Subgroups — #18090372

Order 4864.

866 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926545	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926511	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926313	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926312	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926308	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11926306	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#417	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂²×#64520	C₂²	1	1	yes	characteristic
10	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
12	#11926545	—	2	2	no	—
13	#11926545	—	2	2	no	—
14	C₂×#10597292	—	2	1	no	—
15	C₂×#10597289	—	2	1	no	—
16	#11926511	—	2	2	no	—
17	#11926511	—	2	2	no	—
18	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
19	#11926313	—	2	2	no	—
20	#11926312	—	2	2	no	—
21	#11926308	—	2	2	no	—
22	#11926306	—	2	2	no	—
23	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#417	—	2	2	no	—
27	C₁₉×#417	C₄	1	4	yes	complemented
28	C₂×C₁₉×#103	—	2	1	no	—
29	C₂×C₁₉×#102	—	2	1	no	—
30	C₂×#41×C₁₉	—	2	1	no	—
31	C₂×#41×C₁₉	—	2	1	no	—
32	C₂×#41×C₁₉	—	2	1	no	—
33	C₂×#41×C₁₉	—	2	1	no	—
34	C₂×#41×C₁₉	—	2	1	no	—
35	C₂×#41×C₁₉	—	2	1	no	—
36	C₂×#41×C₁₉	—	2	1	no	—
37	C₂×#41×C₁₉	—	2	1	no	—
38	C₂×#41×C₁₉	—	2	1	no	—
39	C₂×#41×C₁₉	—	2	1	no	—
40	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
41	C₂×#41×C₁₉	D₄	1	2	yes	—
42	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
43	C₂²×D₄×C₁₉	—	2	1	no	—
44	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂³×C₄×C₁₉	—	2	1	no	—
47	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂³×Dic₁₉	—	2	1	no	—
49	C₂×M₁₆×C₁₉	—	2	1	no	—
50	C₂×M₁₆×C₁₉	—	2	1	no	—
51	C₂×M₁₆×C₁₉	—	2	1	no	—
52	C₂×M₁₆×C₁₉	—	2	1	no	—
53	C₂×M₁₆×C₁₉	—	2	1	no	—
54	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
55	C₂²×C₈×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
62	C₂×C₄⋊Dic₁₉	—	2	1	no	—
63	C₂×C₄⋊Dic₁₉	—	2	1	no	—
64	C₂×C₄⋊Dic₁₉	—	2	1	no	—
65	C₂×C₄⋊Dic₁₉	—	2	1	no	—
66	C₂×C₄⋊Dic₁₉	—	2	1	no	—
67	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
68	C₂×#64520	—	2	1	no	—
69	C₂×#64520	—	2	1	no	—
70	C₂×#64520	—	2	1	no	—
71	C₂×#64520	—	2	1	no	—
72	C₂×#64520	—	2	1	no	—
73	C₂×#64520	—	2	1	no	—
74	C₂×#64520	—	2	1	no	—
75	C₂×#64520	—	2	1	no	—
76	C₂×#64520	—	2	1	no	—
77	C₂×#64520	—	2	1	no	—
78	C₂×#64520	D₄	1	2	yes	—
79	C₂×#64520	D₄	1	2	yes	—
80	C₂²×C₁₉⋊C₈	—	2	1	no	—
81	C₂²×C₁₉⋊C₈	—	2	1	no	—
82	C₂²×C₁₉⋊C₈	—	2	1	no	—
83	C₂²×C₁₉⋊C₈	—	2	1	no	—
84	C₂²×C₁₉⋊C₈	—	2	1	no	—
85	C₂²×C₁₉⋊C₈	—	2	1	no	—
86	C₂²×C₁₉⋊C₈	—	2	1	no	—
87	C₂²×C₁₉⋊C₈	—	2	1	no	—
88	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
