Subgroups — C₈₉×#35541 #36413389

Order 22784.

2774 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#535×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#518×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2447	C₂	1	4	yes	maximal, complemented
4	C₈₉×#2445	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2422	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2420	C₂	1	4	yes	maximal, complemented
7	C₈₉×#2412	C₂	1	8	yes	maximal, complemented
8	C₈₉×#2316	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2311	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2297	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#390×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2285	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
15	#535×C₈₉	—	2	8	no	—
16	C₂×#127×C₈₉	C₂²	1	2	yes	—
17	C₂×#124×C₈₉	C₂²	1	2	yes	—
18	C₂×#123×C₈₉	C₂²	1	8	yes	complemented
19	C₂×#121×C₈₉	C₂²	1	4	yes	—
20	C₂×#120×C₈₉	C₂²	1	4	yes	—
21	#518×C₈₉	—	2	8	no	—
22	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
23	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
24	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
29	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
30	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
31	#397×C₈₉	C₂²	1	8	yes	complemented
32	#397×C₈₉	C₂²	1	8	yes	complemented
33	#394×C₈₉	C₂²	1	8	yes	complemented
34	#394×C₈₉	C₂²	1	8	yes	complemented
35	#391×C₈₉	C₂²	1	2	yes	complemented
36	#391×C₈₉	C₂²	1	2	yes	complemented
37	#390×C₈₉	C₂²	1	2	yes	—
38	#390×C₈₉	C₂²	1	2	yes	—
39	#390×C₈₉	C₂²	1	4	yes	—
40	#390×C₈₉	C₂²	1	2	yes	complemented
41	#390×C₈₉	C₂²	1	2	yes	complemented
42	#389×C₈₉	C₂²	1	4	yes	complemented
43	#389×C₈₉	C₂²	1	4	yes	complemented
44	#386×C₈₉	C₂²	1	4	yes	—
45	#386×C₈₉	C₂²	1	4	yes	—
46	#386×C₈₉	C₂²	1	8	yes	complemented
47	#385×C₈₉	C₂²	1	8	yes	complemented
48	#384×C₈₉	C₂²	1	2	yes	complemented
49	#382×C₈₉	C₂²	1	2	yes	complemented
50	#381×C₈₉	C₂²	1	8	yes	complemented
51	#380×C₈₉	C₂²	1	4	yes	—
52	#380×C₈₉	C₂²	1	4	yes	—
53	#380×C₈₉	C₂²	1	4	yes	complemented
54	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	complemented
55	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
57	C₂⁵×C₈₉	C₂³	1	2	yes	—
58	C₂×#41×C₈₉	—	2	4	no	—
59	C₂×#41×C₈₉	—	2	4	no	—
60	C₂×#41×C₈₉	—	2	4	no	—
61	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₈₉	—	2	4	no	—
63	C₂²×D₄×C₈₉	—	2	4	no	—
64	C₂²×D₄×C₈₉	D₄	1	8	yes	—
65	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
66	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
68	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
69	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
70	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
71	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
72	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
73	C₂³×C₄×C₈₉	C₂³	1	8	yes	—
74	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
75	#127×C₈₉	—	2	8	no	—
76	#124×C₈₉	—	2	8	no	—
77	#123×C₈₉	—	4	16	no	—
78	#121×C₈₉	—	2	16	no	—
79	#120×C₈₉	—	2	16	no	—
80	C₄×D₄×C₈₉	—	2	16	no	—
81	C₄×D₄×C₈₉	—	2	16	no	—
82	#117×C₈₉	—	2	4	no	—
83	#117×C₈₉	—	2	4	no	—
84	#117×C₈₉	—	2	4	no	—
85	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
86	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
94	C₂×C₂²⋊C₄×C₈₉	—	2	16	no	—
95	C₂×C₂²⋊C₄×C₈₉	—	4	8	no	—
96	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
98	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
