Subgroups — #15768884

Order 3328.

974 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88054	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718116	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718142	C₂	1	1	yes	maximal, characteristic
4	C₂×#11718142	C₂	1	1	yes	maximal, characteristic
5	C₂×#11718142	C₂	1	1	yes	maximal, characteristic
6	C₄×#88071	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
13	C₂³×#1055	C₂²	1	1	yes	characteristic
14	C₂³×#1055	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₃	—	2	2	no	—
16	C₂×C₄×C₈×C₁₃	—	2	2	no	—
17	C₂×C₄×C₈×C₁₃	—	2	2	no	—
18	C₂×#88071	C₄	1	2	yes	—
19	C₂×#88071	C₄	1	2	yes	—
20	C₂×#88054	—	2	2	no	—
21	C₂×#88054	—	2	2	no	—
22	C₂×#88054	C₄	1	4	yes	complemented
23	#11718142	—	2	2	no	—
24	#11718142	—	2	2	no	—
25	#11718142	C₄	1	4	yes	complemented
26	#11718116	—	2	2	no	—
27	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
28	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
29	C₂³×Dic₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂³×Dic₁₃	C₂×C₄	1	2	yes	—
31	C₂³×Dic₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₃	—	2	1	no	—
33	C₂²×C₈×C₁₃	—	2	1	no	—
34	C₂²×C₈×C₁₃	—	2	1	no	—
35	C₂²×C₈×C₁₃	—	2	1	no	—
36	C₂²×C₈×C₁₃	—	2	1	no	—
37	C₂²×C₈×C₁₃	—	2	1	no	—
38	C₂²×C₈×C₁₃	—	2	1	no	—
39	C₂²×C₈×C₁₃	—	2	1	no	—
40	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
41	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
42	C₂²×C₈×C₁₃	D₄	1	2	yes	—
43	C₂²×C₈×C₁₃	D₄	1	2	yes	—
44	C₂²×C₈×C₁₃	D₄	1	2	yes	—
45	C₂²×C₈×C₁₃	Q₈	1	2	yes	—
46	C₂×C₄²×C₁₃	—	2	1	no	—
47	C₂×C₄²×C₁₃	—	2	1	no	—
48	C₂×C₄²×C₁₃	—	2	1	no	—
49	C₂×C₄²×C₁₃	—	2	1	no	—
50	C₂×C₄²×C₁₃	D₄	1	2	yes	—
51	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
52	C₂×C₄×Dic₁₃	—	2	1	no	—
53	C₂×C₄×Dic₁₃	—	2	1	no	—
54	C₂×C₄×Dic₁₃	—	2	1	no	—
55	C₂×C₄×Dic₁₃	—	2	1	no	—
56	C₂×C₄×Dic₁₃	—	2	1	no	—
57	C₂×C₄×Dic₁₃	—	2	1	no	—
58	C₂×C₄×Dic₁₃	—	2	1	no	—
59	C₂×C₄×Dic₁₃	—	2	1	no	—
60	C₂×C₄×Dic₁₃	—	2	1	no	—
61	C₂×C₄×Dic₁₃	—	2	1	no	—
62	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
63	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
64	C₂²×#1055	—	2	1	no	—
65	C₂²×#1055	—	2	1	no	—
66	C₂²×#1055	—	2	1	no	—
67	C₂²×#1055	—	2	1	no	—
68	C₂²×#1055	—	2	1	no	—
69	C₂²×#1055	—	2	1	no	—
70	C₂²×#1055	—	2	1	no	—
71	C₂²×#1055	—	2	1	no	—
72	C₂²×#1055	—	2	1	no	—
73	C₂²×#1055	—	2	1	no	—
74	C₂²×#1055	—	2	1	no	—
75	C₂²×#1055	—	2	1	no	—
76	C₂²×#1055	C₂×C₄	1	2	yes	—
77	C₂²×#1055	C₂×C₄	1	2	yes	—
78	C₄×C₈×C₁₃	—	2	8	no	—
79	#88071	—	2	4	no	—
80	#88071	C₈	1	8	yes	complemented
81	#88054	—	2	8	no	—
82	#10876	—	13	1	no	maximal, Sylow