89	C₁₉×#103	—	2	4	no	—
90	C₁₉×#102	—	2	4	no	—
91	#10597292	—	2	4	no	—
92	#10597289	—	2	4	no	—
93	C₂²⋊(C₁₉⋊C₈)	—	2	8	no	—
94	C₂⁴×C₁₉	—	2	1	no	—
95	C₂⁴×C₁₉	#41	1	1	yes	characteristic
96	#41×C₁₉	—	2	2	no	—
97	#41×C₁₉	—	2	2	no	—
98	#41×C₁₉	—	2	2	no	—
99	#41×C₁₉	—	2	2	no	—
100	#41×C₁₉	—	2	2	no	—
101	#41×C₁₉	—	2	2	no	—
102	#41×C₁₉	—	2	2	no	—
103	#41×C₁₉	—	2	2	no	—
104	#41×C₁₉	—	4	1	no	—
105	#41×C₁₉	—	4	1	no	—
106	#41×C₁₉	—	4	1	no	—
107	#41×C₁₉	—	4	1	no	—
108	#41×C₁₉	—	4	1	no	—
109	#41×C₁₉	—	4	1	no	—
110	#41×C₁₉	—	4	1	no	—
111	#41×C₁₉	—	4	1	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	1	no	—
114	C₂×Q₈×C₁₉	—	2	1	no	—
115	C₂×Q₈×C₁₉	—	2	1	no	—
116	C₂×Q₈×C₁₉	—	2	1	no	—
117	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
118	C₂×D₄×C₁₉	—	2	2	no	—
119	C₂×D₄×C₁₉	—	2	2	no	—
120	C₂×D₄×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	2	1	no	—
123	C₂×D₄×C₁₉	—	2	1	no	—
124	C₂×D₄×C₁₉	—	2	1	no	—
125	C₂×D₄×C₁₉	—	4	1	no	—
126	C₂×D₄×C₁₉	—	4	1	no	—
127	C₂×D₄×C₁₉	—	4	1	no	—
128	C₂×D₄×C₁₉	—	4	1	no	—
129	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
130	C₂²×C₄×C₁₉	—	2	1	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	4	1	no	—
135	C₂²×C₄×C₁₉	—	4	1	no	—
136	C₂²×C₄×C₁₉	—	4	1	no	—
137	C₂²×C₄×C₁₉	—	4	1	no	—
138	C₂²×C₄×C₁₉	—	4	1	no	—
139	C₂²×C₄×C₁₉	—	4	1	no	—
140	C₂²×C₄×C₁₉	—	8	1	no	—
141	C₂²×C₄×C₁₉	—	8	1	no	—
142	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
156	C₂²×Dic₁₉	—	2	2	no	—
157	C₂²×Dic₁₉	—	4	1	no	—
158	C₂²×Dic₁₉	—	4	1	no	—
159	C₂²×Dic₁₉	—	8	1	no	—
160	C₂²×Dic₁₉	—	8	1	no	—
161	M₁₆×C₁₉	—	2	2	no	—
162	M₁₆×C₁₉	—	2	2	no	—
163	M₁₆×C₁₉	—	4	1	no	—
164	M₁₆×C₁₉	—	4	1	no	—
165	C₂×C₈×C₁₉	—	2	2	no	—
166	C₂×C₈×C₁₉	—	4	1	no	—
167	C₂×C₈×C₁₉	—	4	1	no	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	2	2	no	—
170	C₄⋊C₄×C₁₉	—	4	1	no	—
171	C₄⋊C₄×C₁₉	—	4	1	no	—
172	C₄⋊Dic₁₉	—	2	2	no	—
173	C₄⋊Dic₁₉	—	2	2	no	—
174	C₄⋊Dic₁₉	—	4	1	no	—
175	C₄⋊Dic₁₉	—	4	1	no	—
176	#64520	—	2	2	no	—
177	#64520	—	2	2	no	—
178	#64520	—	2	2	no	—
179	#64520	—	2	2	no	—
180	#64520	—	4	1	no	—
181	#64520	—	4	1	no	—
182	#64520	—	4	1	no	—
183	#64520	—	4	1	no	—
184	C₂×C₁₉⋊C₈	—	2	2	no	—
185	C₂×C₁₉⋊C₈	—	2	2	no	—
186	C₂×C₁₉⋊C₈	—	2	2	no	—
187	C₂×C₁₉⋊C₈	—	2	2	no	—
188	C₂×C₁₉⋊C₈	—	2	2	no	—
189	C₂×C₁₉⋊C₈	—	4	1	no	—
190	C₂×C₁₉⋊C₈	—	4	1	no	—
191	C₂×C₁₉⋊C₈	—	4	1	no	—
192	C₂×C₁₉⋊C₈	—	4	1	no	—
193	C₂×C₁₉⋊C₈	—	4	1	no	—
194	C₂×C₁₉⋊C₈	—	4	1	no	—
195	C₂×C₁₉⋊C₈	—	4	1	no	—
196	C₂×C₁₉⋊C₈	—	4	1	no	—
197	#11192	—	19	1	no	maximal, Sylow
198	C₂³×C₁₉	—	2	1	no	—
199	C₂³×C₁₉	—	2	1	no	—
200	C₂³×C₁₉	—	2	1	no	—
201	C₂³×C₁₉	—	2	1	no	—
202	C₂³×C₁₉	—	2	2	no	—
203	C₂³×C₁₉	—	4	1	no	—
204	C₂³×C₁₉	—	4	1	no	—
205	C₂³×C₁₉	—	4	1	no	—