99	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
100	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
101	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
102	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
103	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
105	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
106	C₂×C₄²×C₈₉	—	2	4	no	—
107	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
110	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
111	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
112	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
113	#95×C₈₉	C₂³	1	4	yes	—
114	#95×C₈₉	C₂³	1	4	yes	—
115	#95×C₈₉	C₂³	1	4	yes	—
116	#95×C₈₉	C₂³	1	4	yes	—
117	#95×C₈₉	C₂³	1	8	yes	—
118	#95×C₈₉	C₂³	1	8	yes	—
119	C₂⁴×C₈₉	—	2	4	no	—
120	C₂⁴×C₈₉	—	2	4	no	—
121	C₂⁴×C₈₉	—	4	4	no	—
122	C₂⁴×C₈₉	—	4	4	no	—
123	C₂⁴×C₈₉	C₂×D₄	1	8	yes	—
124	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
125	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
126	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
127	#41×C₈₉	—	4	16	no	—
128	C₂×Q₈×C₈₉	—	2	2	no	—
129	C₂×Q₈×C₈₉	—	2	2	no	—
130	C₂×Q₈×C₈₉	—	2	2	no	—
131	C₂×D₄×C₈₉	—	2	4	no	—
132	C₂×D₄×C₈₉	—	2	4	no	—
133	C₂×D₄×C₈₉	—	2	4	no	—
134	C₂×D₄×C₈₉	—	2	16	no	—
135	C₂×D₄×C₈₉	—	2	32	no	—
136	C₂×D₄×C₈₉	—	2	2	no	—
137	C₂×D₄×C₈₉	—	2	4	no	—
138	C₂×D₄×C₈₉	—	2	4	no	—
139	C₂×D₄×C₈₉	—	2	4	no	—
140	C₂×D₄×C₈₉	—	2	4	no	—
141	C₂×D₄×C₈₉	—	2	2	no	—
142	C₂×D₄×C₈₉	—	2	2	no	—
143	C₂×D₄×C₈₉	—	4	8	no	—
144	C₂×D₄×C₈₉	—	4	8	no	—
145	C₂×D₄×C₈₉	C₂×D₄	1	8	yes	—
146	C₂×D₄×C₈₉	C₂×D₄	1	8	yes	—
147	C₂²×C₄×C₈₉	—	2	4	no	—
148	C₂²×C₄×C₈₉	—	2	16	no	—
149	C₂²×C₄×C₈₉	—	2	4	no	—
150	C₂²×C₄×C₈₉	—	2	4	no	—
151	C₂²×C₄×C₈₉	—	2	4	no	—
152	C₂²×C₄×C₈₉	—	2	4	no	—
153	C₂²×C₄×C₈₉	—	2	4	no	—
154	C₂²×C₄×C₈₉	—	4	2	no	—
155	C₂²×C₄×C₈₉	—	4	4	no	—
156	C₂²×C₄×C₈₉	—	4	8	no	—
157	C₂²×C₄×C₈₉	—	4	8	no	—
158	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
159	C₂²×C₄×C₈₉	#41	1	4	yes	—
160	C₂²×C₄×C₈₉	#41	1	4	yes	—
161	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
164	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
167	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
169	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
170	C₄⋊C₄×C₈₉	—	2	4	no	—
171	C₄⋊C₄×C₈₉	—	2	4	no	—
172	C₄⋊C₄×C₈₉	—	2	4	no	—
173	C₄⋊C₄×C₈₉	—	2	4	no	—
174	C₄⋊C₄×C₈₉	—	2	4	no	—
175	C₄⋊C₄×C₈₉	—	2	8	no	—
176	C₄⋊C₄×C₈₉	—	4	4	no	—
177	C₄⋊C₄×C₈₉	—	4	8	no	—
178	C₂²⋊C₄×C₈₉	—	2	4	no	—
179	C₂²⋊C₄×C₈₉	—	2	4	no	—
180	C₂²⋊C₄×C₈₉	—	2	16	no	—
181	C₂²⋊C₄×C₈₉	—	2	4	no	—
182	C₂²⋊C₄×C₈₉	—	2	16	no	—
183	C₂²⋊C₄×C₈₉	—	2	16	no	—
184	C₂²⋊C₄×C₈₉	—	2	8	no	—
185	C₂²⋊C₄×C₈₉	—	4	8	no	—
186	C₂²⋊C₄×C₈₉	—	4	4	no	—
187	C₂²⋊C₄×C₈₉	—	4	8	no	—
188	C₄²×C₈₉	—	2	4	no	—
189	C₄²×C₈₉	—	2	4	no	—
190	C₄²×C₈₉	—	2	4	no	—
191	C₄²×C₈₉	—	2	2	no	—
192	C₄²×C₈₉	—	2	4	no	—
193	C₄²×C₈₉	—	2	2	no	—
194	C₂³×C₈₉	—	2	2	no	—
195	C₂³×C₈₉	—	2	2	no	—
196	C₂³×C₈₉	—	2	4	no	—
197	C₂³×C₈₉	—	2	4	no	—
198	C₂³×C₈₉	—	2	8	no	—
199	C₂³×C₈₉	—	2	8	no	—
200	C₂³×C₈₉	—	2	16	no	—
201	C₂³×C₈₉	—	2	2	no	—
202	C₂³×C₈₉	—	2	2	no	—
203	C₂³×C₈₉	—	2	2	no	—
204	C₂³×C₈₉	—	2	4	no	—
205	C₂³×C₈₉	—	2	4	no	—
206	C₂³×C₈₉	—	4	16	no	—
207	C₂³×C₈₉	—	8	8	no	—
208	C₂³×C₈₉	—	8	4	no	—
209	C₂³×C₈₉	—	8	4	no	—
210	C₂³×C₈₉	C₂²×D₄	1	8	yes	—
211	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
212	C₂³×C₈₉	C₂×#41	1	2	yes	—
213	C₂³×C₈₉	C₂×#41	1	2	yes	—
214	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
