Subgroups — C₂×C₈₉×#2569 #36412690

Order 22784.

2486 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2569	C₂	1	16	yes	maximal, direct product factor
2	C₂×#400×C₈₉	C₂	1	2	yes	maximal, complemented
3	C₂×#398×C₈₉	C₂	1	2	yes	maximal, complemented
4	C₂×#387×C₈₉	C₂	1	2	yes	maximal, complemented
5	C₂×#387×C₈₉	C₂	1	2	yes	maximal, complemented
6	C₂×#385×C₈₉	C₂	1	2	yes	maximal
7	C₂×#380×C₈₉	C₂	1	2	yes	maximal
8	C₂×#380×C₈₉	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×C₂²⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic
10	C₂²×#95×C₈₉	C₂	1	1	yes	maximal, characteristic
11	C₂⁴×C₄×C₈₉	C₂²	1	2	yes	—
12	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
21	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
22	#400×C₈₉	C₂²	1	16	yes	complemented
23	#398×C₈₉	C₂²	1	16	yes	complemented
24	#387×C₈₉	C₂²	1	16	yes	complemented
25	#387×C₈₉	C₂²	1	16	yes	complemented
26	#385×C₈₉	C₂²	1	16	yes	—
27	#380×C₈₉	C₂²	1	8	yes	—
28	#380×C₈₉	C₂²	1	16	yes	—
29	C₄×C₂²⋊C₄×C₈₉	C₂²	1	8	yes	—
30	C₂×#95×C₈₉	C₂²	1	8	yes	—
31	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#95×C₈₉	C₂²	1	2	yes	—
33	C₂×#95×C₈₉	C₂²	1	2	yes	—
34	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#95×C₈₉	C₂²	1	2	yes	—
36	C₂×#95×C₈₉	C₂²	1	2	yes	—
37	C₂×#95×C₈₉	C₂²	1	2	yes	—
38	C₂×#95×C₈₉	C₂²	1	2	yes	—
39	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
41	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₈₉	—	2	8	no	—
43	C₂³×C₄×C₈₉	—	2	8	no	—
44	C₂³×C₄×C₈₉	—	4	4	no	—
45	C₂³×C₄×C₈₉	—	4	4	no	—
46	C₂³×C₄×C₈₉	Q₈	1	8	yes	—
47	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
48	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
49	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
50	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
51	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
52	C₂³×C₄×C₈₉	C₂³	1	8	yes	—
53	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
56	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
57	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
58	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
59	C₂×C₄⋊C₄×C₈₉	—	4	4	no	—
60	C₂×C₄⋊C₄×C₈₉	—	4	4	no	—
61	C₂×C₄⋊C₄×C₈₉	—	4	4	no	—
62	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
63	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
64	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
65	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
66	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
67	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
69	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
71	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
72	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
73	C₂×C₄²×C₈₉	—	4	4	no	—
74	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
75	#95×C₈₉	C₂³	1	8	yes	—
76	#95×C₈₉	C₂³	1	4	yes	—
77	#95×C₈₉	C₂³	1	4	yes	—
78	#95×C₈₉	C₂³	1	8	yes	—
79	#95×C₈₉	C₂³	1	4	yes	—
80	#95×C₈₉	C₂³	1	4	yes	—
81	#95×C₈₉	C₂³	1	8	yes	—
