Subgroups — #18089310

Order 4864.

1270 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926561	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11926540	C₂	1	1	yes	maximal, characteristic, complemented
3	#14572080	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926511	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926316	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11926308	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#575	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	C₂×#10597372	C₂²	1	1	yes	characteristic
12	#11926561	—	2	2	no	—
13	#11926561	—	2	2	no	—
14	C₂×#10597294	—	2	2	no	—
15	#11926540	—	2	2	no	—
16	#11926540	—	2	2	no	—
17	C₂×#10597292	—	2	1	no	—
18	C₂×#10597289	—	2	1	no	—
19	#11926511	—	2	2	no	—
20	#11926511	—	2	2	no	—
21	#11926511	—	2	2	no	—
22	#11926511	—	2	2	no	—
23	#11926508	—	2	2	no	—
24	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
25	#11926316	—	2	2	no	—
26	#11926308	—	2	2	no	—
27	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
28	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#575	—	2	2	no	—
30	C₁₉×#575	—	2	2	no	—
31	C₁₉×#575	—	2	2	no	—
32	C₁₉×#575	—	2	2	no	—
33	C₂×C₁₉×#137	—	2	1	no	—
34	C₂×C₁₉×#137	C₄	1	2	yes	complemented
35	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
36	C₂×C₁₉×AGL(1,ℤ/8)	C₄	1	2	yes	complemented
37	C₂×C₁₉×#135	—	2	2	no	—
38	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
39	C₂×#41×C₁₉	—	2	1	no	—
40	C₂×#41×C₁₉	—	2	1	no	—
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂×#41×C₁₉	—	2	1	no	—
43	C₂×#41×C₁₉	—	2	1	no	—
44	C₂×#41×C₁₉	—	2	1	no	—
45	C₂×#41×C₁₉	—	2	1	no	—
46	C₂×#41×C₁₉	—	2	1	no	—
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂×#41×C₁₉	—	2	1	no	—
49	C₂×#41×C₁₉	—	2	1	no	—
50	C₂×#41×C₁₉	—	2	1	no	—
51	C₂×#41×C₁₉	—	2	1	no	—
52	C₂×#41×C₁₉	—	2	1	no	—
53	C₂×#41×C₁₉	—	2	1	no	—
54	C₂×#41×C₁₉	—	2	1	no	—
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂×#41×C₁₉	—	2	1	no	—
57	C₂×#41×C₁₉	—	2	1	no	—
58	C₂×#41×C₁₉	—	2	1	no	—
59	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
60	C₂×#41×C₁₉	D₄	1	2	yes	—
61	C₂×#41×C₁₉	D₄	1	2	yes	—
62	C₂×#41×C₁₉	D₄	1	2	yes	—
63	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
64	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
65	C₂²×D₄×C₁₉	—	2	1	no	—
66	C₂²×D₄×C₁₉	—	2	1	no	—
67	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
68	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
69	C₂³×C₄×C₁₉	—	2	1	no	—
70	C₂³×C₄×C₁₉	—	2	1	no	—
71	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₁₉×#137	—	2	4	no	—
73	C₁₉×#137	—	2	4	no	—
74	C₁₉×#137	—	2	4	no	—
75	C₁₉×#137	—	2	4	no	—
76	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
77	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
78	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
79	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
80	C₁₉×#135	—	2	8	no	—
81	C₁₉×#135	—	2	8	no	—
