Subgroups — C₂×C₈₉×#3260 #36438759

Order 22784.

1882 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#541×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#540×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3260	C₂	1	16	yes	maximal, direct product factor
4	C₂×#479×C₈₉	C₂	1	2	yes	maximal, complemented
5	C₂×#478×C₈₉	C₂	1	2	yes	maximal, complemented
6	C₂×#468×C₈₉	C₂	1	2	yes	maximal, complemented
7	C₂×#465×C₈₉	C₂	1	2	yes	maximal, complemented
8	C₂×#460×C₈₉	C₂	1	2	yes	maximal, complemented
9	C₂×#461×C₈₉	C₂	1	2	yes	maximal, complemented
10	C₂×#424×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×SD₁₆×C₈₉	C₂²	1	2	yes	—
12	C₂²×SD₁₆×C₈₉	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
15	#541×C₈₉	—	2	4	no	—
16	#541×C₈₉	C₂²	1	8	yes	complemented
17	#540×C₈₉	—	2	4	no	—
18	#540×C₈₉	C₂²	1	8	yes	—
19	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#126×C₈₉	—	2	2	no	—
22	C₂×#125×C₈₉	—	2	2	no	—
23	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#123×C₈₉	—	2	2	no	—
26	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
27	C₂×#121×C₈₉	—	2	2	no	—
28	C₂×#121×C₈₉	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
31	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
32	#479×C₈₉	C₂²	1	16	yes	complemented
33	#478×C₈₉	C₂²	1	16	yes	complemented
34	#468×C₈₉	C₂²	1	16	yes	complemented
35	#465×C₈₉	C₂²	1	16	yes	complemented
36	#461×C₈₉	C₂²	1	16	yes	complemented
37	#460×C₈₉	C₂²	1	16	yes	complemented
38	C₂×#107×C₈₉	C₂²	1	2	yes	—
39	C₂×#106×C₈₉	C₂²	1	2	yes	—
40	#424×C₈₉	C₂²	1	8	yes	complemented
41	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
42	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
43	C₂×#103×C₈₉	C₂²	1	2	yes	—
44	C₂×#103×C₈₉	C₂²	1	2	yes	—
45	C₂×#102×C₈₉	C₂²	1	2	yes	—
46	C₂×#102×C₈₉	C₂²	1	2	yes	—
47	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
48	C₂²×D₄×C₈₉	—	2	2	no	—
49	C₂²×D₄×C₈₉	—	2	2	no	—
50	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
51	C₂³×C₄×C₈₉	—	2	2	no	—
52	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
53	C₂×SD₁₆×C₈₉	—	4	4	no	—
54	C₂×SD₁₆×C₈₉	—	4	4	no	—
55	C₂×SD₁₆×C₈₉	C₂³	1	8	yes	—
56	C₂×SD₁₆×C₈₉	C₂³	1	8	yes	—
57	C₂×M₁₆×C₈₉	—	4	2	no	—
58	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
59	C₂²×C₈×C₈₉	—	4	2	no	—
60	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
61	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
62	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
63	C₄⋊Q₈×C₈₉	—	2	2	no	—
64	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
65	#127×C₈₉	—	2	2	no	—
66	#127×C₈₉	C₂³	1	4	yes	—
67	#126×C₈₉	—	2	16	no	—
68	#125×C₈₉	—	2	16	no	—
69	#125×C₈₉	—	2	2	no	—
70	#125×C₈₉	—	2	2	no	—
71	#125×C₈₉	C₂³	1	4	yes	—
72	#125×C₈₉	C₂³	1	4	yes	—
73	#123×C₈₉	—	2	16	no	—
74	C₂²⋊Q₈×C₈₉	—	2	4	no	—
75	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
76	#121×C₈₉	—	2	4	no	—
77	#121×C₈₉	—	2	16	no	—
78	#121×C₈₉	C₂³	1	8	yes	—
79	C₄×Q₈×C₈₉	—	2	4	no	—
80	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
81	C₄×D₄×C₈₉	—	2	4	no	—
82	C₄×D₄×C₈₉	C₂³	1	8	yes	—
83	#117×C₈₉	D₄	1	4	yes	—
84	#117×C₈₉	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
