Subgroups — C₈₉×#35170 #36413018

Order 22784.

2264 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#542×C₈₉	C₂	1	2	yes	maximal, complemented
2	C₈₉×#2857	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2854	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2663	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2551	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2547	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2542	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2537	C₂	1	1	yes	maximal, characteristic
9	C₈₉×#2521	C₂	1	4	yes	maximal, complemented
10	C₈₉×#2496	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2492	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2491	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2427	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2323	C₂	1	2	yes	maximal, complemented
15	C₄×C₄⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2293	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄²×D₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#542×C₈₉	—	2	16	no	—
19	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
20	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
22	C₂×#126×C₈₉	C₂²	1	4	yes	—
23	C₂×#124×C₈₉	C₂²	1	2	yes	—
24	C₂×#124×C₈₉	C₂²	1	4	yes	—
25	C₂×#123×C₈₉	C₂²	1	4	yes	—
26	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
28	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
29	C₂×#121×C₈₉	C₂²	1	2	yes	—
30	C₂×#121×C₈₉	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#117×C₈₉	C₂²	1	2	yes	—
37	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
38	#400×C₈₉	C₂²	1	4	yes	—
39	#399×C₈₉	C₂²	1	4	yes	—
40	#397×C₈₉	C₂²	1	4	yes	—
41	#397×C₈₉	C₂²	1	4	yes	—
42	#395×C₈₉	C₂²	1	4	yes	—
43	#394×C₈₉	C₂²	1	4	yes	—
44	#394×C₈₉	C₂²	1	4	yes	—
45	#393×C₈₉	C₂²	1	4	yes	—
46	#391×C₈₉	C₂²	1	2	yes	—
47	#391×C₈₉	C₂²	1	2	yes	—
48	#391×C₈₉	C₂²	1	4	yes	—
49	#390×C₈₉	C₂²	1	1	yes	characteristic
50	#390×C₈₉	C₂²	1	2	yes	—
51	#390×C₈₉	C₂²	1	1	yes	characteristic
52	#389×C₈₉	C₂²	1	2	yes	—
53	#389×C₈₉	C₂²	1	2	yes	—
54	#389×C₈₉	C₂²	1	2	yes	—
55	#389×C₈₉	C₂²	1	2	yes	—
56	#389×C₈₉	C₂²	1	4	yes	—
57	#389×C₈₉	C₂²	1	1	yes	characteristic
58	#389×C₈₉	C₂²	1	1	yes	characteristic
59	#388×C₈₉	C₂²	1	4	yes	—
60	#388×C₈₉	C₂²	1	4	yes	—
61	#388×C₈₉	C₂²	1	4	yes	—
62	#388×C₈₉	C₂²	1	2	yes	—
63	#388×C₈₉	C₂²	1	2	yes	—
64	#387×C₈₉	C₂²	1	4	yes	—
65	#386×C₈₉	C₂²	1	4	yes	—
66	#384×C₈₉	C₂²	1	1	yes	characteristic
67	#384×C₈₉	C₂²	1	2	yes	—
68	#380×C₈₉	C₂²	1	2	yes	—
69	#380×C₈₉	C₂²	1	2	yes	—
70	#380×C₈₉	C₂²	1	4	yes	—
71	#380×C₈₉	C₂²	1	2	yes	—
72	#380×C₈₉	C₂²	1	2	yes	—
73	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
74	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
75	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
76	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
77	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
78	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
79	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
81	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
83	C₄³×C₈₉	C₂²	1	1	yes	characteristic
84	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
