Subgroups — #15771180

Order 3328.

886 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718121	C₂	1	2	yes	maximal
2	C₂×#11718121	C₂	1	2	yes	maximal
3	C₂×#11718116	C₂	1	1	yes	maximal, characteristic
4	#13113066	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#384	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
7	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
8	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
12	C₂³×#1055	C₂²	1	2	yes	—
13	C₁₃×#384	—	2	4	no	—
14	C₂×#88071	—	2	1	no	—
15	C₂×#88071	—	2	1	no	—
16	#11718121	—	2	4	no	—
17	#11718121	—	2	4	no	—
18	#11718116	C₄	1	4	yes	complemented
19	C₂³×C₄×C₁₃	—	2	2	no	—
20	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
23	C₂³×Dic₁₃	—	2	1	no	—
24	C₂³×Dic₁₃	—	2	1	no	—
25	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
28	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
29	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
30	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
31	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
32	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
33	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
34	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
35	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
36	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
37	C₂×C₄²×C₁₃	—	2	2	no	—
38	C₂×C₄²×C₁₃	—	2	2	no	—
39	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
40	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
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	1	no	—
46	C₂×C₄⋊Dic₁₃	—	2	1	no	—
47	C₂×C₄⋊Dic₁₃	D₄	1	2	yes	—
48	C₂×C₄⋊Dic₁₃	Q₈	1	2	yes	—
49	C₂²×#1055	—	2	2	no	—
50	C₂²×#1055	—	2	2	no	—
51	C₂²×#1055	—	2	2	no	—
52	C₂²×#1055	—	2	2	no	—
53	C₂²×#1055	—	2	2	no	—
54	C₂²×#1055	—	2	2	no	—
55	C₂²×#1055	C₂×C₄	1	4	yes	—
56	#88071	—	4	2	no	—
57	#88071	—	4	2	no	—
58	#11267	—	13	1	no	maximal, Sylow
59	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₃	—	2	1	no	—
61	C₂²×C₄×C₁₃	—	2	1	no	—
62	C₂²×C₄×C₁₃	—	2	1	no	—
63	C₂²×C₄×C₁₃	—	2	1	no	—
64	C₂²×C₄×C₁₃	—	2	1	no	—
65	C₂²×C₄×C₁₃	—	2	1	no	—
66	C₂²×C₄×C₁₃	—	2	1	no	—
67	C₂²×C₄×C₁₃	—	2	1	no	—
68	C₂²×C₄×C₁₃	—	2	4	no	—
69	C₂²×C₄×C₁₃	—	4	2	no	—
70	C₂²×C₄×C₁₃	—	4	2	no	—
71	C₂²×C₄×C₁₃	—	4	2	no	—
72	C₂²×C₄×C₁₃	—	4	2	no	—
73	C₂²×C₄×C₁₃	—	4	2	no	—
74	C₂²×C₄×C₁₃	—	4	2	no	—
75	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
76	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
77	C₂²×C₄×C₁₃	D₈	1	2	yes	—
78	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
79	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
80	C₂²×C₄×C₁₃	Q₁₆	1	2	yes	—
81	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	#41	1	2	yes	—
87	C₂²×C₄×C₁₃	#41	1	2	yes	—
88	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	#41	1	2	yes	—
90	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
91	C₂²×Dic₁₃	—	2	2	no	—
92	C₂²×Dic₁₃	—	2	2	no	—
93	C₂²×Dic₁₃	—	4	1	no	—
94	C₂²×Dic₁₃	—	4	1	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	1	no	—
101	C₂²×Dic₁₃	—	4	1	no	—
102	C₂²×Dic₁₃	—	4	1	no	—
