Subgroups — C₂×C₈₉×#3050 #36438285

Order 22784.

3046 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#525×C₈₉	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3050	C₂	1	16	yes	maximal, direct product factor
5	C₂×#467×C₈₉	C₂	1	2	yes	maximal, complemented
6	C₂×#466×C₈₉	C₂	1	2	yes	maximal, complemented
7	C₂×#465×C₈₉	C₂	1	4	yes	maximal, complemented
8	C₂×#427×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#416×C₈₉	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₈₉	C₂²	1	2	yes	—
11	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
12	C₂×#135×C₈₉	—	2	8	no	—
13	C₂×#135×C₈₉	C₂²	1	8	yes	complemented
14	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
15	C₂²×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
16	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
17	C₂³×C₈×C₈₉	—	2	8	no	—
18	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₈₉	C₂²	1	2	yes	—
20	C₂³×C₈×C₈₉	C₂²	1	2	yes	—
21	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₈₉	C₂²	1	8	yes	complemented
23	#525×C₈₉	—	2	8	no	—
24	#525×C₈₉	C₂²	1	16	yes	complemented
25	C₂×#123×C₈₉	—	2	2	no	—
26	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
27	C₂×#121×C₈₉	C₂²	1	4	yes	—
28	C₂×#120×C₈₉	—	2	2	no	—
29	C₂×C₄×D₄×C₈₉	—	2	4	no	—
30	C₂×#117×C₈₉	C₂²	1	2	yes	—
31	#467×C₈₉	C₂²	1	16	yes	complemented
32	#466×C₈₉	C₂²	1	16	yes	complemented
33	#465×C₈₉	C₂²	1	32	yes	complemented
34	#427×C₈₉	C₂²	1	8	yes	complemented
35	C₂×#107×C₈₉	C₂²	1	2	yes	complemented
36	C₂×#106×C₈₉	C₂²	1	2	yes	complemented
37	#416×C₈₉	C₂²	1	16	yes	complemented
38	C₂×#103×C₈₉	C₂²	1	4	yes	complemented
39	C₂×#102×C₈₉	C₂²	1	4	yes	complemented
40	C₂⁵×C₈₉	D₄	1	1	yes	characteristic
41	C₂×#41×C₈₉	—	2	4	no	—
42	C₂×#41×C₈₉	—	2	8	no	—
43	C₂×#41×C₈₉	—	2	8	no	—
44	C₂×#41×C₈₉	C₂³	1	8	yes	—
45	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
46	C₂²×D₄×C₈₉	—	2	4	no	—
47	C₂²×D₄×C₈₉	—	2	2	no	—
48	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
49	C₂³×C₄×C₈₉	—	2	4	no	—
50	C₂³×C₄×C₈₉	—	2	4	no	—
51	C₂³×C₄×C₈₉	—	2	2	no	—
52	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₈₉	D₄	1	4	yes	—
54	C₂³×C₄×C₈₉	D₄	1	2	yes	—
55	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
56	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
57	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
58	#135×C₈₉	—	2	32	no	—
59	C₂×Q₁₆×C₈₉	—	2	4	no	—
60	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	complemented
61	C₂×SD₁₆×C₈₉	—	2	8	no	—
62	C₂×SD₁₆×C₈₉	C₂³	1	8	yes	complemented
63	C₂×D₈×C₈₉	—	2	4	no	—
64	C₂×D₈×C₈₉	C₂³	1	4	yes	complemented
65	C₂²×C₈×C₈₉	—	2	4	no	—
66	C₂²×C₈×C₈₉	—	2	8	no	—
67	C₂²×C₈×C₈₉	—	2	8	no	—
68	C₂²×C₈×C₈₉	—	2	32	no	—
69	C₂²×C₈×C₈₉	D₄	1	8	yes	complemented
70	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
71	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
72	C₂²×C₈×C₈₉	C₂³	1	8	yes	—
73	C₂²×C₈×C₈₉	C₂³	1	8	yes	—
74	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
77	#123×C₈₉	—	2	16	no	—
78	C₂²⋊Q₈×C₈₉	—	2	8	no	—
