Subgroups — C₂×C₈₉×#3540 #36440576

Order 22784.

7418 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3540	C₂	1	32	yes	maximal, direct product factor
2	C₂×H(3,𝔽₄)×C₈₉	C₂	1	2	yes	maximal, complemented
3	C₂×#560×C₈₉	C₂	1	2	yes	maximal, complemented
4	C₂×#559×C₈₉	C₂	1	2	yes	maximal, complemented
5	C₂×#556×C₈₉	C₂	1	2	yes	maximal, complemented
6	C₂×#555×C₈₉	C₂	1	2	yes	maximal, complemented
7	C₂×#551×C₈₉	C₂	1	2	yes	maximal, complemented
8	C₂×#548×C₈₉	C₂	1	2	yes	maximal, complemented
9	C₂×#546×C₈₉	C₂	1	2	yes	maximal, complemented
10	C₂×#542×C₈₉	C₂	1	2	yes	maximal, complemented
11	C₂×#542×C₈₉	C₂	1	4	yes	maximal, complemented
12	C₂×#538×C₈₉	C₂	1	4	yes	maximal, complemented
13	C₂×#536×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#535×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#525×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#525×C₈₉	C₂	1	2	yes	maximal, complemented
17	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×#41×C₈₉	C₂²	1	2	yes	—
19	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
20	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
21	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
22	H(3,𝔽₄)×C₈₉	C₂²	1	32	yes	complemented
23	#560×C₈₉	C₂²	1	32	yes	complemented
24	#559×C₈₉	C₂²	1	32	yes	complemented
25	#556×C₈₉	C₂²	1	32	yes	complemented
26	#555×C₈₉	C₂²	1	32	yes	complemented
27	#551×C₈₉	C₂²	1	32	yes	complemented
28	#548×C₈₉	C₂²	1	32	yes	complemented
29	#546×C₈₉	C₂²	1	32	yes	complemented
30	#542×C₈₉	C₂²	1	32	yes	complemented
31	#542×C₈₉	C₂²	1	64	yes	complemented
32	#538×C₈₉	C₂²	1	64	yes	complemented
33	#536×C₈₉	C₂²	1	16	yes	complemented
34	#535×C₈₉	C₂²	1	16	yes	complemented
35	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
36	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
37	C₂×#127×C₈₉	C₂²	1	2	yes	—
38	C₂×#126×C₈₉	C₂²	1	4	yes	complemented
39	C₂×#126×C₈₉	C₂²	1	4	yes	complemented
40	C₂×#126×C₈₉	C₂²	1	4	yes	complemented
41	C₂×#124×C₈₉	C₂²	1	2	yes	—
42	C₂×#124×C₈₉	C₂²	1	4	yes	—
43	C₂×#124×C₈₉	C₂²	1	2	yes	complemented
44	C₂×#124×C₈₉	C₂²	1	4	yes	complemented
45	C₂×#124×C₈₉	C₂²	1	2	yes	complemented
46	C₂×#124×C₈₉	C₂²	1	4	yes	complemented
47	C₂×#124×C₈₉	C₂²	1	4	yes	complemented
48	C₂×#124×C₈₉	C₂²	1	4	yes	complemented
49	#525×C₈₉	C₂²	1	16	yes	complemented
50	#525×C₈₉	C₂²	1	32	yes	complemented
51	C₂×#123×C₈₉	C₂²	1	1	yes	characteristic
52	C₂×#123×C₈₉	C₂²	1	4	yes	complemented
53	C₂×#123×C₈₉	C₂²	1	1	yes	characteristic, complemented
54	C₂×#123×C₈₉	C₂²	1	2	yes	complemented
55	C₂×#123×C₈₉	C₂²	1	2	yes	complemented
56	C₂×#123×C₈₉	C₂²	1	4	yes	complemented
57	C₂×#123×C₈₉	C₂²	1	4	yes	complemented
58	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
59	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
60	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
61	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
62	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
63	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
64	C₂×#121×C₈₉	C₂²	1	2	yes	—
65	C₂×#121×C₈₉	C₂²	1	2	yes	—
66	C₂×#121×C₈₉	C₂²	1	2	yes	—
67	C₂×#121×C₈₉	C₂²	1	4	yes	—
68	C₂×#121×C₈₉	C₂²	1	2	yes	complemented
69	C₂×#121×C₈₉	C₂²	1	4	yes	complemented
70	C₂×#121×C₈₉	C₂²	1	4	yes	complemented
71	C₂×#120×C₈₉	C₂²	1	1	yes	characteristic
72	C₂×#120×C₈₉	C₂²	1	2	yes	—
73	C₂×#120×C₈₉	C₂²	1	4	yes	—
74	C₂×#120×C₈₉	C₂²	1	1	yes	characteristic, complemented
75	C₂×#120×C₈₉	C₂²	1	4	yes	complemented
76	C₂×#120×C₈₉	C₂²	1	2	yes	complemented
77	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
78	C₂×C₄×Q₈×C₈₉	C₂²	1	4	yes	complemented
79	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
80	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
81	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
82	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
83	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
84	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
85	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
86	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
87	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
88	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
89	C₂×#117×C₈₉	C₂²	1	4	yes	complemented
90	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	complemented
91	C₂⁵×C₈₉	C₂³	1	2	yes	—
92	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
93	C₂×#41×C₈₉	—	4	4	no	—
94	C₂×#41×C₈₉	—	4	8	no	—
95	C₂×#41×C₈₉	C₂³	1	8	yes	—
96	C₂×#41×C₈₉	C₂³	1	16	yes	—
97	C₂²×Q₈×C₈₉	—	4	4	no	—
98	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
99	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
100	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
101	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₈₉	C₂³	1	8	yes	complemented
103	C₂²×D₄×C₈₉	—	4	4	no	—
104	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
105	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
106	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
107	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
108	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
109	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
110	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