103	C₂²×Dic₁₃	—	4	1	no	—
104	C₂²×Dic₁₃	—	4	1	no	—
105	C₁₃×C₄⋊C₄	—	2	4	no	—
106	C₁₃×C₄⋊C₄	—	2	4	no	—
107	C₁₃×C₄⋊C₄	—	4	8	no	—
108	C₁₃×C₄⋊C₄	—	4	8	no	—
109	C₁₃×C₄⋊C₄	—	4	2	no	—
110	C₁₃×C₄⋊C₄	—	4	2	no	—
111	C₄²×C₁₃	—	2	4	no	—
112	C₄²×C₁₃	—	2	4	no	—
113	C₄⋊Dic₁₃	—	2	4	no	—
114	C₄⋊Dic₁₃	—	2	4	no	—
115	C₄⋊Dic₁₃	—	4	2	no	—
116	C₄⋊Dic₁₃	—	4	2	no	—
117	C₂×#1055	—	2	4	no	—
118	C₂×#1055	—	2	4	no	—
119	C₂×#1055	—	2	4	no	—
120	C₂×#1055	—	4	2	no	—
121	C₂×#1055	—	4	2	no	—
122	C₂×#1055	—	4	2	no	—
123	C₂×#1055	—	4	2	no	—
124	C₂×#384	D₁₃	1	1	yes	characteristic
125	C₂×#340	—	13	2	no	—
126	C₂×#340	—	13	2	no	—
127	C₂×#336	—	13	1	no	—
128	C₄⋊#95	—	13	1	no	—
129	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂³×C₁₃	#120	1	1	yes	characteristic
131	C₂³×C₁₃	#121	1	1	yes	characteristic
132	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
133	C₂³×C₁₃	#123	1	1	yes	characteristic
134	C₂³×C₁₃	#124	1	1	yes	characteristic
135	C₂³×C₁₃	#124	1	1	yes	characteristic
136	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
137	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
138	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
139	C₂³×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
140	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
141	C₂³×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
142	C₂³×C₁₃	#137	1	1	yes	characteristic
143	C₂³×C₁₃	#137	1	1	yes	characteristic
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
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	—	4	4	no	—
157	C₂×C₄×C₁₃	—	4	4	no	—
158	C₂×C₄×C₁₃	—	4	4	no	—
159	C₂×C₄×C₁₃	—	8	2	no	—
160	C₂×C₄×C₁₃	—	8	2	no	—
161	C₂×C₄×C₁₃	—	8	2	no	—
162	C₂×C₄×C₁₃	—	8	2	no	—
163	C₂×C₄×C₁₃	#106	1	4	yes	—
164	C₂×C₄×C₁₃	#107	1	4	yes	—
165	C₂×C₄×C₁₃	#117	1	2	yes	—
166	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
169	C₂×C₄×C₁₃	#121	1	2	yes	—
170	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
171	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
172	C₂×C₄×C₁₃	#123	1	2	yes	—
173	C₂×C₄×C₁₃	#123	1	2	yes	—
174	C₂×C₄×C₁₃	#124	1	2	yes	—
175	C₂×C₄×C₁₃	#125	1	2	yes	—
176	C₂×C₄×C₁₃	#125	1	2	yes	—
177	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
178	C₂×C₄×C₁₃	#126	1	2	yes	—
179	C₂×C₄×C₁₃	#126	1	2	yes	—
180	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
181	C₂×Dic₁₃	—	4	2	no	—
182	C₂×Dic₁₃	—	4	2	no	—
183	C₂×Dic₁₃	—	4	2	no	—
184	C₂×Dic₁₃	—	4	2	no	—
185	C₂×Dic₁₃	—	4	2	no	—
186	C₂×Dic₁₃	—	4	2	no	—
187	C₂×Dic₁₃	—	8	1	no	—
188	C₂×Dic₁₃	—	8	1	no	—
189	C₂×Dic₁₃	—	8	1	no	—
190	C₂×Dic₁₃	—	8	1	no	—
191	C₂×Dic₁₃	—	8	1	no	—
192	C₂×Dic₁₃	—	8	1	no	—
193	C₂×Dic₁₃	—	8	1	no	—
194	C₂×Dic₁₃	—	8	1	no	—
195	#1055	—	4	4	no	—
196	C₂³×C₈	—	13	2	no	—
197	C₂²×C₄⋊C₄	—	2	1	no	—
198	C₂²×C₄⋊C₄	—	2	1	no	—
199	C₂²×C₄⋊C₄	—	13	1	no	—
200	C₂²×C₄⋊C₄	—	13	1	no	—
201	C₂²×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
202	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
203	#384	—	2	4	no	—
204	C₂×#95	—	26	1	no	—
205	C₂×#95	—	26	1	no	—
206	#340	—	26	4	no	—
207	#340	—	26	4	no	—
208	#336	—	13	4	no	—
