Subgroups — #18089203

Order 4864.

1292 conjugacy classes of subgroups.

The subgroup lattice has 806 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	#14572154	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11926528	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926518	C₂	1	1	yes	maximal, characteristic, complemented
5	#14563345	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11926300	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3449	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	1	no	—
16	#11926549	—	2	1	no	—
17	#11926545	—	2	2	no	—
18	#11926540	—	2	2	no	—
19	#11926528	—	2	2	no	—
20	#11926528	—	2	2	no	—
21	C₂×#10597293	—	2	1	no	—
22	C₂×#10597290	—	2	1	no	—
23	#11926518	—	2	2	no	—
24	#11926518	—	2	2	no	—
25	C₂×#10597291	—	2	2	no	—
26	#11926304	—	2	2	no	—
27	#11926300	—	2	2	no	—
28	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
29	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×#537	—	2	2	no	—
31	C₁₉×#536	—	2	1	no	—
32	C₁₉×#536	—	2	1	no	—
33	C₁₉×#535	—	2	1	no	—
34	C₁₉×#535	—	2	1	no	—
35	C₁₉×#534	—	2	2	no	—
36	C₁₉×#532	—	2	2	no	—
37	C₁₉×#525	—	2	2	no	—
38	C₁₉×#525	C₄	1	4	yes	complemented
39	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
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	—	2	1	no	—
60	C₂×#41×C₁₉	—	2	1	no	—
61	C₂×#41×C₁₉	—	2	1	no	—
62	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
63	C₂×#41×C₁₉	D₄	1	2	yes	—
64	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
65	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
66	C₂²×D₄×C₁₉	—	2	1	no	—
67	C₂²×D₄×C₁₉	D₄	1	2	yes	—
68	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
69	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
70	C₂³×C₄×C₁₉	—	2	1	no	—
71	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
72	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₁₉×C₄⋊Q₈	—	2	2	no	—
74	C₁₉×#127	—	2	2	no	—
75	C₁₉×#124	—	2	2	no	—
76	C₁₉×#124	—	2	2	no	—
77	C₁₉×#123	—	2	4	no	—
78	C₁₉×#123	—	2	4	no	—
79	C₁₉×C₂²⋊Q₈	—	2	4	no	—
80	C₁₉×C₂²⋊Q₈	—	2	4	no	—
81	C₁₉×#121	—	2	4	no	—
82	C₁₉×#121	—	2	8	no	—
83	C₁₉×#121	—	2	4	no	—
84	C₁₉×#120	—	2	4	no	—
85	C₁₉×#120	—	2	4	no	—
86	C₄×D₄×C₁₉	—	2	8	no	—
87	C₁₉×#117	—	2	1	no	—
88	C₁₉×#117	—	2	1	no	—
89	C₁₉×#117	C₂×C₄	1	2	yes	—
90	C₁₉×#117	D₄	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₄²×C₁₉	D₄	1	2	yes	—
94	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
95	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
96	#10597372	—	2	1	no	—
97	#10597372	—	2	1	no	—
98	#10597372	—	2	1	no	—
99	#10597372	—	2	1	no	—
100	#10597372	—	2	1	no	—
101	#10597372	—	2	1	no	—
102	#10597372	D₄	1	2	yes	complemented
103	#10597372	D₄	1	2	yes	complemented
104	C₂×C₄⋊Dic₁₉	—	2	1	no	—
105	C₂×C₄⋊Dic₁₉	—	2	1	no	—
106	C₂×C₄×Dic₁₉	—	2	1	no	—
107	C₂×C₄×Dic₁₉	—	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	—	2	1	no	—
