Subgroups — C₂×C₈₉×#2505 #36412596

Order 22784.

2486 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2505	C₂	1	16	yes	maximal, direct product factor
2	C₂×#400×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#400×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#400×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#398×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#389×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#387×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#387×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#385×C₈₉	C₂	1	1	yes	maximal, characteristic
10	C₂×#385×C₈₉	C₂	1	1	yes	maximal, characteristic
11	C₂×#385×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂×#385×C₈₉	C₂	1	1	yes	maximal, characteristic
13	C₂×#382×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#380×C₈₉	C₂	1	1	yes	maximal, characteristic
15	C₂×C₄×C₂²⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic
16	C₂²×#95×C₈₉	C₂	1	1	yes	maximal, characteristic
17	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
36	#400×C₈₉	C₂²	1	8	yes	complemented
37	#400×C₈₉	C₂²	1	8	yes	complemented
38	#400×C₈₉	C₂²	1	8	yes	complemented
39	#398×C₈₉	C₂²	1	8	yes	complemented
40	#389×C₈₉	C₂²	1	8	yes	complemented
41	#387×C₈₉	C₂²	1	8	yes	complemented
42	#387×C₈₉	C₂²	1	8	yes	complemented
43	#385×C₈₉	C₂²	1	8	yes	—
44	#385×C₈₉	C₂²	1	8	yes	—
45	#385×C₈₉	C₂²	1	8	yes	—
46	#385×C₈₉	C₂²	1	8	yes	—
47	#382×C₈₉	C₂²	1	8	yes	complemented
48	#380×C₈₉	C₂²	1	8	yes	—
49	C₄×C₂²⋊C₄×C₈₉	C₂²	1	8	yes	—
50	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
51	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
52	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
54	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
55	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
56	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
57	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
58	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
59	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
60	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
61	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
62	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
63	C₂×#95×C₈₉	C₂²	1	8	yes	—
64	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
65	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
66	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
67	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₈₉	—	2	4	no	—
69	C₂³×C₄×C₈₉	—	2	4	no	—
70	C₂³×C₄×C₈₉	—	2	4	no	—
71	C₂³×C₄×C₈₉	—	2	4	no	—
72	C₂³×C₄×C₈₉	—	2	4	no	—
73	C₂³×C₄×C₈₉	—	4	2	no	—
74	C₂³×C₄×C₈₉	—	4	2	no	—
75	C₂³×C₄×C₈₉	—	4	2	no	—
76	C₂³×C₄×C₈₉	—	4	2	no	—
77	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
88	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
89	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
95	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
96	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
97	C₂×C₄⋊C₄×C₈₉	—	4	2	no	—
98	C₂×C₄⋊C₄×C₈₉	—	4	2	no	—
99	C₂×C₄⋊C₄×C₈₉	—	4	2	no	—
100	C₂×C₄⋊C₄×C₈₉	—	4	2	no	—
101	C₂×C₄⋊C₄×C₈₉	—	4	2	no	—
102	C₂×C₄⋊C₄×C₈₉	—	4	2	no	—