86	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
87	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
88	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
89	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
90	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
91	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
93	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
97	C₂×C₄²×C₈₉	—	2	2	no	—
98	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
100	#107×C₈₉	C₂³	1	8	yes	—
101	#106×C₈₉	C₂³	1	8	yes	—
102	C₄⋊C₈×C₈₉	C₂³	1	8	yes	—
103	C₄⋊C₈×C₈₉	C₂³	1	8	yes	—
104	#103×C₈₉	C₂³	1	8	yes	—
105	#103×C₈₉	C₂³	1	8	yes	—
106	#102×C₈₉	C₂³	1	8	yes	—
107	#102×C₈₉	C₂³	1	8	yes	—
108	C₂⁴×C₈₉	—	2	2	no	—
109	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
110	C₂×Q₈×C₈₉	—	2	2	no	—
111	C₂×Q₈×C₈₉	—	2	4	no	—
112	C₂×Q₈×C₈₉	—	2	4	no	—
113	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
114	C₂×D₄×C₈₉	—	2	8	no	—
115	C₂×D₄×C₈₉	—	2	2	no	—
116	C₂×D₄×C₈₉	—	2	8	no	—
117	C₂×D₄×C₈₉	—	2	4	no	—
118	C₂×D₄×C₈₉	—	2	4	no	—
119	C₂×D₄×C₈₉	—	8	4	no	—
120	C₂×D₄×C₈₉	—	8	4	no	—
121	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₈₉	—	2	2	no	—
123	C₂²×C₄×C₈₉	—	2	2	no	—
124	C₂²×C₄×C₈₉	—	2	2	no	—
125	C₂²×C₄×C₈₉	—	2	2	no	—
126	C₂²×C₄×C₈₉	—	2	2	no	—
127	C₂²×C₄×C₈₉	—	2	8	no	—
128	C₂²×C₄×C₈₉	—	8	4	no	—
129	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
135	SD₁₆×C₈₉	—	4	8	no	—
136	SD₁₆×C₈₉	—	4	8	no	—
137	M₁₆×C₈₉	—	4	4	no	—
138	C₂×C₈×C₈₉	—	2	4	no	—
139	C₂×C₈×C₈₉	—	2	4	no	—
140	C₂×C₈×C₈₉	—	4	4	no	—
141	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
142	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
143	C₄⋊C₄×C₈₉	—	2	8	no	—
144	C₄⋊C₄×C₈₉	—	2	8	no	—
145	C₄⋊C₄×C₈₉	—	2	8	no	—
146	C₄⋊C₄×C₈₉	—	2	8	no	—
147	C₄⋊C₄×C₈₉	—	2	8	no	—
148	C₄⋊C₄×C₈₉	—	2	2	no	—
149	C₄⋊C₄×C₈₉	—	2	2	no	—
150	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
151	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
152	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
153	C₂²⋊C₄×C₈₉	—	2	8	no	—
154	C₂²⋊C₄×C₈₉	—	2	8	no	—
155	C₂²⋊C₄×C₈₉	—	2	8	no	—
156	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
157	C₄²×C₈₉	—	2	8	no	—
158	C₄²×C₈₉	C₂×D₄	1	2	yes	—
159	C₄²×C₈₉	C₂×D₄	1	2	yes	—
160	C₄²×C₈₉	C₂⁴	1	2	yes	—
161	C₄²×C₈₉	C₂⁴	1	2	yes	—
162	C₂³×C₈₉	—	2	2	no	—
163	C₂³×C₈₉	—	2	4	no	—
164	C₂³×C₈₉	—	2	4	no	—
165	C₂³×C₈₉	—	4	4	no	—
166	C₂³×C₈₉	—	4	4	no	—
167	C₂³×C₈₉	—	4	4	no	—
168	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
169	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
170	Q₈×C₈₉	—	2	4	no	—
171	Q₈×C₈₉	—	2	4	no	—
172	Q₈×C₈₉	—	4	4	no	—
173	D₄×C₈₉	—	2	4	no	—
174	D₄×C₈₉	—	2	4	no	—
175	D₄×C₈₉	—	4	4	no	—
176	D₄×C₈₉	—	8	8	no	—
177	D₄×C₈₉	—	8	8	no	—
178	C₂×C₄×C₈₉	—	2	2	no	—
179	C₂×C₄×C₈₉	—	2	4	no	—
180	C₂×C₄×C₈₉	—	2	4	no	—
181	C₂×C₄×C₈₉	—	2	4	no	—
182	C₂×C₄×C₈₉	—	2	2	no	—
183	C₂×C₄×C₈₉	—	2	2	no	—
184	C₂×C₄×C₈₉	—	2	4	no	—
185	C₂×C₄×C₈₉	—	2	4	no	—
186	C₂×C₄×C₈₉	—	2	4	no	—
187	C₂×C₄×C₈₉	—	4	4	no	—
188	C₂×C₄×C₈₉	—	4	4	no	—
189	C₂×C₄×C₈₉	—	4	4	no	—
190	C₂×C₄×C₈₉	—	8	8	no	—