113	C₂×#64520	—	2	1	no	—
114	C₂×#64520	—	2	1	no	—
115	C₂×#64520	—	2	1	no	—
116	C₂×#64520	—	2	1	no	—
117	C₂×#64520	—	2	1	no	—
118	C₂×#64520	D₄	1	2	yes	complemented
119	C₂×#64520	D₄	1	2	yes	complemented
120	C₂²×C₁₉⋊C₈	—	2	1	no	—
121	C₂²×C₁₉⋊C₈	—	2	1	no	—
122	#10597294	—	2	8	no	—
123	#10597293	—	2	4	no	—
124	#10597292	—	2	4	no	—
125	#10597291	—	2	8	no	—
126	#10597290	—	2	4	no	—
127	#10597289	—	2	4	no	—
128	C₂⁴×C₁₉	—	2	1	no	—
129	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
130	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
140	#41×C₁₉	—	4	1	no	—
141	#41×C₁₉	—	4	1	no	—
142	#41×C₁₉	—	4	1	no	—
143	#41×C₁₉	—	4	1	no	—
144	#41×C₁₉	—	4	1	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	#41×C₁₉	—	4	1	no	—
162	#41×C₁₉	—	4	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	—	2	1	no	—
172	C₂×Q₈×C₁₉	—	2	1	no	—
173	C₂×Q₈×C₁₉	—	2	1	no	—
174	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
175	C₂×D₄×C₁₉	—	2	2	no	—
176	C₂×D₄×C₁₉	—	2	2	no	—
177	C₂×D₄×C₁₉	—	2	2	no	—
178	C₂×D₄×C₁₉	—	2	2	no	—
179	C₂×D₄×C₁₉	—	2	2	no	—
180	C₂×D₄×C₁₉	—	2	2	no	—
181	C₂×D₄×C₁₉	—	2	2	no	—
182	C₂×D₄×C₁₉	—	2	2	no	—
183	C₂×D₄×C₁₉	—	2	8	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	—	2	1	no	—
188	C₂×D₄×C₁₉	—	2	1	no	—
189	C₂×D₄×C₁₉	—	2	1	no	—
190	C₂×D₄×C₁₉	—	2	1	no	—
191	C₂×D₄×C₁₉	—	2	1	no	—
192	C₂×D₄×C₁₉	—	2	1	no	—
193	C₂×D₄×C₁₉	—	2	1	no	—
194	C₂×D₄×C₁₉	—	2	1	no	—
195	C₂×D₄×C₁₉	—	4	1	no	—
196	C₂×D₄×C₁₉	—	4	1	no	—
197	C₂×D₄×C₁₉	—	4	1	no	—
198	C₂×D₄×C₁₉	—	4	1	no	—
199	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
200	C₂²×C₄×C₁₉	—	2	1	no	—
201	C₂²×C₄×C₁₉	—	2	2	no	—
202	C₂²×C₄×C₁₉	—	2	2	no	—
203	C₂²×C₄×C₁₉	—	2	2	no	—
204	C₂²×C₄×C₁₉	—	2	2	no	—
205	C₂²×C₄×C₁₉	—	2	2	no	—
206	C₂²×C₄×C₁₉	—	2	2	no	—
207	C₂²×C₄×C₁₉	—	2	2	no	—
208	C₂²×C₄×C₁₉	—	2	2	no	—
209	C₂²×C₄×C₁₉	—	2	2	no	—
210	C₂²×C₄×C₁₉	—	4	1	no	—
211	C₂²×C₄×C₁₉	—	4	1	no	—
212	C₂²×C₄×C₁₉	—	4	1	no	—
213	C₂²×C₄×C₁₉	—	4	1	no	—
214	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
215	C₂²×C₄×C₁₉	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
226	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
227	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
228	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
229	C₂²×Dic₁₉	—	4	1	no	—
230	C₂²×Dic₁₉	—	4	1	no	—
231	C₄⋊C₄×C₁₉	—	2	8	no	—
232	C₄⋊C₄×C₁₉	—	2	2	no	—
233	C₄⋊C₄×C₁₉	—	2	2	no	—
234	C₂²⋊C₄×C₁₉	—	2	8	no	—
235	C₂²⋊C₄×C₁₉	—	2	8	no	—
236	C₂²⋊C₄×C₁₉	—	2	2	no	—
237	C₂²⋊C₄×C₁₉	—	2	2	no	—
238	C₄²×C₁₉	—	2	2	no	—
239	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
240	C₂²⋊Dic₁₉	—	2	2	no	—
241	C₂²⋊Dic₁₉	—	2	2	no	—
242	C₂²⋊Dic₁₉	—	4	1	no	—
243	C₂²⋊Dic₁₉	—	4	1	no	—
244	C₄⋊Dic₁₉	—	2	2	no	—
245	C₄⋊Dic₁₉	—	2	2	no	—
246	C₄⋊Dic₁₉	—	4	1	no	—
247	C₄⋊Dic₁₉	—	4	1	no	—
248	C₄×Dic₁₉	—	2	2	no	—
249	C₄×Dic₁₉	—	2	2	no	—
250	C₄×Dic₁₉	—	4	1	no	—