103	C₂×C₄⋊C₄×C₈₉	—	4	2	no	—
104	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
105	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
106	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
107	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
108	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
115	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
116	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
117	C₂×C₂²⋊C₄×C₈₉	Q₈	1	8	yes	—
118	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
119	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
122	C₂×C₄²×C₈₉	—	2	4	no	—
123	C₂×C₄²×C₈₉	—	4	2	no	—
124	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
125	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
126	#95×C₈₉	C₂³	1	4	yes	—
127	#95×C₈₉	C₂³	1	4	yes	—
128	#95×C₈₉	C₂³	1	4	yes	—
129	#95×C₈₉	C₂³	1	4	yes	—
130	#95×C₈₉	C₂³	1	4	yes	—
131	#95×C₈₉	C₂³	1	4	yes	—
132	#95×C₈₉	C₂³	1	4	yes	—
133	#95×C₈₉	C₂³	1	4	yes	—
134	#95×C₈₉	C₂³	1	4	yes	—
135	#95×C₈₉	C₂³	1	4	yes	—
136	#95×C₈₉	C₂³	1	4	yes	—
137	#95×C₈₉	C₂³	1	4	yes	—
138	#95×C₈₉	C₂³	1	4	yes	—
139	#95×C₈₉	C₂³	1	4	yes	—
140	#95×C₈₉	C₂³	1	4	yes	—
141	#95×C₈₉	C₂³	1	4	yes	—
142	C₂⁴×C₈₉	—	2	2	no	—
143	C₂⁴×C₈₉	—	2	2	no	—
144	C₂⁴×C₈₉	—	2	2	no	—
145	C₂⁴×C₈₉	—	2	2	no	—
146	C₂⁴×C₈₉	C₂×Q₈	1	4	yes	—
147	C₂⁴×C₈₉	#41	1	4	yes	—
148	C₂⁴×C₈₉	#41	1	4	yes	—
149	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
150	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
151	C₂²×C₄×C₈₉	—	2	2	no	—
152	C₂²×C₄×C₈₉	—	2	2	no	—
153	C₂²×C₄×C₈₉	—	2	2	no	—
154	C₂²×C₄×C₈₉	—	2	2	no	—
155	C₂²×C₄×C₈₉	—	2	2	no	—
156	C₂²×C₄×C₈₉	—	2	2	no	—
157	C₂²×C₄×C₈₉	—	2	2	no	—
158	C₂²×C₄×C₈₉	—	2	2	no	—
159	C₂²×C₄×C₈₉	—	2	2	no	—
160	C₂²×C₄×C₈₉	—	2	2	no	—
161	C₂²×C₄×C₈₉	—	2	2	no	—
162	C₂²×C₄×C₈₉	—	2	2	no	—
163	C₂²×C₄×C₈₉	—	2	2	no	—
164	C₂²×C₄×C₈₉	—	2	2	no	—
165	C₂²×C₄×C₈₉	—	2	2	no	—
166	C₂²×C₄×C₈₉	—	2	2	no	—
167	C₂²×C₄×C₈₉	—	2	2	no	—
168	C₂²×C₄×C₈₉	—	2	2	no	—
169	C₂²×C₄×C₈₉	—	2	2	no	—
170	C₂²×C₄×C₈₉	—	2	2	no	—
171	C₂²×C₄×C₈₉	—	2	8	no	—
172	C₂²×C₄×C₈₉	—	2	8	no	—
173	C₂²×C₄×C₈₉	—	2	8	no	—
174	C₂²×C₄×C₈₉	—	2	2	no	—
175	C₂²×C₄×C₈₉	—	2	2	no	—
176	C₂²×C₄×C₈₉	—	2	2	no	—
177	C₂²×C₄×C₈₉	—	2	2	no	—
178	C₂²×C₄×C₈₉	—	2	2	no	—
179	C₂²×C₄×C₈₉	—	2	2	no	—
180	C₂²×C₄×C₈₉	—	2	2	no	—
181	C₂²×C₄×C₈₉	—	2	2	no	—
182	C₂²×C₄×C₈₉	—	2	2	no	—
183	C₂²×C₄×C₈₉	—	2	2	no	—
184	C₂²×C₄×C₈₉	—	2	2	no	—
185	C₂²×C₄×C₈₉	—	2	2	no	—
186	C₂²×C₄×C₈₉	—	2	2	no	—
187	C₂²×C₄×C₈₉	—	2	2	no	—
188	C₂²×C₄×C₈₉	—	2	2	no	—
189	C₂²×C₄×C₈₉	—	2	2	no	—
190	C₂²×C₄×C₈₉	—	2	2	no	—
191	C₂²×C₄×C₈₉	—	2	2	no	—
192	C₂²×C₄×C₈₉	—	2	8	no	—
193	C₂²×C₄×C₈₉	—	2	8	no	—
194	C₂²×C₄×C₈₉	—	4	4	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	16	no	—
199	C₂²×C₄×C₈₉	—	4	16	no	—
200	C₂²×C₄×C₈₉	—	4	16	no	—
201	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
202	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
203	C₂²×C₄×C₈₉	#41	1	4	yes	—
204	C₂²×C₄×C₈₉	#41	1	4	yes	—
205	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
219	C₄⋊C₄×C₈₉	—	2	8	no	—
220	C₄⋊C₄×C₈₉	—	2	8	no	—
221	C₄⋊C₄×C₈₉	—	2	8	no	—
222	C₄⋊C₄×C₈₉	—	4	4	no	—
223	C₄⋊C₄×C₈₉	—	4	4	no	—
224	C₄⋊C₄×C₈₉	—	4	4	no	—
225	C₄⋊C₄×C₈₉	—	4	4	no	—
226	C₄⋊C₄×C₈₉	—	4	4	no	—
