Subgroups — C₂×#24921099 #36312288

Order 21248.

14438 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14581837	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₄×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#24921099	C₂	1	32	yes	maximal, direct product factor
4	C₂×#19128346	C₂	1	8	yes	maximal, complemented
5	C₂×D₄×D₃₃₂	C₂	1	8	yes	maximal, complemented
6	C₂×#19128270	C₂	1	2	yes	maximal, complemented
7	C₂×#19128263	C₂	1	4	yes	maximal, complemented
8	C₂×#19128213	C₂	1	2	yes	maximal, complemented
9	C₂²×#14581762	C₂	1	4	yes	maximal, complemented
10	C₂×#518×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁵×D₈₃	C₂²	1	2	yes	complemented
12	C₂×#14581837	—	2	16	no	—
13	C₂×#14581837	C₂²	1	16	yes	complemented
14	C₂²×#13050590	C₂²	1	2	yes	complemented
15	C₂²×#13050589	C₂²	1	4	yes	complemented
16	C₂³×D₃₃₂	C₂²	1	1	yes	characteristic, complemented
17	C₂³×D₃₃₂	C₂²	1	8	yes	complemented
18	C₂³×C₂²⋊D₈₃	C₂²	1	2	yes	complemented
19	C₂³×C₂²⋊D₈₃	C₂²	1	4	yes	complemented
20	C₂²×D₄×D₈₃	—	2	16	no	—
21	C₂²×D₄×D₈₃	C₂²	1	8	yes	complemented
22	C₂²×D₄×D₈₃	C₂²	1	16	yes	complemented
23	C₂²×D₄×D₈₃	C₂²	1	4	yes	complemented
24	C₂³×C₄×D₈₃	C₂²	1	1	yes	characteristic, complemented
25	#19128346	C₂²	1	128	yes	complemented
26	D₄×D₃₃₂	C₂²	1	128	yes	complemented
27	#19128270	C₂²	1	32	yes	complemented
28	#19128263	C₂²	1	64	yes	complemented
29	C₂×#14581789	C₂²	1	4	yes	complemented
30	C₂×#14581780	C₂²	1	4	yes	complemented
31	#19128213	C₂²	1	32	yes	complemented
32	C₂×#14581776	C₂²	1	4	yes	complemented
33	C₂×#14581776	C₂²	1	8	yes	complemented
34	C₂×#14581772	C₂²	1	4	yes	complemented
35	C₂×#14581767	C₂²	1	4	yes	complemented
36	C₂×#14581767	C₂²	1	8	yes	complemented
37	C₂×#14581766	C₂²	1	16	yes	complemented
38	C₂×#14581762	C₂²	1	4	yes	complemented
39	C₂×#14581762	C₂²	1	8	yes	complemented
40	C₂×#14581762	C₂²	1	8	yes	complemented
41	C₂×#14581762	C₂²	1	16	yes	complemented
42	C₂×#14581762	C₂²	1	64	yes	complemented
43	C₂×C₄×D₃₃₂	C₂²	1	8	yes	complemented
44	C₂²×(C₂×D₈₃)⋊C₄	C₂²	1	8	yes	complemented
45	C₂³×D₄×C₈₃	C₂²	1	1	yes	characteristic
46	#518×C₈₃	C₂²	1	16	yes	complemented
47	C₂×C₄×D₄×C₈₃	C₂²	1	8	yes	complemented
48	C₂×#117×C₈₃	C₂²	1	2	yes	complemented
49	C₂²×C₂²⋊C₄×C₈₃	C₂²	1	4	yes	complemented
50	C₂⁴×D₈₃	—	2	16	no	—
51	C₂⁴×D₈₃	—	4	16	no	—
52	C₂⁴×D₈₃	C₂³	1	1	yes	characteristic
53	C₂⁴×D₈₃	C₂³	1	8	yes	—
54	C₂⁴×D₈₃	C₂³	1	2	yes	—
55	C₂⁴×D₈₃	C₂³	1	16	yes	complemented
56	C₂⁴×D₈₃	C₂³	1	4	yes	complemented
57	#14581837	—	2	128	no	—
58	C₂×#13050590	—	2	16	no	—
59	C₂×#13050590	C₂³	1	16	yes	complemented
60	C₂×#13050589	—	2	32	no	—
61	C₂×#13050589	C₂³	1	32	yes	complemented
62	C₂²×Dic₁₆₆	C₂³	1	2	yes	complemented
63	C₂²×D₃₃₂	—	2	8	no	—
64	C₂²×D₃₃₂	—	4	32	no	—
65	C₂²×D₃₃₂	C₂³	1	8	yes	—