206	C₂³×C₁₉	—	4	1	no	—
207	C₂³×C₁₉	—	4	1	no	—
208	C₂³×C₁₉	—	4	1	no	—
209	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
210	C₂³×C₁₉	#121	1	1	yes	characteristic
211	C₂³×C₁₉	#123	1	1	yes	characteristic
212	C₂³×C₁₉	#123	1	1	yes	characteristic
213	C₂³×C₁₉	#124	1	1	yes	characteristic
214	C₂³×C₁₉	#126	1	1	yes	characteristic
215	C₂³×C₁₉	#126	1	1	yes	characteristic
216	Q₈×C₁₉	—	2	2	no	—
217	Q₈×C₁₉	—	2	2	no	—
218	Q₈×C₁₉	—	4	1	no	—
219	Q₈×C₁₉	—	4	1	no	—
220	D₄×C₁₉	—	2	2	no	—
221	D₄×C₁₉	—	2	2	no	—
222	D₄×C₁₉	—	4	2	no	—
223	D₄×C₁₉	—	4	2	no	—
224	D₄×C₁₉	—	4	2	no	—
225	D₄×C₁₉	—	4	2	no	—
226	D₄×C₁₉	—	4	1	no	—
227	D₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	4	2	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	8	2	no	—
237	C₂×C₄×C₁₉	—	8	1	no	—
238	C₂×C₄×C₁₉	—	8	1	no	—
239	C₂×C₄×C₁₉	—	8	2	no	—
240	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
242	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
247	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
248	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
249	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
250	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
251	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
252	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
253	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
254	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
255	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
256	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
257	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
258	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
259	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
260	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
261	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
262	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
263	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
264	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
265	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
266	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
267	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
268	C₂×Dic₁₉	—	4	2	no	—
269	C₂×Dic₁₉	—	8	2	no	—
270	C₂×Dic₁₉	—	8	1	no	—
271	C₂×Dic₁₉	—	8	1	no	—
272	C₂×Dic₁₉	—	8	2	no	—
273	C₈×C₁₉	—	4	2	no	—
274	C₁₉⋊C₈	—	4	2	no	—
275	C₁₉⋊C₈	—	4	2	no	—
276	C₁₉⋊C₈	—	4	2	no	—
277	C₂×#417	—	19	1	no	—
278	C₂×#417	D₁₉	1	1	yes	characteristic
279	C₂×#408	—	19	1	no	—
280	C₂×#343	—	19	1	no	—
281	C₂×#343	—	19	1	no	—
282	C₂×#341	—	19	1	no	—
283	C₂×#340	—	19	1	no	—
284	C₂²×C₁₉	—	2	1	no	—
285	C₂²×C₁₉	—	2	1	no	—
286	C₂²×C₁₉	—	2	1	no	—
287	C₂²×C₁₉	—	2	1	no	—
