Subgroups — C₈₉×#35198 #36413046

Order 22784.

2400 conjugacy classes of subgroups.

The subgroup lattice has 760 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×#2860	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2858	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2662	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2551	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2548	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2541	C₂	1	1	yes	maximal, characteristic
8	C₈₉×#2538	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2491	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2461	C₂	1	4	yes	maximal, complemented
11	C₈₉×#2452	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2445	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2426	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2324	C₂	1	2	yes	maximal, complemented
15	C₄×#127×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2293	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄²×Q₈×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	2	yes	—
21	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#127×C₈₉	C₂²	1	2	yes	—
23	C₂×#126×C₈₉	C₂²	1	4	yes	—
24	C₂×#124×C₈₉	C₂²	1	4	yes	—
25	C₂×#124×C₈₉	C₂²	1	2	yes	—
26	C₂×#124×C₈₉	C₂²	1	4	yes	—
27	C₂×#123×C₈₉	C₂²	1	4	yes	—
28	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
30	C₂×#121×C₈₉	C₂²	1	2	yes	—
31	C₂×#121×C₈₉	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
39	C₂×#117×C₈₉	C₂²	1	2	yes	—
40	#396×C₈₉	C₂²	1	4	yes	—
41	#396×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	#394×C₈₉	C₂²	1	4	yes	—
46	#393×C₈₉	C₂²	1	4	yes	—
47	#392×C₈₉	C₂²	1	4	yes	—
48	#390×C₈₉	C₂²	1	2	yes	—
49	#390×C₈₉	C₂²	1	2	yes	—
50	#390×C₈₉	C₂²	1	2	yes	—
51	#390×C₈₉	C₂²	1	4	yes	—
52	#390×C₈₉	C₂²	1	2	yes	—
53	#390×C₈₉	C₂²	1	1	yes	characteristic
54	#390×C₈₉	C₂²	1	4	yes	—
55	#390×C₈₉	C₂²	1	2	yes	—
56	#390×C₈₉	C₂²	1	2	yes	—
57	#390×C₈₉	C₂²	1	2	yes	—
58	#390×C₈₉	C₂²	1	2	yes	—
59	#390×C₈₉	C₂²	1	1	yes	characteristic
60	#389×C₈₉	C₂²	1	2	yes	—
61	#389×C₈₉	C₂²	1	2	yes	—
62	#389×C₈₉	C₂²	1	1	yes	characteristic
63	#389×C₈₉	C₂²	1	2	yes	—
64	#389×C₈₉	C₂²	1	1	yes	characteristic
65	#388×C₈₉	C₂²	1	4	yes	—
66	#388×C₈₉	C₂²	1	4	yes	—
67	#388×C₈₉	C₂²	1	4	yes	—
68	#388×C₈₉	C₂²	1	2	yes	—
69	#388×C₈₉	C₂²	1	2	yes	—
70	#386×C₈₉	C₂²	1	4	yes	—
71	#385×C₈₉	C₂²	1	4	yes	—
72	#384×C₈₉	C₂²	1	1	yes	characteristic
73	#380×C₈₉	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
75	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
76	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
77	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
81	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
82	C₄³×C₈₉	C₂²	1	1	yes	characteristic
83	C₄³×C₈₉	C₂²	1	2	yes	—
84	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
86	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
89	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
90	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
91	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
92	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
93	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