79	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
80	#121×C₈₉	—	2	8	no	—
81	#121×C₈₉	C₂³	1	16	yes	—
82	#120×C₈₉	—	2	16	no	—
83	C₄×D₄×C₈₉	—	2	32	no	—
84	#117×C₈₉	—	2	4	no	—
85	#117×C₈₉	C₂³	1	8	yes	—
86	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
87	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
88	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
90	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
91	C₂×C₄²×C₈₉	—	2	2	no	—
92	#107×C₈₉	C₂³	1	8	yes	complemented
93	#106×C₈₉	C₂³	1	8	yes	complemented
94	#103×C₈₉	C₂³	1	16	yes	complemented
95	#102×C₈₉	C₂³	1	16	yes	complemented
96	C₂⁴×C₈₉	—	2	4	no	—
97	C₂⁴×C₈₉	—	2	8	no	—
98	C₂⁴×C₈₉	—	2	2	no	—
99	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
100	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
101	C₂⁴×C₈₉	C₂×D₄	1	2	yes	—
102	#41×C₈₉	—	2	16	no	—
103	#41×C₈₉	—	2	16	no	—
104	#41×C₈₉	—	4	16	no	—
105	C₂×Q₈×C₈₉	—	2	2	no	—
106	C₂×Q₈×C₈₉	—	2	4	no	—
107	C₂×Q₈×C₈₉	—	2	4	no	—
108	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
109	C₂×D₄×C₈₉	—	2	16	no	—
110	C₂×D₄×C₈₉	—	2	8	no	—
111	C₂×D₄×C₈₉	—	2	4	no	—
112	C₂×D₄×C₈₉	—	2	2	no	—
113	C₂×D₄×C₈₉	—	2	4	no	—
114	C₂×D₄×C₈₉	—	4	8	no	—
115	C₂×D₄×C₈₉	—	4	16	no	—
116	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
117	C₂²×C₄×C₈₉	—	2	4	no	—
118	C₂²×C₄×C₈₉	—	2	8	no	—
119	C₂²×C₄×C₈₉	—	2	16	no	—
120	C₂²×C₄×C₈₉	—	2	4	no	—
121	C₂²×C₄×C₈₉	—	2	8	no	—
122	C₂²×C₄×C₈₉	—	2	4	no	—
123	C₂²×C₄×C₈₉	—	2	8	no	—
124	C₂²×C₄×C₈₉	—	2	4	no	—
125	C₂²×C₄×C₈₉	—	2	2	no	—
126	C₂²×C₄×C₈₉	—	2	8	no	—
127	C₂²×C₄×C₈₉	—	4	8	no	—
128	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
130	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
134	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₈₉	#41	1	4	yes	—
136	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
139	Q₁₆×C₈₉	—	2	8	no	—
140	SD₁₆×C₈₉	—	2	16	no	—
141	D₈×C₈₉	—	2	8	no	—
142	C₂×C₈×C₈₉	—	2	4	no	—
143	C₂×C₈×C₈₉	—	2	8	no	—
144	C₂×C₈×C₈₉	—	2	16	no	—
145	C₂×C₈×C₈₉	—	2	16	no	—
146	C₂×C₈×C₈₉	C₂×D₄	1	4	yes	—
147	C₂×C₈×C₈₉	C₂×D₄	1	4	yes	—
148	C₂×C₈×C₈₉	C₂×D₄	1	16	yes	complemented
149	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
150	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
151	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
152	C₄⋊C₄×C₈₉	—	2	16	no	—
153	C₄⋊C₄×C₈₉	—	2	4	no	—
154	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
155	C₂²⋊C₄×C₈₉	—	2	8	no	—
156	C₂²⋊C₄×C₈₉	—	2	16	no	—
157	C₂²⋊C₄×C₈₉	—	2	16	no	—
158	C₄²×C₈₉	—	2	8	no	—
159	C₂³×C₈₉	—	2	32	no	—
160	C₂³×C₈₉	—	2	8	no	—
161	C₂³×C₈₉	—	2	4	no	—
162	C₂³×C₈₉	—	2	4	no	—
163	C₂³×C₈₉	—	2	4	no	—
164	C₂³×C₈₉	—	2	16	no	—
165	C₂³×C₈₉	—	2	4	no	—
166	C₂³×C₈₉	—	4	4	no	—
167	C₂³×C₈₉	—	4	8	no	—
168	C₂³×C₈₉	#121	1	4	yes	—
169	C₂³×C₈₉	#135	1	8	yes	complemented
170	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
171	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
172	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₈₉	—	2	4	no	—
174	Q₈×C₈₉	—	2	4	no	—
175	Q₈×C₈₉	—	4	4	no	—
176	D₄×C₈₉	—	2	4	no	—