82	#95×C₈₉	C₂³	1	8	yes	—
83	#95×C₈₉	C₂³	1	8	yes	—
84	#95×C₈₉	C₂³	1	8	yes	—
85	C₂⁴×C₈₉	—	2	4	no	—
86	C₂⁴×C₈₉	—	2	4	no	—
87	C₂⁴×C₈₉	C₂×Q₈	1	4	yes	—
88	C₂⁴×C₈₉	#41	1	4	yes	—
89	C₂⁴×C₈₉	#41	1	4	yes	—
90	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
91	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
92	C₂²×C₄×C₈₉	—	2	4	no	—
93	C₂²×C₄×C₈₉	—	2	4	no	—
94	C₂²×C₄×C₈₉	—	2	4	no	—
95	C₂²×C₄×C₈₉	—	2	4	no	—
96	C₂²×C₄×C₈₉	—	2	4	no	—
97	C₂²×C₄×C₈₉	—	2	4	no	—
98	C₂²×C₄×C₈₉	—	2	4	no	—
99	C₂²×C₄×C₈₉	—	2	4	no	—
100	C₂²×C₄×C₈₉	—	2	4	no	—
101	C₂²×C₄×C₈₉	—	2	4	no	—
102	C₂²×C₄×C₈₉	—	2	4	no	—
103	C₂²×C₄×C₈₉	—	2	4	no	—
104	C₂²×C₄×C₈₉	—	2	16	no	—
105	C₂²×C₄×C₈₉	—	2	4	no	—
106	C₂²×C₄×C₈₉	—	2	4	no	—
107	C₂²×C₄×C₈₉	—	2	4	no	—
108	C₂²×C₄×C₈₉	—	2	4	no	—
109	C₂²×C₄×C₈₉	—	2	4	no	—
110	C₂²×C₄×C₈₉	—	2	4	no	—
111	C₂²×C₄×C₈₉	—	2	4	no	—
112	C₂²×C₄×C₈₉	—	2	16	no	—
113	C₂²×C₄×C₈₉	—	4	16	no	—
114	C₂²×C₄×C₈₉	—	4	8	no	—
115	C₂²×C₄×C₈₉	—	4	8	no	—
116	C₂²×C₄×C₈₉	—	4	32	no	—
117	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
118	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
119	C₂²×C₄×C₈₉	C₂×Q₈	1	16	yes	—
120	C₂²×C₄×C₈₉	#41	1	8	yes	—
121	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
123	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
124	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
125	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
127	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
128	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
129	C₄⋊C₄×C₈₉	—	2	16	no	—
130	C₄⋊C₄×C₈₉	—	2	16	no	—
131	C₄⋊C₄×C₈₉	—	4	8	no	—
132	C₄⋊C₄×C₈₉	—	4	8	no	—
133	C₄⋊C₄×C₈₉	—	4	8	no	—
134	C₂²⋊C₄×C₈₉	—	2	8	no	—
135	C₂²⋊C₄×C₈₉	—	2	16	no	—
136	C₂²⋊C₄×C₈₉	—	2	8	no	—
137	C₄²×C₈₉	—	4	8	no	—
138	C₂³×C₈₉	—	2	8	no	—
139	C₂³×C₈₉	—	2	8	no	—
140	C₂³×C₈₉	—	2	16	no	—
141	C₂³×C₈₉	—	2	16	no	—
142	C₂³×C₈₉	—	2	4	no	—
143	C₂³×C₈₉	—	2	4	no	—
144	C₂³×C₈₉	#125	1	16	yes	—
145	C₂³×C₈₉	C₂²×Q₈	1	4	yes	—
146	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
147	C₂³×C₈₉	C₂×#41	1	4	yes	—
148	C₂³×C₈₉	C₂×#41	1	4	yes	—
149	C₂³×C₈₉	C₂×#41	1	2	yes	—
150	C₂³×C₈₉	C₂×#41	1	2	yes	—
151	C₂³×C₈₉	C₂×#41	1	4	yes	—
152	C₂³×C₈₉	H(5,𝔽₂)	1	4	yes	—
153	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
154	C₂×C₄×C₈₉	—	2	8	no	—
155	C₂×C₄×C₈₉	—	2	8	no	—
156	C₂×C₄×C₈₉	—	2	16	no	—
157	C₂×C₄×C₈₉	—	2	4	no	—
158	C₂×C₄×C₈₉	—	2	4	no	—
159	C₂×C₄×C₈₉	—	2	4	no	—
160	C₂×C₄×C₈₉	—	2	4	no	—
161	C₂×C₄×C₈₉	—	2	4	no	—
162	C₂×C₄×C₈₉	—	2	4	no	—
163	C₂×C₄×C₈₉	—	2	4	no	—
164	C₂×C₄×C₈₉	—	2	4	no	—
165	C₂×C₄×C₈₉	—	2	4	no	—
166	C₂×C₄×C₈₉	—	2	4	no	—
167	C₂×C₄×C₈₉	—	2	4	no	—
168	C₂×C₄×C₈₉	—	2	4	no	—
169	C₂×C₄×C₈₉	—	2	4	no	—
170	C₂×C₄×C₈₉	—	2	4	no	—
171	C₂×C₄×C₈₉	—	2	4	no	—
172	C₂×C₄×C₈₉	—	2	4	no	—
173	C₂×C₄×C₈₉	—	2	4	no	—
174	C₂×C₄×C₈₉	—	2	4	no	—
175	C₂×C₄×C₈₉	—	2	4	no	—
176	C₂×C₄×C₈₉	—	4	16	no	—
177	C₂×C₄×C₈₉	—	4	32	no	—
178	C₂×C₄×C₈₉	—	4	8	no	—
179	C₂×C₄×C₈₉	—	4	8	no	—
180	C₂×C₄×C₈₉	—	4	8	no	—
181	C₂×C₄×C₈₉	—	4	8	no	—
