Subgroups — #28404712

Order 14464.

1058 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299351	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299349	C₂	1	2	yes	maximal, complemented
3	#20299345	C₂	1	2	yes	maximal, complemented
4	#20299344	C₂	1	2	yes	maximal, complemented
5	#20299343	C₂	1	2	yes	maximal, complemented
6	#20299341	C₂	1	1	yes	maximal, characteristic, complemented
7	#20299338	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299337	C₂	1	2	yes	maximal, complemented
9	#20299337	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299336	C₂	1	2	yes	maximal, complemented
11	#20299145	C₂	1	2	yes	maximal, complemented
12	#20299144	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299130	C₂	1	2	yes	maximal, complemented
14	#20299128	C₂	1	2	yes	maximal, complemented
15	#20299126	C₂	1	2	yes	maximal, complemented
16	#20299109	C₂	1	2	yes	maximal, complemented
17	#20299107	C₂	1	2	yes	maximal, complemented
18	#20299105	C₂	1	1	yes	maximal, characteristic, complemented
19	#525×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14268647	C₂²	1	2	yes	—
21	C₂×#14268647	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
23	#16813621	C₂²	1	2	yes	complemented
24	#16813620	C₂²	1	1	yes	characteristic, complemented
25	#16813618	C₂²	1	2	yes	—
26	#16813618	C₂²	1	1	yes	characteristic
27	#16813617	C₂²	1	2	yes	complemented
28	#16813617	C₂²	1	2	yes	complemented
29	#16813615	C₂²	1	2	yes	complemented
30	#16813615	C₂²	1	2	yes	complemented
31	#16813615	C₂²	1	2	yes	complemented
32	#16813615	C₂²	1	2	yes	complemented
33	#16813613	C₂²	1	2	yes	complemented
34	#16813612	C₂²	1	2	yes	complemented
35	#16813612	C₂²	1	2	yes	complemented
36	#16813611	C₂²	1	1	yes	characteristic, complemented
37	#16813609	C₂²	1	2	yes	—
38	#16813609	C₂²	1	1	yes	characteristic
39	#16813608	C₂²	1	2	yes	—
40	#16813608	C₂²	1	2	yes	—
41	#16813608	C₂²	1	2	yes	—
42	#16813608	C₂²	1	2	yes	complemented
43	#16813607	C₂²	1	2	yes	complemented
44	#16813607	C₂²	1	2	yes	complemented
45	#16813606	C₂²	1	2	yes	complemented
46	#16813605	C₂²	1	2	yes	—
47	#16813605	C₂²	1	2	yes	complemented
48	#16813604	C₂²	1	2	yes	—
49	#16813604	C₂²	1	2	yes	complemented
50	#16813604	C₂²	1	2	yes	complemented
51	#16813604	C₂²	1	2	yes	complemented
52	#16813603	C₂²	1	1	yes	characteristic
53	#16813603	C₂²	1	2	yes	complemented
54	#16813603	C₂²	1	1	yes	characteristic, complemented
55	#16813602	C₂²	1	2	yes	complemented
56	#16813601	C₂²	1	2	yes	complemented
57	#16813601	C₂²	1	2	yes	complemented
58	#16813600	C₂²	1	2	yes	complemented
59	#16813600	C₂²	1	2	yes	complemented
60	#16813599	C₂²	1	2	yes	complemented
61	#16813599	C₂²	1	2	yes	complemented
62	#16813598	C₂²	1	2	yes	complemented
63	#16813597	C₂²	1	2	yes	complemented
64	#16813596	C₂²	1	2	yes	—
65	#16813596	C₂²	1	2	yes	—
66	#16813595	C₂²	1	2	yes	—
67	#16813595	C₂²	1	2	yes	—
68	#16813595	C₂²	1	2	yes	complemented
69	#16813595	C₂²	1	2	yes	complemented
70	#16813594	C₂²	1	2	yes	—
71	#16813594	C₂²	1	2	yes	—
72	#16813594	C₂²	1	2	yes	complemented
73	#16813594	C₂²	1	2	yes	complemented
74	#16813593	C₂²	1	2	yes	—
75	#16813593	C₂²	1	2	yes	—
76	#16813593	C₂²	1	2	yes	complemented
77	#16813592	C₂²	1	2	yes	complemented
