Subgroups — C₈₉×#34494 #36412342

Order 22784.

2660 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#550×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2377	C₂	1	4	yes	maximal, complemented
3	C₈₉×#2366	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2366	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2361	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2355	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2349	C₂	1	2	yes	maximal, complemented
8	D₄×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2339	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2328	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2325	C₂	1	4	yes	maximal, complemented
12	C₈₉×#2324	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2319	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2311	C₂	1	2	yes	maximal, complemented
15	C₄×#127×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2295	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2293	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₈₉	C₂²	1	2	yes	—
19	#550×C₈₉	C₄	1	16	yes	complemented
20	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#127×C₈₉	C₂²	1	2	yes	—
22	C₂×#121×C₈₉	C₂²	1	2	yes	—
23	C₂×#121×C₈₉	C₂²	1	4	yes	—
24	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
30	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#117×C₈₉	C₂²	1	2	yes	—
35	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
36	#391×C₈₉	C₂²	1	1	yes	characteristic
37	#391×C₈₉	C₂²	1	1	yes	characteristic
38	#391×C₈₉	C₂²	1	2	yes	—
39	#390×C₈₉	C₂²	1	2	yes	—
40	#390×C₈₉	C₂²	1	2	yes	—
41	#390×C₈₉	C₂²	1	2	yes	—
42	#390×C₈₉	C₂²	1	2	yes	—
43	#390×C₈₉	C₂²	1	2	yes	—
44	#390×C₈₉	C₂²	1	4	yes	—
45	#390×C₈₉	C₂²	1	1	yes	characteristic
46	#390×C₈₉	C₂²	1	1	yes	characteristic
47	#389×C₈₉	C₂²	1	1	yes	characteristic
48	#389×C₈₉	C₂²	1	1	yes	characteristic
49	#389×C₈₉	C₂²	1	1	yes	characteristic
50	#389×C₈₉	C₂²	1	2	yes	—
51	#389×C₈₉	C₂²	1	1	yes	characteristic
52	#388×C₈₉	C₂²	1	4	yes	—
53	#388×C₈₉	C₂²	1	4	yes	—
54	#388×C₈₉	C₂²	1	2	yes	—
55	#388×C₈₉	C₂²	1	2	yes	—
56	#387×C₈₉	C₂²	1	2	yes	—
57	#387×C₈₉	C₂²	1	2	yes	—
58	#387×C₈₉	C₂²	1	4	yes	—
59	#386×C₈₉	C₂²	1	4	yes	—
60	#386×C₈₉	C₂²	1	4	yes	—
61	#386×C₈₉	C₂²	1	4	yes	—
62	#386×C₈₉	C₂²	1	4	yes	—
63	#386×C₈₉	C₂²	1	4	yes	—
64	#386×C₈₉	C₂²	1	4	yes	—
65	#386×C₈₉	C₂²	1	4	yes	—
66	#385×C₈₉	C₂²	1	4	yes	—
67	#385×C₈₉	C₂²	1	4	yes	—
68	#385×C₈₉	C₂²	1	4	yes	—
69	#384×C₈₉	C₂²	1	1	yes	characteristic
70	#382×C₈₉	C₂²	1	2	yes	—
71	#381×C₈₉	C₂²	1	4	yes	—
72	#380×C₈₉	C₂²	1	4	yes	—
73	#380×C₈₉	C₂²	1	4	yes	—
74	#380×C₈₉	C₂²	1	2	yes	—
75	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
76	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
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	1	yes	characteristic
80	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
81	#376×C₈₉	C₂²	1	2	yes	—
82	C₂×#95×C₈₉	C₂²	1	4	yes	—