227	C₄⋊C₄×C₈₉	—	4	4	no	—
228	C₄⋊C₄×C₈₉	—	4	4	no	—
229	C₂²⋊C₄×C₈₉	—	2	8	no	—
230	C₂²⋊C₄×C₈₉	—	2	8	no	—
231	C₂²⋊C₄×C₈₉	—	2	8	no	—
232	C₂²⋊C₄×C₈₉	C₂×Q₈	1	16	yes	—
233	C₄²×C₈₉	—	2	8	no	—
234	C₄²×C₈₉	—	4	4	no	—
235	C₂³×C₈₉	—	2	8	no	—
236	C₂³×C₈₉	—	2	8	no	—
237	C₂³×C₈₉	—	2	8	no	—
238	C₂³×C₈₉	—	2	8	no	—
239	C₂³×C₈₉	—	2	8	no	—
240	C₂³×C₈₉	—	2	8	no	—
241	C₂³×C₈₉	—	2	2	no	—
242	C₂³×C₈₉	—	2	2	no	—
243	C₂³×C₈₉	—	2	2	no	—
244	C₂³×C₈₉	—	2	2	no	—
245	C₂³×C₈₉	#125	1	16	yes	—
246	C₂³×C₈₉	C₂²×Q₈	1	4	yes	—
247	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
248	C₂³×C₈₉	C₂×#41	1	4	yes	—
249	C₂³×C₈₉	C₂×#41	1	4	yes	—
250	C₂³×C₈₉	C₂×#41	1	2	yes	—
251	C₂³×C₈₉	C₂×#41	1	2	yes	—
252	C₂³×C₈₉	C₂×#41	1	2	yes	—
253	C₂³×C₈₉	C₂×#41	1	2	yes	—
254	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
255	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
256	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
257	C₂×C₄×C₈₉	—	2	8	no	—
258	C₂×C₄×C₈₉	—	2	8	no	—
259	C₂×C₄×C₈₉	—	2	8	no	—
260	C₂×C₄×C₈₉	—	2	8	no	—
261	C₂×C₄×C₈₉	—	2	2	no	—
262	C₂×C₄×C₈₉	—	2	2	no	—
263	C₂×C₄×C₈₉	—	2	2	no	—
264	C₂×C₄×C₈₉	—	2	2	no	—
265	C₂×C₄×C₈₉	—	2	2	no	—
266	C₂×C₄×C₈₉	—	2	2	no	—
267	C₂×C₄×C₈₉	—	2	2	no	—
268	C₂×C₄×C₈₉	—	2	2	no	—
269	C₂×C₄×C₈₉	—	2	2	no	—
270	C₂×C₄×C₈₉	—	2	2	no	—
271	C₂×C₄×C₈₉	—	2	2	no	—
272	C₂×C₄×C₈₉	—	2	2	no	—
273	C₂×C₄×C₈₉	—	2	2	no	—
274	C₂×C₄×C₈₉	—	2	2	no	—
275	C₂×C₄×C₈₉	—	2	2	no	—
276	C₂×C₄×C₈₉	—	2	2	no	—
277	C₂×C₄×C₈₉	—	2	2	no	—
278	C₂×C₄×C₈₉	—	2	2	no	—
279	C₂×C₄×C₈₉	—	2	2	no	—
280	C₂×C₄×C₈₉	—	2	2	no	—
281	C₂×C₄×C₈₉	—	2	2	no	—
282	C₂×C₄×C₈₉	—	2	2	no	—
283	C₂×C₄×C₈₉	—	2	2	no	—
284	C₂×C₄×C₈₉	—	2	2	no	—
285	C₂×C₄×C₈₉	—	2	2	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	2	no	—
292	C₂×C₄×C₈₉	—	2	2	no	—
293	C₂×C₄×C₈₉	—	2	2	no	—
294	C₂×C₄×C₈₉	—	2	2	no	—
295	C₂×C₄×C₈₉	—	2	2	no	—
296	C₂×C₄×C₈₉	—	2	2	no	—
297	C₂×C₄×C₈₉	—	2	2	no	—
298	C₂×C₄×C₈₉	—	2	2	no	—
299	C₂×C₄×C₈₉	—	4	16	no	—
300	C₂×C₄×C₈₉	—	4	16	no	—
301	C₂×C₄×C₈₉	—	4	16	no	—
302	C₂×C₄×C₈₉	—	4	4	no	—
303	C₂×C₄×C₈₉	—	4	4	no	—
304	C₂×C₄×C₈₉	—	4	4	no	—
305	C₂×C₄×C₈₉	—	4	4	no	—
306	C₂×C₄×C₈₉	—	4	4	no	—
307	C₂×C₄×C₈₉	—	4	4	no	—
308	C₂×C₄×C₈₉	—	4	4	no	—
309	C₂×C₄×C₈₉	—	4	4	no	—
310	C₂×C₄×C₈₉	—	4	4	no	—
311	C₂×C₄×C₈₉	—	4	4	no	—
312	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
313	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
314	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
315	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
316	C₂²×C₈₉	—	2	4	no	—
317	C₂²×C₈₉	—	2	4	no	—
318	C₂²×C₈₉	—	2	4	no	—
319	C₂²×C₈₉	—	2	4	no	—
320	C₂²×C₈₉	—	2	4	no	—
321	C₂²×C₈₉	—	2	4	no	—
322	C₂²×C₈₉	—	2	32	no	—
323	C₂²×C₈₉	C₂×#125	1	8	yes	—
324	C₂²×C₈₉	C₂×#125	1	4	yes	—
325	C₂²×C₈₉	#529	1	4	yes	—
326	C₂²×C₈₉	#538	1	4	yes	—
327	C₂²×C₈₉	#551	1	4	yes	—
328	C₂²×C₈₉	#551	1	4	yes	—
329	C₂²×C₈₉	#554	1	4	yes	—
330	C₂²×C₈₉	#554	1	4	yes	—
331	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
332	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
333	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
334	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
335	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
336	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
