—	4	2	no	—
54	C₂×C₄⋊Dic₁₃	—	4	2	no	—
55	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
57	C₂×C₄⋊Dic₁₃	D₄	1	4	yes	—
58	C₂×C₄⋊Dic₁₃	D₄	1	2	yes	—
59	C₂×C₄⋊Dic₁₃	Q₈	1	2	yes	—
60	C₂×#6101	—	2	4	no	—
61	C₂×#6101	—	4	2	no	—
62	C₂×#6101	—	4	2	no	—
63	#88071	—	2	4	no	—
64	#11207	—	13	1	no	maximal, Sylow
65	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₃	—	2	1	no	—
67	C₂²×C₄×C₁₃	—	2	1	no	—
68	C₂²×C₄×C₁₃	—	2	1	no	—
69	C₂²×C₄×C₁₃	—	2	1	no	—
70	C₂²×C₄×C₁₃	—	2	1	no	—
71	C₂²×C₄×C₁₃	—	2	1	no	—
72	C₂²×C₄×C₁₃	—	2	1	no	—
73	C₂²×C₄×C₁₃	—	2	1	no	—
74	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
75	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
76	C₂²×C₄×C₁₃	D₈	1	2	yes	—
77	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
78	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
79	C₂²×C₄×C₁₃	Q₁₆	1	2	yes	—
80	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
83	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
85	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	#41	1	2	yes	—
87	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	#41	1	2	yes	—
89	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
90	C₂²×Dic₁₃	—	2	2	no	—
91	C₂²×Dic₁₃	—	2	2	no	—
92	C₂²×Dic₁₃	—	2	2	no	—
93	C₂²×Dic₁₃	—	2	2	no	—
94	C₂²×Dic₁₃	—	2	4	no	—
95	C₂²×Dic₁₃	—	4	1	no	—
96	C₂²×Dic₁₃	—	4	1	no	—
97	C₂²×Dic₁₃	—	4	1	no	—
98	C₂²×Dic₁₃	—	4	1	no	—
99	C₂²×Dic₁₃	—	4	1	no	—
100	C₂²×Dic₁₃	—	4	2	no	—
101	C₂²×Dic₁₃	—	4	1	no	—
102	C₂²×Dic₁₃	—	4	2	no	—
103	C₂²×Dic₁₃	—	4	1	no	—
104	C₂²×Dic₁₃	—	4	2	no	—
105	C₂²×Dic₁₃	—	4	1	no	—
106	C₂²×Dic₁₃	—	4	2	no	—
107	C₂²×Dic₁₃	—	4	2	no	—
108	C₂²×Dic₁₃	—	4	2	no	—
109	C₂²×Dic₁₃	—	4	1	no	—
110	C₂²×Dic₁₃	—	4	1	no	—
111	C₂×C₈×C₁₃	—	2	4	no	—
112	C₂×C₈×C₁₃	—	2	4	no	—
113	C₂×C₈×C₁₃	—	2	4	no	—
114	C₂×C₈×C₁₃	—	4	2	no	—
115	C₂×C₈×C₁₃	—	4	2	no	—
116	C₂×C₈×C₁₃	—	4	2	no	—
117	C₂×C₈×C₁₃	—	4	2	no	—
118	C₄²×C₁₃	—	2	4	no	—
119	C₄²×C₁₃	—	2	4	no	—
120	C₄⋊Dic₁₃	—	2	2	no	—
121	C₄⋊Dic₁₃	—	2	2	no	—
122	C₄⋊Dic₁₃	—	2	2	no	—
123	C₄⋊Dic₁₃	—	2	4	no	—
124	C₄⋊Dic₁₃	—	2	4	no	—
125	C₄⋊Dic₁₃	—	2	4	no	—
126	C₄⋊Dic₁₃	—	4	8	no	—
127	C₄⋊Dic₁₃	—	4	8	no	—
128	C₄⋊Dic₁₃	—	4	2	no	—
129	C₄⋊Dic₁₃	—	4	2	no	—
130	C₄⋊Dic₁₃	—	4	2	no	—
131	C₄⋊Dic₁₃	C₄⋊C₄	1	4	yes	complemented
132	#6101	—	4	8	no	—
133	C₂×#389	—	13	1	no	—
134	C₂×#384	—	13	1	no	—
135	C₂×#340	—	13	2	no	—
136	C₂×#340	—	13	2	no	—
137	C₂×#336	D₁₃	1	1	yes	characteristic