83	C₄³×C₈₉	C₂²	1	1	yes	characteristic
84	C₂×#41×C₈₉	—	4	4	no	—
85	C₂×#41×C₈₉	—	4	4	no	—
86	C₂×#41×C₈₉	C₂×C₄	1	16	yes	complemented
87	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
89	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
91	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
92	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
93	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
94	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
95	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
96	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
97	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
98	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
99	#127×C₈₉	C₂×C₄	1	8	yes	complemented
100	#127×C₈₉	C₂×C₄	1	16	yes	complemented
101	#121×C₈₉	C₂×C₄	1	16	yes	complemented
102	#121×C₈₉	C₂×C₄	1	32	yes	complemented
103	C₄×Q₈×C₈₉	C₂×C₄	1	8	yes	complemented
104	C₄×D₄×C₈₉	—	4	4	no	—
105	C₄×D₄×C₈₉	—	4	4	no	—
106	C₄×D₄×C₈₉	—	4	4	no	—
107	C₄×D₄×C₈₉	—	4	4	no	—
108	C₄×D₄×C₈₉	—	4	4	no	—
109	C₄×D₄×C₈₉	—	4	4	no	—
110	C₄×D₄×C₈₉	—	4	8	no	—
111	C₄×D₄×C₈₉	C₂×C₄	1	8	yes	complemented
112	C₄×D₄×C₈₉	C₂×C₄	1	16	yes	complemented
113	#117×C₈₉	—	4	4	no	—
114	C₂×C₄⋊C₄×C₈₉	—	4	4	no	—
115	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
120	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	4	yes	—
137	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	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	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
151	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
152	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
154	#95×C₈₉	C₂³	1	2	yes	—
155	#95×C₈₉	C₂³	1	2	yes	—
156	#95×C₈₉	C₂³	1	4	yes	—
157	#95×C₈₉	C₂³	1	4	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	2	yes	—
162	#95×C₈₉	C₂³	1	2	yes	—
163	#95×C₈₉	C₂³	1	2	yes	—
164	#95×C₈₉	C₂³	1	4	yes	—
165	#95×C₈₉	C₂³	1	4	yes	—
166	#95×C₈₉	C₂³	1	2	yes	—
167	#95×C₈₉	C₂³	1	2	yes	—
168	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
169	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
170	#41×C₈₉	—	4	32	no	—
171	C₂×Q₈×C₈₉	—	2	2	no	—
172	C₂×Q₈×C₈₉	—	2	2	no	—
173	C₂×Q₈×C₈₉	C₂²×C₄	1	4	yes	—
174	C₂×D₄×C₈₉	—	2	2	no	—
175	C₂×D₄×C₈₉	—	2	4	no	—
176	C₂×D₄×C₈₉	—	2	4	no	—
177	C₂×D₄×C₈₉	—	2	4	no	—
178	C₂×D₄×C₈₉	—	2	4	no	—
179	C₂×D₄×C₈₉	—	2	2	no	—
180	C₂×D₄×C₈₉	—	4	2	no	—
181	C₂×D₄×C₈₉	—	4	4	no	—
182	C₂×D₄×C₈₉	—	4	2	no	—
183	C₂×D₄×C₈₉	—	4	4	no	—
184	C₂×D₄×C₈₉	—	4	4	no	—
185	C₂×D₄×C₈₉	—	4	4	no	—
186	C₂×D₄×C₈₉	C₂²×C₄	1	4	yes	—
187	C₂×D₄×C₈₉	C₂²×C₄	1	8	yes	—
188	C₂×D₄×C₈₉	C₂²×C₄	1	8	yes	—
189	C₂×D₄×C₈₉	C₂²×C₄	1	16	yes	—
190	C₂×D₄×C₈₉	C₂²×C₄	1	8	yes	—
191	C₂×D₄×C₈₉	C₂²×C₄	1	16	yes	—
192	C₂²×C₄×C₈₉	—	2	4	no	—
193	C₂²×C₄×C₈₉	—	2	4	no	—
194	C₂²×C₄×C₈₉	—	2	8	no	—
195	C₂²×C₄×C₈₉	—	4	4	no	—
196	C₂²×C₄×C₈₉	—	4	4	no	—
197	C₂²×C₄×C₈₉	—	4	4	no	—
198	C₂²×C₄×C₈₉	—	4	4	no	—
199	C₂²×C₄×C₈₉	—	4	4	no	—
200	C₂²×C₄×C₈₉	—	4	4	no	—