85	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
86	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
89	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
90	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
91	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
92	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
93	C₄⋊Q₈×C₈₉	—	2	8	no	—
94	C₄⋊Q₈×C₈₉	—	2	4	no	—
95	C₄⋊Q₈×C₈₉	—	4	4	no	—
96	#126×C₈₉	—	2	16	no	—
97	#124×C₈₉	—	2	8	no	—
98	#124×C₈₉	—	2	16	no	—
99	#123×C₈₉	—	2	16	no	—
100	C₂²⋊Q₈×C₈₉	—	2	16	no	—
101	C₂²⋊Q₈×C₈₉	—	2	8	no	—
102	C₂²⋊Q₈×C₈₉	—	2	8	no	—
103	#121×C₈₉	—	2	8	no	—
104	#121×C₈₉	—	4	4	no	—
105	C₄×Q₈×C₈₉	—	2	8	no	—
106	C₄×D₄×C₈₉	—	2	4	no	—
107	C₄×D₄×C₈₉	—	2	4	no	—
108	C₄×D₄×C₈₉	—	2	4	no	—
109	C₄×D₄×C₈₉	D₄	1	8	yes	complemented
110	#117×C₈₉	—	2	8	no	—
111	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
143	C₂×C₄²×C₈₉	—	4	4	no	—
144	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
149	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
150	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
151	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
153	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
154	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
156	#95×C₈₉	C₂³	1	2	yes	—
157	#95×C₈₉	C₂³	1	2	yes	—
158	#95×C₈₉	C₂³	1	2	yes	—
159	#95×C₈₉	C₂³	1	2	yes	—
160	#95×C₈₉	C₂³	1	2	yes	—
161	#95×C₈₉	C₂³	1	4	yes	—
162	#95×C₈₉	C₂³	1	2	yes	—
163	#95×C₈₉	C₂³	1	4	yes	—
164	#95×C₈₉	C₂³	1	4	yes	—
165	#95×C₈₉	C₂³	1	4	yes	—
166	#95×C₈₉	C₂³	1	4	yes	—
167	#95×C₈₉	C₂³	1	4	yes	—
168	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
169	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
170	C₂×Q₈×C₈₉	—	2	4	no	—
171	C₂×Q₈×C₈₉	—	2	8	no	—
172	C₂×Q₈×C₈₉	—	2	4	no	—
173	C₂×Q₈×C₈₉	—	2	4	no	—
174	C₂×Q₈×C₈₉	—	4	4	no	—
175	C₂×Q₈×C₈₉	—	4	4	no	—
176	C₂×D₄×C₈₉	—	2	8	no	—
177	C₂×D₄×C₈₉	—	2	2	no	—
178	C₂×D₄×C₈₉	—	2	2	no	—
179	C₂×D₄×C₈₉	—	2	2	no	—
180	C₂×D₄×C₈₉	—	2	2	no	—
181	C₂×D₄×C₈₉	—	2	2	no	—
182	C₂×D₄×C₈₉	—	4	4	no	—
183	C₂×D₄×C₈₉	—	4	4	no	—
184	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
185	C₂²×C₄×C₈₉	—	2	4	no	—
186	C₂²×C₄×C₈₉	—	2	4	no	—
187	C₂²×C₄×C₈₉	—	2	4	no	—
188	C₂²×C₄×C₈₉	—	2	4	no	—
189	C₂²×C₄×C₈₉	—	2	4	no	—
190	C₂²×C₄×C₈₉	—	2	4	no	—
191	C₂²×C₄×C₈₉	—	2	4	no	—
192	C₂²×C₄×C₈₉	—	2	4	no	—
193	C₂²×C₄×C₈₉	—	4	2	no	—
194	C₂²×C₄×C₈₉	—	4	2	no	—
195	C₂²×C₄×C₈₉	—	4	2	no	—
196	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
197	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
203	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
212	C₄⋊C₄×C₈₉	—	2	4	no	—
213	C₄⋊C₄×C₈₉	—	2	4	no	—
214	C₄⋊C₄×C₈₉	—	2	4	no	—
215	C₄⋊C₄×C₈₉	—	2	8	no	—
216	C₄⋊C₄×C₈₉	—	2	8	no	—
217	C₄⋊C₄×C₈₉	—	2	8	no	—
218	C₄⋊C₄×C₈₉	—	2	2	no	—
219	C₄⋊C₄×C₈₉	—	2	2	no	—
220	C₄⋊C₄×C₈₉	—	2	8	no	—
221	C₄⋊C₄×C₈₉	—	2	4	no	—
222	C₄⋊C₄×C₈₉	—	2	4	no	—
223	C₄⋊C₄×C₈₉	—	2	4	no	—
224	C₄⋊C₄×C₈₉	—	2	2	no	—
225	C₄⋊C₄×C₈₉	—	2	2	no	—
226	C₄⋊C₄×C₈₉	—	4	2	no	—
227	C₄⋊C₄×C₈₉	—	4	4	no	—
228	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
229	C₄⋊C₄×C₈₉	#41	1	4	yes	—
230	C₂²⋊C₄×C₈₉	—	2	8	no	—
231	C₂²⋊C₄×C₈₉	—	2	8	no	—
232	C₂²⋊C₄×C₈₉	—	2	8	no	—
233	C₂²⋊C₄×C₈₉	—	2	4	no	—
234	C₂²⋊C₄×C₈₉	—	2	4	no	—
235	C₂²⋊C₄×C₈₉	—	2	8	no	—
