Subgroups — #18089234

Order 4864.

1270 conjugacy classes of subgroups.

The subgroup lattice has 744 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
2	#14572154	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926553	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926553	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926314	C₂	1	1	yes	maximal, characteristic, complemented
6	#14563367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#536	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂²×#64520	C₂²	1	1	yes	characteristic
10	C₂×#10597372	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	#11926553	—	2	2	no	—
16	#11926553	—	2	2	no	—
17	#11926553	—	2	2	no	—
18	#11926553	—	2	2	no	—
19	#11926553	—	2	1	no	—
20	#11926549	—	2	1	no	—
21	#11926545	—	2	2	no	—
22	#11926540	—	2	2	no	—
23	C₂×#10597292	—	2	2	no	—
24	C₂×#10597292	—	2	2	no	—
25	#11926314	—	2	2	no	—
26	#11926310	—	2	2	no	—
27	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
28	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#536	—	2	2	no	—
30	C₁₉×#536	—	2	2	no	—
31	C₁₉×#536	—	2	2	no	—
32	C₁₉×#536	C₄	1	4	yes	complemented
33	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
34	C₂×C₁₉×#124	—	2	1	no	—
35	C₂×C₁₉×#123	—	2	2	no	—
36	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
37	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
38	C₂×#41×C₁₉	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
49	C₂×#41×C₁₉	D₄	1	2	yes	—
50	C₂²×Q₈×C₁₉	—	2	1	no	—
51	C₂²×Q₈×C₁₉	—	2	1	no	—
52	C₂²×Q₈×C₁₉	—	2	1	no	—
53	C₂²×Q₈×C₁₉	—	2	1	no	—
54	C₂²×Q₈×C₁₉	—	2	1	no	—
55	C₂²×Q₈×C₁₉	—	2	1	no	—
56	C₂²×Q₈×C₁₉	—	2	1	no	—
57	C₂²×Q₈×C₁₉	—	2	1	no	—
58	C₂²×Q₈×C₁₉	—	2	1	no	—
59	C₂²×Q₈×C₁₉	—	2	1	no	—
60	C₂²×Q₈×C₁₉	—	2	1	no	—
61	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
62	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
63	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
64	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
65	C₂²×D₄×C₁₉	—	2	1	no	—
66	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
67	C₂³×C₄×C₁₉	—	2	1	no	—
68	C₂³×C₄×C₁₉	—	2	1	no	—
69	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₁₉×C₄⋊Q₈	—	2	4	no	—
71	C₁₉×C₄⋊Q₈	—	2	4	no	—
72	C₁₉×#124	—	2	4	no	—
73	C₁₉×#124	—	2	4	no	—
74	C₁₉×#123	—	2	8	no	—
75	C₁₉×#123	—	2	8	no	—
76	C₁₉×C₂²⋊Q₈	—	2	8	no	—
77	C₁₉×C₂²⋊Q₈	—	2	8	no	—
78	C₁₉×#117	—	2	1	no	—
79	C₁₉×#117	—	2	1	no	—
80	C₁₉×#117	C₂×C₄	1	2	yes	—
81	C₁₉×#117	D₄	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
85	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
86	C₂×C₄²×C₁₉	—	2	1	no	—
87	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
88	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
