Subgroups — #19148256

Order 5504.

1658 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063371	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#10621898	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583570	C₂	1	2	yes	maximal, complemented
4	#14583558	C₂	1	2	yes	maximal, complemented
5	#14583545	C₂	1	2	yes	maximal, complemented
6	#14583541	C₂	1	4	yes	maximal, complemented
7	D₄×D₁₇₂	C₂	1	2	yes	maximal, complemented
8	#14583531	C₂	1	4	yes	maximal, complemented
9	#14583479	C₂	1	2	yes	maximal, complemented
10	#14583477	C₂	1	1	yes	maximal, characteristic, complemented
11	#14583468	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583465	C₂	1	2	yes	maximal, complemented
13	#14583412	C₂	1	2	yes	maximal, complemented
14	C₂×#13063299	C₂	1	1	yes	maximal, characteristic, complemented
15	#121×D₄₃	C₂	1	2	yes	maximal, complemented
16	#14583379	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
18	#13063371	—	2	8	no	—
19	C₂×#10621902	C₂²	1	2	yes	complemented
20	C₂×#10621898	—	2	8	no	—
21	C₂×#10621898	C₂²	1	1	yes	characteristic
22	C₂×#10621898	C₂²	1	2	yes	complemented
23	C₂×#10621898	C₂²	1	1	yes	characteristic, complemented
24	C₂×#10621898	C₂²	1	2	yes	complemented
25	C₂×#10621898	C₂²	1	1	yes	characteristic, complemented
26	C₂×#10621898	C₂²	1	2	yes	complemented
27	C₂×#10621898	C₂²	1	1	yes	characteristic, complemented
28	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
29	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
30	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
31	C₂²×D₁₇₂	C₂²	1	2	yes	complemented
32	C₂²×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
33	C₂²×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
34	C₂×D₄×D₄₃	C₂²	1	2	yes	complemented
35	C₂×D₄×D₄₃	C₂²	1	4	yes	complemented
36	C₂×D₄×D₄₃	C₂²	1	4	yes	complemented
37	C₂²×C₄×D₄₃	C₂²	1	2	yes	complemented
38	#13063322	C₂²	1	2	yes	complemented
39	#13063321	C₂²	1	4	yes	complemented
40	#13063313	C₂²	1	2	yes	complemented
41	#13063311	C₂²	1	4	yes	complemented
42	#13063310	C₂²	1	4	yes	complemented
43	#13063304	C₂²	1	2	yes	complemented
44	#13063303	C₂²	1	4	yes	complemented
45	#13063301	C₂²	1	2	yes	complemented
46	#13063300	C₂²	1	2	yes	complemented
47	#13063300	C₂²	1	2	yes	complemented
48	#13063300	C₂²	1	4	yes	complemented
49	#13063299	C₂²	1	2	yes	complemented
50	#13063299	C₂²	1	2	yes	complemented
51	#13063299	C₂²	1	2	yes	complemented
52	#13063299	C₂²	1	2	yes	complemented
53	#13063299	C₂²	1	2	yes	complemented
54	#13063298	C₂²	1	4	yes	complemented
55	#13063298	C₂²	1	4	yes	complemented
56	#13063298	C₂²	1	4	yes	complemented
57	#13063297	C₂²	1	4	yes	complemented
