Subgroups — #28404546

Order 14464.

1014 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299325	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299304	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299303	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299301	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299296	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299286	C₂	1	1	yes	maximal, characteristic, complemented
7	#20299283	C₂	1	2	yes	maximal, complemented
8	#20299283	C₂	1	1	yes	maximal, characteristic, complemented
9	#20299280	C₂	1	2	yes	maximal, complemented
10	#20299280	C₂	1	2	yes	maximal, complemented
11	#20299249	C₂	1	2	yes	maximal, complemented
12	#20299249	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299207	C₂	1	2	yes	maximal, complemented
14	#20299196	C₂	1	2	yes	maximal, complemented
15	#20299195	C₂	1	2	yes	maximal, complemented
16	#20299154	C₂	1	1	yes	maximal, characteristic, complemented
17	#20299133	C₂	1	1	yes	maximal, characteristic, complemented
18	#20299133	C₂	1	1	yes	maximal, characteristic, complemented
19	#20299132	C₂	1	1	yes	maximal, characteristic, complemented
20	#125×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#20299079	C₂	1	2	yes	maximal, complemented
22	C₄×#14268647	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#125×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14268647	C₂²	1	1	yes	characteristic
25	C₂×#14268647	C₂²	1	2	yes	—
26	#16813621	C₂²	1	1	yes	characteristic
27	#16813621	C₂²	1	1	yes	characteristic
28	#16813621	C₂²	1	2	yes	—
29	#16813617	C₂²	1	2	yes	—
30	#16813617	C₂²	1	2	yes	—
31	#16813617	C₂²	1	2	yes	—
32	#16813617	C₂²	1	2	yes	—
33	#16813617	C₂²	1	2	yes	—
34	#16813617	C₂²	1	2	yes	—
35	#16813616	C₂²	1	2	yes	—
36	#16813614	C₂²	1	1	yes	characteristic
37	#16813613	C₂²	1	2	yes	—
38	#16813613	C₂²	1	1	yes	characteristic
39	#16813613	C₂²	1	1	yes	characteristic
40	#16813612	C₂²	1	2	yes	—
41	#16813612	C₂²	1	2	yes	—
42	#16813612	C₂²	1	2	yes	—
43	#16813612	C₂²	1	2	yes	—
44	#16813612	C₂²	1	2	yes	—
45	#16813612	C₂²	1	2	yes	—
46	#16813610	C₂²	1	1	yes	characteristic
47	#16813607	C₂²	1	2	yes	—
48	#16813607	C₂²	1	2	yes	—
49	#16813607	C₂²	1	2	yes	—
50	#16813607	C₂²	1	2	yes	—
51	#16813607	C₂²	1	2	yes	—
52	#16813607	C₂²	1	2	yes	—
53	#16813605	C₂²	1	2	yes	—
54	#16813605	C₂²	1	2	yes	—
55	#16813605	C₂²	1	2	yes	—
56	#16813602	C₂²	1	1	yes	characteristic
57	#16813602	C₂²	1	2	yes	—
58	#16813602	C₂²	1	1	yes	characteristic
59	#16813601	C₂²	1	1	yes	characteristic
60	#16813601	C₂²	1	2	yes	—
61	#16813600	C₂²	1	2	yes	—
62	#16813600	C₂²	1	2	yes	—
63	#16813600	C₂²	1	2	yes	—
64	#16813600	C₂²	1	2	yes	—
65	#16813600	C₂²	1	2	yes	—
66	#16813600	C₂²	1	2	yes	—
67	#16813597	C₂²	1	1	yes	characteristic
68	#16813597	C₂²	1	1	yes	characteristic
69	#16813597	C₂²	1	2	yes	—
70	#16813596	C₂²	1	1	yes	characteristic
71	#16813596	C₂²	1	2	yes	—
72	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
73	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
74	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
75	#16813587	C₂²	1	2	yes	—
76	#16813587	C₂²	1	2	yes	—
77	#16813587	C₂²	1	1	yes	characteristic
78	#16813587	C₂²	1	1	yes	characteristic
79	#16813587	C₂²	1	2	yes	—
80	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
81	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
82	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
83	#16813584	C₂²	1	2	yes	—
84	#16813584	C₂²	1	2	yes	—
85	#16813584	C₂²	1	1	yes	characteristic
86	#16813584	C₂²	1	1	yes	characteristic