209	C₂²×C₁₃	#382	1	1	yes	characteristic
210	C₂²×C₁₃	#385	1	1	yes	characteristic
211	C₂²×C₁₃	#389	1	1	yes	characteristic
212	C₂²×C₁₃	#393	1	1	yes	characteristic
213	C₂²×C₁₃	#394	1	1	yes	characteristic
214	C₂²×C₁₃	#397	1	1	yes	characteristic
215	C₂²×C₁₃	#400	1	1	yes	characteristic
216	C₂²×C₁₃	C₂×#106	1	1	yes	characteristic
217	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
218	C₂²×C₁₃	#428	1	1	yes	characteristic
219	C₂²×C₁₃	#428	1	1	yes	characteristic
220	C₂²×C₁₃	#447	1	1	yes	characteristic
221	C₂²×C₁₃	#448	1	1	yes	characteristic
222	C₂²×C₁₃	#450	1	1	yes	characteristic
223	C₂²×C₁₃	#451	1	1	yes	characteristic
224	C₂²×C₁₃	#459	1	1	yes	characteristic
225	C₂²×C₁₃	#460	1	1	yes	characteristic
226	C₂²×C₁₃	#461	1	1	yes	characteristic
227	C₂²×C₁₃	#462	1	1	yes	characteristic
228	C₂²×C₁₃	#474	1	1	yes	characteristic
229	C₂²×C₁₃	#475	1	1	yes	characteristic
230	C₂²×C₁₃	#476	1	1	yes	characteristic
231	C₂²×C₁₃	#477	1	1	yes	characteristic
232	C₂²×C₁₃	#480	1	1	yes	characteristic
233	C₂²×C₁₃	#481	1	1	yes	characteristic
234	C₂²×C₁₃	#483	1	1	yes	characteristic
235	C₂²×C₁₃	#484	1	1	yes	characteristic
236	C₂²×C₁₃	#486	1	1	yes	characteristic
237	C₂²×C₁₃	#486	1	1	yes	characteristic
238	C₂²×C₁₃	#487	1	1	yes	characteristic
239	C₂²×C₁₃	#487	1	1	yes	characteristic
240	C₂²×C₁₃	#489	1	1	yes	characteristic
241	C₂²×C₁₃	#489	1	1	yes	characteristic
242	C₂²×C₁₃	#490	1	1	yes	characteristic
243	C₂²×C₁₃	#491	1	1	yes	characteristic
244	C₄×C₁₃	—	2	4	no	—
245	C₄×C₁₃	—	2	4	no	—
246	C₄×C₁₃	—	8	4	no	—
247	C₄×C₁₃	#387	1	2	yes	—
248	C₄×C₁₃	#388	1	2	yes	—
249	C₄×C₁₃	#398	1	2	yes	—
250	C₄×C₁₃	#400	1	2	yes	—
251	Dic₁₃	—	8	2	no	—
252	Dic₁₃	—	8	2	no	—
253	C₂³×C₄	—	2	2	no	—
254	C₂³×C₄	—	26	1	no	—
255	C₂³×C₄	—	26	1	no	—
256	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
257	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
258	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
259	C₂²×C₈	—	13	4	no	—
260	C₂²×C₈	—	26	2	no	—
261	C₂²×C₈	—	26	2	no	—
262	C₂²×C₈	—	26	2	no	—
263	C₂²×C₈	—	26	2	no	—
264	C₂²×C₈	—	26	2	no	—
265	C₂²×C₈	—	26	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	4	no	—
271	C₂×C₄⋊C₄	—	2	4	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	4	2	no	—
274	C₂×C₄⋊C₄	—	4	2	no	—
275	C₂×C₄⋊C₄	—	4	2	no	—
276	C₂×C₄⋊C₄	—	4	2	no	—
277	C₂×C₄⋊C₄	—	13	2	no	—
278	C₂×C₄⋊C₄	—	13	2	no	—
279	C₂×C₄⋊C₄	—	26	2	no	—
280	C₂×C₄⋊C₄	—	26	2	no	—
281	C₂×C₄⋊C₄	—	26	2	no	—
282	C₂×C₄⋊C₄	—	26	2	no	—
283	C₂×C₄⋊C₄	—	26	1	no	—
284	C₂×C₄⋊C₄	—	26	1	no	—
285	C₂×C₄⋊C₄	C₂²⋊D₁₃	1	4	yes	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	—	2	2	no	—
288	C₂×C₄²	Dic₂₆	1	2	yes	—
289	C₂×C₄²	C₄×D₁₃	1	2	yes	—
290	#95	—	52	2	no	—
291	#95	—	52	2	no	—
292	C₂×C₁₃	#1442	1	1	yes	characteristic
293	C₂×C₁₃	#1834	1	1	yes	characteristic
294	C₂×C₁₃	#1836	1	1	yes	characteristic
295	C₂×C₁₃	#1852	1	1	yes	characteristic
296	C₂×C₁₃	#1853	1	1	yes	characteristic
297	C₂×C₁₃	#1947	1	1	yes	characteristic
298	C₂×C₁₃	#1948	1	1	yes	characteristic
299	C₂×C₁₃	#2023	1	1	yes	characteristic
300	C₂×C₁₃	#2024	1	1	yes	characteristic
301	C₂×C₁₃	#2041	1	1	yes	characteristic