177	D₄×C₈₉	—	2	4	no	—
178	D₄×C₈₉	—	4	16	no	—
179	D₄×C₈₉	—	4	32	no	—
180	D₄×C₈₉	—	4	4	no	—
181	C₂×C₄×C₈₉	—	2	8	no	—
182	C₂×C₄×C₈₉	—	2	4	no	—
183	C₂×C₄×C₈₉	—	2	16	no	—
184	C₂×C₄×C₈₉	—	2	8	no	—
185	C₂×C₄×C₈₉	—	2	4	no	—
186	C₂×C₄×C₈₉	—	2	4	no	—
187	C₂×C₄×C₈₉	—	2	8	no	—
188	C₂×C₄×C₈₉	—	2	4	no	—
189	C₂×C₄×C₈₉	—	4	4	no	—
190	C₂×C₄×C₈₉	—	4	8	no	—
191	C₂×C₄×C₈₉	—	4	16	no	—
192	C₂×C₄×C₈₉	#121	1	4	yes	—
193	C₂×C₄×C₈₉	#121	1	8	yes	—
194	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
195	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
196	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
199	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
200	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
201	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
202	C₈×C₈₉	—	2	4	no	—
203	C₈×C₈₉	C₂²×D₄	1	4	yes	—
204	C₈×C₈₉	C₂²×D₄	1	4	yes	—
205	C₂²×C₈₉	—	2	32	no	—
206	C₂²×C₈₉	—	2	4	no	—
207	C₂²×C₈₉	—	2	8	no	—
208	C₂²×C₈₉	—	2	16	no	—
209	C₂²×C₈₉	—	2	4	no	—
210	C₂²×C₈₉	—	2	4	no	—
211	C₂²×C₈₉	—	4	4	no	—
212	C₂²×C₈₉	—	4	8	no	—
213	C₂²×C₈₉	—	8	8	no	—
214	C₂²×C₈₉	C₂×#121	1	4	yes	—
215	C₂²×C₈₉	C₂×#121	1	2	yes	—
216	C₂²×C₈₉	C₂×#135	1	4	yes	—
217	C₂²×C₈₉	C₂×#135	1	8	yes	complemented
218	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
219	C₄×C₈₉	—	2	4	no	—
220	C₄×C₈₉	—	4	4	no	—
221	C₄×C₈₉	—	4	8	no	—
222	C₄×C₈₉	C₂×#121	1	4	yes	—
223	C₄×C₈₉	C₂×#121	1	2	yes	—
224	C₄×C₈₉	C₂³×D₄	1	1	yes	characteristic
225	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
226	C₂×#3050	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂×C₈₉	—	2	4	no	—
228	C₂×C₈₉	—	2	8	no	—
229	C₂×C₈₉	—	8	4	no	—
230	C₂×C₈₉	#3050	1	4	yes	direct product factor
231	C₂×C₈₉	C₂²×#121	1	1	yes	characteristic
232	C₂×C₈₉	C₂²×#135	1	2	yes	—
233	C₂²×#135	C₂×C₈₉	1	1	yes	characteristic, complemented
234	C₂⁴×C₈	C₂×C₈₉	1	1	yes	characteristic, complemented
235	C₂×#525	C₂×C₈₉	1	2	yes	complemented
236	#3050	C₂×C₈₉	1	16	yes	direct product factor
237	C₂×#467	C₂×C₈₉	1	2	yes	complemented
238	C₂×#466	C₂×C₈₉	1	2	yes	complemented
239	C₂×#465	C₂×C₈₉	1	4	yes	complemented
240	C₂×#427	C₂×C₈₉	1	1	yes	characteristic, complemented
241	C₂×#416	C₂×C₈₉	1	2	yes	complemented
242	C₈₉	C₂×#3050	1	1	yes	characteristic, direct product factor, Sylow
243	C₂²×#41	C₂²×C₈₉	1	2	yes	—
244	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
245	C₂×#135	—	2	8	no	—
246	C₂×#135	C₂²×C₈₉	1	8	yes	complemented
247	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
248	C₂²×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
249	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
250	C₂³×C₈	—	2	8	no	—
251	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
252	C₂³×C₈	C₂²×C₈₉	1	2	yes	—
253	C₂³×C₈	C₂²×C₈₉	1	2	yes	—
254	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
255	C₂³×C₈	C₂²×C₈₉	1	8	yes	complemented
256	#525	—	2	8	no	—
257	#525	C₂²×C₈₉	1	16	yes	complemented
258	C₂×#123	—	2	2	no	—
259	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
260	C₂×#121	C₂²×C₈₉	1	4	yes	—