89	#10597372	—	2	1	no	—
90	#10597372	—	2	1	no	—
91	#10597372	—	2	1	no	—
92	#10597372	—	2	1	no	—
93	#10597372	—	2	1	no	—
94	#10597372	—	2	1	no	—
95	#10597372	—	2	1	no	—
96	#10597372	D₄	1	2	yes	—
97	C₂×C₄⋊Dic₁₉	—	2	1	no	—
98	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
99	C₂×C₄×Dic₁₉	—	2	1	no	—
100	C₂×C₄×Dic₁₉	—	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	—	2	1	no	—
112	C₂×#64520	D₄	1	2	yes	—
113	C₂²×C₁₉⋊C₈	—	2	1	no	—
114	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
115	#10597294	—	2	8	no	—
116	#10597292	—	2	8	no	—
117	#10597292	—	2	8	no	—
118	#10597292	—	2	4	no	—
119	#10597289	—	2	4	no	—
120	C₂⁴×C₁₉	—	2	1	no	—
121	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
122	#41×C₁₉	—	2	2	no	—
123	#41×C₁₉	—	2	2	no	—
124	#41×C₁₉	—	2	2	no	—
125	#41×C₁₉	—	2	2	no	—
126	#41×C₁₉	—	2	2	no	—
127	#41×C₁₉	—	2	2	no	—
128	#41×C₁₉	—	2	2	no	—
129	#41×C₁₉	—	2	2	no	—
130	#41×C₁₉	—	4	1	no	—
131	#41×C₁₉	—	4	1	no	—
132	#41×C₁₉	—	4	1	no	—
133	#41×C₁₉	—	4	1	no	—
134	#41×C₁₉	—	4	1	no	—
135	#41×C₁₉	—	4	1	no	—
136	#41×C₁₉	—	4	1	no	—
137	#41×C₁₉	—	4	1	no	—
138	C₂×Q₈×C₁₉	—	2	2	no	—
139	C₂×Q₈×C₁₉	—	2	2	no	—
140	C₂×Q₈×C₁₉	—	2	2	no	—
141	C₂×Q₈×C₁₉	—	2	1	no	—
142	C₂×Q₈×C₁₉	—	2	2	no	—
143	C₂×Q₈×C₁₉	—	2	2	no	—
144	C₂×Q₈×C₁₉	—	2	2	no	—
145	C₂×Q₈×C₁₉	—	2	2	no	—
146	C₂×Q₈×C₁₉	—	2	2	no	—
147	C₂×Q₈×C₁₉	—	2	2	no	—
148	C₂×Q₈×C₁₉	—	2	1	no	—
149	C₂×Q₈×C₁₉	—	2	2	no	—
150	C₂×Q₈×C₁₉	—	2	2	no	—
151	C₂×Q₈×C₁₉	—	2	2	no	—
152	C₂×Q₈×C₁₉	—	2	2	no	—
153	C₂×Q₈×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	—	2	1	no	—
155	C₂×Q₈×C₁₉	—	2	2	no	—
156	C₂×Q₈×C₁₉	—	2	2	no	—
157	C₂×Q₈×C₁₉	—	2	1	no	—
158	C₂×Q₈×C₁₉	—	4	1	no	—
159	C₂×Q₈×C₁₉	—	4	1	no	—
160	C₂×Q₈×C₁₉	—	4	1	no	—
161	C₂×Q₈×C₁₉	—	4	1	no	—
162	C₂×Q₈×C₁₉	—	4	1	no	—
163	C₂×Q₈×C₁₉	—	4	1	no	—
164	C₂×Q₈×C₁₉	—	4	1	no	—
165	C₂×Q₈×C₁₉	—	4	1	no	—
166	C₂×Q₈×C₁₉	—	4	1	no	—
167	C₂×Q₈×C₁₉	—	4	1	no	—
168	C₂×Q₈×C₁₉	—	4	1	no	—
169	C₂×Q₈×C₁₉	—	4	1	no	—
170	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
171	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
172	C₂×D₄×C₁₉	—	2	2	no	—
173	C₂×D₄×C₁₉	—	2	2	no	—
174	C₂×D₄×C₁₉	—	2	1	no	—
175	C₂×D₄×C₁₉	—	2	1	no	—
176	C₂×D₄×C₁₉	—	2	1	no	—
177	C₂×D₄×C₁₉	—	2	1	no	—
178	C₂×D₄×C₁₉	—	2	1	no	—
179	C₂×D₄×C₁₉	—	4	1	no	—
180	C₂×D₄×C₁₉	—	4	1	no	—
181	C₂×D₄×C₁₉	—	4	1	no	—
182	C₂×D₄×C₁₉	—	4	1	no	—
183	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
184	C₂²×C₄×C₁₉	—	2	2	no	—
185	C₂²×C₄×C₁₉	—	2	2	no	—
186	C₂²×C₄×C₁₉	—	2	2	no	—
187	C₂²×C₄×C₁₉	—	2	1	no	—
188	C₂²×C₄×C₁₉	—	2	2	no	—
189	C₂²×C₄×C₁₉	—	2	2	no	—
190	C₂²×C₄×C₁₉	—	2	2	no	—
191	C₂²×C₄×C₁₉	—	4	1	no	—
192	C₂²×C₄×C₁₉	—	4	1	no	—
193	C₂²×C₄×C₁₉	—	4	1	no	—
194	C₂²×C₄×C₁₉	—	4	1	no	—
195	C₂²×C₄×C₁₉	—	4	1	no	—