82	C₂×Q₁₆×C₁₉	—	2	2	no	—
83	C₂×SD₁₆×C₁₉	—	2	2	no	—
84	C₂×SD₁₆×C₁₉	—	2	2	no	—
85	C₂×D₈×C₁₉	—	2	2	no	—
86	C₂×M₁₆×C₁₉	—	2	1	no	—
87	C₂×M₁₆×C₁₉	—	2	1	no	—
88	C₂×M₁₆×C₁₉	—	2	1	no	—
89	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
90	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
91	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
92	C₂²×C₈×C₁₉	—	2	1	no	—
93	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
94	#10597372	—	2	1	no	—
95	#10597372	—	2	1	no	—
96	#10597372	—	2	1	no	—
97	#10597372	D₄	1	2	yes	—
98	C₂×C₄⋊Dic₁₉	—	2	1	no	—
99	C₂×C₄×Dic₁₉	—	2	1	no	—
100	C₂×#64520	—	2	1	no	—
101	C₂×#64520	—	2	1	no	—
102	C₂×#64520	—	2	1	no	—
103	C₂×#64520	—	2	1	no	—
104	C₂×#64520	—	2	1	no	—
105	C₂×#64520	—	2	1	no	—
106	C₂×#64520	—	2	1	no	—
107	C₂×#64520	—	2	1	no	—
108	C₂×#64520	—	2	1	no	—
109	C₂×#64520	—	2	1	no	—
110	C₂×#64520	—	2	1	no	—
111	C₂×#64520	D₄	1	2	yes	—
112	C₂²×C₁₉⋊C₈	—	2	1	no	—
113	C₂²×C₁₉⋊C₈	—	2	1	no	—
114	C₂²×C₁₉⋊C₈	—	2	1	no	—
115	C₂²×C₁₉⋊C₈	—	2	1	no	—
116	C₂²×C₁₉⋊C₈	—	2	1	no	—
117	C₂²×C₁₉⋊C₈	—	2	1	no	—
118	C₂²×C₁₉⋊C₈	—	2	1	no	—
119	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
120	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
121	#10597294	—	2	8	no	—
122	#10597292	—	2	4	no	—
123	#10597289	—	2	4	no	—
124	C₂²⋊(C₁₉⋊C₈)	—	2	8	no	—
125	C₂²⋊(C₁₉⋊C₈)	—	2	8	no	—
126	C₂⁴×C₁₉	—	2	1	no	—
127	C₂⁴×C₁₉	—	2	1	no	—
128	C₂⁴×C₁₉	#41	1	1	yes	characteristic
129	#41×C₁₉	—	2	2	no	—
130	#41×C₁₉	—	2	2	no	—
131	#41×C₁₉	—	2	2	no	—
132	#41×C₁₉	—	2	2	no	—
133	#41×C₁₉	—	2	2	no	—
134	#41×C₁₉	—	2	2	no	—
135	#41×C₁₉	—	2	2	no	—
136	#41×C₁₉	—	2	2	no	—
137	#41×C₁₉	—	2	2	no	—
138	#41×C₁₉	—	2	2	no	—
139	#41×C₁₉	—	2	2	no	—
140	#41×C₁₉	—	2	2	no	—
141	#41×C₁₉	—	2	2	no	—
142	#41×C₁₉	—	2	2	no	—
143	#41×C₁₉	—	2	2	no	—
144	#41×C₁₉	—	2	2	no	—
145	#41×C₁₉	—	4	1	no	—
146	#41×C₁₉	—	4	1	no	—
147	#41×C₁₉	—	4	1	no	—
148	#41×C₁₉	—	4	1	no	—
149	#41×C₁₉	—	4	1	no	—
150	#41×C₁₉	—	4	1	no	—
151	#41×C₁₉	—	4	1	no	—
152	#41×C₁₉	—	4	1	no	—
153	#41×C₁₉	—	4	1	no	—
154	#41×C₁₉	—	4	1	no	—
155	#41×C₁₉	—	4	1	no	—
156	#41×C₁₉	—	4	1	no	—
157	#41×C₁₉	—	4	1	no	—
158	#41×C₁₉	—	4	1	no	—
159	#41×C₁₉	—	4	1	no	—
160	#41×C₁₉	—	4	1	no	—
161	C₂×Q₈×C₁₉	—	2	1	no	—
162	C₂×Q₈×C₁₉	—	2	1	no	—
163	C₂×Q₈×C₁₉	—	2	1	no	—
164	C₂×Q₈×C₁₉	—	2	1	no	—
165	C₂×Q₈×C₁₉	—	2	1	no	—
166	C₂×Q₈×C₁₉	—	2	1	no	—
167	C₂×Q₈×C₁₉	—	2	1	no	—
168	C₂×Q₈×C₁₉	—	2	1	no	—
169	C₂×Q₈×C₁₉	—	2	1	no	—
170	C₂×Q₈×C₁₉	—	2	1	no	—
171	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
172	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
173	C₂×D₄×C₁₉	—	2	2	no	—
174	C₂×D₄×C₁₉	—	2	2	no	—
175	C₂×D₄×C₁₉	—	2	2	no	—
176	C₂×D₄×C₁₉	—	2	2	no	—
177	C₂×D₄×C₁₉	—	2	1	no	—
178	C₂×D₄×C₁₉	—	2	1	no	—
179	C₂×D₄×C₁₉	—	2	1	no	—
180	C₂×D₄×C₁₉	—	2	1	no	—
181	C₂×D₄×C₁₉	—	2	1	no	—
182	C₂×D₄×C₁₉	—	2	1	no	—
183	C₂×D₄×C₁₉	—	2	1	no	—
184	C₂×D₄×C₁₉	—	2	1	no	—
185	C₂×D₄×C₁₉	—	2	1	no	—
186	C₂×D₄×C₁₉	—	2	1	no	—