87	#16813584	C₂²	1	2	yes	—
88	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
90	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
91	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
92	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
93	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
94	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
95	#16813581	C₂²	1	1	yes	characteristic
96	#16813581	C₂²	1	2	yes	—
97	#16813580	C₂²	1	2	yes	—
98	#16813580	C₂²	1	2	yes	—
99	#16813580	C₂²	1	1	yes	characteristic
100	#16813580	C₂²	1	1	yes	characteristic
101	#16813580	C₂²	1	2	yes	—
102	#16813579	C₂²	1	1	yes	characteristic
103	#16813579	C₂²	1	1	yes	characteristic
104	#16813579	C₂²	1	2	yes	—
105	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
106	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
107	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
108	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
109	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
110	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
111	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
112	#125×C₁₁₃	C₂²	1	2	yes	—
113	#125×C₁₁₃	C₂²	1	1	yes	characteristic
114	#125×C₁₁₃	C₂²	1	1	yes	characteristic
115	#125×C₁₁₃	C₂²	1	1	yes	characteristic
116	#125×C₁₁₃	C₂²	1	1	yes	characteristic
117	#125×C₁₁₃	C₂²	1	2	yes	—
118	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
120	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
122	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
123	#14268647	—	2	4	no	—
124	#14268647	—	2	8	no	—
125	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
126	C₂×Dic₂₂₆	C₂³	1	2	yes	—
127	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
128	C₂×Dic₂₂₆	C₂³	1	2	yes	—
129	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
130	C₂×D₄₅₂	C₂³	1	2	yes	—
131	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
132	C₂×D₄₅₂	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
141	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
142	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
145	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
146	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
147	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
148	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
149	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
150	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
151	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
152	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
153	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
155	#14268626	C₂³	1	1	yes	characteristic
156	#14268626	C₂³	1	2	yes	—
157	#14268626	C₂³	1	2	yes	—
158	#14268626	C₂³	1	2	yes	—
159	#14268626	C₂³	1	2	yes	—
160	#14268626	C₂³	1	2	yes	—
161	#14268626	C₂³	1	2	yes	—
162	#14268626	C₂³	1	2	yes	—
163	#14268626	C₂³	1	1	yes	characteristic
164	#14268626	C₂³	1	1	yes	characteristic
165	#14268626	C₂³	1	1	yes	characteristic
166	#14268626	C₂³	1	2	yes	—
167	#14268626	C₂³	1	2	yes	—
168	#14268626	C₂³	1	2	yes	—
169	#14268626	C₂³	1	2	yes	—
170	#14268626	C₂³	1	2	yes	—
171	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
174	#14268624	C₂³	1	1	yes	characteristic
175	#14268624	C₂³	1	2	yes	—
176	#14268624	C₂³	1	1	yes	characteristic
177	#14268624	C₂³	1	1	yes	characteristic
178	#14268624	C₂³	1	1	yes	characteristic
179	#14268624	C₂³	1	2	yes	—
180	#14268624	C₂³	1	2	yes	—
181	#14268624	C₂³	1	2	yes	—
182	#14268624	C₂³	1	2	yes	—
