Subgroups — #28404312

Order 14464.

1142 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299314	C₂	1	2	yes	maximal, complemented
2	#20299301	C₂	1	2	yes	maximal, complemented
3	#20299301	C₂	1	2	yes	maximal, complemented
4	#20299275	C₂	1	4	yes	maximal, complemented
5	#20299251	C₂	1	2	yes	maximal, complemented
6	#20299239	C₂	1	4	yes	maximal, complemented
7	#20299222	C₂	1	2	yes	maximal, complemented
8	#20299204	C₂	1	2	yes	maximal, complemented
9	#20299167	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299149	C₂	1	2	yes	maximal, complemented
11	#20299133	C₂	1	2	yes	maximal, complemented
12	#20299110	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#16813597	C₂	1	1	yes	maximal, characteristic, complemented
14	#20299079	C₂	1	1	yes	maximal, characteristic, complemented
15	#20299072	C₂	1	1	yes	maximal, characteristic, complemented
16	#117×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#544×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14268648	C₂²	1	4	yes	complemented
19	C₂×#14268647	C₂²	1	1	yes	characteristic
20	C₂²×D₄₅₂	C₂²	1	1	yes	characteristic
21	C₂²×D₄₅₂	C₂²	1	2	yes	—
22	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
23	#16813619	C₂²	1	2	yes	complemented
24	#16813617	C₂²	1	4	yes	complemented
25	#16813617	C₂²	1	4	yes	complemented
26	#16813611	C₂²	1	4	yes	complemented
27	#16813611	C₂²	1	4	yes	complemented
28	#16813610	C₂²	1	2	yes	complemented
29	#16813607	C₂²	1	4	yes	complemented
30	#16813607	C₂²	1	4	yes	complemented
31	#16813607	C₂²	1	4	yes	complemented
32	#16813607	C₂²	1	4	yes	complemented
33	#16813606	C₂²	1	2	yes	—
34	#16813602	C₂²	1	1	yes	characteristic, complemented
35	#16813602	C₂²	1	1	yes	characteristic, complemented
36	#16813598	C₂²	1	4	yes	complemented
37	#16813597	C₂²	1	2	yes	—
38	#16813597	C₂²	1	2	yes	—
39	#16813597	C₂²	1	2	yes	—
40	#16813597	C₂²	1	2	yes	—
41	#16813597	C₂²	1	2	yes	complemented
42	#16813597	C₂²	1	4	yes	complemented
43	#16813597	C₂²	1	4	yes	complemented
44	#16813597	C₂²	1	2	yes	complemented
45	#16813597	C₂²	1	4	yes	complemented
46	#16813597	C₂²	1	1	yes	characteristic, complemented
47	#16813597	C₂²	1	1	yes	characteristic, complemented
48	#16813592	C₂²	1	4	yes	—
49	#16813592	C₂²	1	2	yes	—
50	#16813587	C₂²	1	2	yes	complemented
51	C₄×D₄₅₂	C₂²	1	2	yes	complemented
52	C₄×D₄₅₂	C₂²	1	2	yes	complemented
53	C₄×D₄₅₂	C₂²	1	2	yes	complemented
54	C₄×D₄₅₂	C₂²	1	2	yes	complemented
55	#16813584	C₂²	1	4	yes	complemented
56	#16813584	C₂²	1	4	yes	complemented
57	#16813584	C₂²	1	2	yes	complemented
58	#16813584	C₂²	1	2	yes	complemented
59	#16813584	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	—
61	#16813581	C₂²	1	1	yes	characteristic
62	#16813580	C₂²	1	4	yes	complemented
63	#16813580	C₂²	1	1	yes	characteristic, complemented
64	#16813580	C₂²	1	2	yes	complemented
65	#16813580	C₂²	1	1	yes	characteristic, complemented
66	#16813579	C₂²	1	2	yes	complemented
67	#16813578	C₂²	1	2	yes	—
68	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
