Subgroups — #26034589

Order 11392.

1004 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152351	C₂	1	2	yes	maximal, complemented
2	#19152350	C₂	1	2	yes	maximal, complemented
3	Q₈×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152312	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152307	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152306	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152289	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152284	C₂	1	2	yes	maximal, complemented
9	#19152282	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152253	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152248	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152246	C₂	1	2	yes	maximal, complemented
13	#19152227	C₂	1	2	yes	maximal, complemented
14	#19152226	C₂	1	1	yes	maximal, characteristic, complemented
15	#19152225	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152217	C₂	1	1	yes	maximal, characteristic, complemented
17	#19152212	C₂	1	2	yes	maximal, complemented
18	#19152171	C₂	1	2	yes	maximal, complemented
19	#19152168	C₂	1	2	yes	maximal, complemented
20	C₄⋊Q₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#19152127	C₂	1	1	yes	maximal, characteristic, complemented
22	#19152126	C₂	1	1	yes	maximal, characteristic, complemented
23	#542×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13083574	C₂²	1	2	yes	—
25	C₂×#13083573	C₂²	1	2	yes	—
26	C₂×Q₈×D₈₉	C₂²	1	2	yes	—
27	#15668012	C₂²	1	1	yes	characteristic
28	#15668012	C₂²	1	2	yes	—
29	#15668012	C₂²	1	1	yes	characteristic
30	#15668011	C₂²	1	1	yes	characteristic
31	#15668011	C₂²	1	1	yes	characteristic
32	#15668011	C₂²	1	2	yes	—
33	#15668011	C₂²	1	2	yes	—
34	#15668011	C₂²	1	2	yes	—
35	#15668011	C₂²	1	1	yes	characteristic
36	#15668011	C₂²	1	2	yes	—
37	#15668010	C₂²	1	2	yes	—
38	#15668010	C₂²	1	2	yes	—
39	#15668007	C₂²	1	1	yes	characteristic
40	#15668006	C₂²	1	2	yes	—
41	#15668005	C₂²	1	2	yes	—
42	#15668005	C₂²	1	2	yes	—
43	#15668005	C₂²	1	2	yes	—
44	#15668005	C₂²	1	1	yes	characteristic
45	#15668004	C₂²	1	1	yes	characteristic
46	#15668004	C₂²	1	1	yes	characteristic
47	#15668003	C₂²	1	1	yes	characteristic
48	#15668003	C₂²	1	2	yes	—
49	#15668002	C₂²	1	2	yes	—
50	#15668002	C₂²	1	1	yes	characteristic
51	#15668002	C₂²	1	2	yes	—
52	#15668002	C₂²	1	2	yes	—
53	#15668002	C₂²	1	2	yes	—
54	#15667999	C₂²	1	2	yes	—
55	#15667998	C₂²	1	2	yes	—
56	#15667998	C₂²	1	2	yes	—
57	#15667998	C₂²	1	1	yes	characteristic
58	#15667997	C₂²	1	1	yes	characteristic
59	#15667997	C₂²	1	2	yes	—
60	#15667996	C₂²	1	2	yes	—
61	#15667994	C₂²	1	1	yes	characteristic
62	#15667994	C₂²	1	2	yes	—
63	#15667994	C₂²	1	2	yes	—
64	#15667994	C₂²	1	2	yes	—
65	#15667994	C₂²	1	2	yes	—
66	#15667994	C₂²	1	2	yes	—
67	#15667993	C₂²	1	2	yes	—
68	#15667992	C₂²	1	2	yes	—