251	C₄×Dic₁₉	—	4	1	no	—
252	#64520	—	2	2	no	—
253	#64520	—	2	2	no	—
254	#64520	—	2	2	no	—
255	#64520	—	2	2	no	—
256	#64520	—	4	1	no	—
257	#64520	—	4	1	no	—
258	#64520	—	4	1	no	—
259	#64520	—	4	1	no	—
260	C₂×C₁₉⋊C₈	—	2	2	no	—
261	C₂×C₁₉⋊C₈	—	2	2	no	—
262	C₂×C₁₉⋊C₈	—	4	1	no	—
263	C₂×C₁₉⋊C₈	—	4	1	no	—
264	C₂×C₁₉⋊C₈	—	4	1	no	—
265	C₂×C₁₉⋊C₈	—	4	1	no	—
266	#11000	—	19	1	no	maximal, Sylow
267	C₂³×C₁₉	—	2	2	no	—
268	C₂³×C₁₉	—	2	2	no	—
269	C₂³×C₁₉	—	2	2	no	—
270	C₂³×C₁₉	—	2	2	no	—
271	C₂³×C₁₉	—	4	1	no	—
272	C₂³×C₁₉	—	4	1	no	—
273	C₂³×C₁₉	—	8	1	no	—
274	C₂³×C₁₉	—	8	2	no	—
275	C₂³×C₁₉	—	8	2	no	—
276	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
277	C₂³×C₁₉	#120	1	1	yes	characteristic
278	C₂³×C₁₉	#120	1	1	yes	characteristic
279	C₂³×C₁₉	#120	1	1	yes	characteristic
280	C₂³×C₁₉	#121	1	1	yes	characteristic
281	C₂³×C₁₉	#121	1	1	yes	characteristic
282	C₂³×C₁₉	#123	1	1	yes	characteristic
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	Q₈×C₁₉	—	4	1	no	—
290	Q₈×C₁₉	—	4	1	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	D₄×C₁₉	—	4	1	no	—
306	D₄×C₁₉	—	4	1	no	—
307	D₄×C₁₉	—	8	8	no	—
308	C₂×C₄×C₁₉	—	2	4	no	—
309	C₂×C₄×C₁₉	—	2	2	no	—
310	C₂×C₄×C₁₉	—	2	2	no	—
311	C₂×C₄×C₁₉	—	2	2	no	—
312	C₂×C₄×C₁₉	—	2	2	no	—
313	C₂×C₄×C₁₉	—	4	1	no	—
314	C₂×C₄×C₁₉	—	4	1	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	—	4	2	no	—
320	C₂×C₄×C₁₉	—	4	2	no	—
321	C₂×C₄×C₁₉	—	4	2	no	—
322	C₂×C₄×C₁₉	—	4	2	no	—
323	C₂×C₄×C₁₉	—	8	2	no	—
324	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
325	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
326	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
327	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
328	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
329	C₂×C₄×C₁₉	C₄×D₄	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	#120	1	1	yes	characteristic
334	C₂×C₄×C₁₉	#120	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	#121	1	1	yes	characteristic
343	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
344	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
345	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
346	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
347	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
348	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
349	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
350	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
351	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
352	C₂×Dic₁₉	—	4	2	no	—
353	C₂×Dic₁₉	—	4	2	no	—
354	C₂×Dic₁₉	—	8	2	no	—
355	C₂×Dic₁₉	—	8	2	no	—
356	C₁₉⋊C₈	—	4	2	no	—
357	C₁₉⋊C₈	—	4	2	no	—
358	#3449	D₁₉	1	1	yes	characteristic
359	C₂×#421	—	19	1	no	—
360	#2896	—	19	1	no	—
361	C₂×#413	—	19	1	no	—
362	C₂×#410	—	19	1	no	—
363	#1733	—	19	1	no	—
364	C₂×H(3,ℤ/4)	—	19	1	no	—
365	C₂²×C₁₉	—	4	1	no	—
366	C₂²×C₁₉	—	4	1	no	—