69	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
70	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
71	C₂×#14268624	C₂²	1	2	yes	—
72	C₂²⋊C₄×D₁₁₃	C₂²	1	4	yes	—
73	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	—
74	C₄²×D₁₁₃	C₂²	1	2	yes	complemented
75	C₄⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
76	C₄⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
77	#125×C₁₁₃	C₂²	1	2	yes	complemented
78	#125×C₁₁₃	C₂²	1	2	yes	complemented
79	C₂²⋊Q₈×C₁₁₃	C₂²	1	4	yes	—
80	#117×C₁₁₃	C₂²	1	1	yes	characteristic
81	#117×C₁₁₃	C₂²	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
83	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
84	C₂³×D₁₁₃	C₂³	1	2	yes	—
85	#14268648	—	4	8	no	—
86	#14268647	—	2	4	no	—
87	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
88	C₂×D₄₅₂	—	2	4	no	—
89	C₂×D₄₅₂	—	4	4	no	—
90	C₂×D₄₅₂	C₂³	1	2	yes	—
91	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
92	C₂×D₄₅₂	C₂³	1	4	yes	—
93	C₂×D₄₅₂	C₂³	1	2	yes	—
94	C₂×D₄₅₂	C₂³	1	2	yes	—
95	C₂×D₄₅₂	C₂³	1	4	yes	—
96	C₂×D₄₅₂	C₂³	1	2	yes	—
97	C₂×D₄₅₂	C₂³	1	4	yes	—
98	C₂×D₄₅₂	C₂³	1	4	yes	—
99	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
100	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₁₁₃	—	2	4	no	—
102	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
103	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
104	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
106	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
109	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
110	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
111	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
112	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
113	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
114	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
115	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
116	#14268626	C₂³	1	2	yes	—
117	#14268626	C₂³	1	2	yes	—
118	#14268626	C₂³	1	4	yes	—
119	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
120	#14268624	C₂³	1	2	yes	—
121	#14268624	C₂³	1	2	yes	—
122	#14268624	C₂³	1	4	yes	—
123	#14268624	C₂³	1	4	yes	—
124	#14268624	C₂³	1	4	yes	—
125	#14268624	C₂³	1	4	yes	—
126	#14268624	C₂³	1	4	yes	—
127	#14268624	C₂³	1	4	yes	—
128	#14268624	C₂³	1	2	yes	—
129	#14268624	C₂³	1	2	yes	—
130	#14268624	C₂³	1	4	yes	—
131	#14268624	C₂³	1	2	yes	—
132	#14268624	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	4	yes	—
137	C₂×Q₈×C₁₁₃	C₂³	1	4	yes	—
138	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
139	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
140	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
141	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
142	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
143	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
144	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
145	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
146	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