94	C₄⋊Q₈×C₈₉	—	2	8	no	—
95	C₄⋊Q₈×C₈₉	—	4	4	no	—
96	#127×C₈₉	—	2	4	no	—
97	#127×C₈₉	—	4	4	no	—
98	#126×C₈₉	—	2	16	no	—
99	#124×C₈₉	—	2	8	no	—
100	#124×C₈₉	—	2	16	no	—
101	#124×C₈₉	—	4	8	no	—
102	#123×C₈₉	—	2	16	no	—
103	C₂²⋊Q₈×C₈₉	—	2	8	no	—
104	C₂²⋊Q₈×C₈₉	—	2	16	no	—
105	#121×C₈₉	—	2	8	no	—
106	#121×C₈₉	—	2	8	no	—
107	C₄×Q₈×C₈₉	—	2	4	no	—
108	C₄×Q₈×C₈₉	—	2	4	no	—
109	C₄×Q₈×C₈₉	D₄	1	8	yes	complemented
110	C₄×D₄×C₈₉	—	2	8	no	—
111	C₄×D₄×C₈₉	—	2	4	no	—
112	C₄×D₄×C₈₉	—	4	4	no	—
113	C₄×D₄×C₈₉	—	4	4	no	—
114	#117×C₈₉	—	2	8	no	—
115	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	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	2	yes	—
124	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
129	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	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	4	yes	—
139	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
148	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
150	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
152	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
154	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
156	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
162	#95×C₈₉	C₂³	1	2	yes	—
163	#95×C₈₉	C₂³	1	2	yes	—
164	#95×C₈₉	C₂³	1	2	yes	—
165	#95×C₈₉	C₂³	1	2	yes	—
166	#95×C₈₉	C₂³	1	2	yes	—
167	#95×C₈₉	C₂³	1	2	yes	—
168	#95×C₈₉	C₂³	1	4	yes	—
169	#95×C₈₉	C₂³	1	4	yes	—
170	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
171	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
172	C₂×Q₈×C₈₉	—	2	8	no	—
173	C₂×Q₈×C₈₉	—	2	2	no	—
174	C₂×Q₈×C₈₉	—	2	2	no	—
175	C₂×Q₈×C₈₉	—	4	4	no	—
176	C₂×Q₈×C₈₉	—	4	4	no	—
177	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
178	C₂×D₄×C₈₉	—	2	4	no	—
179	C₂×D₄×C₈₉	—	2	8	no	—
180	C₂×D₄×C₈₉	—	2	2	no	—
181	C₂×D₄×C₈₉	—	2	4	no	—
182	C₂×D₄×C₈₉	—	2	4	no	—
183	C₂×D₄×C₈₉	—	2	4	no	—
184	C₂×D₄×C₈₉	—	2	4	no	—
185	C₂×D₄×C₈₉	—	2	8	no	—
186	C₂×D₄×C₈₉	—	2	4	no	—
187	C₂×D₄×C₈₉	—	2	2	no	—
188	C₂×D₄×C₈₉	—	2	2	no	—
189	C₂×D₄×C₈₉	—	2	4	no	—
190	C₂×D₄×C₈₉	—	4	2	no	—
191	C₂×D₄×C₈₉	—	4	2	no	—
192	C₂×D₄×C₈₉	—	4	4	no	—
193	C₂×D₄×C₈₉	—	4	4	no	—
194	C₂×D₄×C₈₉	—	4	4	no	—
195	C₂×D₄×C₈₉	—	4	4	no	—
196	C₂²×C₄×C₈₉	—	2	4	no	—
197	C₂²×C₄×C₈₉	—	2	4	no	—
198	C₂²×C₄×C₈₉	—	2	4	no	—
199	C₂²×C₄×C₈₉	—	2	8	no	—
200	C₂²×C₄×C₈₉	—	4	4	no	—
201	C₂²×C₄×C₈₉	—	4	4	no	—
202	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
208	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
217	C₄⋊C₄×C₈₉	—	2	4	no	—
218	C₄⋊C₄×C₈₉	—	2	4	no	—
219	C₄⋊C₄×C₈₉	—	2	4	no	—
220	C₄⋊C₄×C₈₉	—	2	8	no	—
221	C₄⋊C₄×C₈₉	—	2	8	no	—
222	C₄⋊C₄×C₈₉	—	2	2	no	—
223	C₄⋊C₄×C₈₉	—	2	4	no	—
224	C₄⋊C₄×C₈₉	—	2	4	no	—
225	C₄⋊C₄×C₈₉	—	2	2	no	—
226	C₄⋊C₄×C₈₉	—	2	4	no	—
227	C₄⋊C₄×C₈₉	—	2	2	no	—
228	C₄⋊C₄×C₈₉	—	2	2	no	—
229	C₄⋊C₄×C₈₉	—	4	2	no	—
230	C₄⋊C₄×C₈₉	—	4	4	no	—
231	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
232	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
233	C₄⋊C₄×C₈₉	#41	1	4	yes	—
234	C₂²⋊C₄×C₈₉	—	2	4	no	—
235	C₂²⋊C₄×C₈₉	—	2	4	no	—
236	C₂²⋊C₄×C₈₉	—	2	8	no	—
237	C₂²⋊C₄×C₈₉	—	2	8	no	—
238	C₂²⋊C₄×C₈₉	—	2	8	no	—
239	C₂²⋊C₄×C₈₉	—	2	8	no	—
240	C₂²⋊C₄×C₈₉	—	2	8	no	—
241	C₂²⋊C₄×C₈₉	—	2	4	no	—