196	C₂²×C₄×C₁₉	—	4	1	no	—
197	C₂²×C₄×C₁₉	—	4	1	no	—
198	C₂²×C₄×C₁₉	—	4	1	no	—
199	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
210	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
211	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
212	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
213	C₂²×Dic₁₉	—	2	2	no	—
214	C₂²×Dic₁₉	—	4	1	no	—
215	C₄⋊C₄×C₁₉	—	2	16	no	—
216	C₄⋊C₄×C₁₉	—	2	2	no	—
217	C₄⋊C₄×C₁₉	—	2	2	no	—
218	C₂²⋊C₄×C₁₉	—	2	16	no	—
219	C₂²⋊C₄×C₁₉	—	2	2	no	—
220	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
221	C₄²×C₁₉	—	2	2	no	—
222	C₄²×C₁₉	—	2	2	no	—
223	C₂²⋊Dic₁₉	—	2	2	no	—
224	C₂²⋊Dic₁₉	—	4	1	no	—
225	C₂²⋊Dic₁₉	—	4	1	no	—
226	C₂²⋊Dic₁₉	—	4	1	no	—
227	C₄⋊Dic₁₉	—	2	2	no	—
228	C₄⋊Dic₁₉	—	2	2	no	—
229	C₄⋊Dic₁₉	—	2	2	no	—
230	C₄⋊Dic₁₉	—	4	1	no	—
231	C₄×Dic₁₉	—	2	2	no	—
232	C₄×Dic₁₉	—	4	1	no	—
233	C₄×Dic₁₉	—	4	1	no	—
234	C₄×Dic₁₉	—	4	1	no	—
235	#64520	—	2	2	no	—
236	#64520	—	2	2	no	—
237	#64520	—	4	1	no	—
238	#64520	—	4	1	no	—
239	#64520	—	4	1	no	—
240	#64520	—	4	1	no	—
241	#64520	—	4	1	no	—
242	#64520	—	4	1	no	—
243	C₂×C₁₉⋊C₈	—	2	2	no	—
244	C₂×C₁₉⋊C₈	—	2	2	no	—
245	C₂×C₁₉⋊C₈	—	2	2	no	—
246	C₂×C₁₉⋊C₈	—	2	2	no	—
247	C₂×C₁₉⋊C₈	—	4	1	no	—
248	C₂×C₁₉⋊C₈	—	4	1	no	—
249	#11005	—	19	1	no	maximal, Sylow
250	C₂³×C₁₉	—	2	2	no	—
251	C₂³×C₁₉	—	4	2	no	—
252	C₂³×C₁₉	—	4	4	no	—
253	C₂³×C₁₉	—	4	1	no	—
254	C₂³×C₁₉	—	4	1	no	—
255	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂³×C₁₉	#120	1	1	yes	characteristic
257	C₂³×C₁₉	#120	1	1	yes	characteristic
258	C₂³×C₁₉	#121	1	1	yes	characteristic
259	C₂³×C₁₉	#121	1	1	yes	characteristic
260	C₂³×C₁₉	#124	1	1	yes	characteristic
261	C₂³×C₁₉	#127	1	1	yes	characteristic
262	Q₈×C₁₉	—	2	4	no	—
263	Q₈×C₁₉	—	2	4	no	—
264	Q₈×C₁₉	—	2	2	no	—
265	Q₈×C₁₉	—	2	2	no	—
266	Q₈×C₁₉	—	4	2	no	—
267	Q₈×C₁₉	—	4	2	no	—
268	Q₈×C₁₉	—	4	2	no	—
269	Q₈×C₁₉	—	4	2	no	—
270	Q₈×C₁₉	—	4	1	no	—
271	Q₈×C₁₉	—	4	2	no	—
272	Q₈×C₁₉	—	4	2	no	—
273	Q₈×C₁₉	—	4	1	no	—
274	D₄×C₁₉	—	2	2	no	—
275	D₄×C₁₉	—	2	2	no	—
276	D₄×C₁₉	—	4	2	no	—
277	D₄×C₁₉	—	4	2	no	—
278	D₄×C₁₉	—	4	2	no	—
279	D₄×C₁₉	—	4	2	no	—
280	D₄×C₁₉	—	4	1	no	—
281	D₄×C₁₉	—	4	1	no	—
282	C₂×C₄×C₁₉	—	2	4	no	—
283	C₂×C₄×C₁₉	—	2	4	no	—
284	C₂×C₄×C₁₉	—	2	2	no	—
285	C₂×C₄×C₁₉	—	4	4	no	—
286	C₂×C₄×C₁₉	—	4	2	no	—
287	C₂×C₄×C₁₉	—	4	2	no	—
288	C₂×C₄×C₁₉	—	4	1	no	—
289	C₂×C₄×C₁₉	—	4	2	no	—
290	C₂×C₄×C₁₉	—	4	2	no	—
291	C₂×C₄×C₁₉	—	4	1	no	—
292	C₂×C₄×C₁₉	—	4	2	no	—
293	C₂×C₄×C₁₉	—	4	2	no	—
294	C₂×C₄×C₁₉	—	4	2	no	—
295	C₂×C₄×C₁₉	—	4	2	no	—
296	C₂×C₄×C₁₉	—	4	2	no	—
297	C₂×C₄×C₁₉	—	4	2	no	—
298	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
299	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
300	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