112	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
115	C₂²×D₄×C₈₉	C₂³	1	8	yes	complemented
116	C₂³×C₄×C₈₉	—	4	4	no	—
117	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
119	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
122	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
123	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
125	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
126	C₂³×C₄×C₈₉	C₂³	1	8	yes	complemented
127	C₄⋊Q₈×C₈₉	C₂³	1	16	yes	complemented
128	C₄⋊Q₈×C₈₉	C₂³	1	16	yes	complemented
129	#127×C₈₉	C₂³	1	16	yes	—
130	#126×C₈₉	C₂³	1	32	yes	complemented
131	#126×C₈₉	C₂³	1	32	yes	complemented
132	#126×C₈₉	C₂³	1	32	yes	complemented
133	#124×C₈₉	C₂³	1	16	yes	—
134	#124×C₈₉	C₂³	1	32	yes	—
135	#124×C₈₉	C₂³	1	16	yes	complemented
136	#124×C₈₉	C₂³	1	32	yes	complemented
137	#124×C₈₉	C₂³	1	16	yes	complemented
138	#124×C₈₉	C₂³	1	32	yes	complemented
139	#124×C₈₉	C₂³	1	32	yes	complemented
140	#124×C₈₉	C₂³	1	32	yes	complemented
141	#123×C₈₉	C₂³	1	8	yes	—
142	#123×C₈₉	C₂³	1	32	yes	complemented
143	#123×C₈₉	C₂³	1	8	yes	complemented
144	#123×C₈₉	C₂³	1	16	yes	complemented
145	#123×C₈₉	C₂³	1	16	yes	complemented
146	#123×C₈₉	C₂³	1	32	yes	complemented
147	#123×C₈₉	C₂³	1	32	yes	complemented
148	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	complemented
149	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	complemented
150	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	complemented
151	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	complemented
152	C₂²⋊Q₈×C₈₉	C₂³	1	32	yes	complemented
153	C₂²⋊Q₈×C₈₉	C₂³	1	32	yes	complemented
154	#121×C₈₉	C₂³	1	16	yes	—
155	#121×C₈₉	C₂³	1	16	yes	—
156	#121×C₈₉	C₂³	1	16	yes	—
157	#121×C₈₉	C₂³	1	32	yes	—
158	#121×C₈₉	C₂³	1	16	yes	complemented
159	#121×C₈₉	C₂³	1	32	yes	complemented
160	#121×C₈₉	C₂³	1	32	yes	complemented
161	#120×C₈₉	C₂³	1	8	yes	—
162	#120×C₈₉	C₂³	1	16	yes	—
163	#120×C₈₉	C₂³	1	32	yes	—
164	#120×C₈₉	C₂³	1	8	yes	complemented
165	#120×C₈₉	C₂³	1	32	yes	complemented
166	#120×C₈₉	C₂³	1	16	yes	complemented
167	C₄×Q₈×C₈₉	C₂³	1	16	yes	complemented
168	C₄×Q₈×C₈₉	C₂³	1	32	yes	complemented
169	C₄×D₄×C₈₉	C₂³	1	16	yes	—
170	C₄×D₄×C₈₉	C₂³	1	32	yes	complemented
171	C₄×D₄×C₈₉	C₂³	1	16	yes	complemented
172	C₄×D₄×C₈₉	C₂³	1	32	yes	complemented
173	C₄×D₄×C₈₉	C₂³	1	32	yes	complemented
174	C₄×D₄×C₈₉	C₂³	1	16	yes	complemented
175	#117×C₈₉	C₂³	1	8	yes	complemented
176	#117×C₈₉	C₂³	1	16	yes	complemented
177	#117×C₈₉	C₂³	1	8	yes	complemented
178	#117×C₈₉	C₂³	1	8	yes	complemented
179	#117×C₈₉	C₂³	1	32	yes	complemented
180	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
185	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
187	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
188	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
189	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
190	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
192	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
193	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
194	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
196	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
198	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
203	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
205	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
206	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
207	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
208	C₂×C₂²⋊C₄×C₈₉	C₂³	1	32	yes	complemented
209	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
210	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
211	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
212	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
213	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
214	C₂⁴×C₈₉	—	4	2	no	—
215	C₂⁴×C₈₉	—	4	4	no	—
216	C₂⁴×C₈₉	—	4	4	no	—
217	C₂⁴×C₈₉	—	4	8	no	—
218	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
219	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
220	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
221	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
222	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
223	C₂⁴×C₈₉	C₂⁴	1	8	yes	—
224	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
225	#41×C₈₉	—	4	16	no	—
226	#41×C₈₉	—	4	32	no	—
227	C₂×Q₈×C₈₉	—	2	8	no	—
228	C₂×Q₈×C₈₉	—	4	4	no	—
229	C₂×Q₈×C₈₉	—	4	8	no	—
230	C₂×Q₈×C₈₉	—	4	2	no	—
231	C₂×Q₈×C₈₉	—	4	16	no	—
232	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
233	C₂×Q₈×C₈₉	C₂⁴	1	16	yes	—
234	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
235	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
236	C₂×D₄×C₈₉	—	2	8	no	—
237	C₂×D₄×C₈₉	—	4	16	no	—
238	C₂×D₄×C₈₉	—	4	4	no	—
239	C₂×D₄×C₈₉	—	4	4	no	—
240	C₂×D₄×C₈₉	—	4	8	no	—
241	C₂×D₄×C₈₉	—	4	8	no	—
242	C₂×D₄×C₈₉	—	4	8	no	—
243	C₂×D₄×C₈₉	—	4	4	no	—
244	C₂×D₄×C₈₉	—	4	2	no	—
245	C₂×D₄×C₈₉	—	4	2	no	—
246	C₂×D₄×C₈₉	—	4	2	no	—
247	C₂×D₄×C₈₉	—	4	8	no	—
248	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
249	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
250	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
251	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