182	C₂×C₄×C₈₉	—	4	8	no	—
183	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
184	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
185	C₂×C₄×C₈₉	C₂×#41	1	8	yes	—
186	C₂²×C₈₉	—	2	32	no	—
187	C₂²×C₈₉	—	2	4	no	—
188	C₂²×C₈₉	—	2	4	no	—
189	C₂²×C₈₉	—	2	8	no	—
190	C₂²×C₈₉	—	2	8	no	—
191	C₂²×C₈₉	C₂×#125	1	8	yes	—
192	C₂²×C₈₉	C₂×#125	1	4	yes	—
193	C₂²×C₈₉	#533	1	4	yes	—
194	C₂²×C₈₉	#543	1	4	yes	—
195	C₂²×C₈₉	#551	1	8	yes	—
196	C₂²×C₈₉	#553	1	8	yes	—
197	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
198	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
199	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
200	C₂²×C₈₉	C₂²×#41	1	2	yes	—
201	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
202	C₄×C₈₉	—	2	4	no	—
203	C₄×C₈₉	—	2	4	no	—
204	C₄×C₈₉	—	2	8	no	—
205	C₄×C₈₉	—	4	4	no	—
206	C₄×C₈₉	—	4	4	no	—
207	C₄×C₈₉	—	4	4	no	—
208	C₄×C₈₉	—	4	4	no	—
209	C₄×C₈₉	—	4	4	no	—
210	C₂×#2569	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂×C₈₉	—	2	8	no	—
212	C₂×C₈₉	#2569	1	8	yes	direct product factor
213	C₂×C₈₉	C₂²×#125	1	1	yes	characteristic
214	C₂×C₈₉	C₂×#533	1	1	yes	characteristic
215	C₂×C₈₉	C₂×#543	1	1	yes	characteristic
216	C₂×C₈₉	C₂×#551	1	2	yes	—
217	C₂×C₈₉	C₂×#553	1	2	yes	—
218	#2569	C₂×C₈₉	1	16	yes	direct product factor
219	C₂×#400	C₂×C₈₉	1	2	yes	complemented
220	C₂×#398	C₂×C₈₉	1	2	yes	complemented
221	C₂×#387	C₂×C₈₉	1	2	yes	complemented
222	C₂×#387	C₂×C₈₉	1	2	yes	complemented
223	C₂×#385	C₂×C₈₉	1	2	yes	—
224	C₂×#380	C₂×C₈₉	1	2	yes	—
225	C₂×#380	C₂×C₈₉	1	1	yes	characteristic
226	C₂×C₄×C₂²⋊C₄	C₂×C₈₉	1	1	yes	characteristic
227	C₂²×#95	C₂×C₈₉	1	1	yes	characteristic
228	C₈₉	C₂×#2569	1	1	yes	characteristic, direct product factor, Sylow
229	C₂⁴×C₄	C₂²×C₈₉	1	2	yes	—
230	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
231	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
232	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
233	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
234	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
235	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
236	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
237	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
238	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
239	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
240	#400	C₂²×C₈₉	1	16	yes	complemented
241	#398	C₂²×C₈₉	1	16	yes	complemented
242	#387	C₂²×C₈₉	1	16	yes	complemented
243	#387	C₂²×C₈₉	1	16	yes	complemented
244	#385	C₂²×C₈₉	1	16	yes	—
245	#380	C₂²×C₈₉	1	8	yes	—
246	#380	C₂²×C₈₉	1	16	yes	—
247	C₄×C₂²⋊C₄	C₂²×C₈₉	1	8	yes	—
248	C₂×#95	C₂²×C₈₉	1	8	yes	—
249	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
250	C₂×#95	C₂²×C₈₉	1	2	yes	—
251	C₂×#95	C₂²×C₈₉	1	2	yes	—
252	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
253	C₂×#95	C₂²×C₈₉	1	2	yes	—
254	C₂×#95	C₂²×C₈₉	1	2	yes	—
255	C₂×#95	C₂²×C₈₉	1	2	yes	—
256	C₂×#95	C₂²×C₈₉	1	2	yes	—