301	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
302	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
303	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
304	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
305	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
306	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
307	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
308	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
309	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
310	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
311	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
312	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
313	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
314	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
315	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
316	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
317	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
318	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
319	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
320	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
321	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
322	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
323	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
324	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
325	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
326	C₂×Dic₁₉	—	4	2	no	—
327	C₂×Dic₁₉	—	4	2	no	—
328	C₂×Dic₁₉	—	8	2	no	—
329	C₂×Dic₁₉	—	8	2	no	—
330	C₁₉⋊C₈	—	4	2	no	—
331	C₁₉⋊C₈	—	4	2	no	—
332	C₂×#536	D₁₉	1	1	yes	characteristic
333	C₂×#421	—	19	1	no	—
334	#2896	—	19	1	no	—
335	C₂×#419	—	19	1	no	—
336	C₂×#419	—	19	1	no	—
337	C₂×#344	—	19	1	no	—
338	#1740	—	19	1	no	—
339	C₂²×C₁₉	—	2	2	no	—
340	C₂²×C₁₉	—	2	2	no	—
341	C₂²×C₁₉	—	2	2	no	—
342	C₂²×C₁₉	—	4	1	no	—
343	C₂²×C₁₉	—	4	1	no	—
344	C₂²×C₁₉	—	4	1	no	—
345	C₂²×C₁₉	—	4	1	no	—
346	C₂²×C₁₉	—	4	4	no	—
347	C₂²×C₁₉	—	4	2	no	—
348	C₂²×C₁₉	—	8	2	no	—
349	C₂²×C₁₉	—	8	2	no	—
350	C₂²×C₁₉	#379	1	1	yes	characteristic
351	C₂²×C₁₉	#390	1	1	yes	characteristic
352	C₂²×C₁₉	#390	1	1	yes	characteristic
353	C₂²×C₁₉	#392	1	1	yes	characteristic
354	C₂²×C₁₉	#392	1	1	yes	characteristic
355	C₂²×C₁₉	#394	1	1	yes	characteristic
356	C₂²×C₁₉	#394	1	1	yes	characteristic
357	C₄×C₁₉	—	4	4	no	—
358	C₄×C₁₉	—	4	2	no	—
359	C₄×C₁₉	—	4	4	no	—
360	C₄×C₁₉	#386	1	1	yes	characteristic
361	C₄×C₁₉	#386	1	1	yes	characteristic
362	C₄×C₁₉	#386	1	1	yes	characteristic
363	C₄×C₁₉	#386	1	1	yes	characteristic
364	C₄×C₁₉	#392	1	1	yes	characteristic
365	C₄×C₁₉	#392	1	1	yes	characteristic
366	C₄×C₁₉	#394	1	1	yes	characteristic