183	#14268624	C₂³	1	2	yes	—
184	#14268624	C₂³	1	2	yes	—
185	#14268624	C₂³	1	2	yes	—
186	#14268624	C₂³	1	2	yes	—
187	#14268624	C₂³	1	2	yes	—
188	#14268624	C₂³	1	2	yes	—
189	#14268624	C₂³	1	2	yes	—
190	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
191	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
192	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
193	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
194	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
195	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
196	C₄×Dic₁₁₃	C₂³	1	2	yes	—
197	C₄×Dic₁₁₃	C₂³	1	2	yes	—
198	C₄×Dic₁₁₃	C₂³	1	2	yes	—
199	C₄×Dic₁₁₃	C₂³	1	2	yes	—
200	C₄×Dic₁₁₃	C₂³	1	2	yes	—
201	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
202	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
203	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
204	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
205	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
206	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
207	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
208	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
209	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
210	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
215	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
217	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
218	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
219	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
220	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
221	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
222	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
223	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
224	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
225	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
226	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
227	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
228	C₂×C₄×C₁₁₃	—	2	2	no	—
229	C₂×C₄×C₁₁₃	—	2	4	no	—
230	C₂×C₄×C₁₁₃	—	2	2	no	—
231	C₂×C₄×C₁₁₃	—	4	2	no	—
232	C₂×C₄×C₁₁₃	—	4	1	no	—
233	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
234	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
235	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
239	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
240	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
241	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
242	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
243	C₂²⋊D₁₁₃	—	2	2	no	—
244	C₂²⋊D₁₁₃	—	2	4	no	—
245	C₂²⋊D₁₁₃	#41	1	4	yes	—
246	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
249	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
253	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
254	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
255	D₄₅₂	—	2	4	no	—
256	D₄₅₂	—	2	2	no	—
257	D₄₅₂	—	2	2	no	—
258	D₄₅₂	—	4	2	no	—
259	C₄×D₁₁₃	—	2	2	no	—
260	C₄×D₁₁₃	—	2	4	no	—
261	C₄×D₁₁₃	—	2	2	no	—
262	C₄×D₁₁₃	—	2	2	no	—
263	C₄×D₁₁₃	—	2	2	no	—
264	C₄×D₁₁₃	—	2	4	no	—
265	C₄×D₁₁₃	—	4	1	no	—
266	C₄×D₁₁₃	—	4	2	no	—
267	C₄×D₁₁₃	—	4	2	no	—
268	C₄×D₁₁₃	—	4	2	no	—
269	C₄×D₁₁₃	—	4	1	no	—
270	Dic₂₂₆	—	2	2	no	—
271	Dic₂₂₆	—	2	4	no	—
272	Dic₂₂₆	—	2	2	no	—
273	Dic₂₂₆	—	4	2	no	—
274	C₂²×C₁₁₃	—	2	1	no	—
275	C₂²×C₁₁₃	—	2	1	no	—
276	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
277	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
278	C₂×D₁₁₃	—	2	1	no	—
279	C₂×D₁₁₃	—	2	1	no	—
280	C₂×D₁₁₃	—	2	1	no	—