367	C₂²×C₁₉	—	4	1	no	—
368	C₂²×C₁₉	—	4	1	no	—
369	C₂²×C₁₉	—	4	1	no	—
370	C₂²×C₁₉	—	4	1	no	—
371	C₂²×C₁₉	—	4	1	no	—
372	C₂²×C₁₉	—	4	4	no	—
373	C₂²×C₁₉	—	4	4	no	—
374	C₂²×C₁₉	—	4	2	no	—
375	C₂²×C₁₉	—	4	2	no	—
376	C₂²×C₁₉	—	8	2	no	—
377	C₂²×C₁₉	—	8	2	no	—
378	C₂²×C₁₉	—	8	2	no	—
379	C₂²×C₁₉	—	8	2	no	—
380	C₂²×C₁₉	#379	1	1	yes	characteristic
381	C₂²×C₁₉	#386	1	1	yes	characteristic
382	C₂²×C₁₉	#386	1	1	yes	characteristic
383	C₂²×C₁₉	#392	1	1	yes	characteristic
384	C₂²×C₁₉	#392	1	1	yes	characteristic
385	C₂²×C₁₉	#394	1	1	yes	characteristic
386	C₂²×C₁₉	#394	1	1	yes	characteristic
387	C₄×C₁₉	—	4	4	no	—
388	C₄×C₁₉	—	4	2	no	—
389	C₄×C₁₉	—	4	2	no	—
390	C₄×C₁₉	#386	1	1	yes	characteristic
391	C₄×C₁₉	#386	1	1	yes	characteristic
392	C₄×C₁₉	#390	1	1	yes	characteristic
393	C₄×C₁₉	#390	1	1	yes	characteristic
394	C₄×C₁₉	#392	1	1	yes	characteristic
395	C₄×C₁₉	#392	1	1	yes	characteristic
396	C₄×C₁₉	#394	1	1	yes	characteristic
397	C₄×C₁₉	#394	1	1	yes	characteristic
398	Dic₁₉	—	8	2	no	—
399	Dic₁₉	—	8	2	no	—
400	C₂²×#41	C₂×D₁₉	1	1	yes	characteristic
401	C₂²×#41	C₂×D₁₉	1	1	yes	characteristic
402	C₂²×M₁₆	—	19	1	no	—
403	C₂²×M₁₆	—	19	1	no	—
404	#537	—	2	2	no	—
405	#536	—	2	1	no	—
406	#536	—	2	1	no	—
407	#535	—	2	1	no	—
408	#535	—	2	1	no	—
409	#534	—	2	2	no	—
410	#532	—	2	2	no	—
411	#525	—	2	2	no	—
412	#525	Dic₁₉	1	4	yes	complemented
413	C₂×#117	—	19	1	no	—
414	C₂×#117	—	19	1	no	—
415	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
416	#421	—	38	2	no	—
417	#421	—	38	2	no	—
418	C₂×#104	—	38	2	no	—
419	#419	—	38	1	no	—
420	#418	—	38	1	no	—
421	#417	—	38	2	no	—
422	#416	—	38	2	no	—
423	#413	—	38	2	no	—
424	#413	—	38	2	no	—
425	C₂×#101	—	38	1	no	—
426	C₂×#100	—	38	1	no	—
427	#410	—	38	2	no	—
428	#410	—	38	2	no	—
429	C₂×#99	—	38	2	no	—
430	#339	—	38	2	no	—
431	H(3,ℤ/4)	—	38	2	no	—
432	C₂×C₁₉	—	2	1	no	—
433	C₂×C₁₉	—	2	1	no	—
434	C₂×C₁₉	—	2	1	no	—
435	C₂×C₁₉	—	2	1	no	—
436	C₂×C₁₉	—	2	1	no	—
437	C₂×C₁₉	—	2	1	no	—
438	C₂×C₁₉	—	2	1	no	—
439	C₂×C₁₉	—	8	2	no	—
440	C₂×C₁₉	—	8	2	no	—
441	C₂×C₁₉	#1438	1	1	yes	characteristic
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	—	2	1	no	—
455	C₂×#41	—	2	1	no	—
456	C₂×#41	—	2	1	no	—
457	C₂×#41	—	2	1	no	—
458	C₂×#41	—	2	1	no	—
459	C₂×#41	—	2	1	no	—
460	C₂×#41	—	2	1	no	—
461	C₂×#41	—	2	1	no	—
462	C₂×#41	—	2	1	no	—
463	C₂×#41	—	2	1	no	—
464	C₂×#41	C₂×Dic₁₉	1	2	yes	—
465	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
466	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
467	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
468	C₂²×D₄	—	2	1	no	—
469	C₂²×D₄	C₂²⋊D₁₉	1	2	yes	—
470	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
471	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
472	C₂³×C₄	—	2	1	no	—
473	C₂³×C₄	C₂×Dic₁₉	1	2	yes	—
474	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
475	C₂×M₁₆	—	19	2	no	—