288	C₂²×C₁₉	—	2	1	no	—
289	C₂²×C₁₉	—	2	1	no	—
290	C₂²×C₁₉	—	2	1	no	—
291	C₂²×C₁₉	—	2	1	no	—
292	C₂²×C₁₉	—	2	1	no	—
293	C₂²×C₁₉	—	2	1	no	—
294	C₂²×C₁₉	—	2	1	no	—
295	C₂²×C₁₉	—	2	1	no	—
296	C₂²×C₁₉	—	4	2	no	—
297	C₂²×C₁₉	—	4	2	no	—
298	C₂²×C₁₉	—	4	2	no	—
299	C₂²×C₁₉	—	8	1	no	—
300	C₂²×C₁₉	—	8	1	no	—
301	C₂²×C₁₉	—	8	1	no	—
302	C₂²×C₁₉	—	8	1	no	—
303	C₂²×C₁₉	#386	1	1	yes	characteristic
304	C₂²×C₁₉	#388	1	1	yes	characteristic
305	C₂²×C₁₉	#388	1	1	yes	characteristic
306	C₂²×C₁₉	#394	1	1	yes	characteristic
307	C₂²×C₁₉	#397	1	1	yes	characteristic
308	C₂²×C₁₉	#397	1	1	yes	characteristic
309	C₂²×C₁₉	#397	1	1	yes	characteristic
310	C₂²×C₁₉	#471	1	1	yes	characteristic
311	C₂²×C₁₉	#471	1	1	yes	characteristic
312	C₂²×C₁₉	#472	1	1	yes	characteristic
313	C₂²×C₁₉	#473	1	1	yes	characteristic
314	C₄×C₁₉	—	4	2	no	—
315	C₄×C₁₉	—	8	2	no	—
316	C₄×C₁₉	#381	1	1	yes	characteristic
317	C₄×C₁₉	#386	1	1	yes	characteristic
318	C₄×C₁₉	#388	1	1	yes	characteristic
319	C₄×C₁₉	#388	1	1	yes	characteristic
320	C₄×C₁₉	#394	1	1	yes	characteristic
321	C₄×C₁₉	#394	1	1	yes	characteristic
322	C₄×C₁₉	#394	1	1	yes	characteristic
323	C₄×C₁₉	#397	1	1	yes	characteristic
324	Dic₁₉	—	8	2	no	—
325	C₂²×#41	C₂×D₁₉	1	1	yes	characteristic
326	C₂²×M₁₆	—	19	1	no	—
327	C₂²×M₁₆	—	19	1	no	—
328	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
329	C₂³×C₈	—	19	1	no	—
330	C₂²×C₄⋊C₄	—	19	1	no	—
331	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
332	#417	—	2	2	no	—
333	#417	—	38	2	no	—
334	#417	—	38	2	no	—
335	#417	Dic₁₉	1	4	yes	complemented
336	C₂×#103	—	2	1	no	—
337	C₂×#103	—	38	1	no	—
338	C₂×#102	—	2	1	no	—
339	C₂×#102	—	38	1	no	—
340	#408	—	38	2	no	—
341	#408	—	38	2	no	—
342	C₂×C₂²⋊C₈	—	38	2	no	—
343	#343	—	38	2	no	—
344	#343	—	38	2	no	—
345	#341	—	38	2	no	—
346	#340	—	38	2	no	—
347	C₂×C₁₉	—	2	1	no	—
348	C₂×C₁₉	—	2	1	no	—
349	C₂×C₁₉	—	2	1	no	—
350	C₂×C₁₉	—	2	1	no	—
351	C₂×C₁₉	—	8	2	no	—
352	C₂×C₁₉	#1440	1	1	yes	characteristic
353	C₂×C₁₉	#1907	1	1	yes	characteristic
354	C₂×C₁₉	#1908	1	1	yes	characteristic
355	C₂×C₁₉	#2051	1	1	yes	characteristic
356	C₂×C₁₉	#2052	1	1	yes	characteristic
357	C₂×C₁₉	#2078	1	1	yes	characteristic
358	C₂×C₁₉	#2079	1	1	yes	characteristic
359	C₂×#41	—	2	1	no	—
360	C₂×#41	—	2	1	no	—
361	C₂×#41	—	2	1	no	—
362	C₂×#41	—	2	1	no	—
363	C₂×#41	—	2	1	no	—
364	C₂×#41	—	2	1	no	—
365	C₂×#41	—	2	1	no	—
366	C₂×#41	—	2	1	no	—
367	C₂×#41	—	2	1	no	—
368	C₂×#41	—	2	1	no	—
369	C₂×#41	C₂×Dic₁₉	1	2	yes	—
370	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
371	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
372	C₂²×D₄	—	2	1	no	—
373	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
374	C₂³×C₄	—	2	1	no	—