69	#15667991	C₂²	1	2	yes	—
70	#15667991	C₂²	1	2	yes	—
71	#15667990	C₂²	1	2	yes	—
72	#15667990	C₂²	1	1	yes	characteristic
73	#15667989	C₂²	1	2	yes	—
74	#15667989	C₂²	1	2	yes	—
75	#15667989	C₂²	1	2	yes	—
76	#15667989	C₂²	1	2	yes	—
77	#15667989	C₂²	1	2	yes	—
78	#15667989	C₂²	1	2	yes	—
79	#15667989	C₂²	1	2	yes	—
80	#15667988	C₂²	1	2	yes	—
81	#15667988	C₂²	1	1	yes	characteristic
82	#15667988	C₂²	1	1	yes	characteristic
83	#15667985	C₂²	1	1	yes	characteristic
84	#15667984	C₂²	1	2	yes	—
85	#15667983	C₂²	1	1	yes	characteristic
86	#15667983	C₂²	1	1	yes	characteristic
87	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic
88	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic
89	C₄×Dic₁₇₈	C₂²	1	2	yes	—
90	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
91	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
92	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
93	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
94	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
95	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
96	#15667972	C₂²	1	2	yes	—
97	#15667972	C₂²	1	2	yes	—
98	#15667971	C₂²	1	1	yes	characteristic
99	#15667970	C₂²	1	2	yes	—
100	#15667970	C₂²	1	1	yes	characteristic
101	#15667969	C₂²	1	2	yes	—
102	#15667969	C₂²	1	1	yes	characteristic
103	#15667968	C₂²	1	2	yes	—
104	#15667968	C₂²	1	2	yes	—
105	C₂×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
106	C₂×#13083553	C₂²	1	2	yes	—
107	C₄⋊C₄×D₈₉	C₂²	1	2	yes	—
108	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
109	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
110	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
111	C₄²×D₈₉	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
113	#126×C₈₉	C₂²	1	2	yes	—
114	#124×C₈₉	C₂²	1	2	yes	—
115	#124×C₈₉	C₂²	1	1	yes	characteristic
116	#123×C₈₉	C₂²	1	2	yes	—
117	C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
118	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
119	#121×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
122	#117×C₈₉	C₂²	1	1	yes	characteristic
123	#13083574	—	4	4	no	—
124	#13083573	—	4	4	no	—
125	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
126	C₂×Dic₁₇₈	C₂³	1	2	yes	—
127	C₂×Dic₁₇₈	C₂³	1	2	yes	—
128	C₂×Dic₁₇₈	C₂³	1	2	yes	—
129	C₂×Dic₁₇₈	C₂³	1	2	yes	—
130	C₂×Dic₁₇₈	C₂³	1	2	yes	—
131	Q₈×D₈₉	—	4	4	no	—
132	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
137	C₂²×Dic₈₉	C₂³	1	2	yes	—
138	C₂²×Dic₈₉	C₂³	1	2	yes	—
139	C₂²×Dic₈₉	C₂³	1	2	yes	—
140	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₈₉	C₂³	1	2	yes	—
142	C₂×C₄×D₈₉	C₂³	1	2	yes	—
143	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₈₉	C₂³	1	2	yes	—
147	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₈₉	C₂³	1	2	yes	—
149	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