58	#13063297	C₂²	1	4	yes	complemented
59	#13063296	C₂²	1	2	yes	complemented
60	#13063295	C₂²	1	4	yes	complemented
61	#13063295	C₂²	1	4	yes	complemented
62	#13063295	C₂²	1	4	yes	complemented
63	#13063293	C₂²	1	4	yes	complemented
64	C₄×Dic₈₆	C₂²	1	2	yes	complemented
65	C₄×D₁₇₂	C₂²	1	2	yes	complemented
66	#13063287	C₂²	1	4	yes	complemented
67	(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	complemented
68	(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	complemented
69	#13063283	C₂²	1	2	yes	complemented
70	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic, complemented
71	C₄⋊C₄×D₄₃	C₂²	1	2	yes	complemented
72	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	complemented
73	C₂²⋊C₄×D₄₃	C₂²	1	4	yes	complemented
74	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic, complemented
75	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
76	#123×C₄₃	C₂²	1	2	yes	complemented
77	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
78	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
79	#121×C₄₃	C₂²	1	1	yes	characteristic, complemented
80	#121×C₄₃	C₂²	1	1	yes	characteristic, complemented
81	#120×C₄₃	C₂²	1	2	yes	complemented
82	C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
83	C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
84	#117×C₄₃	C₂²	1	1	yes	characteristic, complemented
85	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
86	C₂³×D₄₃	C₂³	1	2	yes	—
87	C₂³×D₄₃	C₂³	1	4	yes	—
88	C₂³×D₄₃	C₂³	1	2	yes	—
89	#41×C₄₃	—	2	4	no	—
90	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
91	C₂×D₄×C₄₃	C₂³	1	2	yes	—
92	C₂×D₄×C₄₃	C₂³	1	2	yes	—
93	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
94	C₂×D₄×C₄₃	C₂³	1	2	yes	—
95	C₂²×C₄×C₄₃	—	2	4	no	—
96	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
99	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
101	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
103	C₂×C₂²⋊D₄₃	—	2	8	no	—
104	C₂×C₂²⋊D₄₃	—	4	4	no	—
105	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
106	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
107	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
108	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
109	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
110	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
111	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
112	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
113	C₂²×Dic₄₃	C₂³	1	2	yes	—
114	C₂²×Dic₄₃	C₂³	1	2	yes	—
115	#10621902	—	2	8	no	—
116	D₄×D₄₃	—	2	16	no	—
117	D₄×D₄₃	—	2	8	no	—
118	D₄×D₄₃	—	4	8	no	—
119	#10621898	—	2	4	no	—