78	#16813591	C₂²	1	2	yes	—
79	#16813591	C₂²	1	2	yes	complemented
80	#16813590	C₂²	1	2	yes	—
81	#16813590	C₂²	1	1	yes	characteristic
82	#16813590	C₂²	1	1	yes	characteristic, complemented
83	C₄×Dic₂₂₆	C₂²	1	2	yes	complemented
84	C₄×D₄₅₂	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
86	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
87	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
88	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
89	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
90	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
91	#16813581	C₂²	1	1	yes	characteristic, complemented
92	#16813581	C₂²	1	2	yes	complemented
93	#16813579	C₂²	1	2	yes	complemented
94	C₂×C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
95	C₄²×D₁₁₃	C₂²	1	2	yes	complemented
96	C₂×#41×C₁₁₃	C₂²	1	1	yes	characteristic
97	C₂³×C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
98	#123×C₁₁₃	C₂²	1	1	yes	characteristic
99	#123×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
100	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
101	#121×C₁₁₃	C₂²	1	2	yes	—
102	#120×C₁₁₃	C₂²	1	1	yes	characteristic
103	#120×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
104	C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
105	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
106	#117×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
108	#14268647	—	4	4	no	—
109	#14268647	—	4	2	no	—
110	C₂×Dic₂₂₆	C₂³	1	2	yes	—
111	C₂×Dic₂₂₆	C₂³	1	2	yes	—
112	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
113	C₂×D₄₅₂	C₂³	1	2	yes	—
114	C₂×D₄₅₂	C₂³	1	2	yes	—
115	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
116	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
122	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
125	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
126	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
127	C₂×C₄×D₁₁₃	—	4	2	no	—
128	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
129	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
130	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
131	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
132	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
133	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
134	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
135	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
136	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
137	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
138	#14268626	C₂³	1	2	yes	—
139	#14268626	C₂³	1	2	yes	—
140	#14268626	C₂³	1	2	yes	—
141	#14268626	C₂³	1	2	yes	—
142	#14268626	C₂³	1	2	yes	—
143	#14268626	C₂³	1	2	yes	—
144	#14268626	C₂³	1	2	yes	—
145	#14268626	C₂³	1	2	yes	—
146	#14268626	C₂³	1	2	yes	—
147	#14268626	C₂³	1	2	yes	—
148	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
149	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
150	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
151	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
152	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
153	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