375	C₂³×C₄	—	2	1	no	—
376	C₂³×C₄	—	38	1	no	—
377	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
378	C₂×M₁₆	—	2	1	no	—
379	C₂×M₁₆	—	2	1	no	—
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	—	19	2	no	—
384	C₂×M₁₆	—	19	2	no	—
385	C₂×M₁₆	—	38	1	no	—
386	C₂×M₁₆	—	38	1	no	—
387	C₂×M₁₆	—	38	1	no	—
388	C₂×M₁₆	—	38	1	no	—
389	C₂×M₁₆	—	38	1	no	—
390	C₂×M₁₆	—	38	1	no	—
391	C₂×M₁₆	—	38	1	no	—
392	C₂×M₁₆	—	38	1	no	—
393	C₂×M₁₆	—	38	1	no	—
394	C₂×M₁₆	—	38	1	no	—
395	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
396	C₂²×C₈	—	2	1	no	—
397	C₂²×C₈	—	19	2	no	—
398	C₂²×C₈	—	38	1	no	—
399	C₂²×C₈	—	38	1	no	—
400	C₂²×C₈	—	38	1	no	—
401	C₂²×C₈	—	38	1	no	—
402	C₂²×C₈	—	38	1	no	—
403	C₂²×C₈	—	38	1	no	—
404	C₂²×C₈	—	38	1	no	—
405	C₂²×C₈	—	38	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	19	2	no	—
412	C₂×C₄⋊C₄	—	38	1	no	—
413	C₂×C₄⋊C₄	—	38	1	no	—
414	C₂×C₄⋊C₄	—	38	1	no	—
415	C₂×C₄⋊C₄	—	38	1	no	—
416	C₂×C₄⋊C₄	—	38	1	no	—
417	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
418	#103	—	2	4	no	—
419	#103	—	38	4	no	—
420	#102	—	2	4	no	—
421	#102	—	38	4	no	—
422	C₂²⋊C₈	—	38	8	no	—
423	C₁₉	#11192	1	1	yes	characteristic, complemented, Sylow
424	C₂⁴	—	2	1	no	—
425	C₂⁴	#64543	1	1	yes	characteristic
426	#41	—	2	2	no	—
427	#41	—	2	2	no	—
428	#41	—	2	2	no	—
429	#41	—	2	2	no	—
430	#41	—	2	2	no	—
431	#41	—	2	2	no	—
432	#41	—	2	2	no	—
433	#41	—	2	2	no	—
434	#41	—	4	1	no	—
435	#41	—	4	1	no	—
436	#41	—	4	1	no	—
437	#41	—	4	1	no	—
438	#41	—	4	1	no	—
439	#41	—	4	1	no	—
440	#41	—	4	1	no	—
441	#41	—	4	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	4	1	no	—
456	C₂×D₄	—	4	1	no	—
457	C₂×D₄	—	4	1	no	—
458	C₂×D₄	—	4	1	no	—
459	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	4	1	no	—
465	C₂²×C₄	—	4	1	no	—
466	C₂²×C₄	—	4	1	no	—
467	C₂²×C₄	—	4	1	no	—
468	C₂²×C₄	—	4	1	no	—
469	C₂²×C₄	—	4	1	no	—
470	C₂²×C₄	—	8	1	no	—
471	C₂²×C₄	—	8	1	no	—
472	C₂²×C₄	—	38	2	no	—
473	C₂²×C₄	—	76	1	no	—
474	C₂²×C₄	—	76	1	no	—
475	C₂²×C₄	—	152	1	no	—
476	C₂²×C₄	—	152	1	no	—
477	C₂²×C₄	#64541	1	1	yes	characteristic
478	C₂²×C₄	#64541	1	1	yes	characteristic
479	C₂²×C₄	#64541	1	1	yes	characteristic
480	C₂²×C₄	#64541	1	1	yes	characteristic
481	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
482	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
483	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
484	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
485	C₂²×C₄	#64543	1	1	yes	characteristic
486	C₂²×C₄	#64543	1	1	yes	characteristic
487	C₂²×C₄	#64543	1	1	yes	characteristic
488	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
489	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