242	C₂²⋊C₄×C₈₉	—	2	8	no	—
243	C₂²⋊C₄×C₈₉	—	2	8	no	—
244	C₂²⋊C₄×C₈₉	—	2	4	no	—
245	C₂²⋊C₄×C₈₉	—	4	2	no	—
246	C₂²⋊C₄×C₈₉	—	4	4	no	—
247	C₂²⋊C₄×C₈₉	—	4	4	no	—
248	C₂²⋊C₄×C₈₉	—	4	4	no	—
249	C₂²⋊C₄×C₈₉	—	4	4	no	—
250	C₄²×C₈₉	—	2	4	no	—
251	C₄²×C₈₉	—	2	4	no	—
252	C₄²×C₈₉	—	2	2	no	—
253	C₄²×C₈₉	—	2	4	no	—
254	C₄²×C₈₉	—	2	2	no	—
255	C₄²×C₈₉	—	2	2	no	—
256	C₄²×C₈₉	—	2	4	no	—
257	C₄²×C₈₉	—	2	4	no	—
258	C₄²×C₈₉	—	2	2	no	—
259	C₄²×C₈₉	—	4	1	no	—
260	C₄²×C₈₉	—	4	2	no	—
261	C₄²×C₈₉	C₂×D₄	1	4	yes	—
262	C₄²×C₈₉	C₂×D₄	1	8	yes	—
263	C₄²×C₈₉	#41	1	4	yes	—
264	C₂³×C₈₉	—	2	2	no	—
265	C₂³×C₈₉	—	2	4	no	—
266	C₂³×C₈₉	—	2	2	no	—
267	C₂³×C₈₉	—	2	4	no	—
268	C₂³×C₈₉	—	2	2	no	—
269	C₂³×C₈₉	—	2	4	no	—
270	C₂³×C₈₉	—	2	2	no	—
271	C₂³×C₈₉	—	2	4	no	—
272	C₂³×C₈₉	—	2	4	no	—
273	C₂³×C₈₉	—	2	2	no	—
274	C₂³×C₈₉	—	2	2	no	—
275	C₂³×C₈₉	—	2	4	no	—
276	C₂³×C₈₉	—	2	4	no	—
277	C₂³×C₈₉	—	2	2	no	—
278	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
279	Q₈×C₈₉	—	2	8	no	—
280	Q₈×C₈₉	—	8	8	no	—
281	D₄×C₈₉	—	4	8	no	—
282	D₄×C₈₉	—	4	8	no	—
283	D₄×C₈₉	—	4	4	no	—
284	D₄×C₈₉	—	4	8	no	—
285	D₄×C₈₉	—	8	8	no	—
286	D₄×C₈₉	—	8	8	no	—
287	C₂×C₄×C₈₉	—	2	1	no	—
288	C₂×C₄×C₈₉	—	2	2	no	—
289	C₂×C₄×C₈₉	—	2	2	no	—
290	C₂×C₄×C₈₉	—	2	1	no	—
291	C₂×C₄×C₈₉	—	2	2	no	—
292	C₂×C₄×C₈₉	—	2	1	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	1	no	—
297	C₂×C₄×C₈₉	—	2	1	no	—
298	C₂×C₄×C₈₉	—	2	1	no	—
299	C₂×C₄×C₈₉	—	2	1	no	—
300	C₂×C₄×C₈₉	—	2	2	no	—
301	C₂×C₄×C₈₉	—	2	2	no	—
302	C₂×C₄×C₈₉	—	2	2	no	—
303	C₂×C₄×C₈₉	—	2	2	no	—
304	C₂×C₄×C₈₉	—	2	4	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	2	no	—
309	C₂×C₄×C₈₉	—	2	2	no	—
310	C₂×C₄×C₈₉	—	2	1	no	—
311	C₂×C₄×C₈₉	—	2	2	no	—
312	C₂×C₄×C₈₉	—	2	4	no	—
313	C₂×C₄×C₈₉	—	2	4	no	—
314	C₂×C₄×C₈₉	—	2	2	no	—
315	C₂×C₄×C₈₉	—	2	2	no	—
316	C₂×C₄×C₈₉	—	2	2	no	—
317	C₂×C₄×C₈₉	—	2	1	no	—
318	C₂×C₄×C₈₉	—	2	2	no	—
319	C₂×C₄×C₈₉	—	4	8	no	—
320	C₂×C₄×C₈₉	—	8	8	no	—
321	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
323	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
325	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
327	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
328	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
329	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
330	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
331	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
332	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
333	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
334	C₂²×C₈₉	—	4	2	no	—
335	C₂²×C₈₉	—	4	4	no	—
336	C₂²×C₈₉	—	4	2	no	—
337	C₂²×C₈₉	—	4	4	no	—
338	C₂²×C₈₉	—	4	4	no	—
339	C₂²×C₈₉	—	4	2	no	—
340	C₂²×C₈₉	—	4	2	no	—
341	C₂²×C₈₉	—	4	4	no	—
342	C₂²×C₈₉	—	4	4	no	—
343	C₂²×C₈₉	—	4	2	no	—
344	C₂²×C₈₉	—	4	2	no	—
345	C₂²×C₈₉	—	4	4	no	—
346	C₂²×C₈₉	—	4	4	no	—
347	C₂²×C₈₉	—	4	2	no	—
348	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
349	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
350	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
351	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
352	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
353	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