83	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	—	2	2	no	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
89	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
90	C₂²×C₄×C₁₃	M₁₆	1	4	yes	—
91	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
105	C₂²×Dic₁₃	—	2	1	no	—
106	C₂²×Dic₁₃	—	2	1	no	—
107	C₂²×Dic₁₃	—	2	2	no	—
108	C₂²×Dic₁₃	—	2	2	no	—
109	C₂²×Dic₁₃	—	2	1	no	—
110	C₂²×Dic₁₃	—	2	1	no	—
111	C₂²×Dic₁₃	—	2	2	no	—
112	C₂²×Dic₁₃	—	2	2	no	—
113	C₂²×Dic₁₃	—	2	2	no	—
114	C₂²×Dic₁₃	—	2	2	no	—
115	C₂²×Dic₁₃	—	2	2	no	—
116	C₂²×Dic₁₃	—	2	2	no	—
117	C₂²×Dic₁₃	—	2	2	no	—
118	C₂²×Dic₁₃	C₄²	1	2	yes	—
119	C₂²×Dic₁₃	C₄²	1	2	yes	—
120	C₂²×Dic₁₃	C₂×C₈	1	4	yes	—
121	C₂²×Dic₁₃	C₂×C₈	1	4	yes	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	2	2	no	—
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	—	2	2	no	—
134	C₂×C₈×C₁₃	C₂²⋊C₄	1	4	yes	—
135	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
136	C₄²×C₁₃	—	2	2	no	—
137	C₄²×C₁₃	—	2	2	no	—
138	C₄²×C₁₃	—	2	2	no	—
139	C₄²×C₁₃	—	2	2	no	—
140	C₄×Dic₁₃	—	2	2	no	—
141	C₄×Dic₁₃	—	2	2	no	—
142	C₄×Dic₁₃	—	2	2	no	—
143	C₄×Dic₁₃	—	2	2	no	—
144	C₄×Dic₁₃	—	4	1	no	—
145	C₄×Dic₁₃	—	4	1	no	—
146	C₄×Dic₁₃	—	4	1	no	—
147	C₄×Dic₁₃	—	4	1	no	—
148	C₂×#1055	—	2	2	no	—
149	C₂×#1055	—	2	2	no	—
150	C₂×#1055	—	2	2	no	—
151	C₂×#1055	—	2	2	no	—
152	C₂×#1055	—	2	2	no	—
153	C₂×#1055	—	2	2	no	—
154	C₂×#1055	—	4	1	no	—
155	C₂×#1055	—	4	1	no	—
156	C₂×#1055	—	4	1	no	—
157	C₂×#1055	—	4	1	no	—
158	C₂×#1055	—	4	1	no	—
159	C₂×#1055	—	4	1	no	—
160	C₂×#1055	—	4	1	no	—
161	C₂×#1055	—	4	1	no	—
162	C₂²×C₄⋊C₈	—	13	1	no	—
163	C₂²×C₄×C₈	D₁₃	1	1	yes	characteristic
164	C₂×#336	—	13	1	no	—
165	C₂×#336	—	13	1	no	—
166	C₂×#336	—	13	1	no	—
167	C₂×#336	—	13	1	no	—
168	C₄×#95	—	13	1	no	—
169	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
170	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂³×C₁₃	#117	1	1	yes	characteristic
172	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
173	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
174	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
175	C₂³×C₁₃	C₄×Q₈	1	1	yes	characteristic
176	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
177	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
178	C₂³×C₁₃	#131	1	2	yes	—
179	C₂³×C₁₃	#131	1	2	yes	—
180	C₂×C₄×C₁₃	—	2	4	no	—
181	C₂×C₄×C₁₃	—	2	4	no	—
182	C₂×C₄×C₁₃	—	2	4	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	2	4	no	—
186	C₂×C₄×C₁₃	C₄⋊C₈	1	8	yes	complemented
187	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
190	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
199	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
200	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