120	#10621898	—	2	8	no	—
121	#10621898	—	2	4	no	—
122	#10621898	—	2	8	no	—
123	#10621898	—	2	4	no	—
124	#10621898	—	2	8	no	—
125	#10621898	D₄	1	8	yes	complemented
126	C₂×D₁₇₂	—	2	4	no	—
127	C₂×D₁₇₂	—	2	4	no	—
128	C₂×D₁₇₂	—	2	8	no	—
129	C₂×D₁₇₂	C₂³	1	2	yes	—
130	C₂×D₁₇₂	C₂³	1	4	yes	—
131	C₂×D₁₇₂	C₂³	1	2	yes	—
132	C₂×D₁₇₂	C₂³	1	2	yes	—
133	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
134	C₂×D₁₇₂	C₂³	1	4	yes	—
135	C₂×D₁₇₂	C₂³	1	4	yes	—
136	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₄₃	—	2	8	no	—
138	C₂×C₄×D₄₃	C₂³	1	2	yes	—
139	C₂×C₄×D₄₃	C₂³	1	4	yes	—
140	C₂×C₄×D₄₃	C₂³	1	2	yes	—
141	C₂×C₄×D₄₃	C₂³	1	2	yes	—
142	C₂×C₄×D₄₃	C₂³	1	4	yes	—
143	C₂×C₄×D₄₃	C₂³	1	2	yes	—
144	C₂×Dic₈₆	—	2	4	no	—
145	C₂×Dic₈₆	C₂³	1	2	yes	—
146	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
147	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
148	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
149	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
150	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
151	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
152	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
153	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
154	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
155	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
156	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
157	C₄²×C₄₃	C₂³	1	2	yes	—
158	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
159	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
160	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
161	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
162	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
163	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
164	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
165	C₄⋊Dic₄₃	C₂³	1	2	yes	—
166	C₄⋊Dic₄₃	C₂³	1	2	yes	—
167	Dic₄₃⋊C₄	C₂³	1	4	yes	—
168	Dic₄₃⋊C₄	C₂³	1	4	yes	—
169	C₄×Dic₄₃	C₂³	1	4	yes	—
170	C₂³×C₄₃	—	2	2	no	—
171	C₂³×C₄₃	—	2	2	no	—
172	C₂³×C₄₃	—	4	1	no	—
173	C₂³×C₄₃	C₂⁴	1	2	yes	—
174	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
175	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
176	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
177	C₂²×D₄₃	—	2	4	no	—
178	C₂²×D₄₃	—	2	4	no	—
179	C₂²×D₄₃	—	2	4	no	—
180	C₂²×D₄₃	—	2	8	no	—
181	C₂²×D₄₃	—	4	2	no	—
182	C₂²×D₄₃	—	4	4	no	—
183	C₂²×D₄₃	—	4	2	no	—
184	C₂²×D₄₃	—	4	4	no	—
185	C₂²×D₄₃	—	4	2	no	—
186	C₂²×D₄₃	C₂⁴	1	4	yes	—
187	C₂²×D₄₃	C₂⁴	1	2	yes	—
188	C₂²×D₄₃	C₂⁴	1	2	yes	—
189	Q₈×C₄₃	—	2	2	no	—
190	D₄×C₄₃	—	2	4	no	—
191	D₄×C₄₃	—	2	4	no	—
192	D₄×C₄₃	—	2	2	no	—