154	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
155	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
156	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
157	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
158	#14268624	C₂³	1	2	yes	—
159	#14268624	C₂³	1	2	yes	—
160	#14268624	C₂³	1	2	yes	—
161	#14268624	C₂³	1	2	yes	—
162	#14268624	C₂³	1	2	yes	—
163	#14268624	C₂³	1	2	yes	—
164	#14268624	C₂³	1	2	yes	—
165	#14268624	C₂³	1	2	yes	—
166	#14268624	C₂³	1	2	yes	—
167	#14268624	C₂³	1	2	yes	—
168	C₄×Dic₁₁₃	C₂³	1	2	yes	—
169	C₄×Dic₁₁₃	C₂³	1	2	yes	—
170	C₄×Dic₁₁₃	C₂³	1	2	yes	—
171	C₄×Dic₁₁₃	C₂³	1	2	yes	—
172	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
173	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
174	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
175	#41×C₁₁₃	—	4	2	no	—
176	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
177	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
178	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
179	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
180	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
181	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
182	C₂²×C₄×C₁₁₃	—	4	2	no	—
183	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
184	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
185	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
186	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
187	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
188	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
189	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
190	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
191	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
194	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
198	C₄²×C₁₁₃	C₂³	1	2	yes	—
199	C₂³×C₁₁₃	—	4	1	no	—
200	C₂³×C₁₁₃	—	4	2	no	—
201	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
202	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
203	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
204	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
205	C₂²×D₁₁₃	—	4	1	no	—
206	C₂²×D₁₁₃	—	4	2	no	—
207	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
208	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
209	Q₈×C₁₁₃	—	4	1	no	—
210	D₄×C₁₁₃	—	4	2	no	—
211	D₄×C₁₁₃	—	4	2	no	—
212	D₄×C₁₁₃	—	4	1	no	—
213	D₄×C₁₁₃	—	4	1	no	—
214	D₄×C₁₁₃	—	4	1	no	—
215	C₂×C₄×C₁₁₃	—	2	2	no	—
216	C₂×C₄×C₁₁₃	—	2	4	no	—
217	C₂×C₄×C₁₁₃	—	2	2	no	—
218	C₂×C₄×C₁₁₃	—	2	2	no	—
219	C₂×C₄×C₁₁₃	—	4	1	no	—
220	C₂×C₄×C₁₁₃	—	4	2	no	—
221	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
222	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
223	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
224	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
225	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
226	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
227	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
228	C₂²⋊D₁₁₃	—	4	2	no	—
229	C₂²⋊D₁₁₃	—	4	2	no	—
230	C₂²⋊D₁₁₃	—	4	2	no	—
231	C₂²⋊D₁₁₃	—	4	2	no	—
232	C₂²⋊D₁₁₃	—	4	2	no	—
233	C₂²⋊D₁₁₃	—	4	2	no	—
234	C₂²⋊D₁₁₃	—	4	2	no	—
235	C₂²⋊D₁₁₃	—	4	2	no	—