138	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂³×C₁₃	#120	1	1	yes	characteristic
140	C₂³×C₁₃	#121	1	1	yes	characteristic
141	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
142	C₂³×C₁₃	#123	1	1	yes	characteristic
143	C₂³×C₁₃	#124	1	1	yes	characteristic
144	C₂³×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
145	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
146	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
147	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
148	C₂³×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
149	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
150	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
151	C₂³×C₁₃	#137	1	1	yes	characteristic
152	C₂³×C₁₃	#137	1	1	yes	characteristic
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	#102	1	4	yes	—
166	C₂×C₄×C₁₃	#103	1	4	yes	—
167	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
171	C₂×C₄×C₁₃	#121	1	2	yes	—
172	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
173	C₂×C₄×C₁₃	#121	1	2	yes	—
174	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
175	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
176	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
177	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
178	C₂×C₄×C₁₃	#123	1	2	yes	—
179	C₂×C₄×C₁₃	#125	1	2	yes	—
180	C₂×C₄×C₁₃	#125	1	2	yes	—
181	C₂×C₄×C₁₃	#126	1	2	yes	—
182	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
183	C₂×Dic₁₃	—	2	4	no	—
184	C₂×Dic₁₃	—	4	2	no	—
185	C₂×Dic₁₃	—	4	2	no	—
186	C₂×Dic₁₃	—	4	2	no	—
187	C₂×Dic₁₃	—	4	2	no	—
188	C₂×Dic₁₃	—	4	2	no	—
189	C₂×Dic₁₃	—	4	2	no	—
190	C₂×Dic₁₃	—	4	2	no	—
191	C₂×Dic₁₃	—	4	4	no	—
192	C₂×Dic₁₃	—	4	2	no	—
193	C₂×Dic₁₃	—	4	2	no	—
194	C₂×Dic₁₃	—	4	4	no	—
195	C₂×Dic₁₃	—	4	4	no	—
196	C₂×Dic₁₃	—	8	1	no	—
197	C₂×Dic₁₃	—	8	1	no	—
198	C₂×Dic₁₃	—	8	2	no	—
199	C₂×Dic₁₃	—	8	2	no	—
200	C₂×Dic₁₃	—	8	1	no	—
201	C₂×Dic₁₃	—	8	1	no	—
202	C₂×Dic₁₃	—	8	2	no	—
203	C₂×Dic₁₃	—	8	2	no	—
204	C₈×C₁₃	—	4	4	no	—
205	C₂³×C₈	C₂×D₁₃	1	2	yes	—
206	C₂²×C₄⋊C₄	—	13	1	no	—
207	C₂²×C₄⋊C₄	—	13	2	no	—
208	C₂²×C₄⋊C₄	—	13	1	no	—
209	C₂²×C₄⋊C₄	—	26	1	no	—
210	C₂²×C₄⋊C₄	—	26	1	no	—
211	C₂²×C₄⋊C₄	—	26	1	no	—
212	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
213	#389	—	13	4	no	—
214	#389	—	26	2	no	—
215	#384	—	26	4	no	—
216	C₂×#95	—	26	1	no	—
217	#340	—	26	4	no	—
218	#340	—	26	4	no	—
219	#336	—	2	2	no	—
220	C₂²×C₁₃	#380	1	1	yes	characteristic