66	C₂²×D₃₃₂	C₂³	1	4	yes	—
67	C₂²×D₃₃₂	C₂³	1	8	yes	complemented
68	C₂²×D₃₃₂	C₂³	1	2	yes	complemented
69	C₂²×D₃₃₂	C₂³	1	16	yes	complemented
70	C₂²×D₃₃₂	C₂³	1	64	yes	complemented
71	C₂²×C₂²⋊D₈₃	—	2	16	no	—
72	C₂²×C₂²⋊D₈₃	—	2	32	no	—
73	C₂²×C₂²⋊D₈₃	C₂³	1	4	yes	—
74	C₂²×C₂²⋊D₈₃	C₂³	1	8	yes	—
75	C₂²×C₂²⋊D₈₃	C₂³	1	16	yes	complemented
76	C₂²×C₂²⋊D₈₃	C₂³	1	8	yes	complemented
77	C₂²×C₂²⋊D₈₃	C₂³	1	32	yes	complemented
78	C₂×D₄×D₈₃	—	2	64	no	—
79	C₂×D₄×D₈₃	—	2	128	no	—
80	C₂×D₄×D₈₃	—	2	32	no	—
81	C₂×D₄×D₈₃	C₂³	1	64	yes	complemented
82	C₂×D₄×D₈₃	C₂³	1	32	yes	complemented
83	C₂³×Dic₈₃	C₂³	1	1	yes	characteristic
84	C₂³×Dic₈₃	C₂³	1	4	yes	complemented
85	C₂²×C₄×D₈₃	—	2	8	no	—
86	C₂²×C₄×D₈₃	C₂³	1	4	yes	—
87	C₂²×C₄×D₈₃	C₂³	1	8	yes	complemented
88	C₂²×C₄×D₈₃	C₂³	1	4	yes	complemented
89	#14581789	C₂³	1	32	yes	complemented
90	#14581780	C₂³	1	32	yes	complemented
91	#14581776	C₂³	1	32	yes	complemented
92	#14581776	C₂³	1	64	yes	complemented
93	#14581772	C₂³	1	32	yes	complemented
94	#14581767	C₂³	1	32	yes	complemented
95	#14581767	C₂³	1	64	yes	complemented
96	#14581766	C₂³	1	128	yes	complemented
97	#14581762	C₂³	1	32	yes	complemented
98	#14581762	C₂³	1	64	yes	complemented
99	#14581762	C₂³	1	128	yes	complemented
100	#14581762	C₂³	1	64	yes	complemented
101	C₄×D₃₃₂	C₂³	1	64	yes	complemented
102	C₂×C₄⋊Dic₈₃	C₂³	1	8	yes	complemented
103	C₂×(C₂×D₈₃)⋊C₄	C₂³	1	8	yes	—
104	C₂×(C₂×D₈₃)⋊C₄	C₂³	1	16	yes	complemented
105	C₂×(C₂×D₈₃)⋊C₄	C₂³	1	8	yes	complemented
106	C₂×(C₂×D₈₃)⋊C₄	C₂³	1	64	yes	complemented
107	C₂⁵×C₈₃	C₂³	1	2	yes	—
108	C₂²×D₄×C₈₃	D₄	1	16	yes	complemented
109	C₂²×D₄×C₈₃	C₂³	1	4	yes	—
110	C₂²×D₄×C₈₃	C₂³	1	8	yes	—
111	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₈₃	C₂³	1	8	yes	complemented
113	C₄×D₄×C₈₃	C₂³	1	64	yes	complemented
114	#117×C₈₃	C₂³	1	16	yes	complemented
115	C₂×C₄⋊C₄×C₈₃	C₂³	1	4	yes	complemented
116	C₂×C₂²⋊C₄×C₈₃	C₂³	1	4	yes	—
117	C₂×C₂²⋊C₄×C₈₃	C₂³	1	32	yes	complemented
118	C₂×C₂²⋊C₄×C₈₃	C₂³	1	8	yes	complemented
119	C₂×C₄²×C₈₃	C₂³	1	4	yes	complemented
120	C₂³×D₈₃	—	2	4	no	—
121	C₂³×D₈₃	—	2	8	no	—
122	C₂³×D₈₃	—	2	32	no	—
123	C₂³×D₈₃	—	2	8	no	—
124	C₂³×D₈₃	—	2	64	no	—
125	C₂³×D₈₃	—	2	16	no	—
126	C₂³×D₈₃	—	2	32	no	—
127	C₂³×D₈₃	—	4	64	no	—
128	C₂³×D₈₃	—	4	16	no	—
129	C₂³×D₈₃	—	4	8	no	—
130	C₂³×D₈₃	—	4	16	no	—
131	C₂³×D₈₃	—	4	128	no	—
132	C₂³×D₈₃	C₂⁴	1	4	yes	—
133	C₂³×D₈₃	C₂⁴	1	4	yes	—
134	C₂³×D₈₃	C₂⁴	1	4	yes	—
135	C₂³×D₈₃	C₂⁴	1	32	yes	—
136	C₂³×D₈₃	C₂⁴	1	2	yes	—
137	C₂³×D₈₃	C₂⁴	1	8	yes	—
138	C₂³×D₈₃	C₂⁴	1	16	yes	complemented
139	#13050590	—	2	64	no	—
140	#13050589	—	2	128	no	—
141	C₂×Dic₁₆₆	—	2	8	no	—
142	C₂×Dic₁₆₆	C₂⁴	1	8	yes	complemented
143	C₂×D₃₃₂	—	2	32	no	—
144	C₂×D₃₃₂	—	2	16	no	—
145	C₂×D₃₃₂	—	2	8	no	—
146	C₂×D₃₃₂	—	2	32	no	—
147	C₂×D₃₃₂	—	4	128	no	—