337	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
338	C₄×C₈₉	—	2	4	no	—
339	C₄×C₈₉	—	2	4	no	—
340	C₄×C₈₉	—	2	4	no	—
341	C₄×C₈₉	—	2	4	no	—
342	C₄×C₈₉	—	4	2	no	—
343	C₄×C₈₉	—	4	2	no	—
344	C₄×C₈₉	—	4	2	no	—
345	C₄×C₈₉	—	4	2	no	—
346	C₄×C₈₉	—	4	2	no	—
347	C₄×C₈₉	—	4	2	no	—
348	C₄×C₈₉	—	4	2	no	—
349	C₄×C₈₉	—	4	2	no	—
350	C₄×C₈₉	—	4	2	no	—
351	C₄×C₈₉	—	4	2	no	—
352	C₂×#2505	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
353	C₂×C₈₉	—	2	8	no	—
354	C₂×C₈₉	#2505	1	8	yes	direct product factor
355	C₂×C₈₉	C₂²×#125	1	1	yes	characteristic
356	C₂×C₈₉	C₂×#529	1	1	yes	characteristic
357	C₂×C₈₉	C₂×#538	1	1	yes	characteristic
358	C₂×C₈₉	C₂×#551	1	1	yes	characteristic
359	C₂×C₈₉	C₂×#551	1	1	yes	characteristic
360	C₂×C₈₉	C₂×#554	1	1	yes	characteristic
361	C₂×C₈₉	C₂×#554	1	1	yes	characteristic
362	#2505	C₂×C₈₉	1	16	yes	direct product factor
363	C₂×#400	C₂×C₈₉	1	1	yes	characteristic, complemented
364	C₂×#400	C₂×C₈₉	1	1	yes	characteristic, complemented
365	C₂×#400	C₂×C₈₉	1	1	yes	characteristic, complemented
366	C₂×#398	C₂×C₈₉	1	1	yes	characteristic, complemented
367	C₂×#389	C₂×C₈₉	1	1	yes	characteristic, complemented
368	C₂×#387	C₂×C₈₉	1	1	yes	characteristic, complemented
369	C₂×#387	C₂×C₈₉	1	1	yes	characteristic, complemented
370	C₂×#385	C₂×C₈₉	1	1	yes	characteristic
371	C₂×#385	C₂×C₈₉	1	1	yes	characteristic
372	C₂×#385	C₂×C₈₉	1	1	yes	characteristic
373	C₂×#385	C₂×C₈₉	1	1	yes	characteristic
374	C₂×#382	C₂×C₈₉	1	1	yes	characteristic, complemented
375	C₂×#380	C₂×C₈₉	1	1	yes	characteristic
376	C₂×C₄×C₂²⋊C₄	C₂×C₈₉	1	1	yes	characteristic
377	C₂²×#95	C₂×C₈₉	1	1	yes	characteristic
378	C₈₉	C₂×#2505	1	1	yes	characteristic, direct product factor, Sylow
379	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
380	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
381	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
382	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
383	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
384	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
385	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
386	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
387	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
388	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
389	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
390	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
391	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
392	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
393	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
394	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
395	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
396	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
397	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
398	#400	C₂²×C₈₉	1	8	yes	complemented
399	#400	C₂²×C₈₉	1	8	yes	complemented
400	#400	C₂²×C₈₉	1	8	yes	complemented
401	#398	C₂²×C₈₉	1	8	yes	complemented
402	#389	C₂²×C₈₉	1	8	yes	complemented
403	#387	C₂²×C₈₉	1	8	yes	complemented
404	#387	C₂²×C₈₉	1	8	yes	complemented
405	#385	C₂²×C₈₉	1	8	yes	—
406	#385	C₂²×C₈₉	1	8	yes	—
407	#385	C₂²×C₈₉	1	8	yes	—