150	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
153	C₄⋊Dic₈₉	C₂³	1	2	yes	—
154	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₈₉	C₂³	1	2	yes	—
156	C₄⋊Dic₈₉	C₂³	1	2	yes	—
157	C₄⋊Dic₈₉	C₂³	1	2	yes	—
158	C₄⋊Dic₈₉	C₂³	1	2	yes	—
159	#13083553	C₂³	1	1	yes	characteristic
160	#13083553	C₂³	1	2	yes	—
161	#13083553	C₂³	1	2	yes	—
162	#13083553	C₂³	1	2	yes	—
163	#13083553	C₂³	1	2	yes	—
164	#13083553	C₂³	1	2	yes	—
165	#13083553	C₂³	1	1	yes	characteristic
166	#13083553	C₂³	1	1	yes	characteristic
167	#13083553	C₂³	1	2	yes	—
168	#13083553	C₂³	1	2	yes	—
169	#13083553	C₂³	1	1	yes	characteristic
170	#13083553	C₂³	1	1	yes	characteristic
171	#13083553	C₂³	1	2	yes	—
172	#13083553	C₂³	1	1	yes	characteristic
173	#13083553	C₂³	1	2	yes	—
174	#13083553	C₂³	1	2	yes	—
175	#13083553	C₂³	1	2	yes	—
176	#13083553	C₂³	1	2	yes	—
177	#13083553	C₂³	1	2	yes	—
178	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
179	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
181	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
184	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
185	#13083551	C₂³	1	1	yes	characteristic
186	#13083551	C₂³	1	2	yes	—
187	#13083551	C₂³	1	1	yes	characteristic
188	#13083551	C₂³	1	1	yes	characteristic
189	#13083551	C₂³	1	1	yes	characteristic
190	#13083551	C₂³	1	2	yes	—
191	#13083551	C₂³	1	2	yes	—
192	#13083551	C₂³	1	1	yes	characteristic
193	#13083551	C₂³	1	1	yes	characteristic
194	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
195	C₄×Dic₈₉	C₂³	1	2	yes	—
196	C₄×Dic₈₉	C₂³	1	2	yes	—
197	C₄×Dic₈₉	C₂³	1	2	yes	—
198	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
199	C₄×Dic₈₉	C₂³	1	2	yes	—
200	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
201	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
202	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
203	C₂×Q₈×C₈₉	C₂³	1	2	yes	—
204	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₈₉	C₂³	1	2	yes	—
206	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
208	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
209	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
211	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
214	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
215	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
216	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
222	C₄²×C₈₉	C₂³	1	2	yes	—
223	C₄²×C₈₉	C₂³	1	1	yes	characteristic
224	C₄²×C₈₉	C₂³	1	1	yes	characteristic
225	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
226	C₂³×C₈₉	C₂⁴	1	2	yes	—
227	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
228	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
229	Q₈×C₈₉	—	2	2	no	—
230	Q₈×C₈₉	—	4	2	no	—
231	D₄×C₈₉	—	2	2	no	—
232	D₄×C₈₉	—	4	2	no	—
233	C₂×C₄×C₈₉	—	2	2	no	—
234	C₂×C₄×C₈₉	—	4	2	no	—