148	C₂×D₃₃₂	—	4	32	no	—
149	C₂×D₃₃₂	C₂⁴	1	32	yes	—
150	C₂×D₃₃₂	C₂⁴	1	16	yes	—
151	C₂×D₃₃₂	C₂⁴	1	8	yes	complemented
152	C₂×D₃₃₂	C₂⁴	1	64	yes	complemented
153	C₂×C₂²⋊D₈₃	—	2	32	no	—
154	C₂×C₂²⋊D₈₃	—	2	32	no	—
155	C₂×C₂²⋊D₈₃	—	2	16	no	—
156	C₂×C₂²⋊D₈₃	—	2	64	no	—
157	C₂×C₂²⋊D₈₃	—	2	128	no	—
158	C₂×C₂²⋊D₈₃	C₂⁴	1	16	yes	—
159	C₂×C₂²⋊D₈₃	C₂⁴	1	32	yes	—
160	C₂×C₂²⋊D₈₃	C₂⁴	1	32	yes	complemented
161	D₄×D₈₃	—	2	256	no	—
162	D₄×D₈₃	—	2	128	no	—
163	C₂²×Dic₈₃	—	2	4	no	—
164	C₂²×Dic₈₃	—	2	16	no	—
165	C₂²×Dic₈₃	C₂⁴	1	4	yes	—
166	C₂²×Dic₈₃	C₂⁴	1	2	yes	—
167	C₂²×Dic₈₃	C₂⁴	1	4	yes	—
168	C₂²×Dic₈₃	C₂⁴	1	16	yes	complemented
169	C₂×C₄×D₈₃	—	2	16	no	—
170	C₂×C₄×D₈₃	—	2	16	no	—
171	C₂×C₄×D₈₃	—	2	32	no	—
172	C₂×C₄×D₈₃	C₂⁴	1	16	yes	—
173	C₂×C₄×D₈₃	C₂⁴	1	16	yes	complemented
174	C₄⋊Dic₈₃	C₂⁴	1	32	yes	complemented
175	(C₂×D₈₃)⋊C₄	C₂⁴	1	32	yes	—
176	(C₂×D₈₃)⋊C₄	C₂⁴	1	32	yes	complemented
177	(C₂×D₈₃)⋊C₄	C₂⁴	1	64	yes	complemented
178	C₂⁴×C₈₃	—	4	8	no	—
179	C₂⁴×C₈₃	C₂×D₄	1	16	yes	complemented
180	C₂⁴×C₈₃	C₂⁴	1	1	yes	characteristic
181	C₂⁴×C₈₃	C₂⁴	1	4	yes	—
182	C₂⁴×C₈₃	C₂⁴	1	8	yes	—
183	C₂×D₄×C₈₃	C₂×D₄	1	32	yes	complemented
184	C₂×D₄×C₈₃	C₂×D₄	1	64	yes	complemented
185	C₂×D₄×C₈₃	C₂⁴	1	16	yes	—
186	C₂²×C₄×C₈₃	—	4	16	no	—
187	C₂²×C₄×C₈₃	C₂×D₄	1	8	yes	complemented
188	C₂²×C₄×C₈₃	C₂⁴	1	8	yes	—
189	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₈₃	C₂⁴	1	4	yes	—
191	C₂²×C₄×C₈₃	C₂⁴	1	32	yes	complemented
192	C₄⋊C₄×C₈₃	C₂⁴	1	16	yes	complemented
193	C₂²⋊C₄×C₈₃	C₂⁴	1	16	yes	—
194	C₂²⋊C₄×C₈₃	C₂⁴	1	32	yes	complemented
195	C₄²×C₈₃	C₂⁴	1	16	yes	complemented
196	C₂³×C₈₃	—	2	16	no	—
197	C₂³×C₈₃	—	2	4	no	—
198	C₂³×C₈₃	—	4	32	no	—
199	C₂³×C₈₃	—	4	16	no	—
200	C₂³×C₈₃	C₂²×D₄	1	4	yes	—
201	C₂³×C₈₃	C₂²×D₄	1	16	yes	—
202	C₂³×C₈₃	C₂²×D₄	1	32	yes	complemented
203	C₂³×C₈₃	C₂⁵	1	2	yes	—
204	C₂³×C₈₃	C₂⁵	1	8	yes	—
205	C₂³×C₈₃	C₂⁵	1	1	yes	characteristic
206	C₂²×D₈₃	—	2	32	no	—
207	C₂²×D₈₃	—	2	8	no	—
208	C₂²×D₈₃	—	2	4	no	—
209	C₂²×D₈₃	—	2	4	no	—
210	C₂²×D₈₃	—	2	16	no	—
211	C₂²×D₈₃	—	2	8	no	—
212	C₂²×D₈₃	—	2	64	no	—
213	C₂²×D₈₃	—	2	16	no	—
214	C₂²×D₈₃	—	2	8	no	—
215	C₂²×D₈₃	—	2	16	no	—
216	C₂²×D₈₃	—	2	16	no	—
217	C₂²×D₈₃	—	2	32	no	—
218	C₂²×D₈₃	—	2	64	no	—
219	C₂²×D₈₃	—	4	32	no	—
220	C₂²×D₈₃	—	4	16	no	—
221	C₂²×D₈₃	—	4	32	no	—
222	C₂²×D₈₃	—	4	128	no	—
223	C₂²×D₈₃	—	4	256	no	—
224	C₂²×D₈₃	—	4	32	no	—
225	C₂²×D₈₃	—	8	32	no	—
226	C₂²×D₈₃	H(5,𝔽₂)	1	8	yes	complemented
227	C₂²×D₈₃	C₂⁵	1	8	yes	—
228	C₂²×D₈₃	C₂⁵	1	8	yes	—
229	C₂²×D₈₃	C₂⁵	1	4	yes	—
230	D₄×C₈₃	C₂²×D₄	1	64	yes	complemented
231	C₂×C₄×C₈₃	—	2	16	no	—
232	C₂×C₄×C₈₃	—	4	32	no	—
233	C₂×C₄×C₈₃	C₂²×D₄	1	8	yes	—
234	C₂×C₄×C₈₃	C₂²×D₄	1	16	yes	complemented
235	C₂×C₄×C₈₃	C₂⁵	1	16	yes	—
236	C₂×C₄×C₈₃	C₂⁵	1	4	yes	—
237	C₂²⋊D₈₃	—	2	64	no	—