408	#385	C₂²×C₈₉	1	8	yes	—
409	#382	C₂²×C₈₉	1	8	yes	complemented
410	#380	C₂²×C₈₉	1	8	yes	—
411	C₄×C₂²⋊C₄	C₂²×C₈₉	1	8	yes	—
412	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
413	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
414	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
415	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
416	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
417	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
418	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
419	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
420	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
421	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
422	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
423	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
424	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
425	C₂×#95	C₂²×C₈₉	1	8	yes	—
426	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
427	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
428	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
429	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
430	C₂³×C₄	—	2	4	no	—
431	C₂³×C₄	—	2	4	no	—
432	C₂³×C₄	—	2	4	no	—
433	C₂³×C₄	—	2	4	no	—
434	C₂³×C₄	—	2	4	no	—
435	C₂³×C₄	—	4	2	no	—
436	C₂³×C₄	—	4	2	no	—
437	C₂³×C₄	—	4	2	no	—
438	C₂³×C₄	—	4	2	no	—
439	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
440	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
441	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
442	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
443	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
444	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
445	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
446	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
447	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
448	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
449	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
450	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
451	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
452	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
454	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
455	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
456	C₂×C₄⋊C₄	—	2	4	no	—
457	C₂×C₄⋊C₄	—	2	4	no	—
458	C₂×C₄⋊C₄	—	2	4	no	—
459	C₂×C₄⋊C₄	—	4	2	no	—
460	C₂×C₄⋊C₄	—	4	2	no	—
461	C₂×C₄⋊C₄	—	4	2	no	—
462	C₂×C₄⋊C₄	—	4	2	no	—
463	C₂×C₄⋊C₄	—	4	2	no	—
464	C₂×C₄⋊C₄	—	4	2	no	—
465	C₂×C₄⋊C₄	—	4	2	no	—
466	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
467	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
468	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
469	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
470	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
471	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
472	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
473	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
474	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
475	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
476	C₂×C₂²⋊C₄	—	2	4	no	—
477	C₂×C₂²⋊C₄	—	2	4	no	—