215	Q₈×C₈₉	—	4	4	no	—
216	D₄×C₈₉	—	2	16	no	—
217	D₄×C₈₉	—	2	16	no	—
218	D₄×C₈₉	—	4	8	no	—
219	D₄×C₈₉	—	4	4	no	—
220	D₄×C₈₉	—	8	16	no	—
221	C₂×C₄×C₈₉	—	2	2	no	—
222	C₂×C₄×C₈₉	—	2	2	no	—
223	C₂×C₄×C₈₉	—	2	4	no	—
224	C₂×C₄×C₈₉	—	2	4	no	—
225	C₂×C₄×C₈₉	—	2	4	no	—
226	C₂×C₄×C₈₉	—	2	2	no	—
227	C₂×C₄×C₈₉	—	2	2	no	—
228	C₂×C₄×C₈₉	—	2	4	no	—
229	C₂×C₄×C₈₉	—	2	2	no	—
230	C₂×C₄×C₈₉	—	2	2	no	—
231	C₂×C₄×C₈₉	—	2	8	no	—
232	C₂×C₄×C₈₉	—	2	4	no	—
233	C₂×C₄×C₈₉	—	2	2	no	—
234	C₂×C₄×C₈₉	—	2	4	no	—
235	C₂×C₄×C₈₉	—	2	4	no	—
236	C₂×C₄×C₈₉	—	2	2	no	—
237	C₂×C₄×C₈₉	—	2	4	no	—
238	C₂×C₄×C₈₉	—	2	4	no	—
239	C₂×C₄×C₈₉	—	2	4	no	—
240	C₂×C₄×C₈₉	—	4	8	no	—
241	C₂×C₄×C₈₉	—	4	8	no	—
242	C₂×C₄×C₈₉	—	8	16	no	—
243	C₂×C₄×C₈₉	—	8	4	no	—
244	C₂×C₄×C₈₉	#123	1	16	yes	complemented
245	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
248	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
249	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
250	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
251	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
252	C₂²×C₈₉	—	2	4	no	—
253	C₂²×C₈₉	—	2	4	no	—
254	C₂²×C₈₉	—	2	2	no	—
255	C₂²×C₈₉	—	2	2	no	—
256	C₂²×C₈₉	—	2	8	no	—
257	C₂²×C₈₉	—	2	16	no	—
258	C₂²×C₈₉	—	4	8	no	—
259	C₂²×C₈₉	—	4	4	no	—
260	C₂²×C₈₉	—	4	4	no	—
261	C₂²×C₈₉	—	4	2	no	—
262	C₂²×C₈₉	—	4	4	no	—
263	C₂²×C₈₉	—	4	4	no	—
264	C₂²×C₈₉	—	4	2	no	—
265	C₂²×C₈₉	—	4	2	no	—
266	C₂²×C₈₉	—	8	16	no	—
267	C₂²×C₈₉	C₂×#123	1	4	yes	—
268	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
269	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
270	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
271	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
272	C₂²×C₈₉	#585	1	2	yes	—
273	C₄×C₈₉	—	2	4	no	—
274	C₄×C₈₉	—	4	2	no	—
275	C₄×C₈₉	—	4	2	no	—
276	C₄×C₈₉	—	4	4	no	—
277	C₄×C₈₉	—	4	4	no	—
278	C₄×C₈₉	—	4	4	no	—
279	C₄×C₈₉	—	4	4	no	—
280	C₄×C₈₉	C₂×#123	1	4	yes	—
281	C₄×C₈₉	C₂×#123	1	4	yes	—
282	#35541	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
283	C₂×C₈₉	—	2	4	no	—
284	C₂×C₈₉	—	4	8	no	—
285	C₂×C₈₉	—	8	2	no	—
286	C₂×C₈₉	C₂²×#123	1	1	yes	characteristic
287	C₂×C₈₉	#3494	1	2	yes	—
288	C₂×C₈₉	#3496	1	2	yes	—
289	C₂×C₈₉	#3508	1	1	yes	characteristic
290	C₂×C₈₉	#3510	1	1	yes	characteristic
291	C₂×#535	C₂×C₈₉	1	1	yes	characteristic
292	C₂×#518	C₂×C₈₉	1	1	yes	characteristic, complemented
293	#2447	C₂×C₈₉	1	4	yes	complemented
294	#2445	C₂×C₈₉	1	4	yes	complemented
295	#2422	C₂×C₈₉	1	4	yes	complemented
296	#2420	C₂×C₈₉	1	4	yes	complemented
297	#2412	C₂×C₈₉	1	8	yes	complemented
298	#2316	C₂×C₈₉	1	1	yes	characteristic, complemented
299	#2311	C₂×C₈₉	1	1	yes	characteristic, complemented
300	#2297	C₂×C₈₉	1	1	yes	characteristic, complemented
301	C₂×#390	C₂×C₈₉	1	1	yes	characteristic, complemented
302	#2285	C₂×C₈₉	1	1	yes	characteristic, complemented
303	C₈₉	#35541	1	1	yes	characteristic, direct product factor, Sylow
304	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
305	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
306	#535	—	2	8	no	—
307	C₂×#127	C₂²×C₈₉	1	2	yes	—
308	C₂×#124	C₂²×C₈₉	1	2	yes	—
309	C₂×#123	C₂²×C₈₉	1	8	yes	complemented
310	C₂×#121	C₂²×C₈₉	1	4	yes	—
311	C₂×#120	C₂²×C₈₉	1	4	yes	—
312	#518	—	2	8	no	—
313	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
314	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
315	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
316	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