201	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
206	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
207	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
208	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
209	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
210	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
211	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
212	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
213	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
215	C₂×Dic₁₃	—	2	2	no	—
216	C₂×Dic₁₃	—	2	2	no	—
217	C₂×Dic₁₃	—	2	4	no	—
218	C₂×Dic₁₃	—	2	4	no	—
219	C₂×Dic₁₃	—	2	2	no	—
220	C₂×Dic₁₃	—	2	2	no	—
221	C₂×Dic₁₃	—	2	2	no	—
222	C₂×Dic₁₃	—	2	4	no	—
223	C₂×Dic₁₃	—	2	4	no	—
224	C₂×Dic₁₃	—	2	4	no	—
225	C₂×Dic₁₃	—	4	2	no	—
226	C₂×Dic₁₃	—	4	2	no	—
227	C₂×Dic₁₃	—	4	2	no	—
228	C₂×Dic₁₃	—	4	2	no	—
229	C₂×Dic₁₃	—	4	2	no	—
230	C₂×Dic₁₃	—	4	2	no	—
231	C₂×Dic₁₃	C₄×C₈	1	4	yes	complemented
232	C₈×C₁₃	—	2	4	no	—
233	C₈×C₁₃	—	2	4	no	—
234	#1055	—	4	2	no	—
235	#1055	—	4	2	no	—
236	C₂³×C₈	—	13	1	no	—
237	C₂³×C₈	—	13	1	no	—
238	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
239	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
240	C₂²×C₄²	—	13	1	no	—
241	C₂²×C₄²	—	13	1	no	—
242	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
243	C₂×C₄⋊C₈	—	13	4	no	—
244	C₂×C₄⋊C₈	—	26	2	no	—
245	C₂×C₄⋊C₈	—	26	2	no	—
246	C₂×C₄×C₈	—	2	2	no	—
247	C₂×C₄×C₈	—	2	2	no	—
248	C₂×C₄×C₈	—	2	2	no	—
249	C₂×#95	—	13	2	no	—
250	C₂×#95	—	13	2	no	—
251	#336	—	13	4	no	—
252	#336	—	26	2	no	—
253	#336	—	26	2	no	—
254	#336	—	26	2	no	—
255	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
256	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
257	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
258	C₂²×C₁₃	#385	1	1	yes	characteristic
259	C₂²×C₁₃	#387	1	1	yes	characteristic
260	C₂²×C₁₃	#388	1	1	yes	characteristic
261	C₂²×C₁₃	#389	1	1	yes	characteristic
262	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
263	C₂²×C₁₃	C₄×M₁₆	1	1	yes	characteristic
264	C₂²×C₁₃	#405	1	1	yes	characteristic
265	C₂²×C₁₃	#405	1	1	yes	characteristic
266	C₂²×C₁₃	C₂×C₄⋊C₈	1	2	yes	—
267	C₂²×C₁₃	#424	1	2	yes	—
268	C₂²×C₁₃	#431	1	2	yes	—
269	C₂²×C₁₃	#433	1	2	yes	—
270	C₂²×C₁₃	C₈×D₄	1	2	yes	—
271	C₂²×C₁₃	C₈×D₄	1	2	yes	—
272	C₂²×C₁₃	C₈×D₄	1	2	yes	—
273	C₂²×C₁₃	#435	1	2	yes	—
274	C₂²×C₁₃	#435	1	2	yes	—
275	C₂²×C₁₃	#436	1	2	yes	—
276	C₂²×C₁₃	C₈×Q₈	1	2	yes	—
277	C₂²×C₁₃	#446	1	2	yes	—
278	C₄×C₁₃	—	2	8	no	—
279	C₄×C₁₃	#385	1	1	yes	characteristic
280	C₄×C₁₃	#386	1	1	yes	characteristic
281	C₄×C₁₃	#387	1	1	yes	characteristic
282	C₄×C₁₃	#387	1	1	yes	characteristic
283	C₄×C₁₃	#387	1	1	yes	characteristic