367	C₄×C₁₉	#394	1	1	yes	characteristic
368	Dic₁₉	—	8	2	no	—
369	Dic₁₉	—	8	2	no	—
370	C₂²×#41	C₂×D₁₉	1	1	yes	characteristic
371	C₂³×Q₈	C₂×D₁₉	1	1	yes	characteristic
372	C₂²×M₁₆	—	19	1	no	—
373	C₂²×M₁₆	—	19	1	no	—
374	#536	—	2	2	no	—
375	#536	—	2	2	no	—
376	#536	—	2	2	no	—
377	#536	Dic₁₉	1	4	yes	complemented
378	C₂×C₄⋊Q₈	—	2	1	no	—
379	C₂×#124	—	2	1	no	—
380	C₂×#123	—	2	2	no	—
381	C₂×C₂²⋊Q₈	—	2	2	no	—
382	C₂×#117	—	19	1	no	—
383	C₂×#117	—	19	1	no	—
384	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
385	#421	—	38	2	no	—
386	#421	—	38	2	no	—
387	C₂×#104	—	38	2	no	—
388	#419	—	38	2	no	—
389	#419	—	38	2	no	—
390	#419	—	38	2	no	—
391	#419	—	38	2	no	—
392	#419	—	38	1	no	—
393	#418	—	38	1	no	—
394	#417	—	38	2	no	—
395	#416	—	38	2	no	—
396	C₂×#103	—	38	2	no	—
397	C₂×#103	—	38	2	no	—
398	#344	—	38	2	no	—
399	#342	—	38	2	no	—
400	C₂×C₁₉	—	2	1	no	—
401	C₂×C₁₉	—	2	1	no	—
402	C₂×C₁₉	—	2	1	no	—
403	C₂×C₁₉	—	2	1	no	—
404	C₂×C₁₉	—	2	1	no	—
405	C₂×C₁₉	—	2	1	no	—
406	C₂×C₁₉	—	8	2	no	—
407	C₂×C₁₉	#1438	1	1	yes	characteristic
408	C₂×C₁₉	#2009	1	2	yes	—
409	C₂×#41	—	2	1	no	—
410	C₂×#41	—	2	1	no	—
411	C₂×#41	—	2	1	no	—
412	C₂×#41	—	2	1	no	—
413	C₂×#41	—	2	1	no	—
414	C₂×#41	—	2	1	no	—
415	C₂×#41	—	2	1	no	—
416	C₂×#41	—	2	1	no	—
417	C₂×#41	—	2	1	no	—
418	C₂×#41	—	2	1	no	—
419	C₂×#41	C₂×Dic₁₉	1	2	yes	—
420	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
421	C₂²×Q₈	—	2	1	no	—
422	C₂²×Q₈	—	2	1	no	—
423	C₂²×Q₈	—	2	1	no	—
424	C₂²×Q₈	—	2	1	no	—
425	C₂²×Q₈	—	2	1	no	—
426	C₂²×Q₈	—	2	1	no	—
427	C₂²×Q₈	—	2	1	no	—
428	C₂²×Q₈	—	2	1	no	—
429	C₂²×Q₈	—	2	1	no	—
430	C₂²×Q₈	—	2	1	no	—
431	C₂²×Q₈	—	2	1	no	—
432	C₂²×Q₈	C₂×Dic₁₉	1	2	yes	—
433	C₂²×Q₈	C₂²⋊D₁₉	1	2	yes	—
434	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
435	C₂²×Q₈	C₂²⋊D₁₉	1	2	yes	—
436	C₂²×D₄	—	2	1	no	—
437	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
438	C₂³×C₄	—	2	1	no	—
439	C₂³×C₄	—	2	1	no	—
440	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
441	C₂×M₁₆	—	19	2	no	—
442	C₂×M₁₆	—	38	1	no	—
443	C₂×M₁₆	—	38	1	no	—
444	C₂×M₁₆	—	38	1	no	—
445	C₂×M₁₆	—	38	1	no	—
446	C₂×M₁₆	—	38	1	no	—
447	C₂×M₁₆	—	38	1	no	—
448	C₂×M₁₆	—	38	1	no	—
449	C₂×M₁₆	—	38	1	no	—
450	C₂×M₁₆	—	38	1	no	—
451	C₂×M₁₆	—	38	1	no	—
452	C₂×M₁₆	—	38	1	no	—
453	C₂²×C₈	—	19	2	no	—
454	C₂²×C₈	—	38	1	no	—
455	C₄⋊Q₈	—	2	4	no	—
456	C₄⋊Q₈	—	2	4	no	—
457	#124	—	2	4	no	—
458	#124	—	2	4	no	—
459	#123	—	2	8	no	—
460	#123	—	2	8	no	—
461	C₂²⋊Q₈	—	2	8	no	—
462	C₂²⋊Q₈	—	2	8	no	—
463	#117	—	2	1	no	—
464	#117	—	2	1	no	—
465	#117	—	19	2	no	—
466	#117	—	38	1	no	—
467	#117	—	38	1	no	—
468	#117	—	38	1	no	—
469	#117	—	38	1	no	—
470	#117	—	38	1	no	—
471	#117	—	38	1	no	—
472	#117	—	38	1	no	—
473	#117	C₂×Dic₁₉	1	2	yes	—