191	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
192	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
193	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
196	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
197	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
198	C₈×C₈₉	—	2	4	no	—
199	C₈×C₈₉	—	2	4	no	—
200	C₂²×C₈₉	—	2	2	no	—
201	C₂²×C₈₉	—	2	4	no	—
202	C₂²×C₈₉	—	4	4	no	—
203	C₂²×C₈₉	—	4	4	no	—
204	C₂²×C₈₉	—	4	4	no	—
205	C₂²×C₈₉	—	4	4	no	—
206	C₂²×C₈₉	—	8	8	no	—
207	C₂²×C₈₉	#537	1	2	yes	—
208	C₂²×C₈₉	#577	1	4	yes	—
209	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
210	C₄×C₈₉	—	2	2	no	—
211	C₄×C₈₉	—	2	4	no	—
212	C₄×C₈₉	—	2	4	no	—
213	C₄×C₈₉	—	4	4	no	—
214	C₄×C₈₉	—	4	4	no	—
215	C₄×C₈₉	—	4	4	no	—
216	C₄×C₈₉	#537	1	2	yes	—
217	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
218	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
219	C₂×#3260	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂×C₈₉	—	4	2	no	—
221	C₂×C₈₉	—	8	4	no	—
222	C₂×C₈₉	#3260	1	4	yes	direct product factor
223	C₂×C₈₉	C₂×#537	1	1	yes	characteristic
224	C₂×C₈₉	C₂×#577	1	2	yes	—
225	C₂×#541	C₂×C₈₉	1	1	yes	characteristic, complemented
226	C₂×#540	C₂×C₈₉	1	1	yes	characteristic
227	#3260	C₂×C₈₉	1	16	yes	direct product factor
228	C₂×#479	C₂×C₈₉	1	2	yes	complemented
229	C₂×#478	C₂×C₈₉	1	2	yes	complemented
230	C₂×#468	C₂×C₈₉	1	2	yes	complemented
231	C₂×#465	C₂×C₈₉	1	2	yes	complemented
232	C₂×#460	C₂×C₈₉	1	2	yes	complemented
233	C₂×#461	C₂×C₈₉	1	2	yes	complemented
234	C₂×#424	C₂×C₈₉	1	1	yes	characteristic, complemented
235	C₈₉	C₂×#3260	1	1	yes	characteristic, direct product factor, Sylow
236	C₂²×SD₁₆	C₂²×C₈₉	1	2	yes	—
237	C₂²×SD₁₆	C₂²×C₈₉	1	2	yes	—
238	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
239	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
240	#541	—	2	4	no	—
241	#541	C₂²×C₈₉	1	8	yes	complemented
242	#540	—	2	4	no	—
243	#540	C₂²×C₈₉	1	8	yes	—
244	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
245	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
246	C₂×#126	—	2	2	no	—
247	C₂×#125	—	2	2	no	—
248	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
249	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
250	C₂×#123	—	2	2	no	—
251	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
252	C₂×#121	—	2	2	no	—
253	C₂×#121	C₂²×C₈₉	1	2	yes	—
254	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
255	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
256	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
257	#479	C₂²×C₈₉	1	16	yes	complemented
258	#478	C₂²×C₈₉	1	16	yes	complemented
259	#468	C₂²×C₈₉	1	16	yes	complemented
260	#465	C₂²×C₈₉	1	16	yes	complemented
261	#461	C₂²×C₈₉	1	16	yes	complemented
262	#460	C₂²×C₈₉	1	16	yes	complemented
263	C₂×#107	C₂²×C₈₉	1	2	yes	—
264	C₂×#106	C₂²×C₈₉	1	2	yes	—
265	#424	C₂²×C₈₉	1	8	yes	complemented
266	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
267	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
268	C₂×#103	C₂²×C₈₉	1	2	yes	—
269	C₂×#103	C₂²×C₈₉	1	2	yes	—
270	C₂×#102	C₂²×C₈₉	1	2	yes	—
271	C₂×#102	C₂²×C₈₉	1	2	yes	—