476	C₂×M₁₆	—	19	2	no	—
477	C₂×M₁₆	—	38	1	no	—
478	C₂×M₁₆	—	38	1	no	—
479	C₂×M₁₆	—	38	1	no	—
480	C₂×M₁₆	—	38	1	no	—
481	C₂×M₁₆	—	38	1	no	—
482	C₂×M₁₆	—	38	1	no	—
483	C₂×M₁₆	—	38	1	no	—
484	C₂×M₁₆	—	38	1	no	—
485	C₂×M₁₆	—	38	1	no	—
486	C₂×M₁₆	—	38	1	no	—
487	C₂²×C₈	—	38	1	no	—
488	C₂²×C₈	—	38	1	no	—
489	C₄⋊Q₈	—	2	2	no	—
490	#127	—	2	2	no	—
491	#124	—	2	2	no	—
492	#124	—	2	2	no	—
493	#123	—	2	4	no	—
494	#123	—	2	4	no	—
495	C₂²⋊Q₈	—	2	4	no	—
496	C₂²⋊Q₈	—	2	4	no	—
497	#121	—	2	4	no	—
498	#121	—	2	8	no	—
499	#121	—	2	4	no	—
500	#120	—	2	4	no	—
501	#120	—	2	4	no	—
502	C₄×D₄	—	2	8	no	—
503	#117	—	2	1	no	—
504	#117	—	2	1	no	—
505	#117	—	19	2	no	—
506	#117	—	19	2	no	—
507	#117	—	38	1	no	—
508	#117	—	38	1	no	—
509	#117	—	38	1	no	—
510	#117	—	38	1	no	—
511	#117	—	38	1	no	—
512	#117	—	38	1	no	—
513	#117	C₂×Dic₁₉	1	2	yes	—
514	#117	C₂²⋊D₁₉	1	2	yes	—
515	C₂×C₄⋊C₄	—	2	1	no	—
516	C₂×C₄⋊C₄	—	38	1	no	—
517	C₂×C₄⋊C₄	—	38	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	—	38	1	no	—
520	C₂×C₂²⋊C₄	—	38	1	no	—
521	C₂×C₄²	—	38	1	no	—
522	C₂×C₄²	—	38	1	no	—
523	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
524	#104	—	38	8	no	—
525	#103	—	38	4	no	—
526	#102	—	38	4	no	—
527	#101	—	38	4	no	—
528	#100	—	38	4	no	—
529	#99	—	38	8	no	—
530	C₁₉	#11000	1	1	yes	characteristic, complemented, Sylow
531	C₂⁴	—	2	1	no	—
532	C₂⁴	C₂²⋊Dic₁₉	1	2	yes	—
533	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
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	—	2	2	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	#41	—	4	1	no	—
558	#41	—	4	1	no	—
559	#41	—	4	1	no	—
560	#41	—	4	1	no	—
561	#41	—	4	1	no	—
562	#41	—	4	1	no	—
563	#41	—	4	1	no	—
564	#41	—	4	1	no	—
565	#41	—	4	1	no	—
566	C₂×Q₈	—	2	1	no	—
567	C₂×Q₈	—	2	1	no	—
568	C₂×Q₈	—	2	1	no	—
569	C₂×Q₈	—	2	1	no	—
570	C₂×Q₈	—	2	1	no	—
571	C₂×Q₈	—	2	1	no	—
572	C₂×Q₈	—	2	1	no	—
573	C₂×Q₈	—	2	1	no	—
574	C₂×Q₈	—	2	1	no	—
575	C₂×Q₈	—	2	1	no	—
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	8	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	1	no	—
596	C₂×D₄	—	2	1	no	—
597	C₂×D₄	—	2	1	no	—
598	C₂×D₄	—	4	1	no	—
599	C₂×D₄	—	4	1	no	—
600	C₂×D₄	—	4	1	no	—
601	C₂×D₄	—	4	1	no	—
602	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	4	1	no	—
614	C₂²×C₄	—	4	1	no	—
615	C₂²×C₄	—	4	1	no	—
616	C₂²×C₄	—	4	1	no	—
617	C₂²×C₄	—	76	1	no	—
618	C₂²×C₄	—	76	1	no	—
619	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
620	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
621	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
622	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
623	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
624	C₂²×C₄	#64543	1	1	yes	characteristic
625	C₂²×C₄	#64543	1	1	yes	characteristic
626	C₂²×C₄	#64543	1	1	yes	characteristic
627	C₂²×C₄	#64543	1	1	yes	characteristic
628	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