193	D₄×C₄₃	—	4	2	no	—
194	C₂×C₄×C₄₃	—	2	2	no	—
195	C₂×C₄×C₄₃	—	2	2	no	—
196	C₂×C₄×C₄₃	—	2	2	no	—
197	C₂×C₄×C₄₃	—	2	4	no	—
198	C₂×C₄×C₄₃	—	2	2	no	—
199	C₂×C₄×C₄₃	—	2	2	no	—
200	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	complemented
201	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
202	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
203	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
204	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
205	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
206	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
207	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
208	C₂²⋊D₄₃	—	2	4	no	—
209	C₂²⋊D₄₃	—	2	8	no	—
210	C₂²⋊D₄₃	—	2	4	no	—
211	C₂²⋊D₄₃	—	2	4	no	—
212	C₂²⋊D₄₃	—	2	8	no	—
213	C₂²⋊D₄₃	—	4	4	no	—
214	C₂²⋊D₄₃	—	4	4	no	—
215	C₂²⋊D₄₃	C₂×D₄	1	8	yes	complemented
216	C₂×Dic₄₃	—	2	4	no	—
217	C₂×Dic₄₃	—	4	2	no	—
218	C₂×Dic₄₃	C₂⁴	1	4	yes	—
219	C₂×Dic₄₃	C₂⁴	1	2	yes	—
220	C₂×Dic₄₃	C₂⁴	1	2	yes	—
221	D₁₇₂	—	2	4	no	—
222	D₁₇₂	—	2	8	no	—
223	D₁₇₂	—	2	4	no	—
224	D₁₇₂	—	2	2	no	—
225	D₁₇₂	—	2	4	no	—
226	D₁₇₂	—	4	4	no	—
227	D₁₇₂	—	4	4	no	—
228	D₁₇₂	C₂×D₄	1	4	yes	complemented
229	C₄×D₄₃	—	2	4	no	—
230	C₄×D₄₃	—	2	4	no	—
231	C₄×D₄₃	—	2	4	no	—
232	C₄×D₄₃	—	2	8	no	—
233	C₄×D₄₃	—	4	4	no	—
234	C₄×D₄₃	C₂×D₄	1	8	yes	complemented
235	Dic₈₆	—	2	2	no	—
236	Dic₈₆	—	2	4	no	—
237	Dic₈₆	C₂×D₄	1	4	yes	complemented
238	C₂²×C₄₃	—	2	1	no	—
239	C₂²×C₄₃	—	2	1	no	—
240	C₂²×C₄₃	—	2	1	no	—
241	C₂²×C₄₃	—	2	1	no	—
242	C₂²×C₄₃	—	2	2	no	—
243	C₂²×C₄₃	—	2	1	no	—
244	C₂²×C₄₃	—	2	2	no	—
245	C₂²×C₄₃	—	2	1	no	—
246	C₂²×C₄₃	—	2	2	no	—
247	C₂²×C₄₃	—	2	1	no	—
248	C₂²×C₄₃	—	4	4	no	—
249	C₂²×C₄₃	C₂²×D₄	1	2	yes	—
250	C₂²×C₄₃	H(5,𝔽₂)	1	2	yes	complemented
251	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
252	C₂×D₄₃	—	2	2	no	—
253	C₂×D₄₃	—	2	2	no	—
254	C₂×D₄₃	—	2	4	no	—
255	C₂×D₄₃	—	2	2	no	—
256	C₂×D₄₃	—	2	2	no	—
257	C₂×D₄₃	—	2	4	no	—
258	C₂×D₄₃	—	2	4	no	—
259	C₂×D₄₃	—	2	2	no	—
260	C₂×D₄₃	—	4	8	no	—
261	C₂×D₄₃	—	8	8	no	—
262	C₂×D₄₃	—	8	4	no	—
263	C₂×D₄₃	C₂²×D₄	1	4	yes	—
264	C₄×C₄₃	—	2	1	no	—
265	C₄×C₄₃	—	2	1	no	—
266	C₄×C₄₃	—	2	2	no	—
267	C₄×C₄₃	—	2	2	no	—
268	C₄×C₄₃	—	2	2	no	—
269	C₄×C₄₃	C₂²×D₄	1	2	yes	—
270	C₄×C₄₃	C₂²×D₄	1	2	yes	—
271	Dic₄₃	—	2	2	no	—
272	Dic₄₃	—	2	4	no	—
273	Dic₄₃	C₂²×D₄	1	4	yes	—
274	#3488	—	43	1	no	maximal, Sylow
275	C₂×C₄₃	—	2	2	no	—
276	C₂×C₄₃	—	2	2	no	—
277	C₂×C₄₃	—	4	2	no	—
278	C₂×C₄₃	—	4	1	no	—
279	C₂×C₄₃	C₂³×D₄	1	1	yes	characteristic
280	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
281	C₂×C₄₃	#585	1	1	yes	characteristic
282	D₄₃	—	2	4	no	—
283	D₄₃	—	4	2	no	—
284	D₄₃	—	4	4	no	—