235	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
238	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
241	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
243	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
244	C₂²⋊D₈₉	—	2	2	no	—
245	C₂²⋊D₈₉	—	2	4	no	—
246	C₂²⋊D₈₉	—	2	2	no	—
247	C₂²⋊D₈₉	—	4	2	no	—
248	C₂×Dic₈₉	—	2	4	no	—
249	C₂×Dic₈₉	—	4	2	no	—
250	C₂×Dic₈₉	—	4	2	no	—
251	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₈₉	C₂⁴	1	2	yes	—
253	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₈₉	C₂⁴	1	2	yes	—
257	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₈₉	C₂⁴	1	2	yes	—
259	C₂×Dic₈₉	C₂⁴	1	2	yes	—
260	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
261	D₃₅₆	—	2	2	no	—
262	C₄×D₈₉	—	2	2	no	—
263	C₄×D₈₉	—	2	4	no	—
264	C₄×D₈₉	—	2	4	no	—
265	C₄×D₈₉	—	2	2	no	—
266	C₄×D₈₉	—	2	2	no	—
267	C₄×D₈₉	—	2	2	no	—
268	C₄×D₈₉	—	4	2	no	—
269	Dic₁₇₈	—	2	2	no	—
270	Dic₁₇₈	—	4	2	no	—
271	Dic₁₇₈	—	4	2	no	—
272	Dic₁₇₈	—	4	2	no	—
273	Dic₁₇₈	—	4	2	no	—
274	Dic₁₇₈	—	4	2	no	—
275	C₂²×C₈₉	—	2	1	no	—
276	C₂²×C₈₉	—	2	2	no	—
277	C₂²×C₈₉	—	2	2	no	—
278	C₂²×C₈₉	—	2	1	no	—
279	C₂²×C₈₉	—	2	1	no	—
280	C₂²×C₈₉	—	2	2	no	—
281	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
282	C₂×D₈₉	—	2	1	no	—
283	C₂×D₈₉	—	2	1	no	—
284	C₂×D₈₉	—	2	1	no	—
285	C₂×D₈₉	—	2	1	no	—
286	C₂×D₈₉	—	2	1	no	—
287	C₂×D₈₉	H(5,𝔽₂)	1	2	yes	—
288	C₄×C₈₉	—	2	2	no	—
289	C₄×C₈₉	—	2	1	no	—
290	C₄×C₈₉	—	2	1	no	—
291	C₄×C₈₉	—	2	2	no	—
292	C₄×C₈₉	—	2	1	no	—
293	C₄×C₈₉	—	2	1	no	—
294	C₄×C₈₉	—	2	1	no	—
295	C₄×C₈₉	—	2	2	no	—
296	C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
297	Dic₈₉	—	2	1	no	—
298	Dic₈₉	—	2	2	no	—
299	Dic₈₉	—	2	2	no	—
300	Dic₈₉	—	2	2	no	—
301	Dic₈₉	—	2	1	no	—
302	Dic₈₉	—	2	1	no	—
303	Dic₈₉	—	2	1	no	—
304	Dic₈₉	—	2	1	no	—
305	Dic₈₉	—	2	2	no	—
306	Dic₈₉	2₋¹⁺⁴	1	2	yes	—
307	C₂×C₈₉	—	4	1	no	—
308	C₂×C₈₉	—	4	2	no	—
309	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
310	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
311	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
312	D₈₉	—	2	2	no	—
313	D₈₉	—	4	1	no	—
314	#3544	—	89	1	no	maximal, Sylow
315	C₈₉	#3544	1	1	yes	characteristic, complemented, Sylow
316	#563	—	89	2	no	—
317	#563	—	89	2	no	—
318	Q₈²	—	89	1	no	—
319	#555	—	89	1	no	—
320	#554	—	89	1	no	—
321	#554	—	89	1	no	—
322	#552	—	89	2	no	—
323	#552	—	89	1	no	—
324	#552	—	89	1	no	—
325	#547	—	89	2	no	—
326	#547	—	89	1	no	—
327	#547	—	89	1	no	—
328	#544	—	89	1	no	—
329	#544	—	89	2	no	—
330	#544	—	89	1	no	—
331	#542	—	89	2	no	—
332	#542	—	89	1	no	—
333	#542	D₈₉	1	1	yes	characteristic, complemented
334	#536	—	89	2	no	—
335	#536	—	89	2	no	—
336	C₂×C₄⋊Q₈	—	89	1	no	—
337	#529	—	89	1	no	—
338	#529	—	89	1	no	—
339	C₂×#41	—	89	2	no	—
340	C₂×#41	—	89	2	no	—
341	C₂²×Q₈	—	89	2	no	—
342	C₄⋊Q₈	—	89	2	no	—
343	C₄⋊Q₈	—	89	2	no	—