187	C₂×D₄×C₁₉	—	4	1	no	—
188	C₂×D₄×C₁₉	—	4	1	no	—
189	C₂×D₄×C₁₉	—	4	1	no	—
190	C₂×D₄×C₁₉	—	4	1	no	—
191	C₂×D₄×C₁₉	—	4	1	no	—
192	C₂×D₄×C₁₉	—	4	1	no	—
193	C₂×D₄×C₁₉	—	4	1	no	—
194	C₂×D₄×C₁₉	—	4	1	no	—
195	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
196	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
197	C₂²×C₄×C₁₉	—	2	1	no	—
198	C₂²×C₄×C₁₉	—	2	1	no	—
199	C₂²×C₄×C₁₉	—	2	2	no	—
200	C₂²×C₄×C₁₉	—	2	2	no	—
201	C₂²×C₄×C₁₉	—	2	2	no	—
202	C₂²×C₄×C₁₉	—	2	2	no	—
203	C₂²×C₄×C₁₉	—	4	1	no	—
204	C₂²×C₄×C₁₉	—	4	1	no	—
205	C₂²×C₄×C₁₉	—	4	1	no	—
206	C₂²×C₄×C₁₉	—	4	1	no	—
207	C₂²×C₄×C₁₉	—	4	1	no	—
208	C₂²×C₄×C₁₉	—	4	1	no	—
209	C₂²×C₄×C₁₉	—	4	1	no	—
210	C₂²×C₄×C₁₉	—	4	1	no	—
211	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
212	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
223	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
224	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
225	C₂²×Dic₁₉	—	4	1	no	—
226	Q₁₆×C₁₉	—	2	8	no	—
227	SD₁₆×C₁₉	—	2	8	no	—
228	SD₁₆×C₁₉	—	2	8	no	—
229	D₈×C₁₉	—	2	8	no	—
230	M₁₆×C₁₉	—	2	2	no	—
231	M₁₆×C₁₉	—	2	2	no	—
232	M₁₆×C₁₉	—	2	2	no	—
233	M₁₆×C₁₉	C₂²⋊C₄	1	4	yes	—
234	C₂×C₈×C₁₉	—	2	2	no	—
235	C₂×C₈×C₁₉	—	2	2	no	—
236	C₂×C₈×C₁₉	—	2	2	no	—
237	C₂²⋊Dic₁₉	—	2	2	no	—
238	C₂²⋊Dic₁₉	—	4	1	no	—
239	C₄⋊Dic₁₉	—	2	2	no	—
240	C₄⋊Dic₁₉	—	4	1	no	—
241	C₄×Dic₁₉	—	2	2	no	—
242	C₄×Dic₁₉	—	4	1	no	—
243	#64520	—	2	2	no	—
244	#64520	—	2	2	no	—
245	#64520	—	4	1	no	—
246	#64520	—	4	1	no	—
247	#64520	—	4	1	no	—
248	#64520	—	4	1	no	—
249	#64520	—	4	1	no	—
250	#64520	—	4	1	no	—
251	C₂×C₁₉⋊C₈	—	2	2	no	—
252	C₂×C₁₉⋊C₈	—	2	2	no	—
253	C₂×C₁₉⋊C₈	—	2	2	no	—
254	C₂×C₁₉⋊C₈	—	2	2	no	—
255	C₂×C₁₉⋊C₈	—	2	2	no	—
256	C₂×C₁₉⋊C₈	—	2	2	no	—
257	C₂×C₁₉⋊C₈	—	2	2	no	—
258	C₂×C₁₉⋊C₈	—	4	1	no	—
259	C₂×C₁₉⋊C₈	—	4	1	no	—
260	C₂×C₁₉⋊C₈	—	4	1	no	—
261	C₂×C₁₉⋊C₈	—	4	1	no	—
262	C₂×C₁₉⋊C₈	—	4	1	no	—
263	C₂×C₁₉⋊C₈	—	4	1	no	—
264	#11018	—	19	1	no	maximal, Sylow
265	C₂³×C₁₉	—	2	2	no	—
266	C₂³×C₁₉	—	2	2	no	—
267	C₂³×C₁₉	—	4	2	no	—
268	C₂³×C₁₉	—	4	4	no	—
269	C₂³×C₁₉	—	4	1	no	—
270	C₂³×C₁₉	—	4	1	no	—
271	C₂³×C₁₉	—	4	1	no	—
272	C₂³×C₁₉	—	4	1	no	—
273	C₂³×C₁₉	—	8	2	no	—
274	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
275	C₂³×C₁₉	#121	1	1	yes	characteristic
276	C₂³×C₁₉	#121	1	1	yes	characteristic
277	C₂³×C₁₉	#121	1	1	yes	characteristic
278	C₂³×C₁₉	#123	1	1	yes	characteristic
279	C₂³×C₁₉	#123	1	1	yes	characteristic
280	C₂³×C₁₉	#124	1	1	yes	characteristic
281	Q₈×C₁₉	—	2	2	no	—
282	Q₈×C₁₉	—	2	2	no	—
283	Q₈×C₁₉	—	2	2	no	—
284	Q₈×C₁₉	—	2	2	no	—
285	Q₈×C₁₉	—	4	1	no	—
286	Q₈×C₁₉	—	4	1	no	—
287	Q₈×C₁₉	—	4	1	no	—
288	Q₈×C₁₉	—	4	1	no	—
289	D₄×C₁₉	—	2	2	no	—
290	D₄×C₁₉	—	2	2	no	—
291	D₄×C₁₉	—	2	2	no	—
292	D₄×C₁₉	—	2	2	no	—
293	D₄×C₁₉	—	4	2	no	—
294	D₄×C₁₉	—	4	2	no	—
295	D₄×C₁₉	—	4	2	no	—
296	D₄×C₁₉	—	4	2	no	—
297	D₄×C₁₉	—	4	2	no	—
298	D₄×C₁₉	—	4	2	no	—
299	D₄×C₁₉	—	4	2	no	—
300	D₄×C₁₉	—	4	2	no	—
301	D₄×C₁₉	—	4	1	no	—
302	D₄×C₁₉	—	4	1	no	—