317	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
318	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
319	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
320	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
321	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
322	#397	C₂²×C₈₉	1	8	yes	complemented
323	#397	C₂²×C₈₉	1	8	yes	complemented
324	#394	C₂²×C₈₉	1	8	yes	complemented
325	#394	C₂²×C₈₉	1	8	yes	complemented
326	#391	C₂²×C₈₉	1	2	yes	complemented
327	#391	C₂²×C₈₉	1	2	yes	complemented
328	#390	C₂²×C₈₉	1	2	yes	—
329	#390	C₂²×C₈₉	1	2	yes	—
330	#390	C₂²×C₈₉	1	4	yes	—
331	#390	C₂²×C₈₉	1	2	yes	complemented
332	#390	C₂²×C₈₉	1	2	yes	complemented
333	#389	C₂²×C₈₉	1	4	yes	complemented
334	#389	C₂²×C₈₉	1	4	yes	complemented
335	#386	C₂²×C₈₉	1	4	yes	—
336	#386	C₂²×C₈₉	1	4	yes	—
337	#386	C₂²×C₈₉	1	8	yes	complemented
338	#385	C₂²×C₈₉	1	8	yes	complemented
339	#384	C₂²×C₈₉	1	2	yes	complemented
340	#382	C₂²×C₈₉	1	2	yes	complemented
341	#381	C₂²×C₈₉	1	8	yes	complemented
342	#380	C₂²×C₈₉	1	4	yes	—
343	#380	C₂²×C₈₉	1	4	yes	—
344	#380	C₂²×C₈₉	1	4	yes	complemented
345	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	complemented
346	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
347	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
348	C₂⁵	C₂³×C₈₉	1	2	yes	—
349	C₂×#41	—	2	4	no	—
350	C₂×#41	—	2	4	no	—
351	C₂×#41	—	2	4	no	—
352	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
353	C₂²×D₄	—	2	4	no	—
354	C₂²×D₄	—	2	4	no	—
355	C₂²×D₄	D₄×C₈₉	1	8	yes	—
356	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
357	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
358	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
359	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
360	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
361	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
362	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
363	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
364	C₂³×C₄	C₂³×C₈₉	1	8	yes	—
365	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
366	#127	—	2	8	no	—
367	#124	—	2	8	no	—
368	#123	—	4	16	no	—
369	#121	—	2	16	no	—
370	#120	—	2	16	no	—
371	C₄×D₄	—	2	16	no	—
372	C₄×D₄	—	2	16	no	—
373	#117	—	2	4	no	—
374	#117	—	2	4	no	—
375	#117	—	2	4	no	—
376	C₂×C₄⋊C₄	—	2	4	no	—
377	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
378	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
379	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
380	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
381	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
382	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
383	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
384	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
385	C₂×C₂²⋊C₄	—	2	16	no	—
386	C₂×C₂²⋊C₄	—	4	8	no	—
387	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
397	C₂×C₄²	—	2	4	no	—
398	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
399	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
400	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
401	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
402	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
403	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
404	#95	C₂³×C₈₉	1	4	yes	—
405	#95	C₂³×C₈₉	1	4	yes	—
406	#95	C₂³×C₈₉	1	4	yes	—
407	#95	C₂³×C₈₉	1	4	yes	—
408	#95	C₂³×C₈₉	1	8	yes	—
409	#95	C₂³×C₈₉	1	8	yes	—