257	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
258	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
259	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
260	C₂³×C₄	—	2	8	no	—
261	C₂³×C₄	—	2	8	no	—
262	C₂³×C₄	—	4	4	no	—
263	C₂³×C₄	—	4	4	no	—
264	C₂³×C₄	Q₈×C₈₉	1	8	yes	—
265	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
266	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
267	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
268	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
269	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
270	C₂³×C₄	C₂³×C₈₉	1	8	yes	—
271	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
272	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
273	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
274	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
275	C₂×C₄⋊C₄	—	2	8	no	—
276	C₂×C₄⋊C₄	—	2	8	no	—
277	C₂×C₄⋊C₄	—	4	4	no	—
278	C₂×C₄⋊C₄	—	4	4	no	—
279	C₂×C₄⋊C₄	—	4	4	no	—
280	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
281	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
282	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
283	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
284	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
285	C₂×C₂²⋊C₄	—	2	4	no	—
286	C₂×C₂²⋊C₄	—	2	8	no	—
287	C₂×C₂²⋊C₄	—	2	4	no	—
288	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
289	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
290	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
291	C₂×C₄²	—	4	4	no	—
292	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
293	#95	C₂³×C₈₉	1	8	yes	—
294	#95	C₂³×C₈₉	1	4	yes	—
295	#95	C₂³×C₈₉	1	4	yes	—
296	#95	C₂³×C₈₉	1	8	yes	—
297	#95	C₂³×C₈₉	1	4	yes	—
298	#95	C₂³×C₈₉	1	4	yes	—
299	#95	C₂³×C₈₉	1	8	yes	—
300	#95	C₂³×C₈₉	1	8	yes	—
301	#95	C₂³×C₈₉	1	8	yes	—
302	#95	C₂³×C₈₉	1	8	yes	—
303	C₂⁴	—	2	4	no	—
304	C₂⁴	—	2	4	no	—
305	C₂⁴	C₂×Q₈×C₈₉	1	4	yes	—
306	C₂⁴	#41×C₈₉	1	4	yes	—
307	C₂⁴	#41×C₈₉	1	4	yes	—
308	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
309	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	16	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	16	no	—
331	C₂²×C₄	—	4	16	no	—
332	C₂²×C₄	—	4	8	no	—
333	C₂²×C₄	—	4	8	no	—
334	C₂²×C₄	—	4	32	no	—
335	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
336	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
337	C₂²×C₄	C₂×Q₈×C₈₉	1	16	yes	—
338	C₂²×C₄	#41×C₈₉	1	8	yes	—
339	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
340	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
341	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
342	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
343	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
344	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
345	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
346	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
347	C₄⋊C₄	—	2	16	no	—
348	C₄⋊C₄	—	2	16	no	—
349	C₄⋊C₄	—	4	8	no	—