221	C₂²×C₁₃	#386	1	1	yes	characteristic
222	C₂²×C₁₃	#391	1	1	yes	characteristic
223	C₂²×C₁₃	#394	1	1	yes	characteristic
224	C₂²×C₁₃	#395	1	1	yes	characteristic
225	C₂²×C₁₃	#398	1	1	yes	characteristic
226	C₂²×C₁₃	#400	1	1	yes	characteristic
227	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
228	C₂²×C₁₃	C₂×#103	1	1	yes	characteristic
229	C₂²×C₁₃	#417	1	1	yes	characteristic
230	C₂²×C₁₃	#417	1	1	yes	characteristic
231	C₂²×C₁₃	#447	1	1	yes	characteristic
232	C₂²×C₁₃	#448	1	1	yes	characteristic
233	C₂²×C₁₃	#450	1	1	yes	characteristic
234	C₂²×C₁₃	#451	1	1	yes	characteristic
235	C₂²×C₁₃	#459	1	1	yes	characteristic
236	C₂²×C₁₃	#460	1	1	yes	characteristic
237	C₂²×C₁₃	#461	1	1	yes	characteristic
238	C₂²×C₁₃	#462	1	1	yes	characteristic
239	C₂²×C₁₃	#474	1	1	yes	characteristic
240	C₂²×C₁₃	#475	1	1	yes	characteristic
241	C₂²×C₁₃	#476	1	1	yes	characteristic
242	C₂²×C₁₃	#477	1	1	yes	characteristic
243	C₂²×C₁₃	#480	1	1	yes	characteristic
244	C₂²×C₁₃	#481	1	1	yes	characteristic
245	C₂²×C₁₃	#483	1	1	yes	characteristic
246	C₂²×C₁₃	#484	1	1	yes	characteristic
247	C₂²×C₁₃	#486	1	1	yes	characteristic
248	C₂²×C₁₃	#487	1	1	yes	characteristic
249	C₂²×C₁₃	#490	1	1	yes	characteristic
250	C₂²×C₁₃	#491	1	1	yes	characteristic
251	C₂²×C₁₃	#498	1	1	yes	characteristic
252	C₂²×C₁₃	#500	1	1	yes	characteristic
253	C₂²×C₁₃	#501	1	1	yes	characteristic
254	C₂²×C₁₃	#501	1	1	yes	characteristic
255	C₄×C₁₃	—	2	4	no	—
256	C₄×C₁₃	—	2	4	no	—
257	C₄×C₁₃	#387	1	2	yes	—
258	C₄×C₁₃	#389	1	2	yes	—
259	C₄×C₁₃	#396	1	2	yes	—
260	C₄×C₁₃	#398	1	2	yes	—
261	Dic₁₃	—	4	4	no	—
262	Dic₁₃	—	8	2	no	—
263	Dic₁₃	—	8	4	no	—
264	C₂³×C₄	—	26	1	no	—
265	C₂³×C₄	—	26	2	no	—
266	C₂³×C₄	—	26	1	no	—
267	C₂³×C₄	D₅₂	1	1	yes	characteristic
268	C₂³×C₄	D₅₂	1	1	yes	characteristic
269	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
270	C₂²×C₈	—	2	2	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	—	2	2	no	—
273	C₂²×C₈	—	2	2	no	—
274	C₂²×C₈	—	2	2	no	—
275	C₂²×C₈	—	2	2	no	—
276	C₂²×C₈	Dic₂₆	1	4	yes	—
277	C₂×C₄⋊C₄	—	13	2	no	—
278	C₂×C₄⋊C₄	—	13	2	no	—
279	C₂×C₄⋊C₄	—	13	2	no	—
280	C₂×C₄⋊C₄	—	13	2	no	—
281	C₂×C₄⋊C₄	—	13	4	no	—
282	C₂×C₄⋊C₄	—	26	1	no	—
283	C₂×C₄⋊C₄	—	26	1	no	—
284	C₂×C₄⋊C₄	—	26	1	no	—
285	C₂×C₄⋊C₄	—	26	2	no	—
286	C₂×C₄⋊C₄	—	26	2	no	—
287	C₂×C₄⋊C₄	—	26	2	no	—
288	C₂×C₄⋊C₄	—	26	2	no	—
289	C₂×C₄⋊C₄	—	26	2	no	—
290	C₂×C₄⋊C₄	—	26	2	no	—
291	C₂×C₄⋊C₄	—	26	4	no	—