236	C₂²⋊C₄×C₈₉	—	2	4	no	—
237	C₂²⋊C₄×C₈₉	—	2	4	no	—
238	C₂²⋊C₄×C₈₉	—	2	4	no	—
239	C₂²⋊C₄×C₈₉	—	2	8	no	—
240	C₂²⋊C₄×C₈₉	—	2	4	no	—
241	C₂²⋊C₄×C₈₉	—	4	2	no	—
242	C₂²⋊C₄×C₈₉	—	4	4	no	—
243	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
244	C₄²×C₈₉	—	2	4	no	—
245	C₄²×C₈₉	—	2	8	no	—
246	C₄²×C₈₉	—	2	2	no	—
247	C₄²×C₈₉	—	2	2	no	—
248	C₄²×C₈₉	—	2	4	no	—
249	C₄²×C₈₉	—	2	2	no	—
250	C₄²×C₈₉	—	2	2	no	—
251	C₄²×C₈₉	—	4	2	no	—
252	C₄²×C₈₉	—	4	2	no	—
253	C₄²×C₈₉	—	4	1	no	—
254	C₄²×C₈₉	C₂×D₄	1	4	yes	—
255	C₄²×C₈₉	#41	1	4	yes	—
256	C₂³×C₈₉	—	2	2	no	—
257	C₂³×C₈₉	—	2	2	no	—
258	C₂³×C₈₉	—	2	2	no	—
259	C₂³×C₈₉	—	2	2	no	—
260	C₂³×C₈₉	—	2	2	no	—
261	C₂³×C₈₉	—	2	2	no	—
262	C₂³×C₈₉	—	2	2	no	—
263	C₂³×C₈₉	—	2	2	no	—
264	C₂³×C₈₉	—	2	2	no	—
265	C₂³×C₈₉	—	2	2	no	—
266	C₂³×C₈₉	—	2	2	no	—
267	C₂³×C₈₉	—	2	2	no	—
268	C₂³×C₈₉	—	2	2	no	—
269	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
270	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
271	Q₈×C₈₉	—	4	8	no	—
272	Q₈×C₈₉	—	8	8	no	—
273	D₄×C₈₉	—	2	8	no	—
274	D₄×C₈₉	—	4	4	no	—
275	D₄×C₈₉	—	8	8	no	—
276	C₂×C₄×C₈₉	—	2	1	no	—
277	C₂×C₄×C₈₉	—	2	1	no	—
278	C₂×C₄×C₈₉	—	2	1	no	—
279	C₂×C₄×C₈₉	—	2	2	no	—
280	C₂×C₄×C₈₉	—	2	2	no	—
281	C₂×C₄×C₈₉	—	2	1	no	—
282	C₂×C₄×C₈₉	—	2	1	no	—
283	C₂×C₄×C₈₉	—	2	1	no	—
284	C₂×C₄×C₈₉	—	2	2	no	—
285	C₂×C₄×C₈₉	—	2	1	no	—
286	C₂×C₄×C₈₉	—	2	1	no	—
287	C₂×C₄×C₈₉	—	2	2	no	—
288	C₂×C₄×C₈₉	—	2	2	no	—
289	C₂×C₄×C₈₉	—	2	4	no	—
290	C₂×C₄×C₈₉	—	2	2	no	—
291	C₂×C₄×C₈₉	—	2	4	no	—
292	C₂×C₄×C₈₉	—	2	2	no	—
293	C₂×C₄×C₈₉	—	2	1	no	—
294	C₂×C₄×C₈₉	—	2	2	no	—
295	C₂×C₄×C₈₉	—	2	2	no	—
296	C₂×C₄×C₈₉	—	2	4	no	—
297	C₂×C₄×C₈₉	—	2	2	no	—
298	C₂×C₄×C₈₉	—	2	4	no	—
299	C₂×C₄×C₈₉	—	2	2	no	—
300	C₂×C₄×C₈₉	—	2	4	no	—
301	C₂×C₄×C₈₉	—	2	2	no	—
302	C₂×C₄×C₈₉	—	2	1	no	—
303	C₂×C₄×C₈₉	—	2	2	no	—
304	C₂×C₄×C₈₉	—	2	2	no	—
305	C₂×C₄×C₈₉	—	2	2	no	—
306	C₂×C₄×C₈₉	—	2	1	no	—
307	C₂×C₄×C₈₉	—	2	2	no	—
308	C₂×C₄×C₈₉	—	2	4	no	—
309	C₂×C₄×C₈₉	—	4	8	no	—
310	C₂×C₄×C₈₉	—	4	8	no	—
311	C₂×C₄×C₈₉	—	4	8	no	—
312	C₂×C₄×C₈₉	—	4	8	no	—
313	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
314	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
315	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
316	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
318	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
319	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
320	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
321	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
322	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
323	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
324	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
325	C₂²×C₈₉	—	2	4	no	—
326	C₂²×C₈₉	—	2	4	no	—
327	C₂²×C₈₉	—	2	4	no	—
328	C₂²×C₈₉	—	4	2	no	—
329	C₂²×C₈₉	—	4	2	no	—
330	C₂²×C₈₉	—	4	2	no	—
331	C₂²×C₈₉	—	4	2	no	—
332	C₂²×C₈₉	—	4	2	no	—
333	C₂²×C₈₉	—	4	2	no	—
334	C₂²×C₈₉	—	4	2	no	—
335	C₂²×C₈₉	—	4	2	no	—
336	C₂²×C₈₉	—	4	2	no	—
337	C₂²×C₈₉	—	4	2	no	—
338	C₂²×C₈₉	—	4	2	no	—
339	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
340	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
341	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