285	C₂×H(5,𝔽₂)	—	43	1	no	—
286	C₂²×#41	—	43	1	no	—
287	#550	—	43	2	no	—
288	#548	—	43	2	no	—
289	#546	—	43	4	no	—
290	#546	—	43	2	no	—
291	D₄²	—	43	4	no	—
292	D₄²	—	43	2	no	—
293	#537	—	43	1	no	—
294	#537	—	43	2	no	—
295	#535	—	43	2	no	—
296	#535	—	43	1	no	—
297	#525	—	43	2	no	—
298	#525	D₄₃	1	1	yes	characteristic, complemented
299	C₂×#121	—	43	1	no	—
300	C₂×#121	—	43	2	no	—
301	#520	—	43	1	no	—
302	C₄₃	#3488	1	1	yes	characteristic, complemented, Sylow
303	H(5,𝔽₂)	—	86	8	no	—
304	C₂×#41	—	43	2	no	—
305	C₂×#41	—	43	1	no	—
306	C₂×#41	—	43	2	no	—
307	C₂×#41	—	43	1	no	—
308	C₂×#41	—	43	1	no	—
309	C₂×#41	—	43	2	no	—
310	C₂×#41	—	43	2	no	—
311	C₂×#41	—	43	1	no	—
312	C₂×#41	—	86	8	no	—
313	C₂×#41	C₂×D₄₃	1	1	yes	characteristic, complemented
314	C₂²×Q₈	—	43	1	no	—
315	C₂²×D₄	—	43	2	no	—
316	C₂²×D₄	—	43	2	no	—
317	C₂²×D₄	—	43	2	no	—
318	C₂²×D₄	—	43	4	no	—
319	C₂²×D₄	—	43	4	no	—
320	C₂²×D₄	—	43	1	no	—
321	C₂²×D₄	—	43	1	no	—
322	C₂²×D₄	—	43	2	no	—
323	C₂³×C₄	—	43	2	no	—
324	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
325	#127	—	43	4	no	—
326	#127	—	43	2	no	—
327	#124	—	43	4	no	—
328	#124	—	43	2	no	—
329	#123	—	43	4	no	—
330	#123	C₂×D₄₃	1	2	yes	complemented
331	C₂²⋊Q₈	—	43	2	no	—
332	C₂²⋊Q₈	—	43	2	no	—
333	C₂²⋊Q₈	—	43	4	no	—
334	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
335	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
336	#121	—	43	2	no	—
337	#121	—	43	4	no	—
338	#121	—	43	4	no	—
339	#121	—	43	2	no	—
340	#121	—	43	2	no	—
341	#121	—	43	2	no	—
342	#121	—	43	2	no	—
343	#121	—	43	2	no	—
344	#121	—	43	2	no	—
345	#121	—	43	2	no	—
346	#121	—	43	4	no	—
347	#121	—	43	4	no	—
348	#121	—	43	4	no	—
349	#121	—	43	4	no	—
350	#121	C₂×D₄₃	1	1	yes	characteristic, complemented
351	#121	C₂×D₄₃	1	1	yes	characteristic, complemented
352	#120	—	43	4	no	—
353	#120	—	43	4	no	—
354	#120	—	43	4	no	—
355	#120	—	43	4	no	—
356	#120	C₂×D₄₃	1	2	yes	complemented
357	C₄×Q₈	—	43	2	no	—
358	C₄×D₄	—	43	4	no	—
359	C₄×D₄	—	43	4	no	—
360	C₄×D₄	—	43	4	no	—
361	C₄×D₄	—	43	2	no	—
362	C₄×D₄	C₂×D₄₃	1	2	yes	complemented
363	C₄×D₄	C₂×D₄₃	1	2	yes	complemented
364	#117	—	43	2	no	—
365	#117	C₂×D₄₃	1	1	yes	characteristic, complemented
366	C₂×C₄⋊C₄	—	43	1	no	—
367	C₂×C₄⋊C₄	—	43	2	no	—
368	C₂×C₂²⋊C₄	—	43	2	no	—
369	C₂×C₂²⋊C₄	—	43	4	no	—
370	C₂⁴	—	43	2	no	—
371	C₂⁴	—	43	4	no	—
372	C₂⁴	—	43	2	no	—
373	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
374	#41	—	2	4	no	—
375	#41	—	43	8	no	—
376	#41	—	86	8	no	—
377	#41	—	86	8	no	—
378	#41	—	86	4	no	—
379	#41	—	86	4	no	—
380	#41	—	86	8	no	—
381	#41	—	86	8	no	—
382	#41	—	86	4	no	—
383	C₂×Q₈	—	43	1	no	—
384	C₂×Q₈	—	43	2	no	—