147	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
148	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
149	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
150	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
151	C₄²×C₁₁₃	C₂³	1	2	yes	—
152	C₄²×C₁₁₃	C₂³	1	2	yes	—
153	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
154	C₂²×D₁₁₃	—	2	2	no	—
155	C₂²×D₁₁₃	—	2	4	no	—
156	C₂²×D₁₁₃	—	2	2	no	—
157	C₂²×D₁₁₃	—	4	1	no	—
158	C₂²×D₁₁₃	—	4	2	no	—
159	C₂²×D₁₁₃	—	4	2	no	—
160	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
161	C₂²×D₁₁₃	C₂⁴	1	4	yes	—
162	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
163	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
164	Q₈×C₁₁₃	—	4	4	no	—
165	C₂×C₄×C₁₁₃	—	4	2	no	—
166	C₂×C₄×C₁₁₃	#41	1	4	yes	complemented
167	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
168	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
169	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
170	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
171	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
172	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
174	C₂²⋊D₁₁₃	—	2	4	no	—
175	C₂×Dic₁₁₃	—	2	2	no	—
176	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
177	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
178	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
179	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
180	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
181	D₄₅₂	—	2	8	no	—
182	D₄₅₂	—	2	4	no	—
183	D₄₅₂	—	2	4	no	—
184	D₄₅₂	—	2	4	no	—
185	D₄₅₂	—	2	2	no	—
186	D₄₅₂	—	4	4	no	—
187	D₄₅₂	—	4	2	no	—
188	D₄₅₂	—	4	4	no	—
189	D₄₅₂	—	4	4	no	—
190	C₄×D₁₁₃	—	2	4	no	—
191	C₄×D₁₁₃	—	2	2	no	—
192	C₄×D₁₁₃	—	2	2	no	—
193	C₄×D₁₁₃	—	2	2	no	—
194	C₄×D₁₁₃	—	2	2	no	—
195	C₄×D₁₁₃	—	2	4	no	—
196	C₄×D₁₁₃	—	4	4	no	—
197	C₄×D₁₁₃	—	4	2	no	—
198	C₄×D₁₁₃	—	4	4	no	—
199	C₄×D₁₁₃	—	4	4	no	—
200	Dic₂₂₆	—	2	2	no	—
201	C₂²×C₁₁₃	—	2	1	no	—
202	C₂²×C₁₁₃	—	2	1	no	—
203	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
204	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
205	C₂×D₁₁₃	—	2	1	no	—
206	C₂×D₁₁₃	—	2	1	no	—
207	C₂×D₁₁₃	—	2	1	no	—
208	C₂×D₁₁₃	—	2	2	no	—
209	C₂×D₁₁₃	—	2	4	no	—
210	C₂×D₁₁₃	—	2	2	no	—
211	C₂×D₁₁₃	—	2	4	no	—
212	C₂×D₁₁₃	—	2	1	no	—
213	C₂×D₁₁₃	—	2	4	no	—
214	C₂×D₁₁₃	—	2	2	no	—
215	C₂×D₁₁₃	—	2	1	no	—
216	C₂×D₁₁₃	—	4	4	no	—
217	C₂×D₁₁₃	—	8	4	no	—
218	C₂×D₁₁₃	H(5,𝔽₂)	1	2	yes	—
219	C₄×C₁₁₃	—	2	2	no	—
220	C₄×C₁₁₃	—	2	2	no	—
221	C₄×C₁₁₃	—	2	4	no	—
222	C₄×C₁₁₃	—	2	2	no	—
223	C₄×C₁₁₃	—	2	2	no	—
224	C₄×C₁₁₃	C₂×#41	1	2	yes	—
225	C₄×C₁₁₃	C₂×#41	1	2	yes	—
226	Dic₁₁₃	—	2	2	no	—
227	Dic₁₁₃	—	2	1	no	—
228	Dic₁₁₃	—	2	1	no	—
229	Dic₁₁₃	—	2	2	no	—
230	Dic₁₁₃	—	2	2	no	—
231	C₂×C₁₁₃	—	2	2	no	—
232	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
233	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×C₁₁₃	#585	1	1	yes	characteristic
235	D₁₁₃	—	2	2	no	—
236	D₁₁₃	—	4	2	no	—
237	D₁₁₃	—	4	1	no	—
238	D₁₁₃	—	4	4	no	—
239	#3494	—	113	1	no	maximal, Sylow