201	C₂²×C₄×C₈₉	—	4	4	no	—
202	C₂²×C₄×C₈₉	—	4	4	no	—
203	C₂²×C₄×C₈₉	—	4	4	no	—
204	C₂²×C₄×C₈₉	—	4	4	no	—
205	C₂²×C₄×C₈₉	C₂²×C₄	1	8	yes	—
206	C₂²×C₄×C₈₉	C₂²×C₄	1	16	yes	—
207	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
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	4	yes	—
214	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	2	no	—
227	C₄⋊C₄×C₈₉	—	2	4	no	—
228	C₄⋊C₄×C₈₉	—	2	2	no	—
229	C₄⋊C₄×C₈₉	—	4	4	no	—
230	C₄⋊C₄×C₈₉	—	4	2	no	—
231	C₄⋊C₄×C₈₉	—	4	2	no	—
232	C₄⋊C₄×C₈₉	—	4	2	no	—
233	C₄⋊C₄×C₈₉	—	4	2	no	—
234	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
235	C₄⋊C₄×C₈₉	C₂²×C₄	1	8	yes	—
236	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
237	C₂²⋊C₄×C₈₉	—	2	4	no	—
238	C₂²⋊C₄×C₈₉	—	4	2	no	—
239	C₂²⋊C₄×C₈₉	—	4	2	no	—
240	C₂²⋊C₄×C₈₉	—	4	2	no	—
241	C₂²⋊C₄×C₈₉	—	4	4	no	—
242	C₂²⋊C₄×C₈₉	—	4	4	no	—
243	C₂²⋊C₄×C₈₉	—	4	4	no	—
244	C₂²⋊C₄×C₈₉	—	4	4	no	—
245	C₂²⋊C₄×C₈₉	—	4	4	no	—
246	C₂²⋊C₄×C₈₉	—	4	4	no	—
247	C₂²⋊C₄×C₈₉	—	4	4	no	—
248	C₂²⋊C₄×C₈₉	C₂²×C₄	1	8	yes	—
249	C₂²⋊C₄×C₈₉	C₂²×C₄	1	16	yes	—
250	C₄²×C₈₉	—	2	2	no	—
251	C₄²×C₈₉	—	2	4	no	—
252	C₄²×C₈₉	—	2	2	no	—
253	C₄²×C₈₉	—	2	2	no	—
254	C₄²×C₈₉	—	2	2	no	—
255	C₄²×C₈₉	—	2	4	no	—
256	C₄²×C₈₉	—	2	2	no	—
257	C₄²×C₈₉	—	4	1	no	—
258	C₄²×C₈₉	—	4	4	no	—
259	C₄²×C₈₉	C₂²×C₄	1	8	yes	—
260	C₄²×C₈₉	C₂²×C₄	1	4	yes	—
261	C₂³×C₈₉	—	2	2	no	—
262	C₂³×C₈₉	—	2	2	no	—
263	C₂³×C₈₉	—	2	4	no	—
264	C₂³×C₈₉	—	2	2	no	—
265	C₂³×C₈₉	—	2	4	no	—
266	C₂³×C₈₉	—	2	4	no	—
267	C₂³×C₈₉	—	2	4	no	—
268	C₂³×C₈₉	—	2	2	no	—
269	C₂³×C₈₉	—	2	2	no	—
270	C₂³×C₈₉	—	2	4	no	—
271	C₂³×C₈₉	—	2	2	no	—
272	C₂³×C₈₉	—	2	4	no	—
273	C₂³×C₈₉	C₂³×C₄	1	4	yes	—
274	C₂³×C₈₉	C₂³×C₄	1	8	yes	—
275	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
276	Q₈×C₈₉	—	2	8	no	—
277	D₄×C₈₉	—	2	16	no	—
278	D₄×C₈₉	—	2	8	no	—
279	D₄×C₈₉	—	2	16	no	—
280	D₄×C₈₉	—	4	8	no	—
281	D₄×C₈₉	—	4	16	no	—
282	D₄×C₈₉	—	4	16	no	—
283	C₂×C₄×C₈₉	—	2	1	no	—
284	C₂×C₄×C₈₉	—	2	1	no	—
285	C₂×C₄×C₈₉	—	2	1	no	—
286	C₂×C₄×C₈₉	—	2	2	no	—
287	C₂×C₄×C₈₉	—	2	2	no	—
288	C₂×C₄×C₈₉	—	2	2	no	—
289	C₂×C₄×C₈₉	—	2	2	no	—
290	C₂×C₄×C₈₉	—	2	2	no	—
291	C₂×C₄×C₈₉	—	2	1	no	—
292	C₂×C₄×C₈₉	—	2	2	no	—
293	C₂×C₄×C₈₉	—	2	16	no	—
294	C₂×C₄×C₈₉	—	2	1	no	—
295	C₂×C₄×C₈₉	—	2	1	no	—
296	C₂×C₄×C₈₉	—	2	1	no	—
297	C₂×C₄×C₈₉	—	2	2	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	4	no	—
306	C₂×C₄×C₈₉	—	2	2	no	—
307	C₂×C₄×C₈₉	—	2	2	no	—
308	C₂×C₄×C₈₉	—	2	2	no	—
309	C₂×C₄×C₈₉	—	2	4	no	—
310	C₂×C₄×C₈₉	—	2	2	no	—
311	C₂×C₄×C₈₉	—	2	1	no	—
312	C₂×C₄×C₈₉	—	2	1	no	—
313	C₂×C₄×C₈₉	—	2	2	no	—
314	C₂×C₄×C₈₉	—	2	1	no	—
315	C₂×C₄×C₈₉	—	2	1	no	—
316	C₂×C₄×C₈₉	—	2	2	no	—
317	C₂×C₄×C₈₉	—	2	2	no	—
318	C₂×C₄×C₈₉	—	4	16	no	—
319	C₂×C₄×C₈₉	—	8	8	no	—
320	C₂×C₄×C₈₉	—	8	8	no	—
321	C₂×C₄×C₈₉	—	8	8	no	—
322	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
323	C₂×C₄×C₈₉	C₂³×C₄	1	4	yes	—
324	C₂×C₄×C₈₉	C₂³×C₄	1	4	yes	—
325	C₂×C₄×C₈₉	C₂³×C₄	1	4	yes	—