261	C₂×#120	—	2	2	no	—
262	C₂×C₄×D₄	—	2	4	no	—
263	C₂×#117	C₂²×C₈₉	1	2	yes	—
264	#467	C₂²×C₈₉	1	16	yes	complemented
265	#466	C₂²×C₈₉	1	16	yes	complemented
266	#465	C₂²×C₈₉	1	32	yes	complemented
267	#427	C₂²×C₈₉	1	8	yes	complemented
268	C₂×#107	C₂²×C₈₉	1	2	yes	complemented
269	C₂×#106	C₂²×C₈₉	1	2	yes	complemented
270	#416	C₂²×C₈₉	1	16	yes	complemented
271	C₂×#103	C₂²×C₈₉	1	4	yes	complemented
272	C₂×#102	C₂²×C₈₉	1	4	yes	complemented
273	C₂⁵	D₄×C₈₉	1	1	yes	characteristic
274	C₂×#41	—	2	4	no	—
275	C₂×#41	—	2	8	no	—
276	C₂×#41	—	2	8	no	—
277	C₂×#41	C₂³×C₈₉	1	8	yes	—
278	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
279	C₂²×D₄	—	2	4	no	—
280	C₂²×D₄	—	2	2	no	—
281	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
282	C₂³×C₄	—	2	4	no	—
283	C₂³×C₄	—	2	4	no	—
284	C₂³×C₄	—	2	2	no	—
285	C₂³×C₄	D₄×C₈₉	1	2	yes	—
286	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
287	C₂³×C₄	D₄×C₈₉	1	4	yes	—
288	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
289	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
290	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
291	#135	—	2	32	no	—
292	C₂×Q₁₆	—	2	4	no	—
293	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	complemented
294	C₂×SD₁₆	—	2	8	no	—
295	C₂×SD₁₆	C₂³×C₈₉	1	8	yes	complemented
296	C₂×D₈	—	2	4	no	—
297	C₂×D₈	C₂³×C₈₉	1	4	yes	complemented
298	C₂²×C₈	—	2	4	no	—
299	C₂²×C₈	—	2	8	no	—
300	C₂²×C₈	—	2	8	no	—
301	C₂²×C₈	—	2	32	no	—
302	C₂²×C₈	D₄×C₈₉	1	8	yes	complemented
303	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
304	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
305	C₂²×C₈	C₂³×C₈₉	1	8	yes	—
306	C₂²×C₈	C₂³×C₈₉	1	8	yes	—
307	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
309	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
310	#123	—	2	16	no	—
311	C₂²⋊Q₈	—	2	8	no	—
312	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
313	#121	—	2	8	no	—
314	#121	C₂³×C₈₉	1	16	yes	—
315	#120	—	2	16	no	—
316	C₄×D₄	—	2	32	no	—
317	#117	—	2	4	no	—
318	#117	C₂³×C₈₉	1	8	yes	—
319	C₂×C₄⋊C₄	—	2	4	no	—
320	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	4	no	—
323	C₂×C₂²⋊C₄	—	2	4	no	—
324	C₂×C₄²	—	2	2	no	—
325	#107	C₂³×C₈₉	1	8	yes	complemented
326	#106	C₂³×C₈₉	1	8	yes	complemented
327	#103	C₂³×C₈₉	1	16	yes	complemented
328	#102	C₂³×C₈₉	1	16	yes	complemented
329	C₂⁴	—	2	4	no	—
330	C₂⁴	—	2	8	no	—
331	C₂⁴	—	2	2	no	—
332	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
333	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
334	C₂⁴	C₂×D₄×C₈₉	1	2	yes	—
335	#41	—	2	16	no	—
336	#41	—	2	16	no	—
337	#41	—	4	16	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	—	2	4	no	—
341	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
342	C₂×D₄	—	2	16	no	—
343	C₂×D₄	—	2	8	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	4	8	no	—
348	C₂×D₄	—	4	16	no	—
349	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	8	no	—
352	C₂²×C₄	—	2	16	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	8	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	8	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	8	no	—