303	D₄×C₁₉	—	4	1	no	—
304	D₄×C₁₉	—	4	1	no	—
305	C₂×C₄×C₁₉	—	2	2	no	—
306	C₂×C₄×C₁₉	—	2	2	no	—
307	C₂×C₄×C₁₉	—	4	1	no	—
308	C₂×C₄×C₁₉	—	4	1	no	—
309	C₂×C₄×C₁₉	—	4	1	no	—
310	C₂×C₄×C₁₉	—	4	1	no	—
311	C₂×C₄×C₁₉	—	4	2	no	—
312	C₂×C₄×C₁₉	—	4	2	no	—
313	C₂×C₄×C₁₉	—	4	2	no	—
314	C₂×C₄×C₁₉	—	4	2	no	—
315	C₂×C₄×C₁₉	—	4	2	no	—
316	C₂×C₄×C₁₉	—	4	2	no	—
317	C₂×C₄×C₁₉	—	4	2	no	—
318	C₂×C₄×C₁₉	—	4	2	no	—
319	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
320	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
321	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
322	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
323	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
324	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
325	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
326	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
327	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
328	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
329	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
330	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
331	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
332	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
333	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
334	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
335	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
336	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
337	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
338	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
339	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
340	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
341	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
342	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
343	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
344	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
345	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
346	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
347	C₂×Dic₁₉	—	4	2	no	—
348	C₂×Dic₁₉	—	8	2	no	—
349	C₈×C₁₉	—	2	4	no	—
350	C₁₉⋊C₈	—	4	2	no	—
351	C₁₉⋊C₈	—	4	2	no	—
352	C₁₉⋊C₈	—	4	2	no	—
353	C₂×#575	D₁₉	1	1	yes	characteristic
354	C₂×#421	—	19	1	no	—
355	C₂×#416	—	19	1	no	—
356	#2879	—	19	1	no	—
357	C₂×#408	—	19	1	no	—
358	C₂×#344	—	19	1	no	—
359	C₂×#341	—	19	1	no	—
360	C₂²×C₁₉	—	2	2	no	—
361	C₂²×C₁₉	—	2	2	no	—
362	C₂²×C₁₉	—	2	2	no	—
363	C₂²×C₁₉	—	4	1	no	—
364	C₂²×C₁₉	—	4	1	no	—
365	C₂²×C₁₉	—	4	1	no	—
366	C₂²×C₁₉	—	4	1	no	—
367	C₂²×C₁₉	—	4	4	no	—
368	C₂²×C₁₉	—	4	4	no	—
369	C₂²×C₁₉	—	4	2	no	—
370	C₂²×C₁₉	—	4	2	no	—
371	C₂²×C₁₉	—	8	2	no	—
372	C₂²×C₁₉	—	8	2	no	—
373	C₂²×C₁₉	—	8	2	no	—
374	C₂²×C₁₉	—	8	2	no	—
375	C₂²×C₁₉	#386	1	1	yes	characteristic
376	C₂²×C₁₉	#386	1	1	yes	characteristic
377	C₂²×C₁₉	#390	1	1	yes	characteristic
378	C₂²×C₁₉	#392	1	1	yes	characteristic