326	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
327	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
328	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
329	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
330	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
331	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
332	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
333	C₂²×C₈₉	—	2	4	no	—
334	C₂²×C₈₉	—	2	8	no	—
335	C₂²×C₈₉	—	2	4	no	—
336	C₂²×C₈₉	—	2	8	no	—
337	C₂²×C₈₉	—	2	4	no	—
338	C₂²×C₈₉	—	2	8	no	—
339	C₂²×C₈₉	—	4	2	no	—
340	C₂²×C₈₉	—	4	4	no	—
341	C₂²×C₈₉	—	4	4	no	—
342	C₂²×C₈₉	—	4	2	no	—
343	C₂²×C₈₉	—	4	2	no	—
344	C₂²×C₈₉	—	4	4	no	—
345	C₂²×C₈₉	—	4	4	no	—
346	C₂²×C₈₉	—	4	2	no	—
347	C₂²×C₈₉	C₂⁴×C₄	1	1	yes	characteristic
348	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
349	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
350	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
351	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
352	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
353	C₂²×C₈₉	#585	1	1	yes	characteristic
354	C₄×C₈₉	—	2	4	no	—
355	C₄×C₈₉	—	2	4	no	—
356	C₄×C₈₉	—	2	2	no	—
357	C₄×C₈₉	—	2	4	no	—
358	C₄×C₈₉	—	2	2	no	—
359	C₄×C₈₉	—	4	2	no	—
360	C₄×C₈₉	—	4	4	no	—
361	C₄×C₈₉	—	4	1	no	—
362	C₄×C₈₉	—	4	2	no	—
363	C₄×C₈₉	—	4	2	no	—
364	C₄×C₈₉	—	4	1	no	—
365	C₄×C₈₉	—	4	2	no	—
366	C₄×C₈₉	—	4	1	no	—
367	C₄×C₈₉	#518	1	4	yes	—
368	C₄×C₈₉	#520	1	4	yes	—
369	#34494	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
370	C₂×C₈₉	—	4	4	no	—
371	C₂×C₈₉	—	4	8	no	—
372	C₂×C₈₉	C₂×#518	1	1	yes	characteristic
373	C₂×C₈₉	C₂×#520	1	1	yes	characteristic
374	C₂×C₈₉	C₄×H(5,𝔽₂)	1	1	yes	characteristic
375	C₂×C₈₉	#3543	1	1	yes	characteristic
376	C₂×C₈₉	#3546	1	1	yes	characteristic
377	C₂×C₈₉	#3548	1	1	yes	characteristic
378	C₂×C₈₉	#3554	1	1	yes	characteristic
379	C₂×#550	C₂×C₈₉	1	1	yes	characteristic
380	#2377	C₂×C₈₉	1	4	yes	complemented
381	#2366	C₂×C₈₉	1	2	yes	complemented
382	#2366	C₂×C₈₉	1	1	yes	characteristic, complemented
383	#2361	C₂×C₈₉	1	2	yes	complemented
384	#2355	C₂×C₈₉	1	1	yes	characteristic, complemented
385	#2349	C₂×C₈₉	1	2	yes	complemented
386	D₄×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
387	#2339	C₂×C₈₉	1	2	yes	complemented
388	#2328	C₂×C₈₉	1	2	yes	complemented
389	#2325	C₂×C₈₉	1	4	yes	complemented
390	#2324	C₂×C₈₉	1	2	yes	complemented
391	#2319	C₂×C₈₉	1	2	yes	complemented
392	#2311	C₂×C₈₉	1	2	yes	complemented
393	C₄×#127	C₂×C₈₉	1	1	yes	characteristic, complemented
394	#2295	C₂×C₈₉	1	1	yes	characteristic, complemented
395	#2293	C₂×C₈₉	1	1	yes	characteristic, complemented
396	C₈₉	#34494	1	1	yes	characteristic, direct product factor, Sylow
397	C₂²×#41	C₂²×C₈₉	1	2	yes	—
398	#550	C₄×C₈₉	1	16	yes	complemented
399	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
400	C₂×#127	C₂²×C₈₉	1	2	yes	—
401	C₂×#121	C₂²×C₈₉	1	2	yes	—
402	C₂×#121	C₂²×C₈₉	1	4	yes	—