292	C₂×C₄⋊C₄	—	26	4	no	—
293	C₂×C₄⋊C₄	—	26	4	no	—
294	C₂×C₄⋊C₄	—	26	2	no	—
295	C₂×C₄⋊C₄	—	26	1	no	—
296	C₂×C₄⋊C₄	—	52	2	no	—
297	C₂×C₄⋊C₄	—	52	2	no	—
298	C₂×C₄⋊C₄	—	52	2	no	—
299	C₂×C₄⋊C₄	—	52	2	no	—
300	C₂×C₄⋊C₄	—	52	2	no	—
301	C₂×C₄⋊C₄	—	52	2	no	—
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	—	2	2	no	—
304	C₂×C₄²	C₄×D₁₃	1	2	yes	—
305	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
306	#95	—	26	4	no	—
307	C₂×C₁₃	#1441	1	1	yes	characteristic
308	C₂×C₁₃	#1802	1	1	yes	characteristic
309	C₂×C₁₃	#1803	1	1	yes	characteristic
310	C₂×C₁₃	#1872	1	1	yes	characteristic
311	C₂×C₁₃	#1874	1	1	yes	characteristic
312	C₂×C₁₃	#1990	1	1	yes	characteristic
313	C₂×C₁₃	#1992	1	1	yes	characteristic
314	C₂×C₁₃	#2041	1	1	yes	characteristic
315	C₂×C₁₃	#2043	1	1	yes	characteristic
316	C₂×C₁₃	#2057	1	1	yes	characteristic
317	C₂×C₁₃	#2058	1	1	yes	characteristic
318	C₂×C₁₃	#2083	1	1	yes	characteristic
319	C₂×C₁₃	#2084	1	1	yes	characteristic
320	C₂×C₁₃	#2099	1	1	yes	characteristic
321	C₂×C₁₃	#2100	1	1	yes	characteristic
322	C₂⁴	C₂×D₅₂	1	1	yes	characteristic
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	26	2	no	—
332	C₂²×C₄	—	26	2	no	—
333	C₂²×C₄	—	26	2	no	—
334	C₂²×C₄	—	26	4	no	—
335	C₂²×C₄	—	26	2	no	—
336	C₂²×C₄	—	52	1	no	—
337	C₂²×C₄	—	52	1	no	—
338	C₂²×C₄	—	52	1	no	—
339	C₂²×C₄	—	52	1	no	—
340	C₂²×C₄	—	52	2	no	—
341	C₂²×C₄	—	52	1	no	—
342	C₂²×C₄	—	52	1	no	—
343	C₂²×C₄	—	52	2	no	—
344	C₂²×C₄	—	52	1	no	—
345	C₂²×C₄	—	52	2	no	—
346	C₂²×C₄	—	52	1	no	—
347	C₂²×C₄	—	52	2	no	—
348	C₂²×C₄	—	52	2	no	—
349	C₂²×C₄	—	52	2	no	—
350	C₂²×C₄	—	52	1	no	—
351	C₂²×C₄	—	52	1	no	—
352	C₂²×C₄	#6095	1	2	yes	—
353	C₂²×C₄	#6095	1	2	yes	—
354	C₂²×C₄	D₁₀₄	1	2	yes	—
355	C₂²×C₄	Dic₅₂	1	2	yes	—
356	C₂²×C₄	#6103	1	2	yes	—
357	C₂²×C₄	#6103	1	2	yes	—
358	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
359	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
360	C₂²×C₄	#6127	1	2	yes	—
361	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
362	C₂²×C₄	D₄×D₁₃	1	2	yes	—
363	C₂²×C₄	#6129	1	1	yes	characteristic
364	C₂²×C₄	#6129	1	2	yes	—
365	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
366	C₂²×C₄	#6131	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
368	C₂×C₈	—	2	4	no	—
369	C₂×C₈	—	2	4	no	—
370	C₂×C₈	—	2	4	no	—
371	C₂×C₈	—	4	2	no	—
372	C₂×C₈	—	4	2	no	—
373	C₂×C₈	—	4	2	no	—
374	C₂×C₈	—	4	2	no	—
375	C₄⋊C₄	—	13	4	no	—
376	C₄⋊C₄	—	26	2	no	—