281	C₂×D₁₁₃	—	2	2	no	—
282	C₂×D₁₁₃	—	2	1	no	—
283	C₂×D₁₁₃	—	2	2	no	—
284	C₂×D₁₁₃	—	2	2	no	—
285	C₂×D₁₁₃	—	2	1	no	—
286	C₂×D₁₁₃	C₂×#41	1	2	yes	—
287	C₄×C₁₁₃	—	2	1	no	—
288	C₄×C₁₁₃	—	2	2	no	—
289	C₄×C₁₁₃	—	2	1	no	—
290	C₄×C₁₁₃	—	2	2	no	—
291	C₄×C₁₁₃	—	2	1	no	—
292	C₄×C₁₁₃	—	2	2	no	—
293	C₄×C₁₁₃	—	2	1	no	—
294	C₄×C₁₁₃	—	2	1	no	—
295	C₄×C₁₁₃	—	2	2	no	—
296	C₄×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
297	Dic₁₁₃	—	2	2	no	—
298	Dic₁₁₃	—	2	1	no	—
299	Dic₁₁₃	—	2	2	no	—
300	Dic₁₁₃	—	2	1	no	—
301	Dic₁₁₃	—	2	1	no	—
302	Dic₁₁₃	—	2	1	no	—
303	Dic₁₁₃	—	2	2	no	—
304	Dic₁₁₃	—	2	1	no	—
305	Dic₁₁₃	C₂×#41	1	2	yes	—
306	C₂×C₁₁₃	—	2	2	no	—
307	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
308	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
309	C₂×C₁₁₃	#585	1	1	yes	characteristic
310	D₁₁₃	—	2	2	no	—
311	D₁₁₃	—	4	1	no	—
312	D₁₁₃	—	4	2	no	—
313	#3515	—	113	1	no	maximal, Sylow
314	C₁₁₃	#3515	1	1	yes	characteristic, complemented, Sylow
315	#557	—	113	1	no	—
316	#554	—	113	1	no	—
317	#554	—	113	1	no	—
318	#553	—	113	1	no	—
319	#553	—	113	1	no	—
320	#552	—	113	2	no	—
321	#552	—	113	2	no	—
322	#552	—	113	1	no	—
323	#552	—	113	2	no	—
324	#552	—	113	1	no	—
325	#547	—	113	1	no	—
326	#547	—	113	2	no	—
327	#541	—	113	2	no	—
328	#539	—	113	2	no	—
329	#539	—	113	2	no	—
330	#533	—	113	1	no	—
331	#529	—	113	1	no	—
332	#529	—	113	1	no	—
333	#529	—	113	1	no	—
334	C₂×#125	—	113	1	no	—
335	C₂×#125	D₁₁₃	1	1	yes	characteristic, complemented
336	#520	—	113	2	no	—
337	C₄×#41	—	113	1	no	—
338	C₂×#41	—	113	1	no	—
339	C₂×#41	—	113	2	no	—
340	C₄⋊Q₈	—	113	1	no	—
341	C₄⋊Q₈	—	113	1	no	—
342	C₄⋊Q₈	—	113	2	no	—
343	#126	—	113	2	no	—
344	#126	—	113	2	no	—
345	#126	—	113	2	no	—
346	#126	—	113	2	no	—
347	#126	—	113	2	no	—
348	#126	—	113	2	no	—
349	#126	—	113	2	no	—
350	#125	—	113	2	no	—
351	#125	—	113	2	no	—
352	#125	—	113	1	no	—
353	#125	—	113	1	no	—
354	#125	—	113	2	no	—
355	#125	—	113	2	no	—
356	#125	—	113	2	no	—
357	#125	—	113	2	no	—
358	#125	—	113	2	no	—
359	#125	—	113	1	no	—
360	#125	C₂×D₁₁₃	1	1	yes	characteristic
361	#125	C₂×D₁₁₃	1	1	yes	characteristic
362	#125	C₂×D₁₁₃	1	2	yes	—
363	#125	C₂×D₁₁₃	1	2	yes	—
364	#125	C₂×D₁₁₃	1	1	yes	characteristic
365	#125	C₂×D₁₁₃	1	1	yes	characteristic
366	#124	—	113	1	no	—
367	#123	—	113	2	no	—
368	#123	—	113	2	no	—
369	#123	—	113	2	no	—
370	#123	—	113	2	no	—
371	#123	—	113	2	no	—
372	#123	—	113	2	no	—
373	#123	—	113	2	no	—
374	#123	—	113	2	no	—
375	#123	—	113	2	no	—
376	C₂²⋊Q₈	—	113	1	no	—
377	C₂²⋊Q₈	—	113	2	no	—
378	C₂²⋊Q₈	—	113	1	no	—
379	C₂²⋊Q₈	—	113	1	no	—
380	C₂²⋊Q₈	—	113	2	no	—
381	C₂²⋊Q₈	—	113	2	no	—
382	C₂²⋊Q₈	—	113	2	no	—
383	C₂²⋊Q₈	—	113	2	no	—
384	C₂²⋊Q₈	—	113	2	no	—
385	C₂²⋊Q₈	—	113	2	no	—
386	C₂²⋊Q₈	—	113	2	no	—
387	#121	—	113	1	no	—
388	#121	—	113	2	no	—
389	#121	—	113	1	no	—
390	#121	—	113	1	no	—
391	#121	—	113	2	no	—
392	C₄×Q₈	—	113	2	no	—
393	C₄×Q₈	—	113	2	no	—
394	C₄×Q₈	—	113	1	no	—
395	C₄×Q₈	—	113	1	no	—
396	C₄×Q₈	—	113	2	no	—
397	C₄×Q₈	—	113	1	no	—
398	C₄×Q₈	—	113	1	no	—
399	C₄×Q₈	—	113	1	no	—
400	C₄×D₄	—	113	1	no	—
401	C₄×D₄	—	113	1	no	—
402	C₄×D₄	—	113	1	no	—
403	C₄×D₄	—	113	1	no	—
404	C₄×D₄	—	113	2	no	—
405	C₄×D₄	—	113	2	no	—
406	C₄×D₄	—	113	2	no	—
407	C₄×D₄	—	113	2	no	—
408	C₄×D₄	—	113	2	no	—
409	C₄×D₄	—	113	2	no	—
410	C₄×D₄	—	113	1	no	—
411	C₄×D₄	—	113	1	no	—
412	C₄×D₄	—	113	1	no	—
413	C₄×D₄	—	113	1	no	—
414	C₄×D₄	—	113	1	no	—
415	#117	—	113	1	no	—
416	#117	—	113	2	no	—
417	#117	—	113	2	no	—
418	#117	—	113	2	no	—
419	#117	—	113	2	no	—
420	#117	—	113	1	no	—
421	#117	—	113	1	no	—