403	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
404	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
405	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
406	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
407	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
408	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
409	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
410	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
411	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
412	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
413	C₂×#117	C₂²×C₈₉	1	2	yes	—
414	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
415	#391	C₂²×C₈₉	1	1	yes	characteristic
416	#391	C₂²×C₈₉	1	2	yes	—
417	#391	C₂²×C₈₉	1	1	yes	characteristic
418	#390	C₂²×C₈₉	1	2	yes	—
419	#390	C₂²×C₈₉	1	2	yes	—
420	#390	C₂²×C₈₉	1	2	yes	—
421	#390	C₂²×C₈₉	1	2	yes	—
422	#390	C₂²×C₈₉	1	2	yes	—
423	#390	C₂²×C₈₉	1	4	yes	—
424	#390	C₂²×C₈₉	1	1	yes	characteristic
425	#390	C₂²×C₈₉	1	1	yes	characteristic
426	#389	C₂²×C₈₉	1	1	yes	characteristic
427	#389	C₂²×C₈₉	1	2	yes	—
428	#389	C₂²×C₈₉	1	1	yes	characteristic
429	#389	C₂²×C₈₉	1	1	yes	characteristic
430	#389	C₂²×C₈₉	1	1	yes	characteristic
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	2	yes	—
436	#387	C₂²×C₈₉	1	4	yes	—
437	#387	C₂²×C₈₉	1	2	yes	—
438	#386	C₂²×C₈₉	1	4	yes	—
439	#386	C₂²×C₈₉	1	4	yes	—
440	#386	C₂²×C₈₉	1	4	yes	—
441	#386	C₂²×C₈₉	1	4	yes	—
442	#386	C₂²×C₈₉	1	4	yes	—
443	#386	C₂²×C₈₉	1	4	yes	—
444	#386	C₂²×C₈₉	1	4	yes	—
445	#385	C₂²×C₈₉	1	4	yes	—
446	#385	C₂²×C₈₉	1	4	yes	—
447	#385	C₂²×C₈₉	1	4	yes	—
448	#384	C₂²×C₈₉	1	1	yes	characteristic
449	#382	C₂²×C₈₉	1	2	yes	—
450	#381	C₂²×C₈₉	1	4	yes	—
451	#380	C₂²×C₈₉	1	4	yes	—
452	#380	C₂²×C₈₉	1	4	yes	—
453	#380	C₂²×C₈₉	1	2	yes	—
454	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
455	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
456	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
457	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
458	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
459	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
460	#376	C₂²×C₈₉	1	2	yes	—
461	C₂×#95	C₂²×C₈₉	1	4	yes	—
462	C₄³	C₂²×C₈₉	1	1	yes	characteristic
463	C₂×#41	—	4	4	no	—
464	C₂×#41	—	4	4	no	—
465	C₂×#41	C₂×C₄×C₈₉	1	16	yes	complemented
466	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
467	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
468	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
469	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
470	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
471	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
472	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
473	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
474	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
475	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