342	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
343	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
344	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
345	C₂²×C₈₉	#585	1	1	yes	characteristic
346	C₄×C₈₉	—	2	2	no	—
347	C₄×C₈₉	—	2	2	no	—
348	C₄×C₈₉	—	2	4	no	—
349	C₄×C₈₉	—	2	2	no	—
350	C₄×C₈₉	—	2	2	no	—
351	C₄×C₈₉	—	2	4	no	—
352	C₄×C₈₉	—	4	2	no	—
353	C₄×C₈₉	—	4	4	no	—
354	C₄×C₈₉	—	4	2	no	—
355	C₄×C₈₉	—	4	4	no	—
356	C₄×C₈₉	—	4	2	no	—
357	C₄×C₈₉	—	4	2	no	—
358	C₄×C₈₉	—	4	1	no	—
359	C₄×C₈₉	#532	1	4	yes	—
360	C₄×C₈₉	#542	1	4	yes	complemented
361	#35170	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
362	C₂×C₈₉	—	4	4	no	—
363	C₂×C₈₉	—	8	2	no	—
364	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
365	C₂×C₈₉	C₂×#542	1	1	yes	characteristic
366	C₂×C₈₉	#3461	1	1	yes	characteristic
367	C₂×C₈₉	#3496	1	1	yes	characteristic
368	C₂×C₈₉	#3499	1	1	yes	characteristic
369	C₂×C₈₉	#3518	1	1	yes	characteristic
370	C₂×C₈₉	#3520	1	1	yes	characteristic
371	C₂×#542	C₂×C₈₉	1	2	yes	complemented
372	#2857	C₂×C₈₉	1	2	yes	complemented
373	#2854	C₂×C₈₉	1	2	yes	complemented
374	#2663	C₂×C₈₉	1	4	yes	complemented
375	#2551	C₂×C₈₉	1	1	yes	characteristic, complemented
376	#2547	C₂×C₈₉	1	1	yes	characteristic, complemented
377	#2542	C₂×C₈₉	1	1	yes	characteristic, complemented
378	#2537	C₂×C₈₉	1	1	yes	characteristic
379	#2521	C₂×C₈₉	1	4	yes	complemented
380	#2496	C₂×C₈₉	1	2	yes	complemented
381	#2492	C₂×C₈₉	1	2	yes	complemented
382	#2491	C₂×C₈₉	1	2	yes	complemented
383	#2427	C₂×C₈₉	1	2	yes	complemented
384	#2323	C₂×C₈₉	1	2	yes	complemented
385	C₄×C₄⋊Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
386	#2293	C₂×C₈₉	1	1	yes	characteristic, complemented
387	C₄²×D₄	C₂×C₈₉	1	1	yes	characteristic, complemented
388	C₈₉	#35170	1	1	yes	characteristic, direct product factor, Sylow
389	#542	—	2	16	no	—
390	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
391	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
392	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
393	C₂×#126	C₂²×C₈₉	1	4	yes	—
394	C₂×#124	C₂²×C₈₉	1	2	yes	—
395	C₂×#124	C₂²×C₈₉	1	4	yes	—
396	C₂×#123	C₂²×C₈₉	1	4	yes	—
397	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
398	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
399	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
400	C₂×#121	C₂²×C₈₉	1	2	yes	—
401	C₂×#121	C₂²×C₈₉	1	2	yes	—
402	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
403	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
404	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
405	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
406	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
407	C₂×#117	C₂²×C₈₉	1	2	yes	—
408	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
409	#400	C₂²×C₈₉	1	4	yes	—
410	#399	C₂²×C₈₉	1	4	yes	—
411	#397	C₂²×C₈₉	1	4	yes	—
412	#397	C₂²×C₈₉	1	4	yes	—
413	#395	C₂²×C₈₉	1	4	yes	—
414	#394	C₂²×C₈₉	1	4	yes	—
415	#394	C₂²×C₈₉	1	4	yes	—
416	#393	C₂²×C₈₉	1	4	yes	—
417	#391	C₂²×C₈₉	1	2	yes	—
418	#391	C₂²×C₈₉	1	2	yes	—
419	#391	C₂²×C₈₉	1	4	yes	—
420	#390	C₂²×C₈₉	1	1	yes	characteristic
421	#390	C₂²×C₈₉	1	2	yes	—
422	#390	C₂²×C₈₉	1	1	yes	characteristic
423	#389	C₂²×C₈₉	1	2	yes	—