490	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
491	M₁₆	—	2	2	no	—
492	M₁₆	—	2	2	no	—
493	M₁₆	—	4	1	no	—
494	M₁₆	—	4	1	no	—
495	M₁₆	—	38	2	no	—
496	M₁₆	—	38	2	no	—
497	M₁₆	—	38	2	no	—
498	M₁₆	—	38	2	no	—
499	M₁₆	—	76	1	no	—
500	M₁₆	—	76	1	no	—
501	M₁₆	—	76	1	no	—
502	M₁₆	—	76	1	no	—
503	C₂×C₈	—	2	2	no	—
504	C₂×C₈	—	4	1	no	—
505	C₂×C₈	—	4	1	no	—
506	C₂×C₈	—	38	2	no	—
507	C₂×C₈	—	38	2	no	—
508	C₂×C₈	—	38	2	no	—
509	C₂×C₈	—	38	2	no	—
510	C₂×C₈	—	38	2	no	—
511	C₂×C₈	—	76	1	no	—
512	C₂×C₈	—	76	1	no	—
513	C₂×C₈	—	76	1	no	—
514	C₂×C₈	—	76	1	no	—
515	C₂×C₈	—	76	1	no	—
516	C₂×C₈	—	76	1	no	—
517	C₂×C₈	—	76	1	no	—
518	C₂×C₈	—	76	1	no	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	4	1	no	—
522	C₄⋊C₄	—	4	1	no	—
523	C₄⋊C₄	—	38	2	no	—
524	C₄⋊C₄	—	38	2	no	—
525	C₄⋊C₄	—	76	1	no	—
526	C₄⋊C₄	—	76	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	4	1	no	—
533	C₂³	—	4	1	no	—
534	C₂³	—	4	1	no	—
535	C₂³	—	4	1	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	4	1	no	—
538	C₂³	#10597325	1	1	yes	characteristic
539	C₂³	#10597325	1	1	yes	characteristic
540	C₂³	#10597329	1	1	yes	characteristic
541	C₂³	#10597331	1	1	yes	characteristic
542	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
543	C₂³	#10597381	1	1	yes	characteristic
544	C₂³	#10597385	1	1	yes	characteristic
545	Q₈	—	2	2	no	—
546	Q₈	—	2	2	no	—
547	Q₈	—	4	1	no	—
548	Q₈	—	4	1	no	—
549	D₄	—	2	2	no	—
550	D₄	—	2	2	no	—
551	D₄	—	4	2	no	—
552	D₄	—	4	2	no	—
553	D₄	—	4	2	no	—
554	D₄	—	4	2	no	—
555	D₄	—	4	1	no	—
556	D₄	—	4	1	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	8	2	no	—
566	C₂×C₄	—	8	1	no	—
567	C₂×C₄	—	8	1	no	—
568	C₂×C₄	—	8	2	no	—
569	C₂×C₄	—	76	2	no	—
570	C₂×C₄	—	152	2	no	—
571	C₂×C₄	—	152	1	no	—
572	C₂×C₄	—	152	1	no	—
573	C₂×C₄	—	152	2	no	—
574	C₂×C₄	#10597325	1	1	yes	characteristic
575	C₂×C₄	#10597325	1	1	yes	characteristic
576	C₂×C₄	#10597329	1	1	yes	characteristic
577	C₂×C₄	#10597329	1	1	yes	characteristic
578	C₂×C₄	#10597329	1	1	yes	characteristic
579	C₂×C₄	#10597330	1	1	yes	characteristic
580	C₂×C₄	#10597330	1	1	yes	characteristic
581	C₂×C₄	#10597330	1	1	yes	characteristic
582	C₂×C₄	#10597330	1	1	yes	characteristic
583	C₂×C₄	#10597331	1	1	yes	characteristic
584	C₂×C₄	#10597331	1	1	yes	characteristic
585	C₂×C₄	#10597331	1	1	yes	characteristic
586	C₂×C₄	#10597372	1	1	yes	characteristic
587	C₂×C₄	#10597372	1	1	yes	characteristic
588	C₂×C₄	#10597375	1	1	yes	characteristic
589	C₂×C₄	#10597375	1	1	yes	characteristic
590	C₂×C₄	#10597375	1	1	yes	characteristic
591	C₂×C₄	#10597375	1	1	yes	characteristic
592	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
593	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