252	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
253	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
254	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
255	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
256	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
257	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
258	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
259	C₂²×C₄×C₈₉	—	2	8	no	—
260	C₂²×C₄×C₈₉	—	2	4	no	—
261	C₂²×C₄×C₈₉	—	2	4	no	—
262	C₂²×C₄×C₈₉	—	2	4	no	—
263	C₂²×C₄×C₈₉	—	4	16	no	—
264	C₂²×C₄×C₈₉	—	4	2	no	—
265	C₂²×C₄×C₈₉	—	4	4	no	—
266	C₂²×C₄×C₈₉	—	4	8	no	—
267	C₂²×C₄×C₈₉	—	4	4	no	—
268	C₂²×C₄×C₈₉	—	4	8	no	—
269	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
270	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
271	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
272	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
273	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
275	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
276	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
281	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
283	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
284	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
285	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
286	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
287	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
288	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
289	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
290	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
291	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
292	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
293	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
294	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
295	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
296	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
297	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
298	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
299	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
300	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
301	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
302	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
303	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
304	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
305	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
306	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
307	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
308	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
309	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
310	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
311	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
312	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
313	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
314	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
315	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
316	C₄²×C₈₉	C₂⁴	1	8	yes	—
317	C₄²×C₈₉	C₂⁴	1	16	yes	—
318	C₄²×C₈₉	C₂⁴	1	8	yes	—
319	C₄²×C₈₉	C₂⁴	1	8	yes	—
320	C₄²×C₈₉	C₂⁴	1	16	yes	—
321	C₂³×C₈₉	—	2	2	no	—
322	C₂³×C₈₉	—	2	4	no	—
323	C₂³×C₈₉	—	2	2	no	—
324	C₂³×C₈₉	—	2	2	no	—
325	C₂³×C₈₉	—	2	8	no	—
326	C₂³×C₈₉	—	2	8	no	—
327	C₂³×C₈₉	—	2	4	no	—
328	C₂³×C₈₉	—	2	4	no	—
329	C₂³×C₈₉	—	2	4	no	—
330	C₂³×C₈₉	—	2	4	no	—
331	C₂³×C₈₉	—	2	8	no	—
332	C₂³×C₈₉	—	2	4	no	—
333	C₂³×C₈₉	—	4	4	no	—
334	C₂³×C₈₉	—	4	8	no	—
335	C₂³×C₈₉	—	4	8	no	—
336	C₂³×C₈₉	—	4	16	no	—
337	C₂³×C₈₉	—	4	16	no	—
338	C₂³×C₈₉	—	8	16	no	—
339	C₂³×C₈₉	C₂⁵	1	2	yes	—
340	C₂³×C₈₉	C₂⁵	1	2	yes	—
341	C₂³×C₈₉	C₂⁵	1	4	yes	—
342	C₂³×C₈₉	C₂⁵	1	8	yes	—
343	C₂³×C₈₉	C₂⁵	1	2	yes	—
344	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
345	Q₈×C₈₉	—	2	16	no	—
346	Q₈×C₈₉	—	4	8	no	—
347	Q₈×C₈₉	—	4	16	no	—
348	Q₈×C₈₉	—	4	4	no	—
349	D₄×C₈₉	—	2	16	no	—
350	D₄×C₈₉	—	4	8	no	—
351	D₄×C₈₉	—	4	8	no	—
352	D₄×C₈₉	—	4	16	no	—
353	D₄×C₈₉	—	4	16	no	—
354	D₄×C₈₉	—	4	16	no	—
355	D₄×C₈₉	—	4	8	no	—
356	D₄×C₈₉	—	4	4	no	—
357	D₄×C₈₉	—	4	4	no	—
358	D₄×C₈₉	—	4	4	no	—
359	D₄×C₈₉	—	4	16	no	—
360	C₂×C₄×C₈₉	—	2	4	no	—
361	C₂×C₄×C₈₉	—	2	2	no	—
362	C₂×C₄×C₈₉	—	2	2	no	—
363	C₂×C₄×C₈₉	—	2	2	no	—
364	C₂×C₄×C₈₉	—	2	8	no	—
365	C₂×C₄×C₈₉	—	2	4	no	—
366	C₂×C₄×C₈₉	—	2	8	no	—
367	C₂×C₄×C₈₉	—	2	8	no	—
368	C₂×C₄×C₈₉	—	2	4	no	—
369	C₂×C₄×C₈₉	—	2	16	no	—
370	C₂×C₄×C₈₉	—	2	8	no	—
371	C₂×C₄×C₈₉	—	2	8	no	—
372	C₂×C₄×C₈₉	—	2	8	no	—
373	C₂×C₄×C₈₉	—	4	4	no	—
374	C₂×C₄×C₈₉	—	4	8	no	—
375	C₂×C₄×C₈₉	—	4	16	no	—
376	C₂×C₄×C₈₉	—	4	8	no	—
377	C₂×C₄×C₈₉	—	4	16	no	—
378	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
379	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
380	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
381	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
382	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
383	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
384	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
385	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
386	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
387	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