238	C₂²⋊D₈₃	—	2	64	no	—
239	C₂²⋊D₈₃	—	2	32	no	—
240	C₂×Dic₈₃	—	2	8	no	—
241	C₂×Dic₈₃	—	2	4	no	—
242	C₂×Dic₈₃	—	2	8	no	—
243	C₂×Dic₈₃	—	2	32	no	—
244	C₂×Dic₈₃	C₂⁵	1	8	yes	—
245	C₂×Dic₈₃	C₂⁵	1	4	yes	—
246	D₃₃₂	—	2	64	no	—
247	D₃₃₂	—	2	32	no	—
248	D₃₃₂	—	2	16	no	—
249	D₃₃₂	—	4	64	no	—
250	C₄×D₈₃	—	2	32	no	—
251	C₄×D₈₃	—	2	32	no	—
252	Dic₁₆₆	—	2	16	no	—
253	C₂²×C₈₃	—	2	16	no	—
254	C₂²×C₈₃	—	2	4	no	—
255	C₂²×C₈₃	—	2	8	no	—
256	C₂²×C₈₃	—	2	32	no	—
257	C₂²×C₈₃	—	4	32	no	—
258	C₂²×C₈₃	C₂³×D₄	1	4	yes	—
259	C₂²×C₈₃	C₂³×D₄	1	16	yes	—
260	C₂²×C₈₃	C₂³×D₄	1	2	yes	—
261	C₂²×C₈₃	C₂×H(5,𝔽₂)	1	4	yes	—
262	C₂²×C₈₃	C₂⁶	1	1	yes	characteristic
263	C₂×D₈₃	—	2	32	no	—
264	C₂×D₈₃	—	2	4	no	—
265	C₂×D₈₃	—	2	4	no	—
266	C₂×D₈₃	—	2	16	no	—
267	C₂×D₈₃	—	2	8	no	—
268	C₂×D₈₃	—	2	8	no	—
269	C₂×D₈₃	—	2	16	no	—
270	C₂×D₈₃	—	2	16	no	—
271	C₂×D₈₃	—	4	128	no	—
272	C₂×D₈₃	—	4	32	no	—
273	C₂×D₈₃	—	4	16	no	—
274	C₂×D₈₃	—	4	16	no	—
275	C₂×D₈₃	—	8	32	no	—
276	C₂×D₈₃	C₂×H(5,𝔽₂)	1	8	yes	complemented
277	C₄×C₈₃	—	2	16	no	—
278	C₄×C₈₃	C₂³×D₄	1	8	yes	—
279	Dic₈₃	—	2	8	no	—
280	Dic₈₃	—	2	4	no	—
281	C₂×#3484	—	83	1	no	maximal, Sylow
282	C₂×C₈₃	—	2	4	no	—
283	C₂×C₈₃	—	2	16	no	—
284	C₂×C₈₃	#3484	1	4	yes	complemented
285	C₂×C₈₃	C₂⁴×D₄	1	1	yes	characteristic
286	C₂×C₈₃	C₂²×H(5,𝔽₂)	1	2	yes	—
287	D₈₃	—	2	8	no	—
288	D₈₃	—	4	8	no	—
289	D₈₃	—	4	8	no	—
290	C₂²×H(5,𝔽₂)	—	83	1	no	—
291	C₂⁴×D₄	—	83	1	no	—
292	#3484	—	83	32	no	—
293	C₂×#546	—	83	8	no	—
294	C₂×D₄²	—	83	8	no	—
295	C₂×#535	—	83	2	no	—
296	C₂×#534	—	83	4	no	—
297	C₂×#525	—	83	2	no	—
298	C₂²×#120	—	83	4	no	—
299	C₂×#518	D₈₃	1	1	yes	characteristic, complemented
300	C₈₃	C₂×#3484	1	1	yes	characteristic, complemented, Sylow
301	C₂⁶	—	83	2	no	—
302	C₂×H(5,𝔽₂)	—	83	16	no	—
303	C₂×H(5,𝔽₂)	—	166	16	no	—
304	C₂²×#41	—	83	4	no	—
305	C₂²×#41	—	83	2	no	—
306	C₂³×D₄	—	83	2	no	—
307	C₂³×D₄	—	83	4	no	—
308	C₂³×D₄	—	83	8	no	—
309	C₂³×D₄	—	83	16	no	—
310	C₂³×D₄	—	83	4	no	—
311	C₂³×D₄	—	83	1	no	—
312	C₂³×D₄	—	83	8	no	—
313	C₂³×D₄	—	166	16	no	—
314	C₂³×D₄	C₂×D₈₃	1	1	yes	characteristic
315	C₂⁴×C₄	—	83	1	no	—
316	#546	—	83	128	no	—
317	D₄²	—	83	128	no	—
318	#535	—	83	32	no	—
319	#534	—	83	64	no	—
320	C₂×#127	—	83	4	no	—
321	C₂×#124	—	83	4	no	—
322	#525	—	83	32	no	—
323	C₂×#123	—	83	4	no	—
324	C₂×#123	—	83	8	no	—
325	C₂×C₂²⋊Q₈	—	83	4	no	—
326	C₂×#121	—	83	16	no	—
327	C₂×#121	—	83	4	no	—
328	C₂×#121	—	83	8	no	—
329	C₂×#120	—	83	4	no	—
330	C₂×#120	—	83	8	no	—
331	C₂×#120	—	83	16	no	—
332	C₂×#120	—	83	64	no	—
333	C₂×#120	—	83	8	no	—
334	#518	C₂×D₈₃	1	16	yes	complemented
335	C₂×C₄×D₄	—	83	8	no	—
336	C₂×C₄×D₄	C₂×D₈₃	1	8	yes	complemented
337	C₂×#117	C₂×D₈₃	1	2	yes	complemented
338	C₂²×C₂²⋊C₄	—	83	8	no	—
339	C₂²×C₂²⋊C₄	C₂×D₈₃	1	4	yes	complemented
340	C₂⁵	—	332	16	no	—