284	C₄×C₁₃	#388	1	1	yes	characteristic
285	C₄×C₁₃	#389	1	1	yes	characteristic
286	C₄×C₁₃	#391	1	1	yes	characteristic
287	Dic₁₃	—	2	4	no	—
288	Dic₁₃	—	4	4	no	—
289	Dic₁₃	—	4	2	no	—
290	C₂³×C₄	—	13	1	no	—
291	C₂³×C₄	—	13	1	no	—
292	C₂³×C₄	—	13	2	no	—
293	C₂³×C₄	C₄×D₁₃	1	2	yes	—
294	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
295	C₂²×C₈	—	2	1	no	—
296	C₂²×C₈	—	2	1	no	—
297	C₂²×C₈	—	2	1	no	—
298	C₂²×C₈	—	2	1	no	—
299	C₂²×C₈	—	2	1	no	—
300	C₂²×C₈	—	2	1	no	—
301	C₂²×C₈	—	2	1	no	—
302	C₂²×C₈	—	2	1	no	—
303	C₂²×C₈	—	13	2	no	—
304	C₂²×C₈	—	13	2	no	—
305	C₂²×C₈	—	26	1	no	—
306	C₂²×C₈	—	26	1	no	—
307	C₂²×C₈	—	26	1	no	—
308	C₂²×C₈	—	26	1	no	—
309	C₂²×C₈	—	26	1	no	—
310	C₂²×C₈	—	26	1	no	—
311	C₂²×C₈	—	26	1	no	—
312	C₂²×C₈	—	26	1	no	—
313	C₂²×C₈	—	26	1	no	—
314	C₂²×C₈	—	26	1	no	—
315	C₂²×C₈	—	26	1	no	—
316	C₂²×C₈	—	26	1	no	—
317	C₂²×C₈	Dic₂₆	1	2	yes	—
318	C₂²×C₈	C₄×D₁₃	1	2	yes	—
319	C₂²×C₈	C₄×D₁₃	1	2	yes	—
320	C₂²×C₈	D₅₂	1	2	yes	—
321	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
322	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	—	13	2	no	—
328	C₂×C₄²	—	13	2	no	—
329	C₂×C₄²	—	26	1	no	—
330	C₂×C₄²	—	26	1	no	—
331	C₂×C₄²	—	26	1	no	—
332	C₂×C₄²	—	26	1	no	—
333	C₂×C₄²	—	26	1	no	—
334	C₂×C₄²	—	26	1	no	—
335	C₂×C₄²	—	26	1	no	—
336	C₂×C₄²	—	26	1	no	—
337	C₂×C₄²	—	26	1	no	—
338	C₂×C₄²	—	26	1	no	—
339	C₂×C₄²	Dic₂₆	1	2	yes	—
340	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
341	C₄⋊C₈	—	26	8	no	—
342	C₄×C₈	—	2	8	no	—
343	#95	—	13	8	no	—
344	#95	—	26	4	no	—
345	C₂×C₁₃	#1436	1	1	yes	characteristic
346	C₂×C₁₃	C₈×C₂²⋊C₄	1	1	yes	characteristic
347	C₂×C₁₃	#1753	1	1	yes	characteristic
348	C₂×C₁₃	C₄×C₄⋊C₈	1	1	yes	characteristic
349	C₂×C₁₃	#1768	1	1	yes	characteristic
350	C₂×C₁₃	C₈×C₄⋊C₄	1	1	yes	characteristic
351	C₂×C₁₃	#1771	1	1	yes	characteristic
352	C₂×C₁₃	#1850	1	2	yes	—
353	C₂×C₁₃	#1916	1	2	yes	—
354	C₂×C₁₃	#1923	1	2	yes	—
355	C₂×C₁₃	#1939	1	2	yes	—
356	C₂⁴	C₂×C₄×D₁₃	1	1	yes	characteristic
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	13	2	no	—
362	C₂²×C₄	—	13	4	no	—
363	C₂²×C₄	—	13	2	no	—
364	C₂²×C₄	—	13	4	no	—
365	C₂²×C₄	—	26	1	no	—
366	C₂²×C₄	—	26	2	no	—
367	C₂²×C₄	—	26	1	no	—
368	C₂²×C₄	—	26	2	no	—
369	C₂²×C₄	—	26	1	no	—
370	C₂²×C₄	—	26	2	no	—
371	C₂²×C₄	—	26	2	no	—
372	C₂²×C₄	—	26	2	no	—
373	C₂²×C₄	—	26	2	no	—
374	C₂²×C₄	—	26	2	no	—
375	C₂²×C₄	—	26	2	no	—
376	C₂²×C₄	—	26	2	no	—
377	C₂²×C₄	—	26	1	no	—
378	C₂²×C₄	C₈×D₁₃	1	4	yes	—
379	C₂²×C₄	#6094	1	4	yes	—
380	C₂²×C₄	#6101	1	4	yes	—
381	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
382	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
386	C₂²×C₄	#6127	1	1	yes	characteristic