388	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
389	C₂²×C₈₉	—	2	2	no	—
390	C₂²×C₈₉	—	2	4	no	—
391	C₂²×C₈₉	—	2	2	no	—
392	C₂²×C₈₉	—	2	2	no	—
393	C₂²×C₈₉	—	2	8	no	—
394	C₂²×C₈₉	—	2	8	no	—
395	C₂²×C₈₉	—	2	4	no	—
396	C₂²×C₈₉	—	2	4	no	—
397	C₂²×C₈₉	—	2	4	no	—
398	C₂²×C₈₉	—	2	4	no	—
399	C₂²×C₈₉	—	2	8	no	—
400	C₂²×C₈₉	—	2	4	no	—
401	C₂²×C₈₉	—	4	16	no	—
402	C₂²×C₈₉	—	4	4	no	—
403	C₂²×C₈₉	—	4	8	no	—
404	C₂²×C₈₉	—	4	4	no	—
405	C₂²×C₈₉	—	4	16	no	—
406	C₂²×C₈₉	—	4	4	no	—
407	C₂²×C₈₉	—	8	16	no	—
408	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
409	C₂²×C₈₉	#585	1	4	yes	—
410	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
411	C₄×C₈₉	—	2	4	no	—
412	C₄×C₈₉	—	2	2	no	—
413	C₄×C₈₉	—	2	2	no	—
414	C₄×C₈₉	—	2	2	no	—
415	C₄×C₈₉	—	2	8	no	—
416	C₄×C₈₉	—	2	4	no	—
417	C₄×C₈₉	—	2	8	no	—
418	C₄×C₈₉	—	2	8	no	—
419	C₄×C₈₉	—	2	4	no	—
420	C₄×C₈₉	C₂×H(5,𝔽₂)	1	4	yes	—
421	C₂×#3540	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
422	C₂×C₈₉	—	4	2	no	—
423	C₂×C₈₉	—	4	4	no	—
424	C₂×C₈₉	—	4	2	no	—
425	C₂×C₈₉	—	4	8	no	—
426	C₂×C₈₉	—	4	2	no	—
427	C₂×C₈₉	#3540	1	4	yes	direct product factor
428	C₂×C₈₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
429	C₂×C₈₉	C₂×#585	1	2	yes	—
430	#3540	C₂×C₈₉	1	32	yes	direct product factor
431	C₂×H(3,𝔽₄)	C₂×C₈₉	1	2	yes	complemented
432	C₂×#560	C₂×C₈₉	1	2	yes	complemented
433	C₂×#559	C₂×C₈₉	1	2	yes	complemented
434	C₂×#556	C₂×C₈₉	1	2	yes	complemented
435	C₂×#555	C₂×C₈₉	1	2	yes	complemented
436	C₂×#551	C₂×C₈₉	1	2	yes	complemented
437	C₂×#548	C₂×C₈₉	1	2	yes	complemented
438	C₂×#546	C₂×C₈₉	1	2	yes	complemented
439	C₂×#542	C₂×C₈₉	1	2	yes	complemented
440	C₂×#542	C₂×C₈₉	1	4	yes	complemented
441	C₂×#538	C₂×C₈₉	1	4	yes	complemented
442	C₂×#536	C₂×C₈₉	1	1	yes	characteristic, complemented
443	C₂×#535	C₂×C₈₉	1	1	yes	characteristic, complemented
444	C₂×#525	C₂×C₈₉	1	1	yes	characteristic, complemented
445	C₂×#525	C₂×C₈₉	1	2	yes	complemented
446	C₈₉	C₂×#3540	1	1	yes	characteristic, direct product factor, Sylow
447	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
448	C₂²×#41	C₂²×C₈₉	1	2	yes	—
449	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
450	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
451	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
452	H(3,𝔽₄)	C₂²×C₈₉	1	32	yes	complemented
453	#560	C₂²×C₈₉	1	32	yes	complemented
454	#559	C₂²×C₈₉	1	32	yes	complemented
455	#556	C₂²×C₈₉	1	32	yes	complemented
456	#555	C₂²×C₈₉	1	32	yes	complemented
457	#551	C₂²×C₈₉	1	32	yes	complemented
458	#548	C₂²×C₈₉	1	32	yes	complemented
459	#546	C₂²×C₈₉	1	32	yes	complemented
460	#542	C₂²×C₈₉	1	32	yes	complemented
461	#542	C₂²×C₈₉	1	64	yes	complemented
462	#538	C₂²×C₈₉	1	64	yes	complemented
463	#536	C₂²×C₈₉	1	16	yes	complemented
464	#535	C₂²×C₈₉	1	16	yes	complemented
465	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
466	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
467	C₂×#127	C₂²×C₈₉	1	2	yes	—
468	C₂×#126	C₂²×C₈₉	1	4	yes	complemented
469	C₂×#126	C₂²×C₈₉	1	4	yes	complemented
470	C₂×#126	C₂²×C₈₉	1	4	yes	complemented
471	C₂×#124	C₂²×C₈₉	1	2	yes	—
472	C₂×#124	C₂²×C₈₉	1	4	yes	—
473	C₂×#124	C₂²×C₈₉	1	2	yes	complemented
474	C₂×#124	C₂²×C₈₉	1	4	yes	complemented
475	C₂×#124	C₂²×C₈₉	1	2	yes	complemented
476	C₂×#124	C₂²×C₈₉	1	4	yes	complemented
477	C₂×#124	C₂²×C₈₉	1	4	yes	complemented
478	C₂×#124	C₂²×C₈₉	1	4	yes	complemented
479	#525	C₂²×C₈₉	1	16	yes	complemented
480	#525	C₂²×C₈₉	1	32	yes	complemented
481	C₂×#123	C₂²×C₈₉	1	1	yes	characteristic
482	C₂×#123	C₂²×C₈₉	1	4	yes	complemented
483	C₂×#123	C₂²×C₈₉	1	1	yes	characteristic, complemented
484	C₂×#123	C₂²×C₈₉	1	2	yes	complemented
485	C₂×#123	C₂²×C₈₉	1	2	yes	complemented
486	C₂×#123	C₂²×C₈₉	1	4	yes	complemented
487	C₂×#123	C₂²×C₈₉	1	4	yes	complemented
488	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
489	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
490	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
491	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
492	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
493	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
494	C₂×#121	C₂²×C₈₉	1	2	yes	—
495	C₂×#121	C₂²×C₈₉	1	2	yes	—
496	C₂×#121	C₂²×C₈₉	1	2	yes	—
497	C₂×#121	C₂²×C₈₉	1	4	yes	—
498	C₂×#121	C₂²×C₈₉	1	2	yes	complemented
499	C₂×#121	C₂²×C₈₉	1	4	yes	complemented
500	C₂×#121	C₂²×C₈₉	1	4	yes	complemented
501	C₂×#120	C₂²×C₈₉	1	1	yes	characteristic
502	C₂×#120	C₂²×C₈₉	1	2	yes	—
503	C₂×#120	C₂²×C₈₉	1	4	yes	—
504	C₂×#120	C₂²×C₈₉	1	1	yes	characteristic, complemented
505	C₂×#120	C₂²×C₈₉	1	4	yes	complemented
506	C₂×#120	C₂²×C₈₉	1	2	yes	complemented
507	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	complemented
508	C₂×C₄×Q₈	C₂²×C₈₉	1	4	yes	complemented
509	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
510	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
511	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
512	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
513	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
514	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
515	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic, complemented