478	C₂×C₂²⋊C₄	—	2	4	no	—
479	C₂×C₂²⋊C₄	Q₈×C₈₉	1	8	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
484	C₂×C₄²	—	2	4	no	—
485	C₂×C₄²	—	4	2	no	—
486	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
487	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
488	#95	C₂³×C₈₉	1	4	yes	—
489	#95	C₂³×C₈₉	1	4	yes	—
490	#95	C₂³×C₈₉	1	4	yes	—
491	#95	C₂³×C₈₉	1	4	yes	—
492	#95	C₂³×C₈₉	1	4	yes	—
493	#95	C₂³×C₈₉	1	4	yes	—
494	#95	C₂³×C₈₉	1	4	yes	—
495	#95	C₂³×C₈₉	1	4	yes	—
496	#95	C₂³×C₈₉	1	4	yes	—
497	#95	C₂³×C₈₉	1	4	yes	—
498	#95	C₂³×C₈₉	1	4	yes	—
499	#95	C₂³×C₈₉	1	4	yes	—
500	#95	C₂³×C₈₉	1	4	yes	—
501	#95	C₂³×C₈₉	1	4	yes	—
502	#95	C₂³×C₈₉	1	4	yes	—
503	#95	C₂³×C₈₉	1	4	yes	—
504	C₂⁴	—	2	2	no	—
505	C₂⁴	—	2	2	no	—
506	C₂⁴	—	2	2	no	—
507	C₂⁴	—	2	2	no	—
508	C₂⁴	C₂×Q₈×C₈₉	1	4	yes	—
509	C₂⁴	#41×C₈₉	1	4	yes	—
510	C₂⁴	#41×C₈₉	1	4	yes	—
511	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
512	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	2	no	—
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	2	2	no	—
523	C₂²×C₄	—	2	2	no	—
524	C₂²×C₄	—	2	2	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	2	no	—
533	C₂²×C₄	—	2	8	no	—
534	C₂²×C₄	—	2	8	no	—
535	C₂²×C₄	—	2	8	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	8	no	—
555	C₂²×C₄	—	2	8	no	—
556	C₂²×C₄	—	4	4	no	—
557	C₂²×C₄	—	4	4	no	—
558	C₂²×C₄	—	4	4	no	—
559	C₂²×C₄	—	4	4	no	—
560	C₂²×C₄	—	4	16	no	—
561	C₂²×C₄	—	4	16	no	—
562	C₂²×C₄	—	4	16	no	—
563	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
564	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
565	C₂²×C₄	#41×C₈₉	1	4	yes	—
566	C₂²×C₄	#41×C₈₉	1	4	yes	—
567	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
570	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
572	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
573	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
581	C₄⋊C₄	—	2	8	no	—
582	C₄⋊C₄	—	2	8	no	—
583	C₄⋊C₄	—	2	8	no	—
584	C₄⋊C₄	—	4	4	no	—
585	C₄⋊C₄	—	4	4	no	—
586	C₄⋊C₄	—	4	4	no	—
587	C₄⋊C₄	—	4	4	no	—
588	C₄⋊C₄	—	4	4	no	—
589	C₄⋊C₄	—	4	4	no	—
590	C₄⋊C₄	—	4	4	no	—
591	C₂²⋊C₄	—	2	8	no	—
592	C₂²⋊C₄	—	2	8	no	—
593	C₂²⋊C₄	—	2	8	no	—
594	C₂²⋊C₄	C₂×Q₈×C₈₉	1	16	yes	—
595	C₄²	—	2	8	no	—
596	C₄²	—	4	4	no	—
597	C₂³	—	2	8	no	—
598	C₂³	—	2	8	no	—
599	C₂³	—	2	8	no	—
600	C₂³	—	2	8	no	—
601	C₂³	—	2	8	no	—
602	C₂³	—	2	8	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	2	2	no	—
607	C₂³	#125×C₈₉	1	16	yes	—
608	C₂³	C₂²×Q₈×C₈₉	1	4	yes	—
609	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
610	C₂³	C₂×#41×C₈₉	1	4	yes	—
611	C₂³	C₂×#41×C₈₉	1	4	yes	—
612	C₂³	C₂×#41×C₈₉	1	2	yes	—
613	C₂³	C₂×#41×C₈₉	1	2	yes	—
614	C₂³	C₂×#41×C₈₉	1	2	yes	—
615	C₂³	C₂×#41×C₈₉	1	2	yes	—
616	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
617	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
618	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
619	C₂×C₄	—	2	8	no	—
620	C₂×C₄	—	2	8	no	—
621	C₂×C₄	—	2	8	no	—
622	C₂×C₄	—	2	8	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	4	16	no	—
662	C₂×C₄	—	4	16	no	—
663	C₂×C₄	—	4	16	no	—
664	C₂×C₄	—	4	4	no	—
665	C₂×C₄	—	4	4	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	4	4	no	—
668	C₂×C₄	—	4	4	no	—