410	C₂⁴	—	2	4	no	—
411	C₂⁴	—	2	4	no	—
412	C₂⁴	—	4	4	no	—
413	C₂⁴	—	4	4	no	—
414	C₂⁴	C₂×D₄×C₈₉	1	8	yes	—
415	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
416	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
417	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
418	#41	—	4	16	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	2	2	no	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	16	no	—
426	C₂×D₄	—	2	32	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	4	no	—
429	C₂×D₄	—	2	4	no	—
430	C₂×D₄	—	2	4	no	—
431	C₂×D₄	—	2	4	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	4	8	no	—
435	C₂×D₄	—	4	8	no	—
436	C₂×D₄	C₂×D₄×C₈₉	1	8	yes	—
437	C₂×D₄	C₂×D₄×C₈₉	1	8	yes	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	16	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	4	2	no	—
446	C₂²×C₄	—	4	4	no	—
447	C₂²×C₄	—	4	8	no	—
448	C₂²×C₄	—	4	8	no	—
449	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
450	C₂²×C₄	#41×C₈₉	1	4	yes	—
451	C₂²×C₄	#41×C₈₉	1	4	yes	—
452	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
453	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
454	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
455	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
456	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
457	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
458	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
459	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
460	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
461	C₄⋊C₄	—	2	4	no	—
462	C₄⋊C₄	—	2	4	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	8	no	—
467	C₄⋊C₄	—	4	8	no	—
468	C₄⋊C₄	—	4	4	no	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	16	no	—
472	C₂²⋊C₄	—	2	4	no	—
473	C₂²⋊C₄	—	2	16	no	—
474	C₂²⋊C₄	—	2	16	no	—
475	C₂²⋊C₄	—	2	8	no	—
476	C₂²⋊C₄	—	4	8	no	—
477	C₂²⋊C₄	—	4	8	no	—
478	C₂²⋊C₄	—	4	4	no	—
479	C₄²	—	2	4	no	—
480	C₄²	—	2	4	no	—
481	C₄²	—	2	4	no	—
482	C₄²	—	2	2	no	—
483	C₄²	—	2	4	no	—
484	C₄²	—	2	2	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	4	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	8	no	—
490	C₂³	—	2	8	no	—
491	C₂³	—	2	16	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	4	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	4	16	no	—
498	C₂³	—	8	8	no	—
499	C₂³	—	8	4	no	—
500	C₂³	—	8	4	no	—
501	C₂³	C₂²×D₄×C₈₉	1	8	yes	—
502	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
503	C₂³	C₂×#41×C₈₉	1	2	yes	—
504	C₂³	C₂×#41×C₈₉	1	2	yes	—
505	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
506	Q₈	—	4	4	no	—
507	D₄	—	2	16	no	—
508	D₄	—	2	16	no	—
509	D₄	—	4	8	no	—
510	D₄	—	4	4	no	—
511	D₄	—	8	16	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	8	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	4	8	no	—
532	C₂×C₄	—	4	8	no	—
533	C₂×C₄	—	8	16	no	—
534	C₂×C₄	—	8	4	no	—
535	C₂×C₄	#123×C₈₉	1	16	yes	complemented
536	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
537	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
538	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
539	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
540	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
541	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
542	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
543	C₂²	—	2	4	no	—
544	C₂²	—	2	4	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	8	no	—
548	C₂²	—	2	16	no	—