379	C₂²×C₁₉	#394	1	1	yes	characteristic
380	C₂²×C₁₉	#394	1	1	yes	characteristic
381	C₂²×C₁₉	#394	1	1	yes	characteristic
382	C₄×C₁₉	—	4	2	no	—
383	C₄×C₁₉	—	4	2	no	—
384	C₄×C₁₉	#379	1	1	yes	characteristic
385	C₄×C₁₉	#386	1	1	yes	characteristic
386	C₄×C₁₉	#386	1	1	yes	characteristic
387	C₄×C₁₉	#390	1	1	yes	characteristic
388	C₄×C₁₉	#392	1	1	yes	characteristic
389	C₄×C₁₉	#392	1	1	yes	characteristic
390	C₄×C₁₉	#392	1	1	yes	characteristic
391	C₄×C₁₉	#394	1	1	yes	characteristic
392	Dic₁₉	—	8	2	no	—
393	C₂²×#41	C₂×D₁₉	1	1	yes	characteristic
394	C₂²×#41	C₂×D₁₉	1	1	yes	characteristic
395	#575	—	2	2	no	—
396	#575	—	2	2	no	—
397	#575	—	2	2	no	—
398	#575	—	2	2	no	—
399	C₂×#137	—	2	1	no	—
400	C₂×#137	Dic₁₉	1	2	yes	complemented
401	C₂×AGL(1,ℤ/8)	—	2	1	no	—
402	C₂×AGL(1,ℤ/8)	Dic₁₉	1	2	yes	complemented
403	C₂×#135	—	2	2	no	—
404	C₂²×M₁₆	—	19	1	no	—
405	C₂²×M₁₆	—	19	1	no	—
406	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
407	C₂³×C₈	—	19	1	no	—
408	C₂×#117	—	19	1	no	—
409	#421	—	38	2	no	—
410	#421	—	38	2	no	—
411	C₂×#104	—	38	2	no	—
412	#416	—	38	2	no	—
413	#416	—	38	2	no	—
414	C₂×#103	—	38	1	no	—
415	C₂×#102	—	38	1	no	—
416	#408	—	38	2	no	—
417	#408	—	38	2	no	—
418	#408	—	38	2	no	—
419	#408	—	38	2	no	—
420	#407	—	38	2	no	—
421	C₂×C₂²⋊C₈	—	38	2	no	—
422	#344	—	38	2	no	—
423	#341	—	38	2	no	—
424	C₂×C₁₉	—	2	1	no	—
425	C₂×C₁₉	—	2	1	no	—
426	C₂×C₁₉	—	2	1	no	—
427	C₂×C₁₉	—	2	1	no	—
428	C₂×C₁₉	—	2	1	no	—
429	C₂×C₁₉	—	2	1	no	—
430	C₂×C₁₉	—	8	2	no	—
431	C₂×C₁₉	—	8	2	no	—
432	C₂×C₁₉	#1438	1	1	yes	characteristic
433	C₂×C₁₉	#1881	1	2	yes	—
434	C₂×#41	—	2	1	no	—
435	C₂×#41	—	2	1	no	—
436	C₂×#41	—	2	1	no	—
437	C₂×#41	—	2	1	no	—
438	C₂×#41	—	2	1	no	—
439	C₂×#41	—	2	1	no	—
440	C₂×#41	—	2	1	no	—
441	C₂×#41	—	2	1	no	—
442	C₂×#41	—	2	1	no	—
443	C₂×#41	—	2	1	no	—
444	C₂×#41	—	2	1	no	—
445	C₂×#41	—	2	1	no	—
446	C₂×#41	—	2	1	no	—
447	C₂×#41	—	2	1	no	—
448	C₂×#41	—	2	1	no	—
449	C₂×#41	—	2	1	no	—
450	C₂×#41	—	2	1	no	—
451	C₂×#41	—	2	1	no	—
452	C₂×#41	—	2	1	no	—
453	C₂×#41	—	2	1	no	—
454	C₂×#41	C₂×Dic₁₉	1	2	yes	—
455	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
456	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
457	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
458	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
459	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
460	C₂²×D₄	—	2	1	no	—
461	C₂²×D₄	—	2	1	no	—
462	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
463	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
464	C₂³×C₄	—	2	1	no	—
465	C₂³×C₄	—	2	1	no	—
466	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
467	#137	—	2	4	no	—
468	#137	—	2	4	no	—
469	#137	—	2	4	no	—
470	#137	—	2	4	no	—
471	AGL(1,ℤ/8)	—	2	4	no	—
472	AGL(1,ℤ/8)	—	2	4	no	—
473	AGL(1,ℤ/8)	—	2	4	no	—
474	AGL(1,ℤ/8)	—	2	4	no	—
475	#135	—	2	8	no	—
476	#135	—	2	8	no	—
477	C₂×Q₁₆	—	2	2	no	—
478	C₂×SD₁₆	—	2	2	no	—
479	C₂×SD₁₆	—	2	2	no	—
480	C₂×D₈	—	2	2	no	—