354	C₂²×C₈₉	#585	1	1	yes	characteristic
355	C₄×C₈₉	—	2	4	no	—
356	C₄×C₈₉	—	2	2	no	—
357	C₄×C₈₉	—	2	2	no	—
358	C₄×C₈₉	—	2	2	no	—
359	C₄×C₈₉	—	2	4	no	—
360	C₄×C₈₉	—	2	4	no	—
361	C₄×C₈₉	—	2	2	no	—
362	C₄×C₈₉	—	4	2	no	—
363	C₄×C₈₉	—	4	2	no	—
364	C₄×C₈₉	—	4	2	no	—
365	C₄×C₈₉	—	4	4	no	—
366	C₄×C₈₉	—	4	2	no	—
367	C₄×C₈₉	—	4	1	no	—
368	C₄×C₈₉	#532	1	4	yes	—
369	C₄×C₈₉	#542	1	4	yes	complemented
370	#35198	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
371	C₂×C₈₉	—	8	2	no	—
372	C₂×C₈₉	—	8	4	no	—
373	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
374	C₂×C₈₉	C₂×#542	1	1	yes	characteristic
375	C₂×C₈₉	#3460	1	1	yes	characteristic
376	C₂×C₈₉	#3497	1	1	yes	characteristic
377	C₂×C₈₉	#3498	1	1	yes	characteristic
378	C₂×C₈₉	#3514	1	1	yes	characteristic
379	C₂×C₈₉	#3522	1	1	yes	characteristic
380	C₂×#542	C₂×C₈₉	1	2	yes	complemented
381	#2860	C₂×C₈₉	1	2	yes	complemented
382	#2858	C₂×C₈₉	1	2	yes	complemented
383	#2662	C₂×C₈₉	1	4	yes	complemented
384	#2551	C₂×C₈₉	1	1	yes	characteristic, complemented
385	#2548	C₂×C₈₉	1	1	yes	characteristic, complemented
386	#2541	C₂×C₈₉	1	1	yes	characteristic
387	#2538	C₂×C₈₉	1	1	yes	characteristic, complemented
388	#2491	C₂×C₈₉	1	2	yes	complemented
389	#2461	C₂×C₈₉	1	4	yes	complemented
390	#2452	C₂×C₈₉	1	2	yes	complemented
391	#2445	C₂×C₈₉	1	2	yes	complemented
392	#2426	C₂×C₈₉	1	2	yes	complemented
393	#2324	C₂×C₈₉	1	2	yes	complemented
394	C₄×#127	C₂×C₈₉	1	1	yes	characteristic, complemented
395	#2293	C₂×C₈₉	1	1	yes	characteristic, complemented
396	C₄²×Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
397	C₈₉	#35198	1	1	yes	characteristic, direct product factor, Sylow
398	#542	—	2	16	no	—
399	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
400	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
401	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
402	C₂×#127	C₂²×C₈₉	1	2	yes	—
403	C₂×#126	C₂²×C₈₉	1	4	yes	—
404	C₂×#124	C₂²×C₈₉	1	4	yes	—
405	C₂×#124	C₂²×C₈₉	1	2	yes	—
406	C₂×#124	C₂²×C₈₉	1	4	yes	—
407	C₂×#123	C₂²×C₈₉	1	4	yes	—
408	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
409	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
410	C₂×#121	C₂²×C₈₉	1	2	yes	—
411	C₂×#121	C₂²×C₈₉	1	2	yes	—
412	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
413	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
414	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
415	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
416	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
417	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
418	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
419	C₂×#117	C₂²×C₈₉	1	2	yes	—
420	#396	C₂²×C₈₉	1	4	yes	—
421	#396	C₂²×C₈₉	1	4	yes	—
422	#395	C₂²×C₈₉	1	4	yes	—
423	#394	C₂²×C₈₉	1	4	yes	—
424	#394	C₂²×C₈₉	1	4	yes	—
425	#394	C₂²×C₈₉	1	4	yes	—
426	#393	C₂²×C₈₉	1	4	yes	—
427	#392	C₂²×C₈₉	1	4	yes	—
428	#390	C₂²×C₈₉	1	2	yes	—
429	#390	C₂²×C₈₉	1	2	yes	—
430	#390	C₂²×C₈₉	1	2	yes	—
431	#390	C₂²×C₈₉	1	4	yes	—
432	#390	C₂²×C₈₉	1	2	yes	—
433	#390	C₂²×C₈₉	1	1	yes	characteristic
434	#390	C₂²×C₈₉	1	4	yes	—
435	#390	C₂²×C₈₉	1	2	yes	—
436	#390	C₂²×C₈₉	1	2	yes	—
437	#390	C₂²×C₈₉	1	2	yes	—