341	C₂⁵	—	83	2	no	—
342	C₂⁵	—	83	16	no	—
343	C₂⁵	—	83	4	no	—
344	C₂⁵	—	83	8	no	—
345	C₂⁵	—	83	1	no	—
346	C₂⁵	—	166	16	no	—
347	C₂⁵	C₂²×D₈₃	1	2	yes	—
348	H(5,𝔽₂)	—	166	128	no	—
349	C₂×#41	—	83	32	no	—
350	C₂×#41	—	83	16	no	—
351	C₂×#41	—	166	32	no	—
352	C₂×#41	—	166	16	no	—
353	C₂²×Q₈	—	83	2	no	—
354	C₂²×D₄	—	332	32	no	—
355	C₂²×D₄	—	83	4	no	—
356	C₂²×D₄	—	83	8	no	—
357	C₂²×D₄	—	83	32	no	—
358	C₂²×D₄	—	83	8	no	—
359	C₂²×D₄	—	83	16	no	—
360	C₂²×D₄	—	83	32	no	—
361	C₂²×D₄	—	83	64	no	—
362	C₂²×D₄	—	83	16	no	—
363	C₂²×D₄	—	83	8	no	—
364	C₂²×D₄	—	83	4	no	—
365	C₂²×D₄	—	83	2	no	—
366	C₂²×D₄	—	83	8	no	—
367	C₂²×D₄	—	83	64	no	—
368	C₂²×D₄	—	166	16	no	—
369	C₂²×D₄	—	166	32	no	—
370	C₂²×D₄	—	166	64	no	—
371	C₂²×D₄	—	166	128	no	—
372	C₂²×D₄	—	166	32	no	—
373	C₂²×D₄	—	166	8	no	—
374	C₂²×D₄	D₃₃₂	1	16	yes	complemented
375	C₂²×D₄	C₂²×D₈₃	1	4	yes	—
376	C₂²×D₄	C₂²×D₈₃	1	8	yes	—
377	C₂³×C₄	—	83	4	no	—
378	C₂³×C₄	—	83	1	no	—
379	C₂³×C₄	—	83	4	no	—
380	C₂³×C₄	—	83	4	no	—
381	C₂³×C₄	—	83	8	no	—
382	C₂³×C₄	—	166	8	no	—
383	C₂³×C₄	C₂²×D₈₃	1	1	yes	characteristic
384	C₂³×C₄	C₂²×D₈₃	1	8	yes	complemented
385	#127	—	83	32	no	—
386	#124	—	83	32	no	—
387	#123	—	83	32	no	—
388	#123	—	83	64	no	—
389	C₂²⋊Q₈	—	83	32	no	—
390	#121	—	83	128	no	—
391	#121	—	83	32	no	—
392	#121	—	83	64	no	—
393	#120	—	83	32	no	—
394	#120	—	83	64	no	—
395	#120	—	83	128	no	—
396	#120	—	83	64	no	—
397	C₄×D₄	—	83	64	no	—
398	C₄×D₄	C₂²×D₈₃	1	64	yes	complemented
399	#117	C₂²×D₈₃	1	16	yes	complemented
400	C₂×C₄⋊C₄	—	83	8	no	—
401	C₂×C₄⋊C₄	C₂²×D₈₃	1	4	yes	complemented
402	C₂×C₂²⋊C₄	—	83	8	no	—
403	C₂×C₂²⋊C₄	—	83	16	no	—
404	C₂×C₂²⋊C₄	—	83	8	no	—
405	C₂×C₂²⋊C₄	—	83	64	no	—
406	C₂×C₂²⋊C₄	C₂²×D₈₃	1	4	yes	—
407	C₂×C₂²⋊C₄	C₂²×D₈₃	1	32	yes	complemented
408	C₂×C₂²⋊C₄	C₂²×D₈₃	1	8	yes	complemented
409	C₂×C₄²	C₂²×D₈₃	1	4	yes	complemented
410	C₂⁴	—	4	8	no	—
411	C₂⁴	—	332	16	no	—
412	C₂⁴	—	332	8	no	—
413	C₂⁴	—	332	16	no	—
414	C₂⁴	—	332	128	no	—
415	C₂⁴	—	332	64	no	—
416	C₂⁴	—	83	8	no	—
417	C₂⁴	—	83	16	no	—
418	C₂⁴	—	83	32	no	—
419	C₂⁴	—	83	2	no	—
420	C₂⁴	—	83	4	no	—
421	C₂⁴	—	83	4	no	—
422	C₂⁴	—	83	4	no	—
423	C₂⁴	—	166	32	no	—
424	C₂⁴	—	166	8	no	—
425	C₂⁴	—	166	8	no	—
426	C₂⁴	—	166	32	no	—
427	C₂⁴	—	166	64	no	—
428	C₂⁴	—	166	16	no	—
429	C₂⁴	—	166	4	no	—
430	C₂⁴	C₂×D₃₃₂	1	16	yes	complemented
431	C₂⁴	C₂³×D₈₃	1	1	yes	characteristic
432	C₂⁴	C₂³×D₈₃	1	4	yes	—
433	C₂⁴	C₂³×D₈₃	1	8	yes	—
434	#41	—	166	128	no	—
435	#41	—	166	64	no	—
436	C₂×Q₈	—	83	8	no	—
437	C₂×Q₈	—	166	8	no	—
438	C₂×D₄	—	332	32	no	—
439	C₂×D₄	—	332	128	no	—
440	C₂×D₄	—	83	16	no	—
441	C₂×D₄	—	83	32	no	—
442	C₂×D₄	—	83	32	no	—
443	C₂×D₄	—	83	64	no	—
444	C₂×D₄	—	83	32	no	—
445	C₂×D₄	—	83	16	no	—
446	C₂×D₄	—	83	8	no	—
447	C₂×D₄	—	166	32	no	—
448	C₂×D₄	—	166	32	no	—