476	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
477	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
478	#127	C₂×C₄×C₈₉	1	8	yes	complemented
479	#127	C₂×C₄×C₈₉	1	16	yes	complemented
480	#121	C₂×C₄×C₈₉	1	16	yes	complemented
481	#121	C₂×C₄×C₈₉	1	32	yes	complemented
482	C₄×Q₈	C₂×C₄×C₈₉	1	8	yes	complemented
483	C₄×D₄	—	4	4	no	—
484	C₄×D₄	—	4	4	no	—
485	C₄×D₄	—	4	4	no	—
486	C₄×D₄	—	4	4	no	—
487	C₄×D₄	—	4	4	no	—
488	C₄×D₄	—	4	4	no	—
489	C₄×D₄	—	4	8	no	—
490	C₄×D₄	C₂×C₄×C₈₉	1	8	yes	complemented
491	C₄×D₄	C₂×C₄×C₈₉	1	16	yes	complemented
492	#117	—	4	4	no	—
493	C₂×C₄⋊C₄	—	4	4	no	—
494	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
502	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	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	4	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	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
522	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
523	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
524	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
525	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
526	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
527	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
528	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
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	#95	C₂³×C₈₉	1	2	yes	—
534	#95	C₂³×C₈₉	1	2	yes	—
535	#95	C₂³×C₈₉	1	4	yes	—
536	#95	C₂³×C₈₉	1	4	yes	—
537	#95	C₂³×C₈₉	1	2	yes	—
538	#95	C₂³×C₈₉	1	2	yes	—
539	#95	C₂³×C₈₉	1	2	yes	—
540	#95	C₂³×C₈₉	1	2	yes	—
541	#95	C₂³×C₈₉	1	2	yes	—
542	#95	C₂³×C₈₉	1	2	yes	—
543	#95	C₂³×C₈₉	1	4	yes	—
544	#95	C₂³×C₈₉	1	4	yes	—
545	#95	C₂³×C₈₉	1	2	yes	—
546	#95	C₂³×C₈₉	1	2	yes	—
547	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
548	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
549	#41	—	4	32	no	—
550	C₂×Q₈	—	2	2	no	—
551	C₂×Q₈	—	2	2	no	—
552	C₂×Q₈	C₂²×C₄×C₈₉	1	4	yes	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	4	no	—
555	C₂×D₄	—	2	4	no	—
556	C₂×D₄	—	2	4	no	—
557	C₂×D₄	—	2	4	no	—
558	C₂×D₄	—	2	2	no	—
559	C₂×D₄	—	4	2	no	—
560	C₂×D₄	—	4	4	no	—
561	C₂×D₄	—	4	4	no	—
562	C₂×D₄	—	4	4	no	—
563	C₂×D₄	—	4	2	no	—
564	C₂×D₄	—	4	4	no	—
565	C₂×D₄	C₂²×C₄×C₈₉	1	4	yes	—
566	C₂×D₄	C₂²×C₄×C₈₉	1	8	yes	—
567	C₂×D₄	C₂²×C₄×C₈₉	1	8	yes	—
568	C₂×D₄	C₂²×C₄×C₈₉	1	16	yes	—
569	C₂×D₄	C₂²×C₄×C₈₉	1	8	yes	—
570	C₂×D₄	C₂²×C₄×C₈₉	1	16	yes	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	—	2	8	no	—
574	C₂²×C₄	—	4	4	no	—
575	C₂²×C₄	—	4	4	no	—
576	C₂²×C₄	—	4	4	no	—
577	C₂²×C₄	—	4	4	no	—
578	C₂²×C₄	—	4	4	no	—
579	C₂²×C₄	—	4	4	no	—
580	C₂²×C₄	—	4	4	no	—
581	C₂²×C₄	—	4	4	no	—
582	C₂²×C₄	—	4	4	no	—
583	C₂²×C₄	—	4	4	no	—
584	C₂²×C₄	C₂²×C₄×C₈₉	1	8	yes	—
585	C₂²×C₄	C₂²×C₄×C₈₉	1	16	yes	—
586	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
587	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