438	#390	C₂²×C₈₉	1	2	yes	—
439	#390	C₂²×C₈₉	1	1	yes	characteristic
440	#389	C₂²×C₈₉	1	2	yes	—
441	#389	C₂²×C₈₉	1	1	yes	characteristic
442	#389	C₂²×C₈₉	1	2	yes	—
443	#389	C₂²×C₈₉	1	2	yes	—
444	#389	C₂²×C₈₉	1	1	yes	characteristic
445	#388	C₂²×C₈₉	1	4	yes	—
446	#388	C₂²×C₈₉	1	4	yes	—
447	#388	C₂²×C₈₉	1	4	yes	—
448	#388	C₂²×C₈₉	1	2	yes	—
449	#388	C₂²×C₈₉	1	2	yes	—
450	#386	C₂²×C₈₉	1	4	yes	—
451	#385	C₂²×C₈₉	1	4	yes	—
452	#384	C₂²×C₈₉	1	1	yes	characteristic
453	#380	C₂²×C₈₉	1	2	yes	—
454	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
455	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
456	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
457	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
458	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
459	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
460	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
461	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
462	C₄³	C₂²×C₈₉	1	1	yes	characteristic
463	C₄³	C₂²×C₈₉	1	2	yes	—
464	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
465	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
466	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
467	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
468	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
469	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
470	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
471	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
472	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
473	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
474	C₄⋊Q₈	—	2	8	no	—
475	C₄⋊Q₈	—	4	4	no	—
476	#127	—	2	4	no	—
477	#127	—	4	4	no	—
478	#126	—	2	16	no	—
479	#124	—	2	8	no	—
480	#124	—	2	16	no	—
481	#124	—	4	8	no	—
482	#123	—	2	16	no	—
483	C₂²⋊Q₈	—	2	8	no	—
484	C₂²⋊Q₈	—	2	16	no	—
485	#121	—	2	8	no	—
486	#121	—	2	8	no	—
487	C₄×Q₈	—	2	4	no	—
488	C₄×Q₈	—	2	4	no	—
489	C₄×Q₈	D₄×C₈₉	1	8	yes	complemented
490	C₄×D₄	—	2	8	no	—
491	C₄×D₄	—	2	4	no	—
492	C₄×D₄	—	4	4	no	—
493	C₄×D₄	—	4	4	no	—
494	#117	—	2	8	no	—
495	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
504	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
505	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
509	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
512	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
528	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
529	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
532	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
533	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
534	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
535	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
536	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
537	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
538	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
539	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
541	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
542	#95	C₂³×C₈₉	1	2	yes	—
543	#95	C₂³×C₈₉	1	2	yes	—
544	#95	C₂³×C₈₉	1	2	yes	—
545	#95	C₂³×C₈₉	1	2	yes	—
546	#95	C₂³×C₈₉	1	2	yes	—