594	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
595	C₂×C₄	#10597381	1	1	yes	characteristic
596	C₂×C₄	#10597383	1	1	yes	characteristic
597	C₂×C₄	#10597383	1	1	yes	characteristic
598	C₂×C₄	#10597385	1	1	yes	characteristic
599	C₂×C₄	#10597385	1	1	yes	characteristic
600	C₂×C₄	#10597385	1	1	yes	characteristic
601	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
602	C₈	—	4	2	no	—
603	C₈	—	76	2	no	—
604	C₈	—	76	2	no	—
605	C₈	—	76	2	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	1	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	4	2	no	—
619	C₂²	—	4	2	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	8	1	no	—
622	C₂²	—	8	1	no	—
623	C₂²	—	8	1	no	—
624	C₂²	—	8	1	no	—
625	C₂²	#11926424	1	1	yes	characteristic
626	C₂²	#11926437	1	1	yes	characteristic
627	C₂²	#11926437	1	1	yes	characteristic
628	C₂²	#11926459	1	1	yes	characteristic
629	C₂²	#11926472	1	1	yes	characteristic
630	C₂²	#11926472	1	1	yes	characteristic
631	C₂²	#11926472	1	1	yes	characteristic
632	C₂²	#11926805	1	1	yes	characteristic
633	C₂²	#11926809	1	1	yes	characteristic
634	C₂²	#11926812	1	1	yes	characteristic
635	C₂²	#11926817	1	1	yes	characteristic
636	C₄	—	4	2	no	—
637	C₄	—	8	2	no	—
638	C₄	—	152	2	no	—
639	C₄	#11926407	1	1	yes	characteristic
640	C₄	#11926424	1	1	yes	characteristic
641	C₄	#11926437	1	1	yes	characteristic
642	C₄	#11926437	1	1	yes	characteristic
643	C₄	#11926459	1	1	yes	characteristic
644	C₄	#11926459	1	1	yes	characteristic
645	C₄	#11926459	1	1	yes	characteristic
646	C₄	#11926472	1	1	yes	characteristic
647	C₂	—	2	1	no	—
648	C₂	—	2	1	no	—
649	C₂	—	2	1	no	—
650	C₂	—	2	1	no	—
651	C₂	—	8	2	no	—
652	C₂	#14561884	1	1	yes	characteristic
653	C₂	#14564145	1	1	yes	characteristic
654	C₂	#14564152	1	1	yes	characteristic
655	C₂	#14564925	1	1	yes	characteristic
656	C₂	#14564932	1	1	yes	characteristic
657	C₂	#14565078	1	1	yes	characteristic
658	C₂	#14565083	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597385
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#417	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂²×#41×C₁₉	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#417	D₁₉
hypocenter	C₁₉	#11192
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#417

Complements

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

N	H ≅ G/N	type
3. C₂×#11926313	C₂	semidirect
4. C₂×#11926312	C₂	semidirect
5. C₂×#11926308	C₂	semidirect
6. C₂×#11926306	C₂	semidirect
27. C₁₉×#417	C₄	semidirect
335. #417	Dic₁₉	semidirect
423. C₁₉	#11192	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926545	2
C₂×#11926511	2
C₂×#11926313	2
C₂×#11926312	2
C₂×#11926308	2
C₂×#11926306	2
C₂×C₁₉×#417	2
#11192	19