629	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
630	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
631	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
632	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
633	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
634	M₁₆	—	38	2	no	—
635	M₁₆	—	38	2	no	—
636	M₁₆	—	38	2	no	—
637	M₁₆	—	38	2	no	—
638	M₁₆	—	76	1	no	—
639	M₁₆	—	76	1	no	—
640	M₁₆	—	76	1	no	—
641	M₁₆	—	76	1	no	—
642	C₂×C₈	—	38	2	no	—
643	C₂×C₈	—	38	2	no	—
644	C₂×C₈	—	76	1	no	—
645	C₂×C₈	—	76	1	no	—
646	C₂×C₈	—	76	1	no	—
647	C₂×C₈	—	76	1	no	—
648	C₄⋊C₄	—	2	8	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	38	2	no	—
652	C₄⋊C₄	—	38	2	no	—
653	C₄⋊C₄	—	76	1	no	—
654	C₄⋊C₄	—	76	1	no	—
655	C₂²⋊C₄	—	2	8	no	—
656	C₂²⋊C₄	—	2	8	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	38	2	no	—
660	C₂²⋊C₄	—	38	2	no	—
661	C₂²⋊C₄	—	76	1	no	—
662	C₂²⋊C₄	—	76	1	no	—
663	C₄²	—	2	2	no	—
664	C₄²	—	38	2	no	—
665	C₄²	—	38	2	no	—
666	C₄²	—	76	1	no	—
667	C₄²	—	76	1	no	—
668	C₄²	C₂²⋊Dic₁₉	1	4	yes	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	4	1	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	8	1	no	—
676	C₂³	—	8	2	no	—
677	C₂³	—	8	2	no	—
678	C₂³	#10597381	1	1	yes	characteristic
679	C₂³	#10597383	1	1	yes	characteristic
680	C₂³	#10597385	1	1	yes	characteristic
681	C₂³	#10597385	1	1	yes	characteristic
682	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
683	C₂³	#10597399	1	1	yes	characteristic
684	C₂³	#10597399	1	1	yes	characteristic
685	Q₈	—	2	2	no	—
686	Q₈	—	2	2	no	—
687	Q₈	—	4	1	no	—
688	Q₈	—	4	1	no	—
689	Q₈	—	4	1	no	—
690	Q₈	—	4	1	no	—
691	Q₈	—	4	1	no	—
692	Q₈	—	4	1	no	—
693	D₄	—	2	2	no	—
694	D₄	—	2	2	no	—
695	D₄	—	4	2	no	—
696	D₄	—	4	2	no	—
697	D₄	—	4	2	no	—
698	D₄	—	4	2	no	—
699	D₄	—	4	2	no	—
700	D₄	—	4	2	no	—
701	D₄	—	4	2	no	—
702	D₄	—	4	2	no	—
703	D₄	—	4	1	no	—
704	D₄	—	4	1	no	—
705	D₄	—	4	1	no	—
706	D₄	—	4	1	no	—
707	D₄	—	4	1	no	—
708	D₄	—	4	1	no	—
709	D₄	—	8	8	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	2	no	—
718	C₂×C₄	—	4	2	no	—
719	C₂×C₄	—	4	2	no	—
720	C₂×C₄	—	4	2	no	—
721	C₂×C₄	—	4	2	no	—
722	C₂×C₄	—	4	2	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	2	no	—
725	C₂×C₄	—	8	2	no	—
726	C₂×C₄	—	76	2	no	—
727	C₂×C₄	—	76	2	no	—
728	C₂×C₄	—	152	2	no	—
729	C₂×C₄	—	152	2	no	—
730	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
731	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
732	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
733	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
734	C₂×C₄	#10597381	1	1	yes	characteristic
735	C₂×C₄	#10597381	1	1	yes	characteristic
736	C₂×C₄	#10597381	1	1	yes	characteristic
737	C₂×C₄	#10597382	1	1	yes	characteristic
738	C₂×C₄	#10597382	1	1	yes	characteristic
739	C₂×C₄	#10597383	1	1	yes	characteristic