424	#389	C₂²×C₈₉	1	2	yes	—
425	#389	C₂²×C₈₉	1	4	yes	—
426	#389	C₂²×C₈₉	1	2	yes	—
427	#389	C₂²×C₈₉	1	2	yes	—
428	#389	C₂²×C₈₉	1	1	yes	characteristic
429	#389	C₂²×C₈₉	1	1	yes	characteristic
430	#388	C₂²×C₈₉	1	4	yes	—
431	#388	C₂²×C₈₉	1	4	yes	—
432	#388	C₂²×C₈₉	1	4	yes	—
433	#388	C₂²×C₈₉	1	2	yes	—
434	#388	C₂²×C₈₉	1	2	yes	—
435	#387	C₂²×C₈₉	1	4	yes	—
436	#386	C₂²×C₈₉	1	4	yes	—
437	#384	C₂²×C₈₉	1	1	yes	characteristic
438	#384	C₂²×C₈₉	1	2	yes	—
439	#380	C₂²×C₈₉	1	2	yes	—
440	#380	C₂²×C₈₉	1	2	yes	—
441	#380	C₂²×C₈₉	1	4	yes	—
442	#380	C₂²×C₈₉	1	2	yes	—
443	#380	C₂²×C₈₉	1	2	yes	—
444	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
445	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
446	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
447	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
448	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
449	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
450	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
451	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
452	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
453	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
454	C₄³	C₂²×C₈₉	1	1	yes	characteristic
455	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
456	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
457	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
458	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
459	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
460	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
461	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
462	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
463	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
464	C₄⋊Q₈	—	2	8	no	—
465	C₄⋊Q₈	—	2	4	no	—
466	C₄⋊Q₈	—	4	4	no	—
467	#126	—	2	16	no	—
468	#124	—	2	8	no	—
469	#124	—	2	16	no	—
470	#123	—	2	16	no	—
471	C₂²⋊Q₈	—	2	16	no	—
472	C₂²⋊Q₈	—	2	8	no	—
473	C₂²⋊Q₈	—	2	8	no	—
474	#121	—	2	8	no	—
475	#121	—	4	4	no	—
476	C₄×Q₈	—	2	8	no	—
477	C₄×D₄	—	2	4	no	—
478	C₄×D₄	—	2	4	no	—
479	C₄×D₄	—	2	4	no	—
480	C₄×D₄	D₄×C₈₉	1	8	yes	complemented
481	#117	—	2	8	no	—
482	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
488	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
490	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
491	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
492	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
497	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
500	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
514	C₂×C₄²	—	4	4	no	—
515	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
516	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
517	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
518	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
519	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
520	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
521	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
522	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
523	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
524	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