360	C₂²×C₄	—	4	8	no	—
361	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
363	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
364	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
365	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
368	C₂²×C₄	#41×C₈₉	1	4	yes	—
369	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
370	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
371	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
372	Q₁₆	—	2	8	no	—
373	SD₁₆	—	2	16	no	—
374	D₈	—	2	8	no	—
375	C₂×C₈	—	2	4	no	—
376	C₂×C₈	—	2	8	no	—
377	C₂×C₈	—	2	16	no	—
378	C₂×C₈	—	2	16	no	—
379	C₂×C₈	C₂×D₄×C₈₉	1	4	yes	—
380	C₂×C₈	C₂×D₄×C₈₉	1	4	yes	—
381	C₂×C₈	C₂×D₄×C₈₉	1	16	yes	complemented
382	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
383	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
384	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
385	C₄⋊C₄	—	2	16	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₂²⋊C₄	—	2	16	no	—
390	C₂²⋊C₄	—	2	16	no	—
391	C₄²	—	2	8	no	—
392	C₂³	—	2	32	no	—
393	C₂³	—	2	8	no	—
394	C₂³	—	2	4	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	2	16	no	—
398	C₂³	—	2	4	no	—
399	C₂³	—	4	4	no	—
400	C₂³	—	4	8	no	—
401	C₂³	#121×C₈₉	1	4	yes	—
402	C₂³	#135×C₈₉	1	8	yes	complemented
403	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
404	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
405	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
406	Q₈	—	2	4	no	—
407	Q₈	—	2	4	no	—
408	Q₈	—	4	4	no	—
409	D₄	—	2	4	no	—
410	D₄	—	2	4	no	—
411	D₄	—	4	16	no	—
412	D₄	—	4	32	no	—
413	D₄	—	4	4	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	16	no	—
417	C₂×C₄	—	2	8	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	8	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	8	no	—
424	C₂×C₄	—	4	16	no	—
425	C₂×C₄	#121×C₈₉	1	4	yes	—
426	C₂×C₄	#121×C₈₉	1	8	yes	—
427	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
428	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
429	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
430	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
431	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
432	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
433	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
434	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
435	C₈	—	2	4	no	—
436	C₈	C₂²×D₄×C₈₉	1	4	yes	—
437	C₈	C₂²×D₄×C₈₉	1	4	yes	—
438	C₂²	—	2	32	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	2	8	no	—
443	C₂²	—	2	16	no	—
444	C₂²	—	4	8	no	—
445	C₂²	—	4	4	no	—
446	C₂²	—	8	8	no	—
447	C₂²	C₂×#121×C₈₉	1	4	yes	—
448	C₂²	C₂×#121×C₈₉	1	2	yes	—
449	C₂²	C₂×#135×C₈₉	1	4	yes	—
450	C₂²	C₂×#135×C₈₉	1	8	yes	complemented
451	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
452	C₄	—	2	4	no	—
453	C₄	—	4	8	no	—
454	C₄	—	4	4	no	—
455	C₄	C₂×#121×C₈₉	1	4	yes	—
456	C₄	C₂×#121×C₈₉	1	2	yes	—
457	C₄	C₂³×D₄×C₈₉	1	1	yes	characteristic