590	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
593	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
594	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
599	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	2	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	4	4	no	—
609	C₄⋊C₄	—	4	2	no	—
610	C₄⋊C₄	—	4	2	no	—
611	C₄⋊C₄	—	4	2	no	—
612	C₄⋊C₄	—	4	2	no	—
613	C₄⋊C₄	C₂²×C₄×C₈₉	1	4	yes	—
614	C₄⋊C₄	C₂²×C₄×C₈₉	1	8	yes	—
615	C₄⋊C₄	C₂²×C₄×C₈₉	1	4	yes	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	4	2	no	—
618	C₂²⋊C₄	—	4	2	no	—
619	C₂²⋊C₄	—	4	4	no	—
620	C₂²⋊C₄	—	4	4	no	—
621	C₂²⋊C₄	—	4	4	no	—
622	C₂²⋊C₄	—	4	4	no	—
623	C₂²⋊C₄	—	4	4	no	—
624	C₂²⋊C₄	—	4	4	no	—
625	C₂²⋊C₄	—	4	4	no	—
626	C₂²⋊C₄	—	4	2	no	—
627	C₂²⋊C₄	C₂²×C₄×C₈₉	1	8	yes	—
628	C₂²⋊C₄	C₂²×C₄×C₈₉	1	16	yes	—
629	C₄²	—	2	2	no	—
630	C₄²	—	2	4	no	—
631	C₄²	—	2	2	no	—
632	C₄²	—	2	2	no	—
633	C₄²	—	2	2	no	—
634	C₄²	—	2	4	no	—
635	C₄²	—	2	2	no	—
636	C₄²	—	4	4	no	—
637	C₄²	—	4	1	no	—
638	C₄²	C₂²×C₄×C₈₉	1	8	yes	—
639	C₄²	C₂²×C₄×C₈₉	1	4	yes	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	4	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	4	no	—
645	C₂³	—	2	4	no	—
646	C₂³	—	2	4	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	4	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	4	no	—
652	C₂³	C₂³×C₄×C₈₉	1	4	yes	—
653	C₂³	C₂³×C₄×C₈₉	1	8	yes	—
654	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
655	Q₈	—	2	8	no	—
656	D₄	—	2	16	no	—
657	D₄	—	2	8	no	—
658	D₄	—	2	16	no	—
659	D₄	—	4	8	no	—
660	D₄	—	4	16	no	—
661	D₄	—	4	16	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	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	16	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	4	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	4	16	no	—
698	C₂×C₄	—	8	8	no	—
699	C₂×C₄	—	8	8	no	—
700	C₂×C₄	—	8	8	no	—
701	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
702	C₂×C₄	C₂³×C₄×C₈₉	1	4	yes	—
703	C₂×C₄	C₂³×C₄×C₈₉	1	4	yes	—
704	C₂×C₄	C₂³×C₄×C₈₉	1	4	yes	—
705	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
706	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
707	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
708	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
709	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
710	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
711	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
712	C₂²	—	2	4	no	—
713	C₂²	—	2	8	no	—
714	C₂²	—	2	4	no	—
715	C₂²	—	2	8	no	—
716	C₂²	—	2	4	no	—
717	C₂²	—	2	8	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	4	no	—
720	C₂²	—	4	4	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	4	no	—
724	C₂²	—	4	4	no	—
725	C₂²	—	4	2	no	—
726	C₂²	C₂⁴×C₄×C₈₉	1	1	yes	characteristic
727	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
728	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
729	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