385	C₂×Q₈	—	43	1	no	—
386	C₂×Q₈	—	86	4	no	—
387	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
388	C₂×D₄	—	43	2	no	—
389	C₂×D₄	—	43	4	no	—
390	C₂×D₄	—	43	2	no	—
391	C₂×D₄	—	43	2	no	—
392	C₂×D₄	—	43	4	no	—
393	C₂×D₄	—	43	2	no	—
394	C₂×D₄	—	43	4	no	—
395	C₂×D₄	—	43	4	no	—
396	C₂×D₄	—	43	1	no	—
397	C₂×D₄	—	43	2	no	—
398	C₂×D₄	—	43	4	no	—
399	C₂×D₄	—	43	2	no	—
400	C₂×D₄	—	43	2	no	—
401	C₂×D₄	—	43	1	no	—
402	C₂×D₄	—	43	4	no	—
403	C₂×D₄	—	43	4	no	—
404	C₂×D₄	—	86	4	no	—
405	C₂×D₄	—	86	8	no	—
406	C₂×D₄	—	86	8	no	—
407	C₂×D₄	—	86	16	no	—
408	C₂×D₄	—	86	8	no	—
409	C₂×D₄	—	86	4	no	—
410	C₂×D₄	—	172	8	no	—
411	C₂×D₄	—	172	4	no	—
412	C₂×D₄	C₂²×D₄₃	1	2	yes	—
413	C₂×D₄	C₂²×D₄₃	1	2	yes	—
414	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
415	C₂×D₄	C₂²×D₄₃	1	2	yes	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	43	2	no	—
418	C₂²×C₄	—	43	2	no	—
419	C₂²×C₄	—	43	2	no	—
420	C₂²×C₄	—	43	2	no	—
421	C₂²×C₄	—	43	2	no	—
422	C₂²×C₄	—	43	4	no	—
423	C₂²×C₄	—	43	2	no	—
424	C₂²×C₄	—	43	4	no	—
425	C₂²×C₄	—	86	8	no	—
426	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
427	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
428	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
429	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
430	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
431	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
432	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
433	C₄⋊C₄	—	43	2	no	—
434	C₄⋊C₄	—	43	4	no	—
435	C₄⋊C₄	—	43	2	no	—
436	C₄⋊C₄	—	43	4	no	—
437	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
438	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
439	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
440	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
441	C₂²⋊C₄	—	43	4	no	—
442	C₂²⋊C₄	—	43	4	no	—
443	C₂²⋊C₄	—	43	4	no	—
444	C₂²⋊C₄	—	43	4	no	—
445	C₂²⋊C₄	—	43	4	no	—
446	C₂²⋊C₄	—	43	4	no	—
447	C₂²⋊C₄	—	43	4	no	—
448	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
449	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
450	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
451	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
452	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
453	C₄²	—	43	4	no	—
454	C₄²	C₂²×D₄₃	1	2	yes	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	43	2	no	—
459	C₂³	—	43	4	no	—
460	C₂³	—	43	2	no	—
461	C₂³	—	86	8	no	—
462	C₂³	—	86	4	no	—
463	C₂³	—	86	4	no	—
464	C₂³	—	86	4	no	—
465	C₂³	—	172	2	no	—
466	C₂³	—	172	4	no	—
467	C₂³	—	172	2	no	—
468	C₂³	—	172	4	no	—
469	C₂³	—	172	2	no	—
470	C₂³	C₂³×D₄₃	1	2	yes	—