547	#95	C₂³×C₈₉	1	2	yes	—
548	#95	C₂³×C₈₉	1	4	yes	—
549	#95	C₂³×C₈₉	1	4	yes	—
550	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
551	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
552	C₂×Q₈	—	2	8	no	—
553	C₂×Q₈	—	2	2	no	—
554	C₂×Q₈	—	2	2	no	—
555	C₂×Q₈	—	4	4	no	—
556	C₂×Q₈	—	4	4	no	—
557	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
558	C₂×D₄	—	2	4	no	—
559	C₂×D₄	—	2	8	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	4	no	—
562	C₂×D₄	—	2	4	no	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	8	no	—
566	C₂×D₄	—	2	4	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	4	2	no	—
571	C₂×D₄	—	4	2	no	—
572	C₂×D₄	—	4	4	no	—
573	C₂×D₄	—	4	4	no	—
574	C₂×D₄	—	4	4	no	—
575	C₂×D₄	—	4	4	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	2	8	no	—
580	C₂²×C₄	—	4	4	no	—
581	C₂²×C₄	—	4	4	no	—
582	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
583	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
588	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
591	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
594	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	8	no	—
601	C₄⋊C₄	—	2	8	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	2	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	4	2	no	—
610	C₄⋊C₄	—	4	4	no	—
611	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
612	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
613	C₄⋊C₄	#41×C₈₉	1	4	yes	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	8	no	—
617	C₂²⋊C₄	—	2	8	no	—
618	C₂²⋊C₄	—	2	8	no	—
619	C₂²⋊C₄	—	2	8	no	—
620	C₂²⋊C₄	—	2	8	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	8	no	—
623	C₂²⋊C₄	—	2	8	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	4	4	no	—
626	C₂²⋊C₄	—	4	4	no	—
627	C₂²⋊C₄	—	4	4	no	—
628	C₂²⋊C₄	—	4	2	no	—
629	C₂²⋊C₄	—	4	4	no	—
630	C₄²	—	2	4	no	—
631	C₄²	—	2	4	no	—
632	C₄²	—	2	2	no	—
633	C₄²	—	2	4	no	—
634	C₄²	—	2	2	no	—
635	C₄²	—	2	2	no	—
636	C₄²	—	2	4	no	—
637	C₄²	—	2	4	no	—
638	C₄²	—	2	2	no	—
639	C₄²	—	4	1	no	—
640	C₄²	—	4	2	no	—
641	C₄²	C₂×D₄×C₈₉	1	4	yes	—
642	C₄²	C₂×D₄×C₈₉	1	8	yes	—
643	C₄²	#41×C₈₉	1	4	yes	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	4	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	4	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	4	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	4	no	—
652	C₂³	—	2	4	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	4	no	—
656	C₂³	—	2	4	no	—
657	C₂³	—	2	2	no	—
658	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
659	Q₈	—	2	8	no	—
660	Q₈	—	8	8	no	—
661	D₄	—	4	8	no	—
662	D₄	—	4	8	no	—
663	D₄	—	4	4	no	—
664	D₄	—	4	8	no	—
665	D₄	—	8	8	no	—
666	D₄	—	8	8	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	4	8	no	—
700	C₂×C₄	—	8	8	no	—
701	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
702	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
703	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
704	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
705	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
706	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
707	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