302	C₂×C₁₃	#2043	1	1	yes	characteristic
303	C₂×C₁₃	#2071	1	1	yes	characteristic
304	C₂×C₁₃	#2072	1	1	yes	characteristic
305	C₂×C₁₃	#2099	1	1	yes	characteristic
306	C₂×C₁₃	#2100	1	1	yes	characteristic
307	C₂⁴	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	—	4	2	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	—	26	2	no	—
324	C₂²×C₄	—	26	2	no	—
325	C₂²×C₄	—	52	1	no	—
326	C₂²×C₄	—	52	1	no	—
327	C₂²×C₄	—	52	1	no	—
328	C₂²×C₄	—	52	1	no	—
329	C₂²×C₄	—	52	1	no	—
330	C₂²×C₄	—	52	1	no	—
331	C₂²×C₄	—	52	1	no	—
332	C₂²×C₄	—	52	1	no	—
333	C₂²×C₄	—	52	1	no	—
334	C₂²×C₄	—	52	1	no	—
335	C₂²×C₄	—	52	1	no	—
336	C₂²×C₄	—	52	1	no	—
337	C₂²×C₄	#6101	1	2	yes	—
338	C₂²×C₄	#6101	1	2	yes	—
339	C₂²×C₄	#6104	1	2	yes	—
340	C₂²×C₄	#6105	1	2	yes	—
341	C₂²×C₄	#6106	1	2	yes	—
342	C₂²×C₄	#6107	1	2	yes	—
343	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
345	C₂²×C₄	#6127	1	2	yes	—
346	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
347	C₂²×C₄	#6129	1	1	yes	characteristic
348	C₂²×C₄	#6129	1	2	yes	—
349	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
350	C₂²×C₄	#6131	1	2	yes	—
351	C₂²×C₄	#6131	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
353	C₂×C₈	—	26	4	no	—
354	C₂×C₈	—	26	4	no	—
355	C₂×C₈	—	26	4	no	—
356	C₂×C₈	—	52	2	no	—
357	C₂×C₈	—	52	2	no	—
358	C₂×C₈	—	52	2	no	—
359	C₂×C₈	—	52	2	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	4	8	no	—
363	C₄⋊C₄	—	4	8	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	—	26	4	no	—
367	C₄⋊C₄	—	26	4	no	—
368	C₄⋊C₄	—	52	2	no	—
369	C₄⋊C₄	—	52	2	no	—
370	C₄²	—	2	4	no	—
371	C₄²	—	2	4	no	—
372	C₁₃	#11267	1	1	yes	characteristic, complemented, Sylow
373	C₂³	C₂×#6101	1	1	yes	characteristic
374	C₂³	#88183	1	1	yes	characteristic
375	C₂³	C₂×#6104	1	1	yes	characteristic
376	C₂³	#88186	1	1	yes	characteristic
377	C₂³	#88186	1	1	yes	characteristic
378	C₂³	C₂×#6105	1	1	yes	characteristic
379	C₂³	#88190	1	1	yes	characteristic
380	C₂³	#88192	1	1	yes	characteristic
381	C₂³	C₂×#6106	1	1	yes	characteristic
382	C₂³	#88196	1	1	yes	characteristic
383	C₂³	#88196	1	1	yes	characteristic
384	C₂³	C₂×#6107	1	1	yes	characteristic
385	C₂³	#88200	1	1	yes	characteristic
386	C₂³	#88201	1	1	yes	characteristic
387	C₂³	#88207	1	1	yes	characteristic
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	8	2	no	—
404	C₂×C₄	—	8	2	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	—	8	2	no	—
407	C₂×C₄	—	52	2	no	—
408	C₂×C₄	—	52	2	no	—
409	C₂×C₄	—	52	2	no	—
410	C₂×C₄	—	52	2	no	—
411	C₂×C₄	—	52	2	no	—
412	C₂×C₄	—	52	2	no	—
413	C₂×C₄	—	104	1	no	—
414	C₂×C₄	—	104	1	no	—
415	C₂×C₄	—	104	1	no	—
416	C₂×C₄	—	104	1	no	—
417	C₂×C₄	—	104	1	no	—
418	C₂×C₄	—	104	1	no	—
419	C₂×C₄	—	104	1	no	—
420	C₂×C₄	—	104	1	no	—
421	C₂×C₄	#88047	1	4	yes	—
422	C₂×C₄	#88048	1	4	yes	—
423	C₂×C₄	#88141	1	1	yes	characteristic
424	C₂×C₄	#88142	1	1	yes	characteristic
425	C₂×C₄	#88143	1	2	yes	—
426	C₂×C₄	#88144	1	2	yes	—
427	C₂×C₄	#88144	1	1	yes	characteristic
428	C₂×C₄	#88146	1	2	yes	—
429	C₂×C₄	#88147	1	1	yes	characteristic
430	C₂×C₄	#88148	1	2	yes	—