272	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
273	C₂²×D₄	—	2	2	no	—
274	C₂²×D₄	—	2	2	no	—
275	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
276	C₂³×C₄	—	2	2	no	—
277	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
278	C₂×SD₁₆	—	4	4	no	—
279	C₂×SD₁₆	—	4	4	no	—
280	C₂×SD₁₆	C₂³×C₈₉	1	8	yes	—
281	C₂×SD₁₆	C₂³×C₈₉	1	8	yes	—
282	C₂×M₁₆	—	4	2	no	—
283	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
284	C₂²×C₈	—	4	2	no	—
285	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
286	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
287	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
288	C₄⋊Q₈	—	2	2	no	—
289	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
290	#127	—	2	2	no	—
291	#127	C₂³×C₈₉	1	4	yes	—
292	#126	—	2	16	no	—
293	#125	—	2	16	no	—
294	#125	—	2	2	no	—
295	#125	—	2	2	no	—
296	#125	C₂³×C₈₉	1	4	yes	—
297	#125	C₂³×C₈₉	1	4	yes	—
298	#123	—	2	16	no	—
299	C₂²⋊Q₈	—	2	4	no	—
300	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
301	#121	—	2	4	no	—
302	#121	—	2	16	no	—
303	#121	C₂³×C₈₉	1	8	yes	—
304	C₄×Q₈	—	2	4	no	—
305	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
306	C₄×D₄	—	2	4	no	—
307	C₄×D₄	C₂³×C₈₉	1	8	yes	—
308	#117	D₄×C₈₉	1	4	yes	—
309	#117	C₂³×C₈₉	1	4	yes	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
317	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
322	C₂×C₄²	—	2	2	no	—
323	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
324	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
325	#107	C₂³×C₈₉	1	8	yes	—
326	#106	C₂³×C₈₉	1	8	yes	—
327	C₄⋊C₈	C₂³×C₈₉	1	8	yes	—
328	C₄⋊C₈	C₂³×C₈₉	1	8	yes	—
329	#103	C₂³×C₈₉	1	8	yes	—
330	#103	C₂³×C₈₉	1	8	yes	—
331	#102	C₂³×C₈₉	1	8	yes	—
332	#102	C₂³×C₈₉	1	8	yes	—
333	C₂⁴	—	2	2	no	—
334	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	—	2	4	no	—
338	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
339	C₂×D₄	—	2	8	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	8	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	8	4	no	—
345	C₂×D₄	—	8	4	no	—
346	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	8	no	—
353	C₂²×C₄	—	8	4	no	—
354	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
359	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
360	SD₁₆	—	4	8	no	—
361	SD₁₆	—	4	8	no	—
362	M₁₆	—	4	4	no	—
363	C₂×C₈	—	2	4	no	—
364	C₂×C₈	—	2	4	no	—
365	C₂×C₈	—	4	4	no	—
366	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
367	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
368	C₄⋊C₄	—	2	8	no	—
369	C₄⋊C₄	—	2	8	no	—
370	C₄⋊C₄	—	2	8	no	—
371	C₄⋊C₄	—	2	8	no	—
372	C₄⋊C₄	—	2	8	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
376	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
377	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
378	C₂²⋊C₄	—	2	8	no	—
379	C₂²⋊C₄	—	2	8	no	—
380	C₂²⋊C₄	—	2	8	no	—
381	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
382	C₄²	—	2	8	no	—
383	C₄²	C₂×D₄×C₈₉	1	2	yes	—
384	C₄²	C₂×D₄×C₈₉	1	2	yes	—
385	C₄²	C₂⁴×C₈₉	1	2	yes	—
386	C₄²	C₂⁴×C₈₉	1	2	yes	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	2	4	no	—