377	C₄⋊C₄	—	26	2	no	—
378	C₄⋊C₄	—	26	2	no	—
379	C₄⋊C₄	—	26	4	no	—
380	C₄⋊C₄	—	26	4	no	—
381	C₄⋊C₄	—	26	4	no	—
382	C₄⋊C₄	—	52	8	no	—
383	C₄⋊C₄	—	52	8	no	—
384	C₄⋊C₄	—	52	2	no	—
385	C₄⋊C₄	—	52	2	no	—
386	C₄⋊C₄	—	52	2	no	—
387	C₄⋊C₄	—	52	8	no	—
388	C₄²	—	2	4	no	—
389	C₄²	—	2	4	no	—
390	C₁₃	#11207	1	1	yes	characteristic, complemented, Sylow
391	C₂³	#88123	1	1	yes	characteristic
392	C₂³	#88129	1	1	yes	characteristic
393	C₂³	#88136	1	1	yes	characteristic
394	C₂³	#88140	1	1	yes	characteristic
395	C₂³	#88149	1	1	yes	characteristic
396	C₂³	#88151	1	1	yes	characteristic
397	C₂³	C₂×#6095	1	1	yes	characteristic
398	C₂³	C₂×#6095	1	1	yes	characteristic
399	C₂³	C₂×D₁₀₄	1	1	yes	characteristic
400	C₂³	C₂×Dic₅₂	1	1	yes	characteristic
401	C₂³	#88162	1	1	yes	characteristic
402	C₂³	#88162	1	1	yes	characteristic
403	C₂³	#88163	1	1	yes	characteristic
404	C₂³	#88163	1	1	yes	characteristic
405	C₂³	C₂×#6103	1	1	yes	characteristic
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	26	4	no	—
419	C₂×C₄	—	52	2	no	—
420	C₂×C₄	—	52	2	no	—
421	C₂×C₄	—	52	2	no	—
422	C₂×C₄	—	52	2	no	—
423	C₂×C₄	—	52	2	no	—
424	C₂×C₄	—	52	2	no	—
425	C₂×C₄	—	52	2	no	—
426	C₂×C₄	—	52	2	no	—
427	C₂×C₄	—	52	4	no	—
428	C₂×C₄	—	52	2	no	—
429	C₂×C₄	—	52	4	no	—
430	C₂×C₄	—	52	4	no	—
431	C₂×C₄	—	104	2	no	—
432	C₂×C₄	—	104	2	no	—
433	C₂×C₄	—	104	2	no	—
434	C₂×C₄	—	104	2	no	—
435	C₂×C₄	—	104	1	no	—
436	C₂×C₄	—	104	1	no	—
437	C₂×C₄	—	104	1	no	—
438	C₂×C₄	—	104	1	no	—
439	C₂×C₄	#88056	1	4	yes	—
440	C₂×C₄	#88061	1	4	yes	—
441	C₂×C₄	C₄×Dic₂₆	1	2	yes	—
442	C₂×C₄	#88132	1	2	yes	—
443	C₂×C₄	#88132	1	2	yes	—
444	C₂×C₄	#88133	1	2	yes	—
445	C₂×C₄	#88135	1	2	yes	—
446	C₂×C₄	#88138	1	2	yes	—
447	C₂×C₄	#88142	1	2	yes	—
448	C₂×C₄	#88143	1	2	yes	—
449	C₂×C₄	#88144	1	2	yes	—
450	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
451	C₂×C₄	#88146	1	1	yes	characteristic
452	C₂×C₄	#88148	1	2	yes	—
453	C₂×C₄	#88178	1	2	yes	—
454	C₂×C₄	#88192	1	1	yes	characteristic
455	C₂×C₄	#88193	1	2	yes	—
456	C₂×C₄	#88200	1	1	yes	characteristic
457	C₈	—	4	4	no	—
458	C₂²	#11718317	1	1	yes	characteristic
459	C₂²	#11718320	1	1	yes	characteristic
460	C₂²	#11718322	1	1	yes	characteristic
461	C₂²	#11718333	1	1	yes	characteristic
462	C₂²	#11718341	1	1	yes	characteristic
463	C₂²	#11718342	1	1	yes	characteristic
464	C₂²	#11718343	1	1	yes	characteristic
465	C₂²	#11718355	1	1	yes	characteristic
466	C₂²	#11718363	1	1	yes	characteristic