431	C₂×C₄	#88152	1	2	yes	—
432	C₂×C₄	#88152	1	2	yes	—
433	C₂×C₄	#88178	1	2	yes	—
434	C₂×C₄	C₄×C₂²⋊D₁₃	1	2	yes	—
435	C₂×C₄	#88189	1	2	yes	—
436	C₂×C₄	#88193	1	2	yes	—
437	C₂×C₄	#88200	1	2	yes	—
438	C₂×C₄	#88201	1	2	yes	—
439	C₈	—	52	4	no	—
440	C₂²	C₂×#88047	1	1	yes	characteristic
441	C₂²	C₂×#88048	1	1	yes	characteristic
442	C₂²	#11718625	1	1	yes	characteristic
443	C₂²	#11718625	1	1	yes	characteristic
444	C₂²	#11718628	1	1	yes	characteristic
445	C₂²	#11718629	1	1	yes	characteristic
446	C₂²	#11718631	1	1	yes	characteristic
447	C₂²	#11718632	1	1	yes	characteristic
448	C₂²	#11718634	1	1	yes	characteristic
449	C₂²	#11718638	1	1	yes	characteristic
450	C₂²	#11718643	1	1	yes	characteristic
451	C₂²	#11718654	1	1	yes	characteristic
452	C₂²	#11718731	1	1	yes	characteristic
453	C₂²	#11718732	1	1	yes	characteristic
454	C₂²	#11718733	1	1	yes	characteristic
455	C₂²	#11718736	1	1	yes	characteristic
456	C₂²	#11718742	1	1	yes	characteristic
457	C₂²	#11718743	1	1	yes	characteristic
458	C₂²	#11718744	1	1	yes	characteristic
459	C₂²	#11718745	1	1	yes	characteristic
460	C₂²	#11718748	1	1	yes	characteristic
461	C₂²	#11718749	1	1	yes	characteristic
462	C₂²	#11718750	1	1	yes	characteristic
463	C₂²	#11718750	1	1	yes	characteristic
464	C₂²	#11718751	1	1	yes	characteristic
465	C₂²	#11718752	1	1	yes	characteristic
466	C₂²	#11718754	1	1	yes	characteristic
467	C₂²	#11718755	1	1	yes	characteristic
468	C₂²	#11718871	1	1	yes	characteristic
469	C₂²	#11718878	1	1	yes	characteristic
470	C₂²	#11718879	1	1	yes	characteristic
471	C₂²	#11718883	1	1	yes	characteristic
472	C₂²	#11718888	1	1	yes	characteristic
473	C₂²	#11718889	1	1	yes	characteristic
474	C₂²	#11718892	1	1	yes	characteristic
475	C₄	—	2	4	no	—
476	C₄	—	2	4	no	—
477	C₄	—	8	4	no	—
478	C₄	—	104	2	no	—
479	C₄	—	104	2	no	—
480	C₄	#11718639	1	2	yes	—
481	C₄	#11718645	1	2	yes	—
482	C₄	#11718647	1	2	yes	—
483	C₄	#11718651	1	2	yes	—
484	C₂	#13113095	1	1	yes	characteristic
485	C₂	#13114963	1	1	yes	characteristic
486	C₂	#13114971	1	1	yes	characteristic
487	C₂	#13115024	1	1	yes	characteristic
488	C₂	#13115029	1	1	yes	characteristic
489	C₂	#13115592	1	1	yes	characteristic
490	C₂	#13115597	1	1	yes	characteristic
491	C₂	#13115969	1	1	yes	characteristic
492	C₂	#13115974	1	1	yes	characteristic
493	C₂	#13116067	1	1	yes	characteristic
494	C₂	#13116079	1	1	yes	characteristic
495	C₂	#13116240	1	1	yes	characteristic
496	C₂	#13116245	1	1	yes	characteristic
497	C₂	#13116393	1	1	yes	characteristic
498	C₂	#13116398	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₁₃
commutator	C₂²×C₄×C₁₃	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂×C₁₃×#384	C₂
socle, prime radical	C₂⁴×C₁₃	C₂×D₄
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂×#384	D₁₃
hypocenter	C₁₃	#11267
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#384

Complements

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

N	H ≅ G/N	type
18. #11718116	C₄	semidirect
372. C₁₃	#11267	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718121	2
C₂×#11718116	2
#13113066	2
C₂×C₁₃×#384	2
#11267	13