549	C₂²	—	4	8	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	4	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	4	no	—
554	C₂²	—	4	4	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	8	16	no	—
558	C₂²	C₂×#123×C₈₉	1	4	yes	—
559	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
560	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
561	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
562	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
563	C₂²	#585×C₈₉	1	2	yes	—
564	C₄	—	2	4	no	—
565	C₄	—	4	2	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	4	no	—
568	C₄	—	4	4	no	—
569	C₄	—	4	4	no	—
570	C₄	—	4	4	no	—
571	C₄	C₂×#123×C₈₉	1	4	yes	—
572	C₄	C₂×#123×C₈₉	1	4	yes	—
573	C₂	—	2	4	no	—
574	C₂	—	4	8	no	—
575	C₂	—	8	2	no	—
576	C₂	C₂²×#123×C₈₉	1	1	yes	characteristic
577	C₂	C₈₉×#3494	1	2	yes	—
578	C₂	C₈₉×#3496	1	2	yes	—
579	C₂	C₈₉×#3508	1	1	yes	characteristic
580	C₂	C₈₉×#3510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂×#535×C₈₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#518×C₈₉	C₂	semidirect
3. C₈₉×#2447	C₂	semidirect
4. C₈₉×#2445	C₂	semidirect
5. C₈₉×#2422	C₂	semidirect
6. C₈₉×#2420	C₂	semidirect
7. C₈₉×#2412	C₂	semidirect
8. C₈₉×#2316	C₂	semidirect
9. C₈₉×#2311	C₂	semidirect
10. C₈₉×#2297	C₂	semidirect
11. C₂×#390×C₈₉	C₂	semidirect
12. C₈₉×#2285	C₂	semidirect
18. C₂×#123×C₈₉	C₂²	semidirect
31. #397×C₈₉	C₂²	semidirect
32. #397×C₈₉	C₂²	semidirect
33. #394×C₈₉	C₂²	semidirect
34. #394×C₈₉	C₂²	semidirect
35. #391×C₈₉	C₂²	semidirect
36. #391×C₈₉	C₂²	semidirect
40. #390×C₈₉	C₂²	semidirect
41. #390×C₈₉	C₂²	semidirect
42. #389×C₈₉	C₂²	semidirect
43. #389×C₈₉	C₂²	semidirect
46. #386×C₈₉	C₂²	semidirect
47. #385×C₈₉	C₂²	semidirect
48. #384×C₈₉	C₂²	semidirect
49. #382×C₈₉	C₂²	semidirect
50. #381×C₈₉	C₂²	semidirect
53. #380×C₈₉	C₂²	semidirect
54. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
55. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
56. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
244. C₂×C₄×C₈₉	#123	semidirect
282. #35541	C₈₉	direct (N × H)
292. C₂×#518	C₂×C₈₉	semidirect
293. #2447	C₂×C₈₉	semidirect
294. #2445	C₂×C₈₉	semidirect
295. #2422	C₂×C₈₉	semidirect
296. #2420	C₂×C₈₉	semidirect
297. #2412	C₂×C₈₉	semidirect
298. #2316	C₂×C₈₉	semidirect
299. #2311	C₂×C₈₉	semidirect
300. #2297	C₂×C₈₉	semidirect
301. C₂×#390	C₂×C₈₉	semidirect
302. #2285	C₂×C₈₉	semidirect
303. C₈₉	#35541	direct (N × H)
309. C₂×#123	C₂²×C₈₉	semidirect
322. #397	C₂²×C₈₉	semidirect
323. #397	C₂²×C₈₉	semidirect
324. #394	C₂²×C₈₉	semidirect
325. #394	C₂²×C₈₉	semidirect
326. #391	C₂²×C₈₉	semidirect
327. #391	C₂²×C₈₉	semidirect
331. #390	C₂²×C₈₉	semidirect
332. #390	C₂²×C₈₉	semidirect
333. #389	C₂²×C₈₉	semidirect
334. #389	C₂²×C₈₉	semidirect
337. #386	C₂²×C₈₉	semidirect
338. #385	C₂²×C₈₉	semidirect
339. #384	C₂²×C₈₉	semidirect
340. #382	C₂²×C₈₉	semidirect
341. #381	C₂²×C₈₉	semidirect
344. #380	C₂²×C₈₉	semidirect
345. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
346. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
347. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
535. C₂×C₄	#123×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#535×C₈₉	2
C₂×#518×C₈₉	2
C₈₉×#2447	2
C₈₉×#2445	2
C₈₉×#2422	2
C₈₉×#2420	2
C₈₉×#2412	2
C₈₉×#2316	2
C₈₉×#2311	2
C₈₉×#2297	2
C₂×#390×C₈₉	2
C₈₉×#2285	2
#35541	89

Subgroups — C89×#35541 #36413389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35541 #36413389