467	C₂²	#11718363	1	1	yes	characteristic
468	C₂²	#11718364	1	1	yes	characteristic
469	C₂²	#11718374	1	1	yes	characteristic
470	C₂²	#11718382	1	1	yes	characteristic
471	C₂²	#11718383	1	1	yes	characteristic
472	C₂²	#11718392	1	1	yes	characteristic
473	C₂²	#11718393	1	1	yes	characteristic
474	C₂²	#11718396	1	1	yes	characteristic
475	C₂²	#11718397	1	1	yes	characteristic
476	C₂²	#11718399	1	1	yes	characteristic
477	C₂²	#11718400	1	1	yes	characteristic
478	C₂²	#11718502	1	1	yes	characteristic
479	C₂²	#11718503	1	1	yes	characteristic
480	C₂²	#11718504	1	1	yes	characteristic
481	C₂²	#11718507	1	1	yes	characteristic
482	C₂²	#11718509	1	1	yes	characteristic
483	C₂²	#11718510	1	1	yes	characteristic
484	C₂²	#11718511	1	1	yes	characteristic
485	C₂²	#11718512	1	1	yes	characteristic
486	C₂²	#11718590	1	1	yes	characteristic
487	C₂²	#11718619	1	1	yes	characteristic
488	C₂²	#11718648	1	1	yes	characteristic
489	C₂²	C₂×#88056	1	1	yes	characteristic
490	C₂²	C₂×#88061	1	1	yes	characteristic
491	C₂²	#11718794	1	1	yes	characteristic
492	C₂²	#11718794	1	1	yes	characteristic
493	C₄	—	2	4	no	—
494	C₄	—	2	4	no	—
495	C₄	—	52	4	no	—
496	C₄	—	104	2	no	—
497	C₄	—	104	4	no	—
498	C₄	#11718308	1	2	yes	—
499	C₄	#11718316	1	2	yes	—
500	C₄	#11718609	1	2	yes	—
501	C₄	#11718645	1	2	yes	—
502	C₂	#13113090	1	1	yes	characteristic
503	C₂	#13114837	1	1	yes	characteristic
504	C₂	#13114842	1	1	yes	characteristic
505	C₂	#13115141	1	1	yes	characteristic
506	C₂	#13115151	1	1	yes	characteristic
507	C₂	#13115797	1	1	yes	characteristic
508	C₂	#13115805	1	1	yes	characteristic
509	C₂	#13116071	1	1	yes	characteristic
510	C₂	#13116083	1	1	yes	characteristic
511	C₂	#13116165	1	1	yes	characteristic
512	C₂	#13116170	1	1	yes	characteristic
513	C₂	#13116309	1	1	yes	characteristic
514	C₂	#13116314	1	1	yes	characteristic
515	C₂	#13116395	1	1	yes	characteristic
516	C₂	#13116400	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₅₂
commutator	C₂²×C₄×C₁₃	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂×C₁₃×#336	C₂
socle, prime radical	C₂⁴×C₁₃	C₂×D₄
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂×#336	D₁₃
hypocenter	C₁₃	#11207
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
17. #11718589	C₄	semidirect
131. C₄⋊Dic₁₃	C₄⋊C₄	semidirect
390. C₁₃	#11207	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718589	2
C₂×#11718596	2
C₂×#11718143	2
C₂×C₁₃×#336	2
#11207	13