236	C₂²⋊D₁₁₃	—	4	2	no	—
237	C₂×Dic₁₁₃	—	4	1	no	—
238	C₂×Dic₁₁₃	—	4	2	no	—
239	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
240	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
241	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
242	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
243	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
244	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
245	D₄₅₂	—	4	2	no	—
246	D₄₅₂	—	4	2	no	—
247	D₄₅₂	—	4	1	no	—
248	C₄×D₁₁₃	—	2	4	no	—
249	C₄×D₁₁₃	—	2	4	no	—
250	C₄×D₁₁₃	—	4	2	no	—
251	C₄×D₁₁₃	—	4	2	no	—
252	C₄×D₁₁₃	—	4	2	no	—
253	Dic₂₂₆	—	4	2	no	—
254	Dic₂₂₆	—	4	1	no	—
255	Dic₂₂₆	—	4	2	no	—
256	C₂²×C₁₁₃	—	2	1	no	—
257	C₂²×C₁₁₃	—	2	2	no	—
258	C₂²×C₁₁₃	—	2	1	no	—
259	C₂²×C₁₁₃	—	2	1	no	—
260	C₂²×C₁₁₃	—	2	2	no	—
261	C₂²×C₁₁₃	—	2	2	no	—
262	C₂²×C₁₁₃	—	2	2	no	—
263	C₂²×C₁₁₃	—	2	2	no	—
264	C₂²×C₁₁₃	—	2	2	no	—
265	C₂²×C₁₁₃	—	4	4	no	—
266	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
267	C₂×D₁₁₃	—	2	2	no	—
268	C₂×D₁₁₃	—	2	2	no	—
269	C₂×D₁₁₃	—	2	2	no	—
270	C₂×D₁₁₃	—	2	2	no	—
271	C₂×D₁₁₃	—	2	2	no	—
272	C₂×D₁₁₃	—	2	2	no	—
273	C₂×D₁₁₃	—	4	4	no	—
274	C₄×C₁₁₃	—	2	2	no	—
275	C₄×C₁₁₃	—	2	1	no	—
276	C₄×C₁₁₃	—	2	1	no	—
277	C₄×C₁₁₃	—	2	1	no	—
278	C₄×C₁₁₃	—	2	2	no	—
279	C₄×C₁₁₃	—	2	2	no	—
280	C₄×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
281	Dic₁₁₃	—	2	2	no	—
282	Dic₁₁₃	—	2	2	no	—
283	Dic₁₁₃	—	2	2	no	—
284	Dic₁₁₃	—	2	2	no	—
285	Dic₁₁₃	—	2	2	no	—
286	Dic₁₁₃	—	2	2	no	—
287	C₂×C₁₁₃	—	4	1	no	—
288	C₂×C₁₁₃	—	4	1	no	—
289	C₂×C₁₁₃	—	4	2	no	—
290	C₂×C₁₁₃	—	4	1	no	—
291	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
292	C₂×C₁₁₃	#585	1	2	yes	—
293	D₁₁₃	—	4	2	no	—
294	D₁₁₃	—	4	2	no	—
295	#3529	—	113	1	no	maximal, Sylow
296	C₁₁₃	#3529	1	1	yes	characteristic, complemented, Sylow
297	#563	—	113	1	no	—
298	#563	—	113	2	no	—
299	#562	—	113	2	no	—
300	#562	—	113	2	no	—
301	#562	—	113	2	no	—
302	H(3,𝔽₄)	—	113	1	no	—
303	#560	—	113	1	no	—
304	#560	—	113	2	no	—
305	#560	—	113	1	no	—
306	#560	—	113	2	no	—
307	#532	—	113	1	no	—
308	#532	—	113	2	no	—
309	#529	—	113	2	no	—
310	#529	—	113	2	no	—
311	#529	—	113	2	no	—
312	#525	—	113	1	no	—
313	#525	—	113	2	no	—
314	#525	—	113	2	no	—
315	#525	D₁₁₃	1	1	yes	characteristic, complemented
316	C₂×#41	—	113	2	no	—
317	C₂×#41	—	113	1	no	—
318	C₂×#41	C₂×D₁₁₃	1	1	yes	characteristic
319	C₂³×C₄	—	113	1	no	—
320	C₂³×C₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
321	C₄⋊Q₈	—	113	1	no	—
322	C₄⋊Q₈	—	113	2	no	—
323	#127	—	113	1	no	—
324	#127	—	113	2	no	—
325	#126	—	113	2	no	—
326	#126	—	113	2	no	—
327	#126	—	113	2	no	—
328	#126	—	113	2	no	—
329	#126	—	113	2	no	—
330	#126	—	113	2	no	—
331	#125	—	113	2	no	—
332	#125	—	113	2	no	—
333	#125	—	113	2	no	—
334	#124	—	113	1	no	—
335	#124	—	113	2	no	—
336	#124	—	113	1	no	—
337	#124	—	113	2	no	—
338	#124	—	113	2	no	—
339	#124	—	113	2	no	—
340	#124	—	113	2	no	—
341	#123	—	113	1	no	—
342	#123	—	113	1	no	—
343	#123	—	113	2	no	—
344	#123	—	113	2	no	—
345	#123	—	113	2	no	—
346	#123	—	113	2	no	—
347	#123	—	113	2	no	—
348	#123	—	113	2	no	—
349	#123	—	113	2	no	—
350	#123	—	113	2	no	—
351	#123	—	113	2	no	—
352	#123	—	113	2	no	—
353	#123	C₂×D₁₁₃	1	1	yes	characteristic