240	C₁₁₃	#3494	1	1	yes	characteristic, complemented, Sylow
241	#555	—	113	2	no	—
242	#553	—	113	2	no	—
243	#553	—	113	2	no	—
244	#551	—	113	4	no	—
245	#547	—	113	2	no	—
246	#546	—	113	4	no	—
247	#544	D₁₁₃	1	1	yes	characteristic, complemented
248	#542	—	113	2	no	—
249	#540	—	113	2	no	—
250	#535	—	113	1	no	—
251	#532	—	113	2	no	—
252	#529	—	113	2	no	—
253	#525	—	113	1	no	—
254	C₂×#121	—	113	1	no	—
255	#520	—	113	1	no	—
256	#518	—	113	1	no	—
257	C₂×#117	—	113	1	no	—
258	C₂×#41	—	113	4	no	—
259	C₂×#41	—	113	1	no	—
260	C₂²×D₄	—	113	2	no	—
261	C₂²×D₄	—	113	1	no	—
262	C₂³×C₄	—	113	1	no	—
263	C₄⋊Q₈	C₂×D₁₁₃	1	2	yes	complemented
264	C₄⋊Q₈	C₂×D₁₁₃	1	2	yes	complemented
265	#127	—	113	2	no	—
266	#126	—	113	4	no	—
267	#126	—	113	4	no	—
268	#125	C₂×D₁₁₃	1	2	yes	complemented
269	#125	C₂×D₁₁₃	1	2	yes	complemented
270	#124	—	113	4	no	—
271	#124	—	113	4	no	—
272	#124	—	113	2	no	—
273	#123	—	113	4	no	—
274	#123	—	113	4	no	—
275	#123	—	113	4	no	—
276	#123	—	113	4	no	—
277	#123	—	113	2	no	—
278	C₂²⋊Q₈	—	113	4	no	—
279	C₂²⋊Q₈	—	113	1	no	—
280	C₂²⋊Q₈	—	113	1	no	—
281	C₂²⋊Q₈	C₂×D₁₁₃	1	4	yes	—
282	#121	—	113	2	no	—
283	#121	—	113	2	no	—
284	#121	—	113	2	no	—
285	#121	—	113	2	no	—
286	#121	—	113	1	no	—
287	#121	—	113	1	no	—
288	#121	—	113	4	no	—
289	#121	—	113	2	no	—
290	#121	—	113	2	no	—
291	#121	—	113	4	no	—
292	#121	—	113	4	no	—
293	#120	—	113	2	no	—
294	#120	—	113	4	no	—
295	C₄×Q₈	—	113	2	no	—
296	C₄×D₄	—	113	4	no	—
297	C₄×D₄	—	113	2	no	—
298	C₄×D₄	—	113	2	no	—
299	C₄×D₄	—	113	2	no	—
300	C₄×D₄	—	113	4	no	—
301	C₄×D₄	—	113	4	no	—
302	C₄×D₄	—	113	2	no	—
303	C₄×D₄	—	113	2	no	—
304	C₄×D₄	—	113	2	no	—
305	C₄×D₄	—	113	2	no	—
306	#117	—	113	1	no	—
307	#117	—	113	1	no	—
308	#117	—	113	1	no	—
309	#117	—	113	2	no	—
310	#117	—	113	4	no	—
311	#117	—	113	2	no	—
312	#117	—	113	2	no	—
313	#117	C₂×D₁₁₃	1	1	yes	characteristic
314	#117	C₂×D₁₁₃	1	1	yes	characteristic
315	C₂×C₄⋊C₄	—	113	1	no	—
316	C₂×C₄⋊C₄	—	113	1	no	—
317	C₂×C₄⋊C₄	—	113	2	no	—
318	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
319	C₂×C₂²⋊C₄	—	113	2	no	—
320	C₂×C₂²⋊C₄	—	113	2	no	—
321	C₂×C₂²⋊C₄	—	113	4	no	—
322	C₂×C₄²	—	113	2	no	—
323	C₂⁴	—	113	2	no	—
324	C₂⁴	—	113	1	no	—
325	#41	—	452	8	no	—
326	#41	—	226	4	no	—
327	C₂×Q₈	—	113	1	no	—
328	C₂×Q₈	C₂²×D₁₁₃	1	4	yes	—
329	C₂×D₄	—	113	2	no	—
330	C₂×D₄	—	113	2	no	—
331	C₂×D₄	—	113	4	no	—
332	C₂×D₄	—	113	4	no	—
333	C₂×D₄	—	113	4	no	—
334	C₂×D₄	—	113	2	no	—
335	C₂×D₄	—	113	2	no	—
336	C₂×D₄	—	113	1	no	—
337	C₂×D₄	—	113	2	no	—
338	C₂×D₄	—	113	4	no	—
339	C₂×D₄	—	452	4	no	—
340	C₂×D₄	—	226	4	no	—
341	C₂²×C₄	—	113	1	no	—
342	C₂²×C₄	—	113	2	no	—
343	C₂²×C₄	—	113	4	no	—
344	C₂²×C₄	—	113	4	no	—
345	C₂²×C₄	—	113	4	no	—
346	C₂²×C₄	—	113	1	no	—
347	C₂²×C₄	—	113	2	no	—
348	C₂²×C₄	—	113	1	no	—
349	C₂²×C₄	—	113	2	no	—
350	C₂²×C₄	—	113	1	no	—
351	C₂²×C₄	—	113	1	no	—
352	C₂²×C₄	—	226	4	no	—
353	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
354	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
355	C₄⋊C₄	—	113	1	no	—
356	C₄⋊C₄	—	113	1	no	—