516	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
517	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic, complemented
518	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic, complemented
519	C₂×#117	C₂²×C₈₉	1	4	yes	complemented
520	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	complemented
521	C₂⁵	C₂³×C₈₉	1	2	yes	—
522	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
523	C₂×#41	—	4	4	no	—
524	C₂×#41	—	4	8	no	—
525	C₂×#41	C₂³×C₈₉	1	8	yes	—
526	C₂×#41	C₂³×C₈₉	1	16	yes	—
527	C₂²×Q₈	—	4	4	no	—
528	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
529	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
530	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
531	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
532	C₂²×Q₈	C₂³×C₈₉	1	8	yes	complemented
533	C₂²×D₄	—	4	4	no	—
534	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
535	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
536	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
537	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
538	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
539	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
540	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
541	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
542	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
543	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
544	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
545	C₂²×D₄	C₂³×C₈₉	1	8	yes	complemented
546	C₂³×C₄	—	4	4	no	—
547	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
548	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
549	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
550	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
551	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
552	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
553	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
554	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
555	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
556	C₂³×C₄	C₂³×C₈₉	1	8	yes	complemented
557	C₄⋊Q₈	C₂³×C₈₉	1	16	yes	complemented
558	C₄⋊Q₈	C₂³×C₈₉	1	16	yes	complemented
559	#127	C₂³×C₈₉	1	16	yes	—
560	#126	C₂³×C₈₉	1	32	yes	complemented
561	#126	C₂³×C₈₉	1	32	yes	complemented
562	#126	C₂³×C₈₉	1	32	yes	complemented
563	#124	C₂³×C₈₉	1	16	yes	—
564	#124	C₂³×C₈₉	1	32	yes	—
565	#124	C₂³×C₈₉	1	16	yes	complemented
566	#124	C₂³×C₈₉	1	32	yes	complemented
567	#124	C₂³×C₈₉	1	16	yes	complemented
568	#124	C₂³×C₈₉	1	32	yes	complemented
569	#124	C₂³×C₈₉	1	32	yes	complemented
570	#124	C₂³×C₈₉	1	32	yes	complemented
571	#123	C₂³×C₈₉	1	8	yes	—
572	#123	C₂³×C₈₉	1	32	yes	complemented
573	#123	C₂³×C₈₉	1	8	yes	complemented
574	#123	C₂³×C₈₉	1	16	yes	complemented
575	#123	C₂³×C₈₉	1	16	yes	complemented
576	#123	C₂³×C₈₉	1	32	yes	complemented
577	#123	C₂³×C₈₉	1	32	yes	complemented
578	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	complemented
579	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	complemented
580	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	complemented
581	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	complemented
582	C₂²⋊Q₈	C₂³×C₈₉	1	32	yes	complemented
583	C₂²⋊Q₈	C₂³×C₈₉	1	32	yes	complemented
584	#121	C₂³×C₈₉	1	16	yes	—
585	#121	C₂³×C₈₉	1	16	yes	—
586	#121	C₂³×C₈₉	1	16	yes	—
587	#121	C₂³×C₈₉	1	32	yes	—
588	#121	C₂³×C₈₉	1	16	yes	complemented
589	#121	C₂³×C₈₉	1	32	yes	complemented
590	#121	C₂³×C₈₉	1	32	yes	complemented
591	#120	C₂³×C₈₉	1	8	yes	—
592	#120	C₂³×C₈₉	1	16	yes	—
593	#120	C₂³×C₈₉	1	32	yes	—
594	#120	C₂³×C₈₉	1	8	yes	complemented
595	#120	C₂³×C₈₉	1	32	yes	complemented
596	#120	C₂³×C₈₉	1	16	yes	complemented
597	C₄×Q₈	C₂³×C₈₉	1	16	yes	complemented
598	C₄×Q₈	C₂³×C₈₉	1	32	yes	complemented
599	C₄×D₄	C₂³×C₈₉	1	16	yes	—
600	C₄×D₄	C₂³×C₈₉	1	32	yes	complemented
601	C₄×D₄	C₂³×C₈₉	1	16	yes	complemented
602	C₄×D₄	C₂³×C₈₉	1	32	yes	complemented
603	C₄×D₄	C₂³×C₈₉	1	32	yes	complemented
604	C₄×D₄	C₂³×C₈₉	1	16	yes	complemented
605	#117	C₂³×C₈₉	1	8	yes	complemented
606	#117	C₂³×C₈₉	1	16	yes	complemented
607	#117	C₂³×C₈₉	1	8	yes	complemented
608	#117	C₂³×C₈₉	1	8	yes	complemented
609	#117	C₂³×C₈₉	1	32	yes	complemented
610	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
615	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
617	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
618	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
619	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
627	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₈₉	1	32	yes	complemented
639	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
640	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
641	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
642	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
643	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
644	C₂⁴	—	4	2	no	—
645	C₂⁴	—	4	4	no	—
646	C₂⁴	—	4	4	no	—
647	C₂⁴	—	4	8	no	—
648	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
649	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
650	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
651	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