422	#117	—	113	1	no	—
423	#117	—	113	1	no	—
424	#117	—	113	2	no	—
425	C₂×C₄⋊C₄	—	113	2	no	—
426	C₂×C₄⋊C₄	—	113	2	no	—
427	C₂×C₄⋊C₄	—	113	1	no	—
428	C₂×C₄⋊C₄	—	113	2	no	—
429	C₂×C₄⋊C₄	—	113	1	no	—
430	C₂×C₄⋊C₄	C₂×D₁₁₃	1	2	yes	—
431	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂×D₁₁₃	1	2	yes	—
433	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
434	C₂×C₄²	—	113	1	no	—
435	C₂×C₄²	—	113	1	no	—
436	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic
437	#41	—	226	4	no	—
438	#41	—	226	8	no	—
439	C₂×Q₈	—	113	2	no	—
440	C₂×Q₈	—	113	1	no	—
441	C₂×Q₈	—	113	2	no	—
442	C₂×Q₈	—	113	1	no	—
443	C₂×D₄	—	113	1	no	—
444	C₂×D₄	—	113	1	no	—
445	C₂×D₄	—	113	2	no	—
446	C₂×D₄	—	113	2	no	—
447	C₂×D₄	—	113	1	no	—
448	C₂×D₄	—	113	2	no	—
449	C₂×D₄	—	113	1	no	—
450	C₂²×C₄	—	113	1	no	—
451	C₂²×C₄	—	113	1	no	—
452	C₂²×C₄	—	113	2	no	—
453	C₂²×C₄	—	113	2	no	—
454	C₂²×C₄	—	113	2	no	—
455	C₂²×C₄	—	113	1	no	—
456	C₂²×C₄	—	113	1	no	—
457	C₂²×C₄	—	113	1	no	—
458	C₂²×C₄	—	113	1	no	—
459	C₂²×C₄	—	113	2	no	—
460	C₂²×C₄	—	113	2	no	—
461	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
462	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
463	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
464	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
465	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
466	C₄⋊C₄	—	113	1	no	—
467	C₄⋊C₄	—	113	2	no	—
468	C₄⋊C₄	—	113	1	no	—
469	C₄⋊C₄	—	113	1	no	—
470	C₄⋊C₄	—	113	2	no	—
471	C₄⋊C₄	—	113	2	no	—
472	C₄⋊C₄	—	113	2	no	—
473	C₄⋊C₄	—	113	2	no	—
474	C₄⋊C₄	—	113	2	no	—
475	C₄⋊C₄	—	113	2	no	—
476	C₄⋊C₄	—	113	2	no	—
477	C₄⋊C₄	—	113	2	no	—
478	C₄⋊C₄	—	113	2	no	—
479	C₄⋊C₄	—	113	1	no	—
480	C₄⋊C₄	—	113	1	no	—
481	C₄⋊C₄	—	113	1	no	—
482	C₄⋊C₄	—	113	1	no	—
483	C₄⋊C₄	—	113	1	no	—
484	C₄⋊C₄	—	113	2	no	—
485	C₄⋊C₄	—	113	2	no	—
486	C₄⋊C₄	—	113	2	no	—
487	C₄⋊C₄	—	113	2	no	—
488	C₄⋊C₄	—	113	2	no	—
489	C₄⋊C₄	—	113	2	no	—
490	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
491	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
492	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
493	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
494	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
495	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
496	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
498	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
499	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
500	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
501	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
502	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
503	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
504	C₂²⋊C₄	—	113	1	no	—
505	C₂²⋊C₄	—	113	2	no	—
506	C₂²⋊C₄	—	113	1	no	—
507	C₂²⋊C₄	—	113	1	no	—
508	C₂²⋊C₄	—	113	2	no	—
509	C₂²⋊C₄	—	113	2	no	—
510	C₂²⋊C₄	—	113	2	no	—
511	C₂²⋊C₄	—	113	1	no	—
512	C₂²⋊C₄	—	113	1	no	—
513	C₂²⋊C₄	—	113	1	no	—
514	C₂²⋊C₄	—	113	2	no	—
515	C₂²⋊C₄	—	113	2	no	—
516	C₂²⋊C₄	—	113	2	no	—
517	C₂²⋊C₄	—	113	2	no	—
518	C₂²⋊C₄	—	113	2	no	—
519	C₂²⋊C₄	—	113	2	no	—
520	C₂²⋊C₄	—	113	2	no	—
521	C₂²⋊C₄	—	113	2	no	—
522	C₂²⋊C₄	—	113	2	no	—
523	C₄²	—	113	1	no	—
524	C₄²	—	113	1	no	—
525	C₄²	—	113	1	no	—
526	C₄²	—	113	1	no	—
527	C₄²	—	113	1	no	—
528	C₄²	—	113	1	no	—
529	C₄²	—	113	2	no	—
530	C₄²	—	113	2	no	—
531	C₄²	—	113	2	no	—
532	C₄²	—	113	2	no	—
533	C₄²	—	113	2	no	—
534	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
535	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