730	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
731	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
732	C₂²	#585×C₈₉	1	1	yes	characteristic
733	C₄	—	2	4	no	—
734	C₄	—	2	4	no	—
735	C₄	—	2	2	no	—
736	C₄	—	2	4	no	—
737	C₄	—	2	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	4	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	1	no	—
743	C₄	—	4	1	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	1	no	—
746	C₄	#518×C₈₉	1	4	yes	—
747	C₄	#520×C₈₉	1	4	yes	—
748	C₂	—	4	4	no	—
749	C₂	—	4	8	no	—
750	C₂	C₂×#518×C₈₉	1	1	yes	characteristic
751	C₂	C₂×#520×C₈₉	1	1	yes	characteristic
752	C₂	C₄×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
753	C₂	C₈₉×#3543	1	1	yes	characteristic
754	C₂	C₈₉×#3546	1	1	yes	characteristic
755	C₂	C₈₉×#3548	1	1	yes	characteristic
756	C₂	C₈₉×#3554	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₈₉
Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂×#550×C₈₉	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₉×#2377	C₂	semidirect
3. C₈₉×#2366	C₂	semidirect
4. C₈₉×#2366	C₂	semidirect
5. C₈₉×#2361	C₂	semidirect
6. C₈₉×#2355	C₂	semidirect
7. C₈₉×#2349	C₂	semidirect
8. D₄×C₄⋊C₄×C₈₉	C₂	semidirect
9. C₈₉×#2339	C₂	semidirect
10. C₈₉×#2328	C₂	semidirect
11. C₈₉×#2325	C₂	semidirect
12. C₈₉×#2324	C₂	semidirect
13. C₈₉×#2319	C₂	semidirect
14. C₈₉×#2311	C₂	semidirect
15. C₄×#127×C₈₉	C₂	semidirect
16. C₈₉×#2295	C₂	semidirect
17. C₈₉×#2293	C₂	semidirect
19. #550×C₈₉	C₄	semidirect
86. C₂×#41×C₈₉	C₂×C₄	semidirect
99. #127×C₈₉	C₂×C₄	semidirect
100. #127×C₈₉	C₂×C₄	semidirect
101. #121×C₈₉	C₂×C₄	semidirect
102. #121×C₈₉	C₂×C₄	semidirect
103. C₄×Q₈×C₈₉	C₂×C₄	semidirect
111. C₄×D₄×C₈₉	C₂×C₄	semidirect
112. C₄×D₄×C₈₉	C₂×C₄	semidirect
369. #34494	C₈₉	direct (N × H)
380. #2377	C₂×C₈₉	semidirect
381. #2366	C₂×C₈₉	semidirect
382. #2366	C₂×C₈₉	semidirect
383. #2361	C₂×C₈₉	semidirect
384. #2355	C₂×C₈₉	semidirect
385. #2349	C₂×C₈₉	semidirect
386. D₄×C₄⋊C₄	C₂×C₈₉	semidirect
387. #2339	C₂×C₈₉	semidirect
388. #2328	C₂×C₈₉	semidirect
389. #2325	C₂×C₈₉	semidirect
390. #2324	C₂×C₈₉	semidirect
391. #2319	C₂×C₈₉	semidirect
392. #2311	C₂×C₈₉	semidirect
393. C₄×#127	C₂×C₈₉	semidirect
394. #2295	C₂×C₈₉	semidirect
395. #2293	C₂×C₈₉	semidirect
396. C₈₉	#34494	direct (N × H)
398. #550	C₄×C₈₉	semidirect
465. C₂×#41	C₂×C₄×C₈₉	semidirect
478. #127	C₂×C₄×C₈₉	semidirect
479. #127	C₂×C₄×C₈₉	semidirect
480. #121	C₂×C₄×C₈₉	semidirect
481. #121	C₂×C₄×C₈₉	semidirect
482. C₄×Q₈	C₂×C₄×C₈₉	semidirect
490. C₄×D₄	C₂×C₄×C₈₉	semidirect
491. C₄×D₄	C₂×C₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#550×C₈₉	2
C₈₉×#2377	2
C₈₉×#2366	2
C₈₉×#2361	2
C₈₉×#2355	2
C₈₉×#2349	2
D₄×C₄⋊C₄×C₈₉	2
C₈₉×#2339	2
C₈₉×#2328	2
C₈₉×#2325	2
C₈₉×#2324	2
C₈₉×#2319	2
C₈₉×#2311	2
C₄×#127×C₈₉	2
C₈₉×#2295	2
C₈₉×#2293	2
#34494	89

Subgroups — C89×#34494 #36412342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#34494 #36412342