354	#123	C₂×D₁₁₃	1	1	yes	characteristic, complemented
355	C₂²⋊Q₈	—	113	2	no	—
356	C₂²⋊Q₈	—	113	2	no	—
357	C₂²⋊Q₈	—	113	2	no	—
358	C₂²⋊Q₈	—	113	2	no	—
359	C₂²⋊Q₈	—	113	2	no	—
360	C₂²⋊Q₈	—	113	2	no	—
361	C₂²⋊Q₈	—	113	2	no	—
362	C₂²⋊Q₈	—	113	2	no	—
363	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	complemented
364	#121	—	113	2	no	—
365	#121	—	113	2	no	—
366	#121	—	113	2	no	—
367	#121	—	113	2	no	—
368	#121	—	113	2	no	—
369	#121	—	113	2	no	—
370	#121	—	113	2	no	—
371	#121	—	113	2	no	—
372	#121	—	113	2	no	—
373	#121	—	113	2	no	—
374	#121	—	113	2	no	—
375	#121	—	113	2	no	—
376	#121	—	113	2	no	—
377	#121	—	113	2	no	—
378	#121	C₂×D₁₁₃	1	2	yes	—
379	#120	—	113	2	no	—
380	#120	—	113	2	no	—
381	#120	—	113	1	no	—
382	#120	—	113	2	no	—
383	#120	—	113	1	no	—
384	#120	—	113	2	no	—
385	#120	C₂×D₁₁₃	1	1	yes	characteristic
386	#120	C₂×D₁₁₃	1	1	yes	characteristic, complemented
387	C₄×Q₈	—	113	2	no	—
388	C₄×D₄	—	113	2	no	—
389	C₄×D₄	—	113	2	no	—
390	C₄×D₄	—	113	2	no	—
391	C₄×D₄	—	113	2	no	—
392	C₄×D₄	—	113	2	no	—
393	C₄×D₄	—	113	2	no	—
394	C₄×D₄	—	113	2	no	—
395	C₄×D₄	C₂×D₁₁₃	1	2	yes	—
396	C₄×D₄	C₂×D₁₁₃	1	2	yes	complemented
397	#117	—	113	1	no	—
398	#117	—	113	2	no	—
399	#117	—	113	2	no	—
400	#117	C₂×D₁₁₃	1	1	yes	characteristic, complemented
401	C₂×C₄²	—	113	1	no	—
402	C₂×C₄²	—	113	2	no	—
403	C₂⁴	—	113	1	no	—
404	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
405	#41	—	4	2	no	—
406	#41	—	452	4	no	—
407	#41	—	452	2	no	—
408	C₂×Q₈	—	113	2	no	—
409	C₂×Q₈	—	113	2	no	—
410	C₂×Q₈	—	113	1	no	—
411	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
412	C₂×D₄	—	113	2	no	—
413	C₂×D₄	—	113	2	no	—
414	C₂×D₄	—	113	2	no	—
415	C₂×D₄	—	113	2	no	—
416	C₂×D₄	—	113	2	no	—
417	C₂×D₄	—	113	2	no	—
418	C₂×D₄	—	113	2	no	—
419	C₂×D₄	—	113	2	no	—
420	C₂×D₄	—	113	2	no	—
421	C₂×D₄	—	113	2	no	—
422	C₂×D₄	—	113	2	no	—
423	C₂×D₄	—	113	1	no	—
424	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
425	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
426	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
427	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
428	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
429	C₂²×C₄	—	4	2	no	—
430	C₂²×C₄	—	113	2	no	—
431	C₂²×C₄	—	113	1	no	—
432	C₂²×C₄	—	113	2	no	—
433	C₂²×C₄	—	113	2	no	—
434	C₂²×C₄	—	113	2	no	—
435	C₂²×C₄	—	113	2	no	—
436	C₂²×C₄	—	113	2	no	—
437	C₂²×C₄	—	452	2	no	—
438	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
439	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
440	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
441	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
442	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
443	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
444	C₄⋊C₄	—	113	2	no	—
445	C₄⋊C₄	—	113	2	no	—
446	C₄⋊C₄	—	113	2	no	—
447	C₄⋊C₄	—	113	2	no	—
448	C₄⋊C₄	—	113	2	no	—
449	C₄⋊C₄	—	113	2	no	—
450	C₄⋊C₄	—	113	2	no	—
451	C₄⋊C₄	—	113	2	no	—
452	C₄⋊C₄	—	113	2	no	—
453	C₄⋊C₄	—	113	2	no	—
454	C₄⋊C₄	—	113	2	no	—
455	C₄⋊C₄	—	113	2	no	—
456	C₄⋊C₄	—	113	2	no	—
457	C₄⋊C₄	—	113	2	no	—
458	C₄⋊C₄	—	113	2	no	—
459	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
460	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