471	C₂³	C₂³×D₄₃	1	1	yes	characteristic
472	C₂³	C₂³×D₄₃	1	1	yes	characteristic
473	C₂³	C₂³×D₄₃	1	1	yes	characteristic
474	Q₈	—	2	2	no	—
475	Q₈	—	43	4	no	—
476	Q₈	—	86	4	no	—
477	Q₈	—	86	2	no	—
478	D₄	—	2	4	no	—
479	D₄	—	2	4	no	—
480	D₄	—	2	2	no	—
481	D₄	—	4	2	no	—
482	D₄	—	43	8	no	—
483	D₄	—	43	4	no	—
484	D₄	—	86	8	no	—
485	D₄	—	86	4	no	—
486	D₄	—	86	8	no	—
487	D₄	—	86	4	no	—
488	D₄	—	86	4	no	—
489	D₄	—	86	4	no	—
490	D₄	—	86	8	no	—
491	D₄	—	86	4	no	—
492	D₄	—	86	4	no	—
493	D₄	—	86	2	no	—
494	D₄	—	172	4	no	—
495	D₄	—	172	4	no	—
496	D₄	—	172	4	no	—
497	D₄	—	172	4	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	43	2	no	—
505	C₂×C₄	—	43	8	no	—
506	C₂×C₄	—	43	4	no	—
507	C₂×C₄	—	43	2	no	—
508	C₂×C₄	—	86	4	no	—
509	C₂×C₄	—	86	8	no	—
510	C₂×C₄	—	86	4	no	—
511	C₂×C₄	—	86	4	no	—
512	C₂×C₄	—	86	4	no	—
513	C₂×C₄	—	172	4	no	—
514	C₂×C₄	—	172	2	no	—
515	C₂×C₄	D₄×D₄₃	1	4	yes	complemented
516	C₂×C₄	C₂³×D₄₃	1	2	yes	—
517	C₂×C₄	C₂³×D₄₃	1	2	yes	—
518	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
519	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
520	C₂×C₄	C₂³×D₄₃	1	2	yes	—
521	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
522	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	4	4	no	—
534	C₂²	—	43	4	no	—
535	C₂²	—	86	2	no	—
536	C₂²	—	86	2	no	—
537	C₂²	—	86	2	no	—
538	C₂²	—	86	4	no	—
539	C₂²	—	86	4	no	—
540	C₂²	—	86	2	no	—
541	C₂²	—	86	2	no	—
542	C₂²	—	86	4	no	—
543	C₂²	—	344	4	no	—
544	C₂²	—	344	8	no	—
545	C₂²	—	172	8	no	—
546	C₂²	C₂×D₄×D₄₃	1	2	yes	—
547	C₂²	#13063371	1	2	yes	complemented
548	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	2	no	—
552	C₄	—	2	2	no	—
553	C₄	—	2	2	no	—
554	C₄	—	43	4	no	—
555	C₄	—	86	2	no	—
556	C₄	—	86	4	no	—
557	C₄	C₂×D₄×D₄₃	1	2	yes	—
558	C₄	C₂×D₄×D₄₃	1	2	yes	—
559	C₂	—	2	2	no	—
560	C₂	—	2	2	no	—
561	C₂	—	4	1	no	—
562	C₂	—	4	2	no	—
563	C₂	—	86	4	no	—
564	C₂	—	172	4	no	—
565	C₂	—	172	2	no	—
566	C₂	C₂²×D₄×D₄₃	1	1	yes	characteristic
567	C₂	C₂×#13063371	1	1	yes	characteristic
568	C₂	#14583735	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#525	C₂
hypercenter	#525	D₄₃
hypocenter	C₄₃	#3488
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. C₂×#13063371	C₂	semidirect
2. C₂²×#10621898	C₂	semidirect
3. #14583570	C₂	semidirect
4. #14583558	C₂	semidirect
5. #14583545	C₂	semidirect
6. #14583541	C₂	semidirect
7. D₄×D₁₇₂	C₂	semidirect
8. #14583531	C₂	semidirect
9. #14583479	C₂	semidirect
10. #14583477	C₂	semidirect
11. #14583468	C₂	semidirect
12. #14583465	C₂	semidirect
13. #14583412	C₂	semidirect
14. C₂×#13063299	C₂	semidirect
15. #121×D₄₃	C₂	semidirect
16. #14583379	C₂	semidirect
17. C₄₃×#525	C₂	semidirect