350	C₄⋊C₄	—	4	8	no	—
351	C₄⋊C₄	—	4	8	no	—
352	C₂²⋊C₄	—	2	8	no	—
353	C₂²⋊C₄	—	2	16	no	—
354	C₂²⋊C₄	—	2	8	no	—
355	C₄²	—	4	8	no	—
356	C₂³	—	2	8	no	—
357	C₂³	—	2	8	no	—
358	C₂³	—	2	16	no	—
359	C₂³	—	2	16	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	2	4	no	—
362	C₂³	#125×C₈₉	1	16	yes	—
363	C₂³	C₂²×Q₈×C₈₉	1	4	yes	—
364	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
365	C₂³	C₂×#41×C₈₉	1	4	yes	—
366	C₂³	C₂×#41×C₈₉	1	4	yes	—
367	C₂³	C₂×#41×C₈₉	1	2	yes	—
368	C₂³	C₂×#41×C₈₉	1	2	yes	—
369	C₂³	C₂×#41×C₈₉	1	4	yes	—
370	C₂³	H(5,𝔽₂)×C₈₉	1	4	yes	—
371	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	2	8	no	—
374	C₂×C₄	—	2	16	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	4	16	no	—
395	C₂×C₄	—	4	32	no	—
396	C₂×C₄	—	4	8	no	—
397	C₂×C₄	—	4	8	no	—
398	C₂×C₄	—	4	8	no	—
399	C₂×C₄	—	4	8	no	—
400	C₂×C₄	—	4	8	no	—
401	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
402	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
403	C₂×C₄	C₂×#41×C₈₉	1	8	yes	—
404	C₂²	—	2	32	no	—
405	C₂²	—	2	4	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	2	8	no	—
408	C₂²	—	2	8	no	—
409	C₂²	C₂×#125×C₈₉	1	8	yes	—
410	C₂²	C₂×#125×C₈₉	1	4	yes	—
411	C₂²	#533×C₈₉	1	4	yes	—
412	C₂²	#543×C₈₉	1	4	yes	—
413	C₂²	#551×C₈₉	1	8	yes	—
414	C₂²	#553×C₈₉	1	8	yes	—
415	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
416	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
417	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
418	C₂²	C₂²×#41×C₈₉	1	2	yes	—
419	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
420	C₄	—	2	4	no	—
421	C₄	—	2	4	no	—
422	C₄	—	2	8	no	—
423	C₄	—	4	4	no	—
424	C₄	—	4	4	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	4	no	—
428	C₂	—	2	8	no	—
429	C₂	C₈₉×#2569	1	8	yes	direct product factor
430	C₂	C₂²×#125×C₈₉	1	1	yes	characteristic
431	C₂	C₂×#533×C₈₉	1	1	yes	characteristic
432	C₂	C₂×#543×C₈₉	1	1	yes	characteristic
433	C₂	C₂×#551×C₈₉	1	2	yes	—
434	C₂	C₂×#553×C₈₉	1	2	yes	—

	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×#2569	C₂	direct (N × H)
2. C₂×#400×C₈₉	C₂	semidirect
3. C₂×#398×C₈₉	C₂	semidirect
4. C₂×#387×C₈₉	C₂	semidirect
5. C₂×#387×C₈₉	C₂	semidirect
22. #400×C₈₉	C₂²	semidirect
23. #398×C₈₉	C₂²	semidirect
24. #387×C₈₉	C₂²	semidirect
25. #387×C₈₉	C₂²	semidirect
210. C₂×#2569	C₈₉	direct (N × H)
212. C₂×C₈₉	#2569	direct (N × H)
218. #2569	C₂×C₈₉	direct (N × H)
219. C₂×#400	C₂×C₈₉	semidirect
220. C₂×#398	C₂×C₈₉	semidirect
221. C₂×#387	C₂×C₈₉	semidirect
222. C₂×#387	C₂×C₈₉	semidirect
228. C₈₉	C₂×#2569	direct (N × H)
240. #400	C₂²×C₈₉	semidirect
241. #398	C₂²×C₈₉	semidirect
242. #387	C₂²×C₈₉	semidirect
243. #387	C₂²×C₈₉	semidirect
429. C₂	C₈₉×#2569	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×#2569	2
C₂×#400×C₈₉	2
C₂×#398×C₈₉	2
C₂×#387×C₈₉	2
C₂×#385×C₈₉	2
C₂×#380×C₈₉	2
C₂×C₄×C₂²⋊C₄×C₈₉	2
C₂²×#95×C₈₉	2
C₂×#2569	89

Subgroups — C2×C89×#2569 #36412690

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#2569 #36412690