461	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
462	C₂²⋊C₄	—	113	1	no	—
463	C₂²⋊C₄	—	113	2	no	—
464	C₂²⋊C₄	—	113	1	no	—
465	C₂²⋊C₄	—	113	2	no	—
466	C₂²⋊C₄	—	113	2	no	—
467	C₂²⋊C₄	—	113	2	no	—
468	C₂²⋊C₄	—	113	2	no	—
469	C₂²⋊C₄	—	113	2	no	—
470	C₂²⋊C₄	—	113	2	no	—
471	C₂²⋊C₄	—	113	2	no	—
472	C₂²⋊C₄	—	113	2	no	—
473	C₂²⋊C₄	—	113	2	no	—
474	C₂²⋊C₄	—	113	2	no	—
475	C₂²⋊C₄	—	113	2	no	—
476	C₂²⋊C₄	—	113	2	no	—
477	C₂²⋊C₄	—	113	2	no	—
478	C₂²⋊C₄	—	113	2	no	—
479	C₂²⋊C₄	—	113	2	no	—
480	C₂²⋊C₄	—	113	2	no	—
481	C₂²⋊C₄	—	113	2	no	—
482	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
483	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
484	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
485	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
486	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
487	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
488	C₄²	—	113	1	no	—
489	C₄²	—	113	2	no	—
490	C₄²	—	113	1	no	—
491	C₄²	—	113	2	no	—
492	C₄²	—	113	2	no	—
493	C₄²	—	113	2	no	—
494	C₄²	C₂²×D₁₁₃	1	2	yes	—
495	C₂³	—	4	1	no	—
496	C₂³	—	4	2	no	—
497	C₂³	—	113	2	no	—
498	C₂³	—	113	2	no	—
499	C₂³	—	452	1	no	—
500	C₂³	—	452	2	no	—
501	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
502	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
503	C₂³	C₂³×D₁₁₃	1	2	yes	—
504	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
505	Q₈	—	4	1	no	—
506	Q₈	—	452	2	no	—
507	Q₈	—	452	1	no	—
508	Q₈	—	452	2	no	—
509	D₄	—	4	1	no	—
510	D₄	—	4	1	no	—
511	D₄	—	4	1	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	2	no	—
514	D₄	—	452	2	no	—
515	D₄	—	452	1	no	—
516	D₄	—	452	2	no	—
517	D₄	—	452	2	no	—
518	D₄	—	452	2	no	—
519	D₄	—	452	2	no	—
520	D₄	—	452	2	no	—
521	D₄	—	452	2	no	—
522	D₄	—	452	2	no	—
523	D₄	—	452	2	no	—
524	D₄	—	452	2	no	—
525	D₄	—	452	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	113	2	no	—
533	C₂×C₄	—	113	2	no	—
534	C₂×C₄	—	113	2	no	—
535	C₂×C₄	—	113	2	no	—
536	C₂×C₄	—	113	2	no	—
537	C₂×C₄	—	113	2	no	—
538	C₂×C₄	—	452	2	no	—
539	C₂×C₄	—	452	2	no	—
540	C₂×C₄	—	452	2	no	—
541	C₂×C₄	—	452	1	no	—
542	C₂×C₄	—	452	2	no	—
543	C₂×C₄	—	226	4	no	—
544	C₂×C₄	—	226	4	no	—
545	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
546	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
547	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
548	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
549	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
550	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
551	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
552	C₂²	—	2	1	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	4	4	no	—
562	C₂²	—	452	4	no	—
563	C₂²	—	226	2	no	—
564	C₂²	—	226	2	no	—
565	C₂²	—	226	2	no	—
566	C₂²	—	226	2	no	—
567	C₂²	—	226	2	no	—
568	C₂²	—	226	2	no	—
569	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
570	C₄	—	2	1	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	226	2	no	—
577	C₄	—	226	2	no	—
578	C₄	—	226	2	no	—
579	C₄	—	226	2	no	—
580	C₄	—	226	2	no	—
581	C₄	—	226	2	no	—
582	C₄	#16813667	1	2	yes	—
583	C₂	—	4	1	no	—
584	C₂	—	4	2	no	—
585	C₂	—	4	1	no	—
586	C₂	—	4	1	no	—
587	C₂	—	452	2	no	—