387	C₂²×C₄	#6127	1	1	yes	characteristic
388	C₂²×C₄	#6127	1	1	yes	characteristic
389	C₂²×C₄	#6127	1	1	yes	characteristic
390	C₂²×C₄	#6127	1	1	yes	characteristic
391	C₂²×C₄	#6127	1	1	yes	characteristic
392	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
393	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	26	2	no	—
408	C₂×C₈	—	26	2	no	—
409	C₂×C₈	—	26	2	no	—
410	C₂×C₈	—	26	2	no	—
411	C₂×C₈	—	26	2	no	—
412	C₂×C₈	—	26	2	no	—
413	C₂×C₈	—	52	1	no	—
414	C₂×C₈	—	52	1	no	—
415	C₂×C₈	—	52	1	no	—
416	C₂×C₈	—	52	1	no	—
417	C₂×C₈	—	52	1	no	—
418	C₂×C₈	—	52	1	no	—
419	C₂×C₈	—	52	1	no	—
420	C₂×C₈	—	52	1	no	—
421	C₂×C₈	#6101	1	4	yes	—
422	C₂×C₈	#6103	1	4	yes	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	26	2	no	—
428	C₄²	—	26	2	no	—
429	C₄²	—	26	2	no	—
430	C₄²	—	26	2	no	—
431	C₄²	—	52	1	no	—
432	C₄²	—	52	1	no	—
433	C₄²	—	52	1	no	—
434	C₄²	—	52	1	no	—
435	C₁₃	#10876	1	1	yes	characteristic, complemented, Sylow
436	C₂³	C₄×Dic₂₆	1	1	yes	characteristic
437	C₂³	C₄²×D₁₃	1	1	yes	characteristic
438	C₂³	#88126	1	1	yes	characteristic
439	C₂³	C₄×D₅₂	1	1	yes	characteristic
440	C₂³	C₂×C₈×D₁₃	1	2	yes	—
441	C₂³	C₂×#6094	1	2	yes	—
442	C₂³	#88155	1	2	yes	—
443	C₂³	#88155	1	2	yes	—
444	C₂³	C₂×#6101	1	1	yes	characteristic
445	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
446	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	13	4	no	—
454	C₂×C₄	—	26	4	no	—
455	C₂×C₄	—	26	2	no	—
456	C₂×C₄	—	26	4	no	—
457	C₂×C₄	—	26	2	no	—
458	C₂×C₄	—	26	4	no	—
459	C₂×C₄	—	26	2	no	—
460	C₂×C₄	—	26	4	no	—
461	C₂×C₄	—	26	4	no	—
462	C₂×C₄	—	26	2	no	—
463	C₂×C₄	—	26	2	no	—
464	C₂×C₄	—	52	2	no	—
465	C₂×C₄	—	52	2	no	—
466	C₂×C₄	—	52	2	no	—
467	C₂×C₄	—	52	2	no	—
468	C₂×C₄	—	52	2	no	—
469	C₂×C₄	—	52	2	no	—
470	C₂×C₄	#88054	1	8	yes	complemented
471	C₂×C₄	C₄×Dic₂₆	1	1	yes	characteristic
472	C₂×C₄	C₄×Dic₂₆	1	1	yes	characteristic
473	C₂×C₄	C₄×Dic₂₆	1	1	yes	characteristic
474	C₂×C₄	#88123	1	1	yes	characteristic
475	C₂×C₄	#88124	1	1	yes	characteristic
476	C₂×C₄	#88124	1	1	yes	characteristic
477	C₂×C₄	#88126	1	1	yes	characteristic
478	C₂×C₄	#88126	1	1	yes	characteristic
479	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
480	C₂×C₄	#88129	1	1	yes	characteristic
481	C₂×C₄	#88130	1	1	yes	characteristic
482	C₂×C₄	#88130	1	1	yes	characteristic
483	C₂×C₄	C₂×#6101	1	1	yes	characteristic
484	C₂×C₄	#88178	1	1	yes	characteristic
485	C₂×C₄	#88178	1	1	yes	characteristic
486	C₂×C₄	#88178	1	1	yes	characteristic
487	C₂×C₄	#88178	1	1	yes	characteristic
488	C₂×C₄	C₂×#6103	1	1	yes	characteristic
489	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
490	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