344	C₄⋊Q₈	—	89	1	no	—
345	C₄⋊Q₈	—	89	1	no	—
346	C₄⋊Q₈	—	89	2	no	—
347	C₄⋊Q₈	—	89	2	no	—
348	C₄⋊Q₈	—	89	2	no	—
349	C₄⋊Q₈	—	89	2	no	—
350	C₄⋊Q₈	—	89	1	no	—
351	C₄⋊Q₈	—	89	1	no	—
352	C₄⋊Q₈	—	89	2	no	—
353	C₄⋊Q₈	—	89	1	no	—
354	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
355	#126	—	89	1	no	—
356	#126	—	89	2	no	—
357	#126	—	89	1	no	—
358	#126	—	89	2	no	—
359	#126	—	89	2	no	—
360	#126	—	89	2	no	—
361	#126	C₂×D₈₉	1	2	yes	—
362	#125	—	89	1	no	—
363	#125	—	89	2	no	—
364	#125	—	89	2	no	—
365	#125	—	89	2	no	—
366	#125	—	89	2	no	—
367	#125	—	89	1	no	—
368	#125	—	89	2	no	—
369	#125	—	89	1	no	—
370	#125	—	89	1	no	—
371	#124	—	89	2	no	—
372	#124	—	89	1	no	—
373	#124	—	89	2	no	—
374	#124	—	89	2	no	—
375	#124	C₂×D₈₉	1	1	yes	characteristic
376	#124	C₂×D₈₉	1	2	yes	—
377	#123	—	89	2	no	—
378	#123	—	89	1	no	—
379	#123	—	89	2	no	—
380	#123	—	89	2	no	—
381	#123	—	89	1	no	—
382	#123	—	89	2	no	—
383	#123	—	89	2	no	—
384	#123	—	89	2	no	—
385	#123	—	89	2	no	—
386	#123	—	89	2	no	—
387	#123	C₂×D₈₉	1	2	yes	—
388	C₂²⋊Q₈	—	89	1	no	—
389	C₂²⋊Q₈	—	89	2	no	—
390	C₂²⋊Q₈	—	89	1	no	—
391	C₂²⋊Q₈	—	89	2	no	—
392	C₂²⋊Q₈	—	89	2	no	—
393	C₂²⋊Q₈	—	89	1	no	—
394	C₂²⋊Q₈	—	89	2	no	—
395	C₂²⋊Q₈	—	89	2	no	—
396	C₂²⋊Q₈	—	89	2	no	—
397	C₂²⋊Q₈	—	89	2	no	—
398	C₂²⋊Q₈	—	89	2	no	—
399	C₂²⋊Q₈	—	89	2	no	—
400	C₂²⋊Q₈	—	89	2	no	—
401	C₂²⋊Q₈	—	89	2	no	—
402	C₂²⋊Q₈	—	89	2	no	—
403	C₂²⋊Q₈	C₂×D₈₉	1	2	yes	—
404	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
405	#121	—	89	1	no	—
406	#121	—	89	1	no	—
407	#121	—	89	2	no	—
408	#121	—	89	1	no	—
409	#121	C₂×D₈₉	1	1	yes	characteristic
410	C₄×Q₈	—	89	1	no	—
411	C₄×Q₈	—	89	1	no	—
412	C₄×Q₈	—	89	1	no	—
413	C₄×Q₈	—	89	2	no	—
414	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
415	C₄×D₄	—	89	1	no	—
416	C₄×D₄	—	89	1	no	—
417	C₄×D₄	—	89	1	no	—
418	C₄×D₄	—	89	1	no	—
419	C₄×D₄	—	89	2	no	—
420	C₄×D₄	—	89	2	no	—
421	C₄×D₄	—	89	1	no	—
422	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
423	#117	—	89	1	no	—
424	#117	—	89	2	no	—
425	#117	—	89	1	no	—
426	#117	—	89	2	no	—
427	#117	—	89	2	no	—
428	#117	—	89	1	no	—
429	#117	—	89	2	no	—
430	#117	C₂×D₈₉	1	1	yes	characteristic
431	C₂×C₄⋊C₄	—	89	2	no	—
432	C₂×C₄⋊C₄	—	89	1	no	—
433	C₂×C₄⋊C₄	—	89	2	no	—
434	C₂×C₄⋊C₄	—	89	1	no	—
435	C₂×C₄⋊C₄	—	89	1	no	—
436	C₂×C₄⋊C₄	—	89	1	no	—
437	C₂×C₄²	—	89	1	no	—
438	#41	—	356	4	no	—
439	#41	—	356	4	no	—
440	C₂×Q₈	—	89	2	no	—
441	C₂×Q₈	—	89	2	no	—
442	C₂×Q₈	—	89	2	no	—
443	C₂×Q₈	—	89	2	no	—
444	C₂×Q₈	—	89	2	no	—
445	C₂×Q₈	—	89	1	no	—
446	C₂×Q₈	—	356	4	no	—
447	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
448	C₂×Q₈	C₂²×D₈₉	1	2	yes	—
449	C₂×D₄	—	89	2	no	—
450	C₂×D₄	—	89	1	no	—
451	C₂×D₄	—	89	1	no	—
452	C₂×D₄	—	89	2	no	—
453	C₂×D₄	—	89	1	no	—
454	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
455	C₂×D₄	C₂²×D₈₉	1	2	yes	—