449	C₂×D₄	—	166	16	no	—
450	C₂×D₄	—	166	32	no	—
451	C₂×D₄	—	166	64	no	—
452	C₂×D₄	—	166	128	no	—
453	C₂×D₄	—	166	256	no	—
454	C₂×D₄	—	166	128	no	—
455	C₂×D₄	—	166	16	no	—
456	C₂×D₄	—	166	8	no	—
457	C₂×D₄	—	166	32	no	—
458	C₂×D₄	C₂×D₃₃₂	1	32	yes	complemented
459	C₂×D₄	C₂×D₃₃₂	1	64	yes	complemented
460	C₂×D₄	C₂³×D₈₃	1	16	yes	—
461	C₂²×C₄	—	4	16	no	—
462	C₂²×C₄	—	83	16	no	—
463	C₂²×C₄	—	83	4	no	—
464	C₂²×C₄	—	83	4	no	—
465	C₂²×C₄	—	83	2	no	—
466	C₂²×C₄	—	83	16	no	—
467	C₂²×C₄	—	83	16	no	—
468	C₂²×C₄	—	166	4	no	—
469	C₂²×C₄	—	166	16	no	—
470	C₂²×C₄	—	166	16	no	—
471	C₂²×C₄	—	166	16	no	—
472	C₂²×C₄	—	166	32	no	—
473	C₂²×C₄	C₂×D₃₃₂	1	8	yes	complemented
474	C₂²×C₄	C₂³×D₈₃	1	8	yes	—
475	C₂²×C₄	C₂³×D₈₃	1	2	yes	—
476	C₂²×C₄	C₂³×D₈₃	1	4	yes	—
477	C₂²×C₄	C₂³×D₈₃	1	32	yes	complemented
478	C₄⋊C₄	—	83	32	no	—
479	C₄⋊C₄	C₂³×D₈₃	1	16	yes	complemented
480	C₂²⋊C₄	—	83	32	no	—
481	C₂²⋊C₄	—	83	64	no	—
482	C₂²⋊C₄	—	83	32	no	—
483	C₂²⋊C₄	C₂³×D₈₃	1	16	yes	—
484	C₂²⋊C₄	C₂³×D₈₃	1	32	yes	complemented
485	C₄²	C₂³×D₈₃	1	16	yes	complemented
486	C₂³	—	2	16	no	—
487	C₂³	—	2	4	no	—
488	C₂³	—	4	32	no	—
489	C₂³	—	4	16	no	—
490	C₂³	—	332	32	no	—
491	C₂³	—	332	128	no	—
492	C₂³	—	332	32	no	—
493	C₂³	—	332	16	no	—
494	C₂³	—	332	32	no	—
495	C₂³	—	332	256	no	—
496	C₂³	—	83	8	no	—
497	C₂³	—	83	4	no	—
498	C₂³	—	83	8	no	—
499	C₂³	—	83	8	no	—
500	C₂³	—	664	32	no	—
501	C₂³	—	166	64	no	—
502	C₂³	—	166	16	no	—
503	C₂³	—	166	32	no	—
504	C₂³	—	166	8	no	—
505	C₂³	—	166	16	no	—
506	C₂³	—	166	64	no	—
507	C₂³	—	166	8	no	—
508	C₂³	—	166	16	no	—
509	C₂³	—	166	16	no	—
510	C₂³	—	166	32	no	—
511	C₂³	—	166	8	no	—
512	C₂³	—	166	4	no	—
513	C₂³	—	166	4	no	—
514	C₂³	C₂²×D₃₃₂	1	4	yes	—
515	C₂³	C₂²×D₃₃₂	1	16	yes	—
516	C₂³	C₂²×D₃₃₂	1	32	yes	complemented
517	C₂³	C₂⁴×D₈₃	1	2	yes	—
518	C₂³	C₂⁴×D₈₃	1	8	yes	—
519	C₂³	C₂⁴×D₈₃	1	1	yes	characteristic
520	Q₈	—	166	16	no	—
521	D₄	—	332	64	no	—
522	D₄	—	166	64	no	—
523	D₄	—	166	64	no	—
524	D₄	—	166	32	no	—
525	D₄	—	166	64	no	—
526	D₄	—	166	32	no	—
527	D₄	—	166	16	no	—
528	D₄	C₂²×D₃₃₂	1	64	yes	complemented
529	C₂×C₄	—	2	16	no	—
530	C₂×C₄	—	4	32	no	—
531	C₂×C₄	—	83	8	no	—
532	C₂×C₄	—	83	4	no	—
533	C₂×C₄	—	166	8	no	—
534	C₂×C₄	—	166	4	no	—
535	C₂×C₄	—	166	8	no	—
536	C₂×C₄	—	166	32	no	—
537	C₂×C₄	—	166	32	no	—
538	C₂×C₄	—	166	32	no	—
539	C₂×C₄	C₂²×D₃₃₂	1	8	yes	—
540	C₂×C₄	C₂²×D₃₃₂	1	16	yes	complemented
541	C₂×C₄	C₂⁴×D₈₃	1	16	yes	—
542	C₂×C₄	C₂⁴×D₈₃	1	4	yes	—
543	C₂²	—	2	8	no	—
544	C₂²	—	2	32	no	—
545	C₂²	—	2	16	no	—
546	C₂²	—	2	4	no	—
547	C₂²	—	4	32	no	—
548	C₂²	—	332	32	no	—
549	C₂²	—	332	128	no	—
550	C₂²	—	332	16	no	—
551	C₂²	—	332	16	no	—
552	C₂²	—	83	8	no	—
553	C₂²	—	664	32	no	—
554	C₂²	—	166	32	no	—
555	C₂²	—	166	8	no	—
556	C₂²	—	166	8	no	—
557	C₂²	—	166	16	no	—