474	#117	C₂²⋊D₁₉	1	2	yes	—
475	C₂×C₄⋊C₄	—	2	4	no	—
476	C₂×C₄⋊C₄	—	2	1	no	—
477	C₂×C₄⋊C₄	—	19	2	no	—
478	C₂×C₄⋊C₄	—	38	1	no	—
479	C₂×C₂²⋊C₄	—	2	4	no	—
480	C₂×C₂²⋊C₄	—	38	1	no	—
481	C₂×C₂²⋊C₄	—	38	1	no	—
482	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	2	yes	—
483	C₂×C₄²	—	2	1	no	—
484	C₂×C₄²	—	38	1	no	—
485	C₂×C₄²	—	38	1	no	—
486	#104	—	38	8	no	—
487	#103	—	38	8	no	—
488	#103	—	38	8	no	—
489	#103	—	38	4	no	—
490	#102	—	38	4	no	—
491	C₁₉	#11005	1	1	yes	characteristic, complemented, Sylow
492	C₂⁴	—	2	1	no	—
493	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
494	#41	—	2	2	no	—
495	#41	—	2	2	no	—
496	#41	—	2	2	no	—
497	#41	—	2	2	no	—
498	#41	—	2	2	no	—
499	#41	—	2	2	no	—
500	#41	—	2	2	no	—
501	#41	—	2	2	no	—
502	#41	—	4	1	no	—
503	#41	—	4	1	no	—
504	#41	—	4	1	no	—
505	#41	—	4	1	no	—
506	#41	—	4	1	no	—
507	#41	—	4	1	no	—
508	#41	—	4	1	no	—
509	#41	—	4	1	no	—
510	C₂×Q₈	—	2	2	no	—
511	C₂×Q₈	—	2	2	no	—
512	C₂×Q₈	—	2	2	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	2	2	no	—
515	C₂×Q₈	—	2	2	no	—
516	C₂×Q₈	—	2	2	no	—
517	C₂×Q₈	—	2	2	no	—
518	C₂×Q₈	—	2	2	no	—
519	C₂×Q₈	—	2	2	no	—
520	C₂×Q₈	—	2	1	no	—
521	C₂×Q₈	—	2	2	no	—
522	C₂×Q₈	—	2	2	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	2	no	—
525	C₂×Q₈	—	2	2	no	—
526	C₂×Q₈	—	2	2	no	—
527	C₂×Q₈	—	2	2	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	4	1	no	—
531	C₂×Q₈	—	4	1	no	—
532	C₂×Q₈	—	4	1	no	—
533	C₂×Q₈	—	4	1	no	—
534	C₂×Q₈	—	4	1	no	—
535	C₂×Q₈	—	4	1	no	—
536	C₂×Q₈	—	4	1	no	—
537	C₂×Q₈	—	4	1	no	—
538	C₂×Q₈	—	4	1	no	—
539	C₂×Q₈	—	4	1	no	—
540	C₂×Q₈	—	4	1	no	—
541	C₂×Q₈	—	4	1	no	—
542	C₂×Q₈	C₂²⋊Dic₁₉	1	4	yes	—
543	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
544	C₂×D₄	—	2	2	no	—
545	C₂×D₄	—	2	2	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	4	1	no	—
552	C₂×D₄	—	4	1	no	—
553	C₂×D₄	—	4	1	no	—
554	C₂×D₄	—	4	1	no	—
555	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	4	1	no	—
564	C₂²×C₄	—	4	1	no	—
565	C₂²×C₄	—	4	1	no	—
566	C₂²×C₄	—	4	1	no	—
567	C₂²×C₄	—	4	1	no	—
568	C₂²×C₄	—	4	1	no	—
569	C₂²×C₄	—	4	1	no	—
570	C₂²×C₄	—	4	1	no	—
571	C₂²×C₄	—	38	2	no	—
572	C₂²×C₄	—	76	1	no	—
573	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
574	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
575	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
576	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
577	C₂²×C₄	#64543	1	1	yes	characteristic
578	C₂²×C₄	#64543	1	1	yes	characteristic
579	C₂²×C₄	#64543	1	1	yes	characteristic
580	C₂²×C₄	#64543	1	1	yes	characteristic
581	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
582	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
583	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