481	C₂×M₁₆	—	2	1	no	—
482	C₂×M₁₆	—	2	1	no	—
483	C₂×M₁₆	—	2	1	no	—
484	C₂×M₁₆	—	19	2	no	—
485	C₂×M₁₆	—	38	1	no	—
486	C₂×M₁₆	—	38	1	no	—
487	C₂×M₁₆	—	38	1	no	—
488	C₂×M₁₆	—	38	1	no	—
489	C₂×M₁₆	—	38	1	no	—
490	C₂×M₁₆	—	38	1	no	—
491	C₂×M₁₆	—	38	1	no	—
492	C₂×M₁₆	—	38	1	no	—
493	C₂×M₁₆	—	38	1	no	—
494	C₂×M₁₆	—	38	1	no	—
495	C₂×M₁₆	—	38	1	no	—
496	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
497	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
498	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
499	C₂²×C₈	—	2	1	no	—
500	C₂²×C₈	—	19	2	no	—
501	C₂²×C₈	—	19	2	no	—
502	C₂²×C₈	—	38	1	no	—
503	C₂²×C₈	—	38	1	no	—
504	C₂²×C₈	—	38	1	no	—
505	C₂²×C₈	—	38	1	no	—
506	C₂²×C₈	—	38	1	no	—
507	C₂²×C₈	—	38	1	no	—
508	C₂²×C₈	—	38	1	no	—
509	#117	—	19	2	no	—
510	#117	—	38	1	no	—
511	#117	—	38	1	no	—
512	#117	—	38	1	no	—
513	C₂×C₄⋊C₄	—	38	1	no	—
514	C₂×C₂²⋊C₄	—	38	1	no	—
515	C₂×C₄²	—	38	1	no	—
516	#104	—	38	8	no	—
517	#103	—	38	4	no	—
518	#102	—	38	4	no	—
519	C₂²⋊C₈	—	38	8	no	—
520	C₂²⋊C₈	—	38	8	no	—
521	C₁₉	#11018	1	1	yes	characteristic, complemented, Sylow
522	C₂⁴	—	2	1	no	—
523	C₂⁴	—	2	1	no	—
524	C₂⁴	#64543	1	1	yes	characteristic
525	#41	—	2	2	no	—
526	#41	—	2	2	no	—
527	#41	—	2	2	no	—
528	#41	—	2	2	no	—
529	#41	—	2	2	no	—
530	#41	—	2	2	no	—
531	#41	—	2	2	no	—
532	#41	—	2	2	no	—
533	#41	—	2	2	no	—
534	#41	—	2	2	no	—
535	#41	—	2	2	no	—
536	#41	—	2	2	no	—
537	#41	—	2	2	no	—
538	#41	—	2	2	no	—
539	#41	—	2	2	no	—
540	#41	—	2	2	no	—
541	#41	—	4	1	no	—
542	#41	—	4	1	no	—
543	#41	—	4	1	no	—
544	#41	—	4	1	no	—
545	#41	—	4	1	no	—
546	#41	—	4	1	no	—
547	#41	—	4	1	no	—
548	#41	—	4	1	no	—
549	#41	—	4	1	no	—
550	#41	—	4	1	no	—
551	#41	—	4	1	no	—
552	#41	—	4	1	no	—
553	#41	—	4	1	no	—
554	#41	—	4	1	no	—
555	#41	—	4	1	no	—
556	#41	—	4	1	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	1	no	—
567	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
568	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	1	no	—
583	C₂×D₄	—	4	1	no	—
584	C₂×D₄	—	4	1	no	—
585	C₂×D₄	—	4	1	no	—
586	C₂×D₄	—	4	1	no	—
587	C₂×D₄	—	4	1	no	—
588	C₂×D₄	—	4	1	no	—
589	C₂×D₄	—	4	1	no	—
590	C₂×D₄	—	4	1	no	—
591	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
592	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	4	1	no	—
600	C₂²×C₄	—	4	1	no	—
601	C₂²×C₄	—	4	1	no	—
602	C₂²×C₄	—	4	1	no	—
603	C₂²×C₄	—	4	1	no	—
604	C₂²×C₄	—	4	1	no	—
605	C₂²×C₄	—	4	1	no	—
606	C₂²×C₄	—	4	1	no	—
607	C₂²×C₄	—	76	1	no	—
608	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
609	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
610	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
611	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
612	C₂²×C₄	#64543	1	1	yes	characteristic
613	C₂²×C₄	#64543	1	1	yes	characteristic
614	C₂²×C₄	#64543	1	1	yes	characteristic
615	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
616	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