652	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
653	C₂⁴	C₂⁴×C₈₉	1	8	yes	—
654	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
655	#41	—	4	16	no	—
656	#41	—	4	32	no	—
657	C₂×Q₈	—	2	8	no	—
658	C₂×Q₈	—	4	4	no	—
659	C₂×Q₈	—	4	2	no	—
660	C₂×Q₈	—	4	8	no	—
661	C₂×Q₈	—	4	16	no	—
662	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
663	C₂×Q₈	C₂⁴×C₈₉	1	16	yes	—
664	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
665	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
666	C₂×D₄	—	2	8	no	—
667	C₂×D₄	—	4	16	no	—
668	C₂×D₄	—	4	4	no	—
669	C₂×D₄	—	4	2	no	—
670	C₂×D₄	—	4	2	no	—
671	C₂×D₄	—	4	2	no	—
672	C₂×D₄	—	4	8	no	—
673	C₂×D₄	—	4	4	no	—
674	C₂×D₄	—	4	8	no	—
675	C₂×D₄	—	4	8	no	—
676	C₂×D₄	—	4	8	no	—
677	C₂×D₄	—	4	4	no	—
678	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
679	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
680	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
681	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
682	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
683	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
684	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
685	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
686	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
687	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
688	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
689	C₂²×C₄	—	2	8	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	4	16	no	—
694	C₂²×C₄	—	4	2	no	—
695	C₂²×C₄	—	4	4	no	—
696	C₂²×C₄	—	4	4	no	—
697	C₂²×C₄	—	4	8	no	—
698	C₂²×C₄	—	4	8	no	—
699	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
701	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
702	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
707	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
709	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
710	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
711	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
712	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
713	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
714	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
715	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
716	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
717	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
718	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
719	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
720	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
721	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
722	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
723	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
724	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
725	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
726	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
727	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
728	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
729	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
730	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
731	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
732	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
733	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
734	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
735	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
736	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
737	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
738	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
739	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
740	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
741	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
742	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
743	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
744	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
745	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
746	C₄²	C₂⁴×C₈₉	1	8	yes	—
747	C₄²	C₂⁴×C₈₉	1	16	yes	—
748	C₄²	C₂⁴×C₈₉	1	8	yes	—
749	C₄²	C₂⁴×C₈₉	1	8	yes	—
750	C₄²	C₂⁴×C₈₉	1	16	yes	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	4	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	8	no	—
756	C₂³	—	2	8	no	—
757	C₂³	—	2	4	no	—
758	C₂³	—	2	4	no	—
759	C₂³	—	2	4	no	—
760	C₂³	—	2	4	no	—
761	C₂³	—	2	8	no	—
762	C₂³	—	2	4	no	—
763	C₂³	—	4	4	no	—
764	C₂³	—	4	8	no	—
765	C₂³	—	4	8	no	—
766	C₂³	—	4	16	no	—
767	C₂³	—	4	16	no	—
768	C₂³	—	8	16	no	—
769	C₂³	C₂⁵×C₈₉	1	2	yes	—
770	C₂³	C₂⁵×C₈₉	1	2	yes	—
771	C₂³	C₂⁵×C₈₉	1	4	yes	—
772	C₂³	C₂⁵×C₈₉	1	8	yes	—
773	C₂³	C₂⁵×C₈₉	1	2	yes	—
774	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
775	Q₈	—	2	16	no	—
776	Q₈	—	4	8	no	—
777	Q₈	—	4	16	no	—
778	Q₈	—	4	4	no	—
779	D₄	—	2	16	no	—
780	D₄	—	4	8	no	—
781	D₄	—	4	8	no	—
782	D₄	—	4	16	no	—
783	D₄	—	4	16	no	—
784	D₄	—	4	16	no	—
785	D₄	—	4	8	no	—
786	D₄	—	4	4	no	—
787	D₄	—	4	4	no	—
788	D₄	—	4	4	no	—
789	D₄	—	4	16	no	—
790	C₂×C₄	—	2	4	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	8	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	8	no	—
797	C₂×C₄	—	2	8	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	16	no	—