588	C₂	—	452	2	no	—
589	C₂	C₂×#16813667	1	1	yes	characteristic
590	C₂	#20299434	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₁₃
Fitting	#525×C₁₁₃	C₂
hypercenter	#525	D₁₁₃
hypocenter	C₁₁₃	#3529
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
1. #20299351	C₂	semidirect
2. #20299349	C₂	semidirect
3. #20299345	C₂	semidirect
4. #20299344	C₂	semidirect
5. #20299343	C₂	semidirect
6. #20299341	C₂	semidirect
7. #20299338	C₂	semidirect
8. #20299337	C₂	semidirect
9. #20299337	C₂	semidirect
10. #20299336	C₂	semidirect
11. #20299145	C₂	semidirect
12. #20299144	C₂	semidirect
13. #20299130	C₂	semidirect
14. #20299128	C₂	semidirect
15. #20299126	C₂	semidirect
16. #20299109	C₂	semidirect
17. #20299107	C₂	semidirect
18. #20299105	C₂	semidirect
19. #525×C₁₁₃	C₂	semidirect
21. C₂×#14268647	C₂²	semidirect
22. C₂²×C₄×D₁₁₃	C₂²	semidirect
23. #16813621	C₂²	semidirect
24. #16813620	C₂²	semidirect
27. #16813617	C₂²	semidirect
28. #16813617	C₂²	semidirect
29. #16813615	C₂²	semidirect
30. #16813615	C₂²	semidirect
31. #16813615	C₂²	semidirect
32. #16813615	C₂²	semidirect
33. #16813613	C₂²	semidirect
34. #16813612	C₂²	semidirect
35. #16813612	C₂²	semidirect
36. #16813611	C₂²	semidirect
42. #16813608	C₂²	semidirect
43. #16813607	C₂²	semidirect
44. #16813607	C₂²	semidirect
45. #16813606	C₂²	semidirect
47. #16813605	C₂²	semidirect
49. #16813604	C₂²	semidirect
50. #16813604	C₂²	semidirect
51. #16813604	C₂²	semidirect
53. #16813603	C₂²	semidirect
54. #16813603	C₂²	semidirect
55. #16813602	C₂²	semidirect
56. #16813601	C₂²	semidirect
57. #16813601	C₂²	semidirect
58. #16813600	C₂²	semidirect
59. #16813600	C₂²	semidirect
60. #16813599	C₂²	semidirect
61. #16813599	C₂²	semidirect
62. #16813598	C₂²	semidirect
63. #16813597	C₂²	semidirect
68. #16813595	C₂²	semidirect
69. #16813595	C₂²	semidirect
72. #16813594	C₂²	semidirect
73. #16813594	C₂²	semidirect
76. #16813593	C₂²	semidirect
77. #16813592	C₂²	semidirect
79. #16813591	C₂²	semidirect
82. #16813590	C₂²	semidirect
83. C₄×Dic₂₂₆	C₂²	semidirect
84. C₄×D₄₅₂	C₂²	semidirect
87. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
88. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
89. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
90. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
91. #16813581	C₂²	semidirect
92. #16813581	C₂²	semidirect
93. #16813579	C₂²	semidirect
94. C₂×C₄×Dic₁₁₃	C₂²	semidirect
95. C₄²×D₁₁₃	C₂²	semidirect
97. C₂³×C₄×C₁₁₃	C₂²	semidirect
99. #123×C₁₁₃	C₂²	semidirect
100. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
103. #120×C₁₁₃	C₂²	semidirect
105. C₄×D₄×C₁₁₃	C₂²	semidirect
106. #117×C₁₁₃	C₂²	semidirect
296. C₁₁₃	#3529	semidirect
315. #525	D₁₁₃	semidirect
320. C₂³×C₄	C₂×D₁₁₃	semidirect
354. #123	C₂×D₁₁₃	semidirect
363. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
386. #120	C₂×D₁₁₃	semidirect
396. C₄×D₄	C₂×D₁₁₃	semidirect
400. #117	C₂×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299351	2
#20299349	2
#20299345	2
#20299344	2
#20299343	2
#20299341	2
#20299338	2
#20299337	2
#20299336	2
#20299145	2
#20299144	2
#20299130	2
#20299128	2
#20299126	2
#20299109	2
#20299107	2
#20299105	2
#525×C₁₁₃	2
#3529	113