456	C₂²×C₄	—	89	2	no	—
457	C₂²×C₄	—	89	2	no	—
458	C₂²×C₄	—	89	2	no	—
459	C₂²×C₄	—	89	2	no	—
460	C₂²×C₄	—	89	1	no	—
461	C₂²×C₄	—	89	1	no	—
462	C₂²×C₄	—	89	1	no	—
463	C₂²×C₄	—	89	2	no	—
464	C₂²×C₄	—	89	2	no	—
465	C₂²×C₄	—	89	1	no	—
466	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
467	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
468	C₄⋊C₄	—	89	2	no	—
469	C₄⋊C₄	—	89	1	no	—
470	C₄⋊C₄	—	89	1	no	—
471	C₄⋊C₄	—	89	1	no	—
472	C₄⋊C₄	—	89	2	no	—
473	C₄⋊C₄	—	89	1	no	—
474	C₄⋊C₄	—	89	2	no	—
475	C₄⋊C₄	—	89	2	no	—
476	C₄⋊C₄	—	89	2	no	—
477	C₄⋊C₄	—	89	2	no	—
478	C₄⋊C₄	—	89	2	no	—
479	C₄⋊C₄	—	89	2	no	—
480	C₄⋊C₄	—	89	2	no	—
481	C₄⋊C₄	—	89	1	no	—
482	C₄⋊C₄	—	89	1	no	—
483	C₄⋊C₄	—	89	2	no	—
484	C₄⋊C₄	—	89	2	no	—
485	C₄⋊C₄	—	89	2	no	—
486	C₄⋊C₄	—	89	2	no	—
487	C₄⋊C₄	—	89	1	no	—
488	C₄⋊C₄	—	89	1	no	—
489	C₄⋊C₄	—	89	2	no	—
490	C₄⋊C₄	—	89	1	no	—
491	C₄⋊C₄	—	89	2	no	—
492	C₄⋊C₄	—	89	1	no	—
493	C₄⋊C₄	—	89	1	no	—
494	C₄⋊C₄	—	89	2	no	—
495	C₄⋊C₄	—	89	1	no	—
496	C₄⋊C₄	—	89	2	no	—
497	C₄⋊C₄	—	89	2	no	—
498	C₄⋊C₄	—	89	2	no	—
499	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
502	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
503	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
506	C₂²⋊C₄	—	89	2	no	—
507	C₂²⋊C₄	—	89	2	no	—
508	C₂²⋊C₄	—	89	2	no	—
509	C₂²⋊C₄	—	89	2	no	—
510	C₂²⋊C₄	—	89	2	no	—
511	C₂²⋊C₄	—	89	1	no	—
512	C₂²⋊C₄	—	89	1	no	—
513	C₂²⋊C₄	—	89	1	no	—
514	C₂²⋊C₄	—	89	2	no	—
515	C₂²⋊C₄	—	89	1	no	—
516	C₂²⋊C₄	—	89	1	no	—
517	C₂²⋊C₄	—	89	2	no	—
518	C₂²⋊C₄	—	89	1	no	—
519	C₂²⋊C₄	—	89	2	no	—
520	C₂²⋊C₄	—	89	1	no	—
521	C₂²⋊C₄	—	89	1	no	—
522	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
523	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
524	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
525	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
526	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
527	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
528	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
529	C₄²	—	89	1	no	—
530	C₄²	—	89	1	no	—
531	C₄²	—	89	1	no	—
532	C₄²	—	89	2	no	—
533	C₄²	—	89	2	no	—
534	C₄²	—	89	2	no	—
535	C₄²	—	89	1	no	—
536	C₄²	—	89	2	no	—
537	C₄²	C₂²×D₈₉	1	1	yes	characteristic
538	C₄²	C₂²×D₈₉	1	2	yes	—
539	C₄²	C₂²×D₈₉	1	1	yes	characteristic
540	C₂³	—	89	1	no	—
541	C₂³	—	89	1	no	—
542	C₂³	C₂³×D₈₉	1	2	yes	—
543	C₂³	C₂³×D₈₉	1	1	yes	characteristic
544	Q₈	—	2	2	no	—
545	Q₈	—	4	2	no	—
546	Q₈	—	356	2	no	—
547	Q₈	—	356	2	no	—
548	Q₈	—	356	2	no	—
549	Q₈	—	356	2	no	—
550	Q₈	—	356	2	no	—
551	Q₈	—	178	2	no	—
552	D₄	—	2	2	no	—
553	D₄	—	4	2	no	—
554	D₄	—	356	2	no	—
555	D₄	—	178	2	no	—
556	D₄	—	178	2	no	—
557	D₄	—	178	4	no	—
558	D₄	—	178	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	89	1	no	—
562	C₂×C₄	—	89	1	no	—
563	C₂×C₄	—	89	2	no	—
564	C₂×C₄	—	89	1	no	—