357	C₄⋊C₄	—	113	2	no	—
358	C₄⋊C₄	—	113	2	no	—
359	C₄⋊C₄	—	113	4	no	—
360	C₄⋊C₄	—	113	2	no	—
361	C₄⋊C₄	—	113	2	no	—
362	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
363	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
364	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
365	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
366	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
367	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
368	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
369	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
370	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
371	C₂²⋊C₄	—	113	2	no	—
372	C₂²⋊C₄	—	113	2	no	—
373	C₂²⋊C₄	—	113	2	no	—
374	C₂²⋊C₄	—	113	4	no	—
375	C₂²⋊C₄	—	113	4	no	—
376	C₂²⋊C₄	—	113	4	no	—
377	C₂²⋊C₄	—	113	4	no	—
378	C₂²⋊C₄	—	113	4	no	—
379	C₂²⋊C₄	—	113	4	no	—
380	C₂²⋊C₄	—	113	2	no	—
381	C₂²⋊C₄	—	113	2	no	—
382	C₂²⋊C₄	—	113	4	no	—
383	C₂²⋊C₄	—	113	2	no	—
384	C₂²⋊C₄	—	113	2	no	—
385	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
386	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
387	C₄²	—	113	2	no	—
388	C₄²	—	113	2	no	—
389	C₄²	—	113	2	no	—
390	C₄²	—	113	4	no	—
391	C₄²	C₂²×D₁₁₃	1	2	yes	—
392	C₄²	C₂²×D₁₁₃	1	2	yes	—
393	C₂³	—	113	1	no	—
394	C₂³	—	113	1	no	—
395	C₂³	—	113	4	no	—
396	C₂³	—	113	2	no	—
397	C₂³	—	452	2	no	—
398	C₂³	—	452	2	no	—
399	C₂³	—	452	1	no	—
400	C₂³	—	226	2	no	—
401	C₂³	—	226	4	no	—
402	C₂³	—	226	2	no	—
403	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
404	Q₈	—	4	4	no	—
405	Q₈	—	226	2	no	—
406	D₄	—	452	4	no	—
407	D₄	—	452	4	no	—
408	D₄	—	452	2	no	—
409	D₄	—	452	4	no	—
410	D₄	—	226	8	no	—
411	D₄	—	226	4	no	—
412	D₄	—	226	4	no	—
413	D₄	—	226	4	no	—
414	D₄	—	226	4	no	—
415	D₄	—	226	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	113	1	no	—
418	C₂×C₄	—	113	2	no	—
419	C₂×C₄	—	113	2	no	—
420	C₂×C₄	—	113	2	no	—
421	C₂×C₄	—	113	1	no	—
422	C₂×C₄	—	452	4	no	—
423	C₂×C₄	—	452	4	no	—
424	C₂×C₄	—	452	4	no	—
425	C₂×C₄	—	452	2	no	—
426	C₂×C₄	—	226	4	no	—
427	C₂×C₄	—	226	2	no	—
428	C₂×C₄	—	226	2	no	—
429	C₂×C₄	—	226	2	no	—
430	C₂×C₄	—	226	2	no	—
431	C₂×C₄	—	226	2	no	—
432	C₂×C₄	—	226	4	no	—
433	C₂×C₄	#14268648	1	4	yes	complemented
434	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
435	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
436	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
437	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
438	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
439	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
440	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	113	2	no	—
444	C₂²	—	904	4	no	—
445	C₂²	—	452	4	no	—
446	C₂²	—	226	1	no	—
447	C₂²	—	226	2	no	—
448	C₂²	—	226	4	no	—
449	C₂²	—	226	2	no	—
450	C₂²	—	226	4	no	—
451	C₂²	—	226	1	no	—
452	C₂²	—	226	4	no	—
453	C₂²	—	226	2	no	—
454	C₂²	—	226	1	no	—
455	C₂²	—	226	1	no	—
456	C₂²	—	226	1	no	—
457	C₂²	C₂×#14268648	1	2	yes	—
458	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