525	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
526	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
527	#95	C₂³×C₈₉	1	2	yes	—
528	#95	C₂³×C₈₉	1	2	yes	—
529	#95	C₂³×C₈₉	1	2	yes	—
530	#95	C₂³×C₈₉	1	2	yes	—
531	#95	C₂³×C₈₉	1	2	yes	—
532	#95	C₂³×C₈₉	1	4	yes	—
533	#95	C₂³×C₈₉	1	2	yes	—
534	#95	C₂³×C₈₉	1	4	yes	—
535	#95	C₂³×C₈₉	1	4	yes	—
536	#95	C₂³×C₈₉	1	4	yes	—
537	#95	C₂³×C₈₉	1	4	yes	—
538	#95	C₂³×C₈₉	1	4	yes	—
539	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
540	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
541	C₂×Q₈	—	2	4	no	—
542	C₂×Q₈	—	2	8	no	—
543	C₂×Q₈	—	2	4	no	—
544	C₂×Q₈	—	2	4	no	—
545	C₂×Q₈	—	4	4	no	—
546	C₂×Q₈	—	4	4	no	—
547	C₂×D₄	—	2	8	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	4	4	no	—
554	C₂×D₄	—	4	4	no	—
555	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
556	C₂²×C₄	—	2	4	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	2	4	no	—
561	C₂²×C₄	—	2	4	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	4	2	no	—
565	C₂²×C₄	—	4	2	no	—
566	C₂²×C₄	—	4	2	no	—
567	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
568	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
569	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
570	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
572	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
573	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
574	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
576	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
578	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
579	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
581	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	8	no	—
587	C₄⋊C₄	—	2	8	no	—
588	C₄⋊C₄	—	2	8	no	—
589	C₄⋊C₄	—	2	2	no	—
590	C₄⋊C₄	—	2	2	no	—
591	C₄⋊C₄	—	2	8	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	4	4	no	—
598	C₄⋊C₄	—	4	2	no	—
599	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
600	C₄⋊C₄	#41×C₈₉	1	4	yes	—
601	C₂²⋊C₄	—	2	8	no	—
602	C₂²⋊C₄	—	2	8	no	—
603	C₂²⋊C₄	—	2	8	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	8	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	8	no	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	—	4	4	no	—
613	C₂²⋊C₄	—	4	2	no	—
614	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
615	C₄²	—	2	4	no	—
616	C₄²	—	2	8	no	—
617	C₄²	—	2	2	no	—
618	C₄²	—	2	2	no	—
619	C₄²	—	2	4	no	—
620	C₄²	—	2	2	no	—
621	C₄²	—	2	2	no	—
622	C₄²	—	4	2	no	—
623	C₄²	—	4	2	no	—
624	C₄²	—	4	1	no	—
625	C₄²	C₂×D₄×C₈₉	1	4	yes	—
626	C₄²	#41×C₈₉	1	4	yes	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	2	no	—
640	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
641	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
642	Q₈	—	4	8	no	—
643	Q₈	—	8	8	no	—
644	D₄	—	2	8	no	—
645	D₄	—	4	4	no	—
646	D₄	—	8	8	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	4	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	4	8	no	—
681	C₂×C₄	—	4	8	no	—
682	C₂×C₄	—	4	8	no	—
683	C₂×C₄	—	4	8	no	—
684	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
685	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
686	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
687	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