19. C₂×#10621902	C₂²	semidirect
22. C₂×#10621898	C₂²	semidirect
23. C₂×#10621898	C₂²	semidirect
24. C₂×#10621898	C₂²	semidirect
25. C₂×#10621898	C₂²	semidirect
26. C₂×#10621898	C₂²	semidirect
27. C₂×#10621898	C₂²	semidirect
28. C₂²×Dic₈₆	C₂²	semidirect
29. C₂²×D₁₇₂	C₂²	semidirect
30. C₂²×D₁₇₂	C₂²	semidirect
31. C₂²×D₁₇₂	C₂²	semidirect
32. C₂²×C₂²⋊D₄₃	C₂²	semidirect
33. C₂²×C₂²⋊D₄₃	C₂²	semidirect
34. C₂×D₄×D₄₃	C₂²	semidirect
35. C₂×D₄×D₄₃	C₂²	semidirect
36. C₂×D₄×D₄₃	C₂²	semidirect
37. C₂²×C₄×D₄₃	C₂²	semidirect
38. #13063322	C₂²	semidirect
39. #13063321	C₂²	semidirect
40. #13063313	C₂²	semidirect
41. #13063311	C₂²	semidirect
42. #13063310	C₂²	semidirect
43. #13063304	C₂²	semidirect
44. #13063303	C₂²	semidirect
45. #13063301	C₂²	semidirect
46. #13063300	C₂²	semidirect
47. #13063300	C₂²	semidirect
48. #13063300	C₂²	semidirect
49. #13063299	C₂²	semidirect
50. #13063299	C₂²	semidirect
51. #13063299	C₂²	semidirect
52. #13063299	C₂²	semidirect
53. #13063299	C₂²	semidirect
54. #13063298	C₂²	semidirect
55. #13063298	C₂²	semidirect
56. #13063298	C₂²	semidirect
57. #13063297	C₂²	semidirect
58. #13063297	C₂²	semidirect
59. #13063296	C₂²	semidirect
60. #13063295	C₂²	semidirect
61. #13063295	C₂²	semidirect
62. #13063295	C₂²	semidirect
63. #13063293	C₂²	semidirect
64. C₄×Dic₈₆	C₂²	semidirect
65. C₄×D₁₇₂	C₂²	semidirect
66. #13063287	C₂²	semidirect
67. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
68. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
69. #13063283	C₂²	semidirect
70. C₂×C₄⋊Dic₄₃	C₂²	semidirect
71. C₄⋊C₄×D₄₃	C₂²	semidirect
72. C₂×(C₂×D₄₃)⋊C₄	C₂²	semidirect
73. C₂²⋊C₄×D₄₃	C₂²	semidirect
74. C₂×#41×C₄₃	C₂²	semidirect
75. C₂³×C₄×C₄₃	C₂²	semidirect
76. #123×C₄₃	C₂²	semidirect
77. C₂²⋊Q₈×C₄₃	C₂²	semidirect
78. C₂²⋊Q₈×C₄₃	C₂²	semidirect
79. #121×C₄₃	C₂²	semidirect
80. #121×C₄₃	C₂²	semidirect
81. #120×C₄₃	C₂²	semidirect
82. C₄×D₄×C₄₃	C₂²	semidirect
83. C₄×D₄×C₄₃	C₂²	semidirect
84. #117×C₄₃	C₂²	semidirect
125. #10621898	D₄	semidirect
200. C₂×C₄×C₄₃	C₂×D₄	semidirect
215. C₂²⋊D₄₃	C₂×D₄	semidirect
228. D₁₇₂	C₂×D₄	semidirect
234. C₄×D₄₃	C₂×D₄	semidirect
237. Dic₈₆	C₂×D₄	semidirect
250. C₂²×C₄₃	H(5,𝔽₂)	semidirect
298. #525	D₄₃	semidirect
302. C₄₃	#3488	semidirect
313. C₂×#41	C₂×D₄₃	semidirect
324. C₂³×C₄	C₂×D₄₃	semidirect
330. #123	C₂×D₄₃	semidirect
334. C₂²⋊Q₈	C₂×D₄₃	semidirect
335. C₂²⋊Q₈	C₂×D₄₃	semidirect
350. #121	C₂×D₄₃	semidirect
351. #121	C₂×D₄₃	semidirect
356. #120	C₂×D₄₃	semidirect
362. C₄×D₄	C₂×D₄₃	semidirect
363. C₄×D₄	C₂×D₄₃	semidirect
365. #117	C₂×D₄₃	semidirect
515. C₂×C₄	D₄×D₄₃	semidirect
547. C₂²	#13063371	semidirect