459	C₄	—	2	4	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	226	1	no	—
465	C₄	—	226	1	no	—
466	C₄	—	226	2	no	—
467	C₄	—	226	2	no	—
468	C₄	—	226	2	no	—
469	C₄	C₂×#14268648	1	2	yes	—
470	C₄	C₂×#14268648	1	2	yes	—
471	C₂	—	2	2	no	—
472	C₂	—	452	4	no	—
473	C₂	—	452	1	no	—
474	C₂	—	452	2	no	—
475	C₂	—	226	2	no	—
476	C₂	C₂²×#14268648	1	1	yes	characteristic
477	C₂	H(5,𝔽₂)×D₁₁₃	1	1	yes	characteristic
478	C₂	#20299435	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#544×C₁₁₃	C₂
hypercenter	#544	D₁₁₃
hypocenter	C₁₁₃	#3494
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #544

Complements

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

N	H ≅ G/N	type
1. #20299314	C₂	semidirect
2. #20299301	C₂	semidirect
3. #20299301	C₂	semidirect
4. #20299275	C₂	semidirect
5. #20299251	C₂	semidirect
6. #20299239	C₂	semidirect
7. #20299222	C₂	semidirect
8. #20299204	C₂	semidirect
9. #20299167	C₂	semidirect
10. #20299149	C₂	semidirect
11. #20299133	C₂	semidirect
12. #20299110	C₂	semidirect
13. C₂×#16813597	C₂	semidirect
14. #20299079	C₂	semidirect
15. #20299072	C₂	semidirect
16. #117×D₁₁₃	C₂	semidirect
17. #544×C₁₁₃	C₂	semidirect
18. C₂×#14268648	C₂²	semidirect
23. #16813619	C₂²	semidirect
24. #16813617	C₂²	semidirect
25. #16813617	C₂²	semidirect
26. #16813611	C₂²	semidirect
27. #16813611	C₂²	semidirect
28. #16813610	C₂²	semidirect
29. #16813607	C₂²	semidirect
30. #16813607	C₂²	semidirect
31. #16813607	C₂²	semidirect
32. #16813607	C₂²	semidirect
34. #16813602	C₂²	semidirect
35. #16813602	C₂²	semidirect
36. #16813598	C₂²	semidirect
41. #16813597	C₂²	semidirect
42. #16813597	C₂²	semidirect
43. #16813597	C₂²	semidirect
44. #16813597	C₂²	semidirect
45. #16813597	C₂²	semidirect
46. #16813597	C₂²	semidirect
47. #16813597	C₂²	semidirect
50. #16813587	C₂²	semidirect
51. C₄×D₄₅₂	C₂²	semidirect
52. C₄×D₄₅₂	C₂²	semidirect
53. C₄×D₄₅₂	C₂²	semidirect
54. C₄×D₄₅₂	C₂²	semidirect
55. #16813584	C₂²	semidirect
56. #16813584	C₂²	semidirect
57. #16813584	C₂²	semidirect
58. #16813584	C₂²	semidirect
59. #16813584	C₂²	semidirect
62. #16813580	C₂²	semidirect
63. #16813580	C₂²	semidirect
64. #16813580	C₂²	semidirect
65. #16813580	C₂²	semidirect
66. #16813579	C₂²	semidirect
68. C₄⋊C₄×D₁₁₃	C₂²	semidirect
69. C₄⋊C₄×D₁₁₃	C₂²	semidirect
70. C₄⋊C₄×D₁₁₃	C₂²	semidirect
74. C₄²×D₁₁₃	C₂²	semidirect
75. C₄⋊Q₈×C₁₁₃	C₂²	semidirect
76. C₄⋊Q₈×C₁₁₃	C₂²	semidirect
77. #125×C₁₁₃	C₂²	semidirect
78. #125×C₁₁₃	C₂²	semidirect
166. C₂×C₄×C₁₁₃	#41	semidirect
240. C₁₁₃	#3494	semidirect
247. #544	D₁₁₃	semidirect
263. C₄⋊Q₈	C₂×D₁₁₃	semidirect
264. C₄⋊Q₈	C₂×D₁₁₃	semidirect
268. #125	C₂×D₁₁₃	semidirect
269. #125	C₂×D₁₁₃	semidirect
433. C₂×C₄	#14268648	semidirect

Maximal subgroups

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

subgroup	index
#20299314	2
#20299301	2
#20299275	2
#20299251	2
#20299239	2
#20299222	2
#20299204	2
#20299167	2
#20299149	2
#20299133	2
#20299110	2
C₂×#16813597	2
#20299079	2
#20299072	2
#117×D₁₁₃	2
#544×C₁₁₃	2
#3494	113