584	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
585	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
586	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
587	M₁₆	—	38	2	no	—
588	M₁₆	—	38	2	no	—
589	M₁₆	—	76	1	no	—
590	M₁₆	—	76	1	no	—
591	M₁₆	—	76	1	no	—
592	M₁₆	—	76	1	no	—
593	M₁₆	—	76	1	no	—
594	M₁₆	—	76	1	no	—
595	C₂×C₈	—	38	2	no	—
596	C₂×C₈	—	38	2	no	—
597	C₂×C₈	—	38	2	no	—
598	C₂×C₈	—	38	2	no	—
599	C₂×C₈	—	76	1	no	—
600	C₂×C₈	—	76	1	no	—
601	C₄⋊C₄	—	2	16	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	38	2	no	—
605	C₄⋊C₄	—	38	2	no	—
606	C₄⋊C₄	—	38	2	no	—
607	C₄⋊C₄	—	76	1	no	—
608	C₂²⋊C₄	—	2	16	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	38	2	no	—
611	C₂²⋊C₄	—	76	1	no	—
612	C₂²⋊C₄	—	76	1	no	—
613	C₂²⋊C₄	—	76	1	no	—
614	C₂²⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
615	C₄²	—	2	2	no	—
616	C₄²	—	2	2	no	—
617	C₄²	—	38	2	no	—
618	C₄²	—	76	1	no	—
619	C₄²	—	76	1	no	—
620	C₄²	—	76	1	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	4	2	no	—
623	C₂³	—	4	4	no	—
624	C₂³	—	4	1	no	—
625	C₂³	—	4	1	no	—
626	C₂³	#10597382	1	1	yes	characteristic
627	C₂³	#10597384	1	1	yes	characteristic
628	C₂³	#10597384	1	1	yes	characteristic
629	C₂³	#10597386	1	1	yes	characteristic
630	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
631	C₂³	#10597399	1	1	yes	characteristic
632	C₂³	#10597399	1	1	yes	characteristic
633	Q₈	—	2	4	no	—
634	Q₈	—	2	4	no	—
635	Q₈	—	2	2	no	—
636	Q₈	—	2	2	no	—
637	Q₈	—	4	2	no	—
638	Q₈	—	4	2	no	—
639	Q₈	—	4	2	no	—
640	Q₈	—	4	2	no	—
641	Q₈	—	4	1	no	—
642	Q₈	—	4	2	no	—
643	Q₈	—	4	2	no	—
644	Q₈	—	4	1	no	—
645	D₄	—	2	2	no	—
646	D₄	—	2	2	no	—
647	D₄	—	4	2	no	—
648	D₄	—	4	2	no	—
649	D₄	—	4	2	no	—
650	D₄	—	4	2	no	—
651	D₄	—	4	1	no	—
652	D₄	—	4	1	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	4	4	no	—
657	C₂×C₄	—	4	2	no	—
658	C₂×C₄	—	4	2	no	—
659	C₂×C₄	—	4	2	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	2	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	2	no	—
664	C₂×C₄	—	4	2	no	—
665	C₂×C₄	—	4	2	no	—
666	C₂×C₄	—	4	2	no	—
667	C₂×C₄	—	4	2	no	—
668	C₂×C₄	—	4	2	no	—
669	C₂×C₄	—	76	2	no	—
670	C₂×C₄	—	76	2	no	—
671	C₂×C₄	—	152	2	no	—
672	C₂×C₄	—	152	2	no	—
673	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
674	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
675	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
676	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
677	C₂×C₄	#10597381	1	1	yes	characteristic
678	C₂×C₄	#10597381	1	1	yes	characteristic
679	C₂×C₄	#10597381	1	1	yes	characteristic
680	C₂×C₄	#10597381	1	1	yes	characteristic
681	C₂×C₄	#10597382	1	1	yes	characteristic
682	C₂×C₄	#10597383	1	1	yes	characteristic