565	C₂×C₄	—	89	1	no	—
566	C₂×C₄	—	89	1	no	—
567	C₂×C₄	—	89	2	no	—
568	C₂×C₄	—	89	1	no	—
569	C₂×C₄	—	89	2	no	—
570	C₂×C₄	—	89	2	no	—
571	C₂×C₄	—	356	2	no	—
572	C₂×C₄	—	356	2	no	—
573	C₂×C₄	—	356	2	no	—
574	C₂×C₄	—	178	2	no	—
575	C₂×C₄	—	178	2	no	—
576	C₂×C₄	—	178	4	no	—
577	C₂×C₄	—	178	4	no	—
578	C₂×C₄	—	178	4	no	—
579	C₂×C₄	—	178	2	no	—
580	C₂×C₄	—	178	2	no	—
581	C₂×C₄	C₂³×D₈₉	1	2	yes	—
582	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
583	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
584	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₈₉	1	2	yes	—
586	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
587	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
588	C₂×C₄	C₂³×D₈₉	1	2	yes	—
589	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
590	C₂²	—	2	2	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	89	2	no	—
597	C₂²	—	178	1	no	—
598	C₂²	—	178	1	no	—
599	C₂²	—	178	1	no	—
600	C₂²	—	178	1	no	—
601	C₂²	—	178	1	no	—
602	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
603	C₄	—	2	1	no	—
604	C₄	—	2	2	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	1	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	2	no	—
611	C₄	—	89	2	no	—
612	C₄	—	178	2	no	—
613	C₄	—	178	2	no	—
614	C₄	—	178	1	no	—
615	C₄	—	178	2	no	—
616	C₄	—	178	1	no	—
617	C₄	—	178	2	no	—
618	C₄	—	178	1	no	—
619	C₄	—	178	1	no	—
620	C₄	—	178	1	no	—
621	C₄	#15668059	1	2	yes	—
622	C₂	—	4	2	no	—
623	C₂	—	4	1	no	—
624	C₂	—	356	1	no	—
625	C₂	—	178	2	no	—
626	C₂	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
627	C₂	2₋¹⁺⁴×D₈₉	1	1	yes	characteristic
628	C₂	C₂×#15668059	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#542×C₈₉	C₂
hypercenter	#542	D₈₉
hypocenter	C₈₉	#3544
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #19152351	C₂	semidirect
2. #19152350	C₂	semidirect
3. Q₈×Dic₁₇₈	C₂	semidirect
4. #19152312	C₂	semidirect
5. #19152307	C₂	semidirect
6. #19152306	C₂	semidirect
7. #19152289	C₂	semidirect
8. #19152284	C₂	semidirect
9. #19152282	C₂	semidirect
10. #19152253	C₂	semidirect
11. #19152248	C₂	semidirect
12. #19152246	C₂	semidirect
13. #19152227	C₂	semidirect
14. #19152226	C₂	semidirect
15. #19152225	C₂	semidirect
16. #19152217	C₂	semidirect
17. #19152212	C₂	semidirect
18. #19152171	C₂	semidirect
19. #19152168	C₂	semidirect
20. C₄⋊Q₈×D₈₉	C₂	semidirect
21. #19152127	C₂	semidirect
22. #19152126	C₂	semidirect
23. #542×C₈₉	C₂	semidirect
315. C₈₉	#3544	semidirect
333. #542	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152351	2
#19152350	2
Q₈×Dic₁₇₈	2
#19152312	2
#19152307	2
#19152306	2
#19152289	2
#19152284	2
#19152282	2
#19152253	2
#19152248	2
#19152246	2
#19152227	2
#19152226	2
#19152225	2
#19152217	2
#19152212	2
#19152171	2
#19152168	2
C₄⋊Q₈×D₈₉	2
#19152127	2
#19152126	2
#542×C₈₉	2
#3544	89