800	C₂×C₄	—	2	8	no	—
801	C₂×C₄	—	2	8	no	—
802	C₂×C₄	—	2	8	no	—
803	C₂×C₄	—	4	4	no	—
804	C₂×C₄	—	4	8	no	—
805	C₂×C₄	—	4	16	no	—
806	C₂×C₄	—	4	8	no	—
807	C₂×C₄	—	4	16	no	—
808	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
809	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
810	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
811	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
812	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
813	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
814	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
815	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
816	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
817	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
818	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	4	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	8	no	—
824	C₂²	—	2	8	no	—
825	C₂²	—	2	4	no	—
826	C₂²	—	2	4	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	8	no	—
830	C₂²	—	2	4	no	—
831	C₂²	—	4	16	no	—
832	C₂²	—	4	8	no	—
833	C₂²	—	4	4	no	—
834	C₂²	—	4	4	no	—
835	C₂²	—	4	16	no	—
836	C₂²	—	4	4	no	—
837	C₂²	—	8	16	no	—
838	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
839	C₂²	#585×C₈₉	1	4	yes	—
840	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
841	C₄	—	2	4	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	8	no	—
846	C₄	—	2	4	no	—
847	C₄	—	2	8	no	—
848	C₄	—	2	8	no	—
849	C₄	—	2	4	no	—
850	C₄	C₂×H(5,𝔽₂)×C₈₉	1	4	yes	—
851	C₂	—	4	2	no	—
852	C₂	—	4	4	no	—
853	C₂	—	4	2	no	—
854	C₂	—	4	8	no	—
855	C₂	—	4	2	no	—
856	C₂	C₈₉×#3540	1	4	yes	direct product factor
857	C₂	C₂²×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
858	C₂	C₂×#585×C₈₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₈₉
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
1. C₈₉×#3540	C₂	direct (N × H)
2. C₂×H(3,𝔽₄)×C₈₉	C₂	semidirect
3. C₂×#560×C₈₉	C₂	semidirect
4. C₂×#559×C₈₉	C₂	semidirect
5. C₂×#556×C₈₉	C₂	semidirect
6. C₂×#555×C₈₉	C₂	semidirect
7. C₂×#551×C₈₉	C₂	semidirect
8. C₂×#548×C₈₉	C₂	semidirect
9. C₂×#546×C₈₉	C₂	semidirect
10. C₂×#542×C₈₉	C₂	semidirect
11. C₂×#542×C₈₉	C₂	semidirect
12. C₂×#538×C₈₉	C₂	semidirect
13. C₂×#536×C₈₉	C₂	semidirect
14. C₂×#535×C₈₉	C₂	semidirect
15. C₂×#525×C₈₉	C₂	semidirect
16. C₂×#525×C₈₉	C₂	semidirect
19. C₂³×Q₈×C₈₉	C₂²	semidirect
20. C₂³×D₄×C₈₉	C₂²	semidirect
21. C₂⁴×C₄×C₈₉	C₂²	semidirect
22. H(3,𝔽₄)×C₈₉	C₂²	semidirect
23. #560×C₈₉	C₂²	semidirect
24. #559×C₈₉	C₂²	semidirect
25. #556×C₈₉	C₂²	semidirect
26. #555×C₈₉	C₂²	semidirect
27. #551×C₈₉	C₂²	semidirect
28. #548×C₈₉	C₂²	semidirect
29. #546×C₈₉	C₂²	semidirect
30. #542×C₈₉	C₂²	semidirect
31. #542×C₈₉	C₂²	semidirect
32. #538×C₈₉	C₂²	semidirect
33. #536×C₈₉	C₂²	semidirect
34. #535×C₈₉	C₂²	semidirect
35. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
36. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
38. C₂×#126×C₈₉	C₂²	semidirect
39. C₂×#126×C₈₉	C₂²	semidirect
40. C₂×#126×C₈₉	C₂²	semidirect
43. C₂×#124×C₈₉	C₂²	semidirect
44. C₂×#124×C₈₉	C₂²	semidirect
45. C₂×#124×C₈₉	C₂²	semidirect
46. C₂×#124×C₈₉	C₂²	semidirect
47. C₂×#124×C₈₉	C₂²	semidirect
48. C₂×#124×C₈₉	C₂²	semidirect
49. #525×C₈₉	C₂²	semidirect
50. #525×C₈₉	C₂²	semidirect
52. C₂×#123×C₈₉	C₂²	semidirect
53. C₂×#123×C₈₉	C₂²	semidirect
54. C₂×#123×C₈₉	C₂²	semidirect
55. C₂×#123×C₈₉	C₂²	semidirect
56. C₂×#123×C₈₉	C₂²	semidirect
57. C₂×#123×C₈₉	C₂²	semidirect
58. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
59. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
60. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
61. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
62. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
63. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
68. C₂×#121×C₈₉	C₂²	semidirect
69. C₂×#121×C₈₉	C₂²	semidirect
70. C₂×#121×C₈₉	C₂²	semidirect
74. C₂×#120×C₈₉	C₂²	semidirect
75. C₂×#120×C₈₉	C₂²	semidirect
76. C₂×#120×C₈₉	C₂²	semidirect
77. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
78. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
80. C₂×C₄×D₄×C₈₉	C₂²	semidirect
81. C₂×C₄×D₄×C₈₉	C₂²	semidirect
82. C₂×C₄×D₄×C₈₉	C₂²	semidirect
83. C₂×C₄×D₄×C₈₉	C₂²	semidirect
84. C₂×C₄×D₄×C₈₉	C₂²	semidirect
85. C₂×#117×C₈₉	C₂²	semidirect
86. C₂×#117×C₈₉	C₂²	semidirect
87. C₂×#117×C₈₉	C₂²	semidirect
88. C₂×#117×C₈₉	C₂²	semidirect
89. C₂×#117×C₈₉	C₂²	semidirect
90. C₂²×C₂²⋊C₄×C₈₉	C₂²	semidirect
102. C₂²×Q₈×C₈₉	C₂³	semidirect
115. C₂²×D₄×C₈₉	C₂³	semidirect
126. C₂³×C₄×C₈₉	C₂³	semidirect
127. C₄⋊Q₈×C₈₉	C₂³	semidirect
128. C₄⋊Q₈×C₈₉	C₂³	semidirect
130. #126×C₈₉	C₂³	semidirect
131. #126×C₈₉	C₂³	semidirect
132. #126×C₈₉	C₂³	semidirect
135. #124×C₈₉	C₂³	semidirect
136. #124×C₈₉	C₂³	semidirect
137. #124×C₈₉	C₂³	semidirect
138. #124×C₈₉	C₂³	semidirect
139. #124×C₈₉	C₂³	semidirect
140. #124×C₈₉	C₂³	semidirect
142. #123×C₈₉	C₂³	semidirect
143. #123×C₈₉	C₂³	semidirect
144. #123×C₈₉	C₂³	semidirect
145. #123×C₈₉	C₂³	semidirect
146. #123×C₈₉	C₂³	semidirect
147. #123×C₈₉	C₂³	semidirect
148. C₂²⋊Q₈×C₈₉	C₂³	semidirect
149. C₂²⋊Q₈×C₈₉	C₂³	semidirect
150. C₂²⋊Q₈×C₈₉	C₂³	semidirect
151. C₂²⋊Q₈×C₈₉	C₂³	semidirect
152. C₂²⋊Q₈×C₈₉	C₂³	semidirect