558	C₂²	—	166	16	no	—
559	C₂²	—	166	16	no	—
560	C₂²	—	166	4	no	—
561	C₂²	—	166	4	no	—
562	C₂²	C₂³×D₃₃₂	1	4	yes	—
563	C₂²	C₂³×D₃₃₂	1	16	yes	—
564	C₂²	C₂³×D₃₃₂	1	2	yes	—
565	C₂²	H(5,𝔽₂)×D₈₃	1	4	yes	—
566	C₂²	C₂⁵×D₈₃	1	1	yes	characteristic
567	C₄	—	2	16	no	—
568	C₄	—	166	4	no	—
569	C₄	—	166	8	no	—
570	C₄	C₂³×D₃₃₂	1	8	yes	—
571	C₂	—	2	4	no	—
572	C₂	—	2	16	no	—
573	C₂	—	332	8	no	—
574	C₂	—	332	8	no	—
575	C₂	—	166	8	no	—
576	C₂	#24921099	1	4	yes	direct product factor
577	C₂	C₂⁴×D₃₃₂	1	1	yes	characteristic
578	C₂	C₂×H(5,𝔽₂)×D₈₃	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₈₃
commutator, cosocle	C₂²×C₈₃	C₂⁶
Frattini	C₂²	C₂⁵×D₈₃
Fitting	C₂×#518×C₈₃	C₂
socle	C₂³×C₈₃	C₂⁵
hypercenter	C₂×#518	D₈₃
hypocenter	C₈₃	C₂×#3484
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂³ ◁ C₂×#518

Complements

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

N	H ≅ G/N	type
1. C₂²×#14581837	C₂	semidirect
2. C₂³×D₄×D₈₃	C₂	semidirect
3. #24921099	C₂	direct (N × H)
4. C₂×#19128346	C₂	semidirect
5. C₂×D₄×D₃₃₂	C₂	semidirect
6. C₂×#19128270	C₂	semidirect
7. C₂×#19128263	C₂	semidirect
8. C₂×#19128213	C₂	semidirect
9. C₂²×#14581762	C₂	semidirect
10. C₂×#518×C₈₃	C₂	semidirect
11. C₂⁵×D₈₃	C₂²	semidirect
13. C₂×#14581837	C₂²	semidirect
14. C₂²×#13050590	C₂²	semidirect
15. C₂²×#13050589	C₂²	semidirect
16. C₂³×D₃₃₂	C₂²	semidirect
17. C₂³×D₃₃₂	C₂²	semidirect
18. C₂³×C₂²⋊D₈₃	C₂²	semidirect
19. C₂³×C₂²⋊D₈₃	C₂²	semidirect
21. C₂²×D₄×D₈₃	C₂²	semidirect
22. C₂²×D₄×D₈₃	C₂²	semidirect
23. C₂²×D₄×D₈₃	C₂²	semidirect
24. C₂³×C₄×D₈₃	C₂²	semidirect
25. #19128346	C₂²	semidirect
26. D₄×D₃₃₂	C₂²	semidirect
27. #19128270	C₂²	semidirect
28. #19128263	C₂²	semidirect
29. C₂×#14581789	C₂²	semidirect
30. C₂×#14581780	C₂²	semidirect
31. #19128213	C₂²	semidirect
32. C₂×#14581776	C₂²	semidirect
33. C₂×#14581776	C₂²	semidirect
34. C₂×#14581772	C₂²	semidirect
35. C₂×#14581767	C₂²	semidirect
36. C₂×#14581767	C₂²	semidirect
37. C₂×#14581766	C₂²	semidirect
38. C₂×#14581762	C₂²	semidirect
39. C₂×#14581762	C₂²	semidirect
40. C₂×#14581762	C₂²	semidirect
41. C₂×#14581762	C₂²	semidirect
42. C₂×#14581762	C₂²	semidirect
43. C₂×C₄×D₃₃₂	C₂²	semidirect
44. C₂²×(C₂×D₈₃)⋊C₄	C₂²	semidirect
46. #518×C₈₃	C₂²	semidirect
47. C₂×C₄×D₄×C₈₃	C₂²	semidirect
48. C₂×#117×C₈₃	C₂²	semidirect
49. C₂²×C₂²⋊C₄×C₈₃	C₂²	semidirect
55. C₂⁴×D₈₃	C₂³	semidirect
56. C₂⁴×D₈₃	C₂³	semidirect
59. C₂×#13050590	C₂³	semidirect
61. C₂×#13050589	C₂³	semidirect
62. C₂²×Dic₁₆₆	C₂³	semidirect
67. C₂²×D₃₃₂	C₂³	semidirect
68. C₂²×D₃₃₂	C₂³	semidirect
69. C₂²×D₃₃₂	C₂³	semidirect
70. C₂²×D₃₃₂	C₂³	semidirect
75. C₂²×C₂²⋊D₈₃	C₂³	semidirect
76. C₂²×C₂²⋊D₈₃	C₂³	semidirect
77. C₂²×C₂²⋊D₈₃	C₂³	semidirect
81. C₂×D₄×D₈₃	C₂³	semidirect
82. C₂×D₄×D₈₃	C₂³	semidirect