617	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
618	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
619	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
620	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
621	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
622	Q₁₆	—	2	8	no	—
623	SD₁₆	—	2	8	no	—
624	SD₁₆	—	2	8	no	—
625	D₈	—	2	8	no	—
626	M₁₆	—	2	2	no	—
627	M₁₆	—	2	2	no	—
628	M₁₆	—	2	2	no	—
629	M₁₆	—	38	2	no	—
630	M₁₆	—	38	2	no	—
631	M₁₆	—	76	1	no	—
632	M₁₆	—	76	1	no	—
633	M₁₆	—	76	1	no	—
634	M₁₆	—	76	1	no	—
635	M₁₆	—	76	1	no	—
636	M₁₆	—	76	1	no	—
637	M₁₆	C₂²⋊Dic₁₉	1	4	yes	—
638	C₂×C₈	—	2	2	no	—
639	C₂×C₈	—	2	2	no	—
640	C₂×C₈	—	2	2	no	—
641	C₂×C₈	—	38	2	no	—
642	C₂×C₈	—	38	2	no	—
643	C₂×C₈	—	38	2	no	—
644	C₂×C₈	—	38	2	no	—
645	C₂×C₈	—	38	2	no	—
646	C₂×C₈	—	38	2	no	—
647	C₂×C₈	—	38	2	no	—
648	C₂×C₈	—	76	1	no	—
649	C₂×C₈	—	76	1	no	—
650	C₂×C₈	—	76	1	no	—
651	C₂×C₈	—	76	1	no	—
652	C₂×C₈	—	76	1	no	—
653	C₂×C₈	—	76	1	no	—
654	C₄⋊C₄	—	38	2	no	—
655	C₄⋊C₄	—	76	1	no	—
656	C₂²⋊C₄	—	38	2	no	—
657	C₂²⋊C₄	—	76	1	no	—
658	C₄²	—	38	2	no	—
659	C₄²	—	76	1	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	4	2	no	—
663	C₂³	—	4	4	no	—
664	C₂³	—	4	1	no	—
665	C₂³	—	4	1	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	8	2	no	—
669	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
670	C₂³	#10597381	1	1	yes	characteristic
671	C₂³	#10597381	1	1	yes	characteristic
672	C₂³	#10597382	1	1	yes	characteristic
673	C₂³	#10597384	1	1	yes	characteristic
674	C₂³	#10597385	1	1	yes	characteristic
675	C₂³	#10597385	1	1	yes	characteristic
676	Q₈	—	2	2	no	—
677	Q₈	—	2	2	no	—
678	Q₈	—	2	2	no	—
679	Q₈	—	2	2	no	—
680	Q₈	—	4	1	no	—
681	Q₈	—	4	1	no	—
682	Q₈	—	4	1	no	—
683	Q₈	—	4	1	no	—
684	D₄	—	2	2	no	—
685	D₄	—	2	2	no	—
686	D₄	—	2	2	no	—
687	D₄	—	2	2	no	—
688	D₄	—	4	2	no	—
689	D₄	—	4	2	no	—
690	D₄	—	4	2	no	—
691	D₄	—	4	2	no	—
692	D₄	—	4	2	no	—
693	D₄	—	4	2	no	—
694	D₄	—	4	2	no	—
695	D₄	—	4	2	no	—
696	D₄	—	4	1	no	—
697	D₄	—	4	1	no	—
698	D₄	—	4	1	no	—
699	D₄	—	4	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	2	no	—
707	C₂×C₄	—	4	2	no	—
708	C₂×C₄	—	4	2	no	—
709	C₂×C₄	—	4	2	no	—
710	C₂×C₄	—	4	2	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	4	2	no	—
713	C₂×C₄	—	4	2	no	—
714	C₂×C₄	—	76	2	no	—
715	C₂×C₄	—	152	2	no	—
716	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
717	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
718	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
719	C₂×C₄	#10597381	1	1	yes	characteristic
720	C₂×C₄	#10597381	1	1	yes	characteristic
721	C₂×C₄	#10597382	1	1	yes	characteristic
722	C₂×C₄	#10597383	1	1	yes	characteristic
723	C₂×C₄	#10597383	1	1	yes	characteristic
724	C₂×C₄	#10597383	1	1	yes	characteristic
725	C₂×C₄	#10597383	1	1	yes	characteristic
726	C₂×C₄	#10597384	1	1	yes	characteristic
727	C₂×C₄	#10597384	1	1	yes	characteristic