153. C₂²⋊Q₈×C₈₉	C₂³	semidirect
158. #121×C₈₉	C₂³	semidirect
159. #121×C₈₉	C₂³	semidirect
160. #121×C₈₉	C₂³	semidirect
164. #120×C₈₉	C₂³	semidirect
165. #120×C₈₉	C₂³	semidirect
166. #120×C₈₉	C₂³	semidirect
167. C₄×Q₈×C₈₉	C₂³	semidirect
168. C₄×Q₈×C₈₉	C₂³	semidirect
170. C₄×D₄×C₈₉	C₂³	semidirect
171. C₄×D₄×C₈₉	C₂³	semidirect
172. C₄×D₄×C₈₉	C₂³	semidirect
173. C₄×D₄×C₈₉	C₂³	semidirect
174. C₄×D₄×C₈₉	C₂³	semidirect
175. #117×C₈₉	C₂³	semidirect
176. #117×C₈₉	C₂³	semidirect
177. #117×C₈₉	C₂³	semidirect
178. #117×C₈₉	C₂³	semidirect
179. #117×C₈₉	C₂³	semidirect
208. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
421. C₂×#3540	C₈₉	direct (N × H)
427. C₂×C₈₉	#3540	direct (N × H)
430. #3540	C₂×C₈₉	direct (N × H)
431. C₂×H(3,𝔽₄)	C₂×C₈₉	semidirect
432. C₂×#560	C₂×C₈₉	semidirect
433. C₂×#559	C₂×C₈₉	semidirect
434. C₂×#556	C₂×C₈₉	semidirect
435. C₂×#555	C₂×C₈₉	semidirect
436. C₂×#551	C₂×C₈₉	semidirect
437. C₂×#548	C₂×C₈₉	semidirect
438. C₂×#546	C₂×C₈₉	semidirect
439. C₂×#542	C₂×C₈₉	semidirect
440. C₂×#542	C₂×C₈₉	semidirect
441. C₂×#538	C₂×C₈₉	semidirect
442. C₂×#536	C₂×C₈₉	semidirect
443. C₂×#535	C₂×C₈₉	semidirect
444. C₂×#525	C₂×C₈₉	semidirect
445. C₂×#525	C₂×C₈₉	semidirect
446. C₈₉	C₂×#3540	direct (N × H)
449. C₂³×Q₈	C₂²×C₈₉	semidirect
450. C₂³×D₄	C₂²×C₈₉	semidirect
451. C₂⁴×C₄	C₂²×C₈₉	semidirect
452. H(3,𝔽₄)	C₂²×C₈₉	semidirect
453. #560	C₂²×C₈₉	semidirect
454. #559	C₂²×C₈₉	semidirect
455. #556	C₂²×C₈₉	semidirect
456. #555	C₂²×C₈₉	semidirect
457. #551	C₂²×C₈₉	semidirect
458. #548	C₂²×C₈₉	semidirect
459. #546	C₂²×C₈₉	semidirect
460. #542	C₂²×C₈₉	semidirect
461. #542	C₂²×C₈₉	semidirect
462. #538	C₂²×C₈₉	semidirect
463. #536	C₂²×C₈₉	semidirect
464. #535	C₂²×C₈₉	semidirect
465. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
466. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
468. C₂×#126	C₂²×C₈₉	semidirect
469. C₂×#126	C₂²×C₈₉	semidirect
470. C₂×#126	C₂²×C₈₉	semidirect
473. C₂×#124	C₂²×C₈₉	semidirect
474. C₂×#124	C₂²×C₈₉	semidirect
475. C₂×#124	C₂²×C₈₉	semidirect
476. C₂×#124	C₂²×C₈₉	semidirect
477. C₂×#124	C₂²×C₈₉	semidirect
478. C₂×#124	C₂²×C₈₉	semidirect
479. #525	C₂²×C₈₉	semidirect
480. #525	C₂²×C₈₉	semidirect
482. C₂×#123	C₂²×C₈₉	semidirect
483. C₂×#123	C₂²×C₈₉	semidirect
484. C₂×#123	C₂²×C₈₉	semidirect
485. C₂×#123	C₂²×C₈₉	semidirect
486. C₂×#123	C₂²×C₈₉	semidirect
487. C₂×#123	C₂²×C₈₉	semidirect
488. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
489. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
490. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
491. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
492. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
493. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
498. C₂×#121	C₂²×C₈₉	semidirect
499. C₂×#121	C₂²×C₈₉	semidirect
500. C₂×#121	C₂²×C₈₉	semidirect
504. C₂×#120	C₂²×C₈₉	semidirect
505. C₂×#120	C₂²×C₈₉	semidirect
506. C₂×#120	C₂²×C₈₉	semidirect
507. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
508. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
510. C₂×C₄×D₄	C₂²×C₈₉	semidirect
511. C₂×C₄×D₄	C₂²×C₈₉	semidirect
512. C₂×C₄×D₄	C₂²×C₈₉	semidirect
513. C₂×C₄×D₄	C₂²×C₈₉	semidirect
514. C₂×C₄×D₄	C₂²×C₈₉	semidirect
515. C₂×#117	C₂²×C₈₉	semidirect
516. C₂×#117	C₂²×C₈₉	semidirect
517. C₂×#117	C₂²×C₈₉	semidirect
518. C₂×#117	C₂²×C₈₉	semidirect
519. C₂×#117	C₂²×C₈₉	semidirect
520. C₂²×C₂²⋊C₄	C₂²×C₈₉	semidirect
532. C₂²×Q₈	C₂³×C₈₉	semidirect
545. C₂²×D₄	C₂³×C₈₉	semidirect
556. C₂³×C₄	C₂³×C₈₉	semidirect
557. C₄⋊Q₈	C₂³×C₈₉	semidirect
558. C₄⋊Q₈	C₂³×C₈₉	semidirect
560. #126	C₂³×C₈₉	semidirect
561. #126	C₂³×C₈₉	semidirect
562. #126	C₂³×C₈₉	semidirect
565. #124	C₂³×C₈₉	semidirect
566. #124	C₂³×C₈₉	semidirect
567. #124	C₂³×C₈₉	semidirect
568. #124	C₂³×C₈₉	semidirect
569. #124	C₂³×C₈₉	semidirect
570. #124	C₂³×C₈₉	semidirect
572. #123	C₂³×C₈₉	semidirect
573. #123	C₂³×C₈₉	semidirect
574. #123	C₂³×C₈₉	semidirect
575. #123	C₂³×C₈₉	semidirect
576. #123	C₂³×C₈₉	semidirect
577. #123	C₂³×C₈₉	semidirect
578. C₂²⋊Q₈	C₂³×C₈₉	semidirect
579. C₂²⋊Q₈	C₂³×C₈₉	semidirect
580. C₂²⋊Q₈	C₂³×C₈₉	semidirect
581. C₂²⋊Q₈	C₂³×C₈₉	semidirect
582. C₂²⋊Q₈	C₂³×C₈₉	semidirect
583. C₂²⋊Q₈	C₂³×C₈₉	semidirect
588. #121	C₂³×C₈₉	semidirect
589. #121	C₂³×C₈₉	semidirect
590. #121	C₂³×C₈₉	semidirect
594. #120	C₂³×C₈₉	semidirect
595. #120	C₂³×C₈₉	semidirect
596. #120	C₂³×C₈₉	semidirect
597. C₄×Q₈	C₂³×C₈₉	semidirect
598. C₄×Q₈	C₂³×C₈₉	semidirect
600. C₄×D₄	C₂³×C₈₉	semidirect
601. C₄×D₄	C₂³×C₈₉	semidirect
602. C₄×D₄	C₂³×C₈₉	semidirect
603. C₄×D₄	C₂³×C₈₉	semidirect
604. C₄×D₄	C₂³×C₈₉	semidirect
605. #117	C₂³×C₈₉	semidirect
606. #117	C₂³×C₈₉	semidirect
607. #117	C₂³×C₈₉	semidirect
608. #117	C₂³×C₈₉	semidirect
609. #117	C₂³×C₈₉	semidirect
638. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
856. C₂	C₈₉×#3540	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#3540	2
C₂×H(3,𝔽₄)×C₈₉	2
C₂×#560×C₈₉	2
C₂×#559×C₈₉	2
C₂×#556×C₈₉	2
C₂×#555×C₈₉	2
C₂×#551×C₈₉	2
C₂×#548×C₈₉	2
C₂×#546×C₈₉	2
C₂×#542×C₈₉	2
C₂×#538×C₈₉	2
C₂×#536×C₈₉	2
C₂×#535×C₈₉	2
C₂×#525×C₈₉	2
C₂×#3540	89

Subgroups — C2×C89×#3540 #36440576

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3540 #36440576