390	C₂³	—	4	4	no	—
391	C₂³	—	4	4	no	—
392	C₂³	—	4	4	no	—
393	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
394	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
395	Q₈	—	2	4	no	—
396	Q₈	—	2	4	no	—
397	Q₈	—	4	4	no	—
398	D₄	—	2	4	no	—
399	D₄	—	2	4	no	—
400	D₄	—	4	4	no	—
401	D₄	—	8	8	no	—
402	D₄	—	8	8	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	8	8	no	—
416	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
417	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
418	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
419	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
420	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
421	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
422	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
423	C₈	—	2	4	no	—
424	C₈	—	2	4	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	4	4	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	4	no	—
431	C₂²	—	8	8	no	—
432	C₂²	#537×C₈₉	1	2	yes	—
433	C₂²	#577×C₈₉	1	4	yes	—
434	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
435	C₄	—	2	4	no	—
436	C₄	—	2	4	no	—
437	C₄	—	2	2	no	—
438	C₄	—	4	4	no	—
439	C₄	—	4	4	no	—
440	C₄	—	4	4	no	—
441	C₄	#537×C₈₉	1	2	yes	—
442	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
443	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
444	C₂	—	4	2	no	—
445	C₂	—	8	4	no	—
446	C₂	C₈₉×#3260	1	4	yes	direct product factor
447	C₂	C₂×#537×C₈₉	1	1	yes	characteristic
448	C₂	C₂×#577×C₈₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₂×#540×C₈₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×#117×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#541×C₈₉	C₂	semidirect
3. C₈₉×#3260	C₂	direct (N × H)
4. C₂×#479×C₈₉	C₂	semidirect
5. C₂×#478×C₈₉	C₂	semidirect
6. C₂×#468×C₈₉	C₂	semidirect
7. C₂×#465×C₈₉	C₂	semidirect
8. C₂×#460×C₈₉	C₂	semidirect
9. C₂×#461×C₈₉	C₂	semidirect
10. C₂×#424×C₈₉	C₂	semidirect
16. #541×C₈₉	C₂²	semidirect
32. #479×C₈₉	C₂²	semidirect
33. #478×C₈₉	C₂²	semidirect
34. #468×C₈₉	C₂²	semidirect
35. #465×C₈₉	C₂²	semidirect
36. #461×C₈₉	C₂²	semidirect
37. #460×C₈₉	C₂²	semidirect
40. #424×C₈₉	C₂²	semidirect
219. C₂×#3260	C₈₉	direct (N × H)
222. C₂×C₈₉	#3260	direct (N × H)
225. C₂×#541	C₂×C₈₉	semidirect
227. #3260	C₂×C₈₉	direct (N × H)
228. C₂×#479	C₂×C₈₉	semidirect
229. C₂×#478	C₂×C₈₉	semidirect
230. C₂×#468	C₂×C₈₉	semidirect
231. C₂×#465	C₂×C₈₉	semidirect
232. C₂×#460	C₂×C₈₉	semidirect
233. C₂×#461	C₂×C₈₉	semidirect
234. C₂×#424	C₂×C₈₉	semidirect
235. C₈₉	C₂×#3260	direct (N × H)
241. #541	C₂²×C₈₉	semidirect
257. #479	C₂²×C₈₉	semidirect
258. #478	C₂²×C₈₉	semidirect
259. #468	C₂²×C₈₉	semidirect
260. #465	C₂²×C₈₉	semidirect
261. #461	C₂²×C₈₉	semidirect
262. #460	C₂²×C₈₉	semidirect
265. #424	C₂²×C₈₉	semidirect
446. C₂	C₈₉×#3260	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#541×C₈₉	2
C₂×#540×C₈₉	2
C₈₉×#3260	2
C₂×#479×C₈₉	2
C₂×#478×C₈₉	2
C₂×#468×C₈₉	2
C₂×#465×C₈₉	2
C₂×#460×C₈₉	2
C₂×#461×C₈₉	2
C₂×#424×C₈₉	2
C₂×#3260	89

Subgroups — C2×C89×#3260 #36438759

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3260 #36438759