708	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
709	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
710	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
711	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
712	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
713	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	4	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	4	no	—
718	C₂²	—	4	4	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	4	no	—
722	C₂²	—	4	4	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	4	no	—
726	C₂²	—	4	4	no	—
727	C₂²	—	4	2	no	—
728	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
729	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
730	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
731	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
732	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
733	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
734	C₂²	#585×C₈₉	1	1	yes	characteristic
735	C₄	—	2	4	no	—
736	C₄	—	2	2	no	—
737	C₄	—	2	2	no	—
738	C₄	—	2	2	no	—
739	C₄	—	2	4	no	—
740	C₄	—	2	4	no	—
741	C₄	—	2	2	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	4	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	1	no	—
748	C₄	#532×C₈₉	1	4	yes	—
749	C₄	#542×C₈₉	1	4	yes	complemented
750	C₂	—	8	2	no	—
751	C₂	—	8	4	no	—
752	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
753	C₂	C₂×#542×C₈₉	1	1	yes	characteristic
754	C₂	C₈₉×#3460	1	1	yes	characteristic
755	C₂	C₈₉×#3497	1	1	yes	characteristic
756	C₂	C₈₉×#3498	1	1	yes	characteristic
757	C₂	C₈₉×#3514	1	1	yes	characteristic
758	C₂	C₈₉×#3522	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₈₉×#2541	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×#2860	C₂	semidirect
3. C₈₉×#2858	C₂	semidirect
4. C₈₉×#2662	C₂	semidirect
5. C₈₉×#2551	C₂	semidirect
6. C₈₉×#2548	C₂	semidirect
8. C₈₉×#2538	C₂	semidirect
9. C₈₉×#2491	C₂	semidirect
10. C₈₉×#2461	C₂	semidirect
11. C₈₉×#2452	C₂	semidirect
12. C₈₉×#2445	C₂	semidirect
13. C₈₉×#2426	C₂	semidirect
14. C₈₉×#2324	C₂	semidirect
15. C₄×#127×C₈₉	C₂	semidirect
16. C₈₉×#2293	C₂	semidirect
17. C₄²×Q₈×C₈₉	C₂	semidirect
109. C₄×Q₈×C₈₉	D₄	semidirect
369. C₄×C₈₉	#542	semidirect
370. #35198	C₈₉	direct (N × H)
380. C₂×#542	C₂×C₈₉	semidirect
381. #2860	C₂×C₈₉	semidirect
382. #2858	C₂×C₈₉	semidirect
383. #2662	C₂×C₈₉	semidirect
384. #2551	C₂×C₈₉	semidirect
385. #2548	C₂×C₈₉	semidirect
387. #2538	C₂×C₈₉	semidirect
388. #2491	C₂×C₈₉	semidirect
389. #2461	C₂×C₈₉	semidirect
390. #2452	C₂×C₈₉	semidirect
391. #2445	C₂×C₈₉	semidirect
392. #2426	C₂×C₈₉	semidirect
393. #2324	C₂×C₈₉	semidirect
394. C₄×#127	C₂×C₈₉	semidirect
395. #2293	C₂×C₈₉	semidirect
396. C₄²×Q₈	C₂×C₈₉	semidirect
397. C₈₉	#35198	direct (N × H)
489. C₄×Q₈	D₄×C₈₉	semidirect
749. 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×#2860	2
C₈₉×#2858	2
C₈₉×#2662	2
C₈₉×#2551	2
C₈₉×#2548	2
C₈₉×#2541	2
C₈₉×#2538	2
C₈₉×#2491	2
C₈₉×#2461	2
C₈₉×#2452	2
C₈₉×#2445	2
C₈₉×#2426	2
C₈₉×#2324	2
C₄×#127×C₈₉	2
C₈₉×#2293	2
C₄²×Q₈×C₈₉	2
#35198	89

Subgroups — C89×#35198 #36413046

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35198 #36413046