740	C₂×C₄	#10597383	1	1	yes	characteristic
741	C₂×C₄	#10597383	1	1	yes	characteristic
742	C₂×C₄	#10597384	1	1	yes	characteristic
743	C₂×C₄	#10597384	1	1	yes	characteristic
744	C₂×C₄	#10597384	1	1	yes	characteristic
745	C₂×C₄	#10597384	1	1	yes	characteristic
746	C₂×C₄	#10597385	1	1	yes	characteristic
747	C₂×C₄	#10597385	1	1	yes	characteristic
748	C₂×C₄	#10597385	1	1	yes	characteristic
749	C₂×C₄	#10597385	1	1	yes	characteristic
750	C₂×C₄	#10597385	1	1	yes	characteristic
751	C₂×C₄	#10597385	1	1	yes	characteristic
752	C₂×C₄	#10597386	1	1	yes	characteristic
753	C₂×C₄	#10597386	1	1	yes	characteristic
754	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
755	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
756	C₂×C₄	#10597399	1	1	yes	characteristic
757	C₂×C₄	#10597399	1	1	yes	characteristic
758	C₈	—	76	2	no	—
759	C₈	—	76	2	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	4	1	no	—
767	C₂²	—	4	4	no	—
768	C₂²	—	4	4	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	8	2	no	—
772	C₂²	—	8	2	no	—
773	C₂²	—	8	2	no	—
774	C₂²	—	8	2	no	—
775	C₂²	#11926400	1	1	yes	characteristic
776	C₂²	#11926424	1	1	yes	characteristic
777	C₂²	#11926424	1	1	yes	characteristic
778	C₂²	#11926452	1	1	yes	characteristic
779	C₂²	#11926452	1	1	yes	characteristic
780	C₂²	#11926458	1	1	yes	characteristic
781	C₂²	#11926458	1	1	yes	characteristic
782	C₄	—	4	4	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	2	no	—
785	C₄	—	152	2	no	—
786	C₄	—	152	2	no	—
787	C₄	#11926424	1	1	yes	characteristic
788	C₄	#11926424	1	1	yes	characteristic
789	C₄	#11926447	1	1	yes	characteristic
790	C₄	#11926447	1	1	yes	characteristic
791	C₄	#11926452	1	1	yes	characteristic
792	C₄	#11926452	1	1	yes	characteristic
793	C₄	#11926458	1	1	yes	characteristic
794	C₄	#11926458	1	1	yes	characteristic
795	C₂	—	2	1	no	—
796	C₂	—	2	1	no	—
797	C₂	—	2	1	no	—
798	C₂	—	2	1	no	—
799	C₂	—	2	1	no	—
800	C₂	—	2	1	no	—
801	C₂	—	2	1	no	—
802	C₂	—	8	2	no	—
803	C₂	—	8	2	no	—
804	C₂	#14561876	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11926447
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3449	C₂
socle	C₂×C₁₉	#1438
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#3449	D₁₉
hypocenter	C₁₉	#11000
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ #3449

Complements

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

N	H ≅ G/N	type
1. C₂×#11926561	C₂	semidirect
2. #14572154	C₂	semidirect
3. C₂×#11926528	C₂	semidirect
4. C₂×#11926518	C₂	semidirect
5. #14563345	C₂	semidirect
6. C₂×#11926300	C₂	semidirect
38. C₁₉×#525	C₄	semidirect
102. #10597372	D₄	semidirect
103. #10597372	D₄	semidirect
118. C₂×#64520	D₄	semidirect
119. C₂×#64520	D₄	semidirect
412. #525	Dic₁₉	semidirect
530. C₁₉	#11000	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×#11926528	2
C₂×#11926518	2
#14563345	2
C₂×#11926300	2
C₁₉×#3449	2
#11000	19