84. C₂³×Dic₈₃	C₂³	semidirect
87. C₂²×C₄×D₈₃	C₂³	semidirect
88. C₂²×C₄×D₈₃	C₂³	semidirect
89. #14581789	C₂³	semidirect
90. #14581780	C₂³	semidirect
91. #14581776	C₂³	semidirect
92. #14581776	C₂³	semidirect
93. #14581772	C₂³	semidirect
94. #14581767	C₂³	semidirect
95. #14581767	C₂³	semidirect
96. #14581766	C₂³	semidirect
97. #14581762	C₂³	semidirect
98. #14581762	C₂³	semidirect
99. #14581762	C₂³	semidirect
100. #14581762	C₂³	semidirect
101. C₄×D₃₃₂	C₂³	semidirect
102. C₂×C₄⋊Dic₈₃	C₂³	semidirect
104. C₂×(C₂×D₈₃)⋊C₄	C₂³	semidirect
105. C₂×(C₂×D₈₃)⋊C₄	C₂³	semidirect
106. C₂×(C₂×D₈₃)⋊C₄	C₂³	semidirect
108. C₂²×D₄×C₈₃	D₄	semidirect
112. C₂³×C₄×C₈₃	C₂³	semidirect
113. C₄×D₄×C₈₃	C₂³	semidirect
114. #117×C₈₃	C₂³	semidirect
115. C₂×C₄⋊C₄×C₈₃	C₂³	semidirect
117. C₂×C₂²⋊C₄×C₈₃	C₂³	semidirect
118. C₂×C₂²⋊C₄×C₈₃	C₂³	semidirect
119. C₂×C₄²×C₈₃	C₂³	semidirect
138. C₂³×D₈₃	C₂⁴	semidirect
142. C₂×Dic₁₆₆	C₂⁴	semidirect
151. C₂×D₃₃₂	C₂⁴	semidirect
152. C₂×D₃₃₂	C₂⁴	semidirect
160. C₂×C₂²⋊D₈₃	C₂⁴	semidirect
168. C₂²×Dic₈₃	C₂⁴	semidirect
173. C₂×C₄×D₈₃	C₂⁴	semidirect
174. C₄⋊Dic₈₃	C₂⁴	semidirect
176. (C₂×D₈₃)⋊C₄	C₂⁴	semidirect
177. (C₂×D₈₃)⋊C₄	C₂⁴	semidirect
179. C₂⁴×C₈₃	C₂×D₄	semidirect
183. C₂×D₄×C₈₃	C₂×D₄	semidirect
184. C₂×D₄×C₈₃	C₂×D₄	semidirect
187. C₂²×C₄×C₈₃	C₂×D₄	semidirect
191. C₂²×C₄×C₈₃	C₂⁴	semidirect
192. C₄⋊C₄×C₈₃	C₂⁴	semidirect
194. C₂²⋊C₄×C₈₃	C₂⁴	semidirect
195. C₄²×C₈₃	C₂⁴	semidirect
202. C₂³×C₈₃	C₂²×D₄	semidirect
226. C₂²×D₈₃	H(5,𝔽₂)	semidirect
230. D₄×C₈₃	C₂²×D₄	semidirect
234. C₂×C₄×C₈₃	C₂²×D₄	semidirect
276. C₂×D₈₃	C₂×H(5,𝔽₂)	semidirect
284. C₂×C₈₃	#3484	semidirect
299. C₂×#518	D₈₃	semidirect
300. C₈₃	C₂×#3484	semidirect
334. #518	C₂×D₈₃	semidirect
336. C₂×C₄×D₄	C₂×D₈₃	semidirect
337. C₂×#117	C₂×D₈₃	semidirect
339. C₂²×C₂²⋊C₄	C₂×D₈₃	semidirect
374. C₂²×D₄	D₃₃₂	semidirect
384. C₂³×C₄	C₂²×D₈₃	semidirect
398. C₄×D₄	C₂²×D₈₃	semidirect
399. #117	C₂²×D₈₃	semidirect
401. C₂×C₄⋊C₄	C₂²×D₈₃	semidirect
407. C₂×C₂²⋊C₄	C₂²×D₈₃	semidirect
408. C₂×C₂²⋊C₄	C₂²×D₈₃	semidirect
409. C₂×C₄²	C₂²×D₈₃	semidirect
430. C₂⁴	C₂×D₃₃₂	semidirect
458. C₂×D₄	C₂×D₃₃₂	semidirect
459. C₂×D₄	C₂×D₃₃₂	semidirect
473. C₂²×C₄	C₂×D₃₃₂	semidirect
477. C₂²×C₄	C₂³×D₈₃	semidirect
479. C₄⋊C₄	C₂³×D₈₃	semidirect
484. C₂²⋊C₄	C₂³×D₈₃	semidirect
485. C₄²	C₂³×D₈₃	semidirect
516. C₂³	C₂²×D₃₃₂	semidirect
528. D₄	C₂²×D₃₃₂	semidirect
540. C₂×C₄	C₂²×D₃₃₂	semidirect
576. C₂	#24921099	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#14581837	2
C₂³×D₄×D₈₃	2
#24921099	2
C₂×#19128346	2
C₂×D₄×D₃₃₂	2
C₂×#19128270	2
C₂×#19128263	2
C₂×#19128213	2
C₂²×#14581762	2
C₂×#518×C₈₃	2
C₂×#3484	83

Subgroups — C2×#24921099 #36312288

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#24921099 #36312288