669	C₂×C₄	—	4	4	no	—
670	C₂×C₄	—	4	4	no	—
671	C₂×C₄	—	4	4	no	—
672	C₂×C₄	—	4	4	no	—
673	C₂×C₄	—	4	4	no	—
674	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
675	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
676	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
677	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
678	C₂²	—	2	4	no	—
679	C₂²	—	2	4	no	—
680	C₂²	—	2	4	no	—
681	C₂²	—	2	4	no	—
682	C₂²	—	2	4	no	—
683	C₂²	—	2	4	no	—
684	C₂²	—	2	32	no	—
685	C₂²	C₂×#125×C₈₉	1	8	yes	—
686	C₂²	C₂×#125×C₈₉	1	4	yes	—
687	C₂²	#529×C₈₉	1	4	yes	—
688	C₂²	#538×C₈₉	1	4	yes	—
689	C₂²	#551×C₈₉	1	4	yes	—
690	C₂²	#551×C₈₉	1	4	yes	—
691	C₂²	#554×C₈₉	1	4	yes	—
692	C₂²	#554×C₈₉	1	4	yes	—
693	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
694	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
695	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
696	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
697	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
698	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
699	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
700	C₄	—	2	4	no	—
701	C₄	—	2	4	no	—
702	C₄	—	2	4	no	—
703	C₄	—	2	4	no	—
704	C₄	—	4	2	no	—
705	C₄	—	4	2	no	—
706	C₄	—	4	2	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	2	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₂	—	2	8	no	—
715	C₂	C₈₉×#2505	1	8	yes	direct product factor
716	C₂	C₂²×#125×C₈₉	1	1	yes	characteristic
717	C₂	C₂×#529×C₈₉	1	1	yes	characteristic
718	C₂	C₂×#538×C₈₉	1	1	yes	characteristic
719	C₂	C₂×#551×C₈₉	1	1	yes	characteristic
720	C₂	C₂×#551×C₈₉	1	1	yes	characteristic
721	C₂	C₂×#554×C₈₉	1	1	yes	characteristic
722	C₂	C₂×#554×C₈₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₈₉×#2505	C₂	direct (N × H)
2. C₂×#400×C₈₉	C₂	semidirect
3. C₂×#400×C₈₉	C₂	semidirect
4. C₂×#400×C₈₉	C₂	semidirect
5. C₂×#398×C₈₉	C₂	semidirect
6. C₂×#389×C₈₉	C₂	semidirect
7. C₂×#387×C₈₉	C₂	semidirect
8. C₂×#387×C₈₉	C₂	semidirect
13. C₂×#382×C₈₉	C₂	semidirect
36. #400×C₈₉	C₂²	semidirect
37. #400×C₈₉	C₂²	semidirect
38. #400×C₈₉	C₂²	semidirect
39. #398×C₈₉	C₂²	semidirect
40. #389×C₈₉	C₂²	semidirect
41. #387×C₈₉	C₂²	semidirect
42. #387×C₈₉	C₂²	semidirect
47. #382×C₈₉	C₂²	semidirect
352. C₂×#2505	C₈₉	direct (N × H)
354. C₂×C₈₉	#2505	direct (N × H)
362. #2505	C₂×C₈₉	direct (N × H)
363. C₂×#400	C₂×C₈₉	semidirect
364. C₂×#400	C₂×C₈₉	semidirect
365. C₂×#400	C₂×C₈₉	semidirect
366. C₂×#398	C₂×C₈₉	semidirect
367. C₂×#389	C₂×C₈₉	semidirect
368. C₂×#387	C₂×C₈₉	semidirect
369. C₂×#387	C₂×C₈₉	semidirect
374. C₂×#382	C₂×C₈₉	semidirect
378. C₈₉	C₂×#2505	direct (N × H)
398. #400	C₂²×C₈₉	semidirect
399. #400	C₂²×C₈₉	semidirect
400. #400	C₂²×C₈₉	semidirect
401. #398	C₂²×C₈₉	semidirect
402. #389	C₂²×C₈₉	semidirect
403. #387	C₂²×C₈₉	semidirect
404. #387	C₂²×C₈₉	semidirect
409. #382	C₂²×C₈₉	semidirect
715. C₂	C₈₉×#2505	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×#2505	2
C₂×#400×C₈₉	2
C₂×#398×C₈₉	2
C₂×#389×C₈₉	2
C₂×#387×C₈₉	2
C₂×#385×C₈₉	2
C₂×#382×C₈₉	2
C₂×#380×C₈₉	2
C₂×C₄×C₂²⋊C₄×C₈₉	2
C₂²×#95×C₈₉	2
C₂×#2505	89

Subgroups — C2×C89×#2505 #36412596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#2505 #36412596