683	C₂×C₄	#10597383	1	1	yes	characteristic
684	C₂×C₄	#10597383	1	1	yes	characteristic
685	C₂×C₄	#10597383	1	1	yes	characteristic
686	C₂×C₄	#10597384	1	1	yes	characteristic
687	C₂×C₄	#10597384	1	1	yes	characteristic
688	C₂×C₄	#10597385	1	1	yes	characteristic
689	C₂×C₄	#10597385	1	1	yes	characteristic
690	C₂×C₄	#10597385	1	1	yes	characteristic
691	C₂×C₄	#10597385	1	1	yes	characteristic
692	C₂×C₄	#10597385	1	1	yes	characteristic
693	C₂×C₄	#10597385	1	1	yes	characteristic
694	C₂×C₄	#10597385	1	1	yes	characteristic
695	C₂×C₄	#10597385	1	1	yes	characteristic
696	C₂×C₄	#10597386	1	1	yes	characteristic
697	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
698	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
699	C₂×C₄	#10597399	1	1	yes	characteristic
700	C₂×C₄	#10597399	1	1	yes	characteristic
701	C₈	—	76	2	no	—
702	C₈	—	76	2	no	—
703	C₂²	—	2	2	no	—
704	C₂²	—	2	2	no	—
705	C₂²	—	2	2	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	1	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	4	4	no	—
711	C₂²	—	4	2	no	—
712	C₂²	—	8	2	no	—
713	C₂²	—	8	2	no	—
714	C₂²	#11926400	1	1	yes	characteristic
715	C₂²	#11926447	1	1	yes	characteristic
716	C₂²	#11926447	1	1	yes	characteristic
717	C₂²	#11926452	1	1	yes	characteristic
718	C₂²	#11926452	1	1	yes	characteristic
719	C₂²	#11926458	1	1	yes	characteristic
720	C₂²	#11926458	1	1	yes	characteristic
721	C₄	—	4	4	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	4	no	—
724	C₄	—	152	2	no	—
725	C₄	—	152	2	no	—
726	C₄	#11926424	1	1	yes	characteristic
727	C₄	#11926424	1	1	yes	characteristic
728	C₄	#11926424	1	1	yes	characteristic
729	C₄	#11926424	1	1	yes	characteristic
730	C₄	#11926452	1	1	yes	characteristic
731	C₄	#11926452	1	1	yes	characteristic
732	C₄	#11926458	1	1	yes	characteristic
733	C₄	#11926458	1	1	yes	characteristic
734	C₂	—	2	1	no	—
735	C₂	—	2	1	no	—
736	C₂	—	2	1	no	—
737	C₂	—	2	1	no	—
738	C₂	—	2	1	no	—
739	C₂	—	2	1	no	—
740	C₂	—	8	2	no	—
741	C₂	#14561876	1	1	yes	characteristic
742	C₂	#14564695	1	2	yes	—

	subgroup	G/H
center	C₂²	#11926452
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#536	C₂
socle	C₂²×C₁₉	#392
prime radical	C₂²×#41×C₁₉	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#536	D₁₉
hypocenter	C₁₉	#11005
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#536

Complements

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

N	H ≅ G/N	type
3. C₂×#11926553	C₂	semidirect
4. C₂×#11926553	C₂	semidirect
5. C₂×#11926314	C₂	semidirect
6. #14563367	C₂	semidirect
32. C₁₉×#536	C₄	semidirect
377. #536	Dic₁₉	semidirect
491. C₁₉	#11005	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
#14572154	2
C₂×#11926553	2
C₂×#11926314	2
#14563367	2
C₂×C₁₉×#536	2
#11005	19