688	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
689	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
690	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
691	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
692	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
693	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
694	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
695	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
696	C₂²	—	2	4	no	—
697	C₂²	—	2	4	no	—
698	C₂²	—	2	4	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
711	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
712	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
713	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
714	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
715	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
716	C₂²	#585×C₈₉	1	1	yes	characteristic
717	C₄	—	2	2	no	—
718	C₄	—	2	2	no	—
719	C₄	—	2	4	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	2	no	—
722	C₄	—	2	4	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	4	no	—
725	C₄	—	4	2	no	—
726	C₄	—	4	4	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	1	no	—
730	C₄	#532×C₈₉	1	4	yes	—
731	C₄	#542×C₈₉	1	4	yes	complemented
732	C₂	—	4	4	no	—
733	C₂	—	8	2	no	—
734	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
735	C₂	C₂×#542×C₈₉	1	1	yes	characteristic
736	C₂	C₈₉×#3461	1	1	yes	characteristic
737	C₂	C₈₉×#3496	1	1	yes	characteristic
738	C₂	C₈₉×#3499	1	1	yes	characteristic
739	C₂	C₈₉×#3518	1	1	yes	characteristic
740	C₂	C₈₉×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₈₉×#2537	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
1. C₂×#542×C₈₉	C₂	semidirect
2. C₈₉×#2857	C₂	semidirect
3. C₈₉×#2854	C₂	semidirect
4. C₈₉×#2663	C₂	semidirect
5. C₈₉×#2551	C₂	semidirect
6. C₈₉×#2547	C₂	semidirect
7. C₈₉×#2542	C₂	semidirect
9. C₈₉×#2521	C₂	semidirect
10. C₈₉×#2496	C₂	semidirect
11. C₈₉×#2492	C₂	semidirect
12. C₈₉×#2491	C₂	semidirect
13. C₈₉×#2427	C₂	semidirect
14. C₈₉×#2323	C₂	semidirect
15. C₄×C₄⋊Q₈×C₈₉	C₂	semidirect
16. C₈₉×#2293	C₂	semidirect
17. C₄²×D₄×C₈₉	C₂	semidirect
109. C₄×D₄×C₈₉	D₄	semidirect
360. C₄×C₈₉	#542	semidirect
361. #35170	C₈₉	direct (N × H)
371. C₂×#542	C₂×C₈₉	semidirect
372. #2857	C₂×C₈₉	semidirect
373. #2854	C₂×C₈₉	semidirect
374. #2663	C₂×C₈₉	semidirect
375. #2551	C₂×C₈₉	semidirect
376. #2547	C₂×C₈₉	semidirect
377. #2542	C₂×C₈₉	semidirect
379. #2521	C₂×C₈₉	semidirect
380. #2496	C₂×C₈₉	semidirect
381. #2492	C₂×C₈₉	semidirect
382. #2491	C₂×C₈₉	semidirect
383. #2427	C₂×C₈₉	semidirect
384. #2323	C₂×C₈₉	semidirect
385. C₄×C₄⋊Q₈	C₂×C₈₉	semidirect
386. #2293	C₂×C₈₉	semidirect
387. C₄²×D₄	C₂×C₈₉	semidirect
388. C₈₉	#35170	direct (N × H)
480. C₄×D₄	D₄×C₈₉	semidirect
731. C₄	#542×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#542×C₈₉	2
C₈₉×#2857	2
C₈₉×#2854	2
C₈₉×#2663	2
C₈₉×#2551	2
C₈₉×#2547	2
C₈₉×#2542	2
C₈₉×#2537	2
C₈₉×#2521	2
C₈₉×#2496	2
C₈₉×#2492	2
C₈₉×#2491	2
C₈₉×#2427	2
C₈₉×#2323	2
C₄×C₄⋊Q₈×C₈₉	2
C₈₉×#2293	2
C₄²×D₄×C₈₉	2
#35170	89

Subgroups — C89×#35170 #36413018

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35170 #36413018