491	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
492	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
493	C₂×C₄	#88183	1	1	yes	characteristic
494	C₂×C₄	#88183	1	1	yes	characteristic
495	C₂×C₄	#88183	1	1	yes	characteristic
496	C₂×C₄	#88184	1	1	yes	characteristic
497	C₂×C₄	#88184	1	1	yes	characteristic
498	C₂×C₄	#88207	1	1	yes	characteristic
499	C₈	—	2	4	no	—
500	C₈	—	2	4	no	—
501	C₈	—	52	2	no	—
502	C₈	—	52	2	no	—
503	C₂²	C₈×Dic₂₆	1	2	yes	—
504	C₂²	#11718340	1	2	yes	—
505	C₂²	C₄×C₈×D₁₃	1	1	yes	characteristic
506	C₂²	#11718346	1	2	yes	—
507	C₂²	C₈×D₅₂	1	2	yes	—
508	C₂²	C₄×#6094	1	1	yes	characteristic
509	C₂²	#11718349	1	2	yes	—
510	C₂²	#11718350	1	1	yes	characteristic
511	C₂²	#11718350	1	1	yes	characteristic
512	C₂²	#11718351	1	2	yes	—
513	C₂²	#11718589	1	1	yes	characteristic
514	C₂²	C₄×#6101	1	1	yes	characteristic
515	C₂²	C₄×#6101	1	1	yes	characteristic
516	C₂²	#11718594	1	1	yes	characteristic
517	C₂²	C₄×#6103	1	1	yes	characteristic
518	C₂²	#11718601	1	1	yes	characteristic
519	C₂²	C₂×#88054	1	2	yes	—
520	C₂²	#11718763	1	2	yes	—
521	C₂²	C₈×C₂²⋊D₁₃	1	2	yes	—
522	C₂²	C₈×C₂²⋊D₁₃	1	2	yes	—
523	C₂²	#11718772	1	2	yes	—
524	C₂²	#11718772	1	2	yes	—
525	C₂²	#11718871	1	1	yes	characteristic
526	C₄	—	2	8	no	—
527	C₄	—	26	4	no	—
528	C₄	—	52	4	no	—
529	C₄	—	52	2	no	—
530	C₄	#11718589	1	1	yes	characteristic
531	C₄	#11718590	1	1	yes	characteristic
532	C₄	#11718594	1	1	yes	characteristic
533	C₄	#11718594	1	1	yes	characteristic
534	C₄	#11718594	1	1	yes	characteristic
535	C₄	#11718601	1	1	yes	characteristic
536	C₄	#11718871	1	1	yes	characteristic
537	C₄	#11718874	1	1	yes	characteristic
538	C₂	#13113069	1	1	yes	characteristic
539	C₂	C₈×#6103	1	1	yes	characteristic
540	C₂	#13114619	1	1	yes	characteristic
541	C₂	C₄×#88054	1	1	yes	characteristic
542	C₂	#13114694	1	1	yes	characteristic
543	C₂	C₈×#6101	1	1	yes	characteristic
544	C₂	#13114710	1	1	yes	characteristic
545	C₂	#13115014	1	2	yes	—
546	C₂	#13115393	1	2	yes	—
547	C₂	#13115442	1	2	yes	—
548	C₂	#13115554	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂×C₄×C₈
Fitting	C₂²×C₄×C₈×C₁₃	C₂
socle, prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂²×C₄×C₈	D₁₃
hypocenter	C₁₃	#10876
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄×C₈

Complements

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

N	H ≅ G/N	type
22. C₂×#88054	C₄	semidirect
25. #11718142	C₄	semidirect
80. #88071	C₈	semidirect
186. C₂×C₄×C₁₃	C₄⋊C₈	semidirect
231. C₂×Dic₁₃	C₄×C₈	semidirect
435. C₁₃	#10876	semidirect
470. C₂×C₄	#88054	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#88054	2
C₂×#11718116	2
C₂×#11718142	2
C₄×#88071	2
C₂²×C₄×C₈×C₁₃	2
#10876	13