728	C₂×C₄	#10597384	1	1	yes	characteristic
729	C₂×C₄	#10597385	1	1	yes	characteristic
730	C₂×C₄	#10597385	1	1	yes	characteristic
731	C₂×C₄	#10597385	1	1	yes	characteristic
732	C₂×C₄	#10597385	1	1	yes	characteristic
733	C₂×C₄	#10597385	1	1	yes	characteristic
734	C₂×C₄	#10597385	1	1	yes	characteristic
735	C₂×C₄	#10597386	1	1	yes	characteristic
736	C₂×C₄	#10597386	1	1	yes	characteristic
737	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
738	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
739	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
740	C₂×C₄	#10597399	1	1	yes	characteristic
741	C₂×C₄	#10597399	1	1	yes	characteristic
742	C₂×C₄	#10597399	1	1	yes	characteristic
743	C₂×C₄	#10597399	1	1	yes	characteristic
744	C₈	—	2	4	no	—
745	C₈	—	76	2	no	—
746	C₈	—	76	2	no	—
747	C₈	—	76	2	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	2	2	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	4	1	no	—
752	C₂²	—	4	1	no	—
753	C₂²	—	4	1	no	—
754	C₂²	—	4	1	no	—
755	C₂²	—	4	4	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	4	no	—
759	C₂²	—	8	2	no	—
760	C₂²	—	8	2	no	—
761	C₂²	—	8	2	no	—
762	C₂²	—	8	2	no	—
763	C₂²	#11926424	1	1	yes	characteristic
764	C₂²	#11926424	1	1	yes	characteristic
765	C₂²	#11926447	1	1	yes	characteristic
766	C₂²	#11926452	1	1	yes	characteristic
767	C₂²	#11926458	1	1	yes	characteristic
768	C₂²	#11926458	1	1	yes	characteristic
769	C₂²	#11926458	1	1	yes	characteristic
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	152	2	no	—
773	C₄	#11926400	1	1	yes	characteristic
774	C₄	#11926424	1	1	yes	characteristic
775	C₄	#11926424	1	1	yes	characteristic
776	C₄	#11926447	1	1	yes	characteristic
777	C₄	#11926452	1	1	yes	characteristic
778	C₄	#11926452	1	1	yes	characteristic
779	C₄	#11926452	1	1	yes	characteristic
780	C₄	#11926458	1	1	yes	characteristic
781	C₂	—	2	1	no	—
782	C₂	—	2	1	no	—
783	C₂	—	2	1	no	—
784	C₂	—	2	1	no	—
785	C₂	—	2	1	no	—
786	C₂	—	2	1	no	—
787	C₂	—	8	2	no	—
788	C₂	—	8	2	no	—
789	C₂	#14561876	1	1	yes	characteristic
790	C₂	#14563999	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10597383
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting, prime radical	C₂×C₁₉×#575	C₂
socle	C₂²×C₁₉	#386
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#575	D₁₉
hypocenter	C₁₉	#11018
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#575

Complements

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

N	H ≅ G/N	type
1. C₂×#11926561	C₂	semidirect
2. C₂×#11926540	C₂	semidirect
3. #14572080	C₂	semidirect
4. C₂×#11926511	C₂	semidirect
5. C₂×#11926316	C₂	semidirect
6. C₂×#11926308	C₂	semidirect
34. C₂×C₁₉×#137	C₄	semidirect
36. C₂×C₁₉×AGL(1,ℤ/8)	C₄	semidirect
400. C₂×#137	Dic₁₉	semidirect
402. C₂×AGL(1,ℤ/8)	Dic₁₉	semidirect
521. C₁₉	#11018	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926561	2
C₂×#11926540	2
#14572080	2
C₂×#11926511	2
C₂×#11926316	2
C₂×#11926308	2
C₂×C₁₉×#575	2
#11018	19