536	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
537	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
538	C₂³	—	113	1	no	—
539	C₂³	—	113	1	no	—
540	C₂³	—	113	2	no	—
541	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
542	Q₈	—	452	2	no	—
543	Q₈	—	226	4	no	—
544	Q₈	—	226	2	no	—
545	Q₈	—	226	2	no	—
546	D₄	—	113	4	no	—
547	D₄	—	452	2	no	—
548	D₄	—	226	4	no	—
549	D₄	—	226	2	no	—
550	D₄	—	226	2	no	—
551	D₄	—	226	4	no	—
552	D₄	—	226	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	113	1	no	—
559	C₂×C₄	—	113	1	no	—
560	C₂×C₄	—	113	1	no	—
561	C₂×C₄	—	113	2	no	—
562	C₂×C₄	—	113	1	no	—
563	C₂×C₄	—	113	1	no	—
564	C₂×C₄	—	113	1	no	—
565	C₂×C₄	—	113	2	no	—
566	C₂×C₄	—	113	2	no	—
567	C₂×C₄	—	452	1	no	—
568	C₂×C₄	—	452	2	no	—
569	C₂×C₄	—	452	1	no	—
570	C₂×C₄	—	452	2	no	—
571	C₂×C₄	—	452	2	no	—
572	C₂×C₄	—	226	2	no	—
573	C₂×C₄	—	226	4	no	—
574	C₂×C₄	—	226	2	no	—
575	C₂×C₄	—	226	4	no	—
576	C₂×C₄	—	226	2	no	—
577	C₂×C₄	—	226	2	no	—
578	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
579	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
580	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
581	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
582	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
583	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
584	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
587	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	113	2	no	—
591	C₂²	—	226	1	no	—
592	C₂²	—	226	2	no	—
593	C₂²	—	226	1	no	—
594	C₂²	—	226	2	no	—
595	C₂²	—	226	2	no	—
596	C₂²	—	226	1	no	—
597	C₂²	—	226	1	no	—
598	C₂²	—	226	1	no	—
599	C₂²	#41×D₁₁₃	1	2	yes	—
600	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
601	C₄	—	2	1	no	—
602	C₄	—	2	2	no	—
603	C₄	—	2	2	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	1	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	2	no	—
610	C₄	—	113	2	no	—
611	C₄	—	226	1	no	—
612	C₄	—	226	2	no	—
613	C₄	—	226	1	no	—
614	C₄	—	226	1	no	—
615	C₄	—	226	2	no	—
616	C₄	—	226	1	no	—
617	C₄	—	226	2	no	—
618	C₄	—	226	1	no	—
619	C₄	#16813670	1	2	yes	—
620	C₂	—	2	2	no	—
621	C₂	—	452	1	no	—
622	C₂	—	452	2	no	—
623	C₂	—	226	2	no	—
624	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
625	C₂	C₂×#16813670	1	1	yes	characteristic
626	C₂	#20299434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	C₂×#125×C₁₁₃	C₂
hypercenter	C₂×#125	D₁₁₃
hypocenter	C₁₁₃	#3515
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×#125

Complements

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

N	H ≅ G/N	type
1. #20299325	C₂	semidirect
2. #20299304	C₂	semidirect
3. #20299303	C₂	semidirect
4. #20299301	C₂	semidirect
5. #20299296	C₂	semidirect
6. #20299286	C₂	semidirect
7. #20299283	C₂	semidirect
8. #20299283	C₂	semidirect
9. #20299280	C₂	semidirect
10. #20299280	C₂	semidirect
11. #20299249	C₂	semidirect
12. #20299249	C₂	semidirect
13. #20299207	C₂	semidirect
14. #20299196	C₂	semidirect
15. #20299195	C₂	semidirect
16. #20299154	C₂	semidirect
17. #20299133	C₂	semidirect
18. #20299133	C₂	semidirect
19. #20299132	C₂	semidirect
20. #125×D₁₁₃	C₂	semidirect
21. #20299079	C₂	semidirect
22. C₄×#14268647	C₂	semidirect
23. C₂×#125×C₁₁₃	C₂	semidirect
314. C₁₁₃	#3515	semidirect
335. C₂×#125	D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299325	2
#20299304	2
#20299303	2
#20299301	2
#20299296	2
#20299286	2
#20299283	2
#20299280	2
#20299249	2
#20299207	2
#20299196	2
#20299195	2
#20299154	2
#20299133	2
#20299132	2
#125×D₁₁₃	2
#20299079	2
C₄×#14268647	2
C₂×#125×C₁₁₃	2
#3515	113