458	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
459	C₂	—	2	4	no	—
460	C₂	—	2	8	no	—
461	C₂	—	8	4	no	—
462	C₂	C₈₉×#3050	1	4	yes	direct product factor
463	C₂	C₂²×#121×C₈₉	1	1	yes	characteristic
464	C₂	C₂²×#135×C₈₉	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₈₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
socle	C₂³×C₈₉	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₈₉ ◁ C₂⁴×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#135×C₈₉	C₂	semidirect
2. C₂⁴×C₈×C₈₉	C₂	semidirect
3. C₂×#525×C₈₉	C₂	semidirect
4. C₈₉×#3050	C₂	direct (N × H)
5. C₂×#467×C₈₉	C₂	semidirect
6. C₂×#466×C₈₉	C₂	semidirect
7. C₂×#465×C₈₉	C₂	semidirect
8. C₂×#427×C₈₉	C₂	semidirect
9. C₂×#416×C₈₉	C₂	semidirect
13. C₂×#135×C₈₉	C₂²	semidirect
14. C₂²×Q₁₆×C₈₉	C₂²	semidirect
15. C₂²×SD₁₆×C₈₉	C₂²	semidirect
16. C₂²×D₈×C₈₉	C₂²	semidirect
22. C₂³×C₈×C₈₉	C₂²	semidirect
24. #525×C₈₉	C₂²	semidirect
31. #467×C₈₉	C₂²	semidirect
32. #466×C₈₉	C₂²	semidirect
33. #465×C₈₉	C₂²	semidirect
34. #427×C₈₉	C₂²	semidirect
35. C₂×#107×C₈₉	C₂²	semidirect
36. C₂×#106×C₈₉	C₂²	semidirect
37. #416×C₈₉	C₂²	semidirect
38. C₂×#103×C₈₉	C₂²	semidirect
39. C₂×#102×C₈₉	C₂²	semidirect
60. C₂×Q₁₆×C₈₉	C₂³	semidirect
62. C₂×SD₁₆×C₈₉	C₂³	semidirect
64. C₂×D₈×C₈₉	C₂³	semidirect
69. C₂²×C₈×C₈₉	D₄	semidirect
92. #107×C₈₉	C₂³	semidirect
93. #106×C₈₉	C₂³	semidirect
94. #103×C₈₉	C₂³	semidirect
95. #102×C₈₉	C₂³	semidirect
148. C₂×C₈×C₈₉	C₂×D₄	semidirect
169. C₂³×C₈₉	#135	semidirect
217. C₂²×C₈₉	C₂×#135	semidirect
226. C₂×#3050	C₈₉	direct (N × H)
230. C₂×C₈₉	#3050	direct (N × H)
233. C₂²×#135	C₂×C₈₉	semidirect
234. C₂⁴×C₈	C₂×C₈₉	semidirect
235. C₂×#525	C₂×C₈₉	semidirect
236. #3050	C₂×C₈₉	direct (N × H)
237. C₂×#467	C₂×C₈₉	semidirect
238. C₂×#466	C₂×C₈₉	semidirect
239. C₂×#465	C₂×C₈₉	semidirect
240. C₂×#427	C₂×C₈₉	semidirect
241. C₂×#416	C₂×C₈₉	semidirect
242. C₈₉	C₂×#3050	direct (N × H)
246. C₂×#135	C₂²×C₈₉	semidirect
247. C₂²×Q₁₆	C₂²×C₈₉	semidirect
248. C₂²×SD₁₆	C₂²×C₈₉	semidirect
249. C₂²×D₈	C₂²×C₈₉	semidirect
255. C₂³×C₈	C₂²×C₈₉	semidirect
257. #525	C₂²×C₈₉	semidirect
264. #467	C₂²×C₈₉	semidirect
265. #466	C₂²×C₈₉	semidirect
266. #465	C₂²×C₈₉	semidirect
267. #427	C₂²×C₈₉	semidirect
268. C₂×#107	C₂²×C₈₉	semidirect
269. C₂×#106	C₂²×C₈₉	semidirect
270. #416	C₂²×C₈₉	semidirect
271. C₂×#103	C₂²×C₈₉	semidirect
272. C₂×#102	C₂²×C₈₉	semidirect
293. C₂×Q₁₆	C₂³×C₈₉	semidirect
295. C₂×SD₁₆	C₂³×C₈₉	semidirect
297. C₂×D₈	C₂³×C₈₉	semidirect
302. C₂²×C₈	D₄×C₈₉	semidirect
325. #107	C₂³×C₈₉	semidirect
326. #106	C₂³×C₈₉	semidirect
327. #103	C₂³×C₈₉	semidirect
328. #102	C₂³×C₈₉	semidirect
381. C₂×C₈	C₂×D₄×C₈₉	semidirect
402. C₂³	#135×C₈₉	semidirect
450. C₂²	C₂×#135×C₈₉	semidirect
462. C₂	C₈₉×#3050	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×#135×C₈₉	2
C₂⁴×C₈×C₈₉	2
C₂×#525×C₈₉	2
C₈₉×#3050	2
C₂×#467×C₈₉	2
C₂×#466×C₈₉	2
C₂×#465×C₈₉	2
C₂×#427×C₈₉	2
C₂×#416×C₈₉	2
C₂×#3050	89

Subgroups — C2×C89×#3050 #36438285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3050 #36438285