Subgroups — #18088973

Order 4864.

966 conjugacy classes of subgroups.

The subgroup lattice has 638 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	C₂×#11926518	C₂	1	1	yes	maximal, characteristic
3	#14565992	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926315	C₂	1	1	yes	maximal, characteristic, complemented
5	#14563354	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11926301	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	C₂×#10597372	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	C₄	1	4	yes	complemented
14	C₂×#10597294	—	2	2	no	—
15	#11926518	—	2	2	no	—
16	#11926518	C₄	1	4	yes	complemented
17	C₂×#10597291	—	2	2	no	—
18	C₄⋊C₄×Dic₁₉	—	2	2	no	—
19	C₄⋊C₄×Dic₁₉	—	2	2	no	—
20	C₄×C₂²⋊Dic₁₉	—	2	2	no	—
21	#11926315	—	2	2	no	—
22	#11926306	—	2	2	no	—
23	#11926301	—	2	2	no	—
24	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#417	—	2	2	no	—
28	C₁₉×#417	—	2	2	no	—
29	C₂×C₁₉×#103	C₄	1	2	yes	complemented
30	C₂×C₁₉×#102	C₄	1	2	yes	complemented
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	—	2	1	no	—
41	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
42	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
43	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₉	—	2	1	no	—
45	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	—	2	1	no	—
47	C₂³×C₄×C₁₉	—	2	1	no	—
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
55	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
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	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
62	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
63	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
64	C₂×C₂²⋊Dic₁₉	D₄	1	2	yes	—
65	#10597372	—	2	1	no	—
66	#10597372	—	2	1	no	—
67	#10597372	—	2	1	no	—
68	#10597372	—	2	1	no	—
69	#10597372	—	2	1	no	—
70	#10597372	—	2	1	no	—
71	#10597372	—	2	1	no	—
72	#10597372	C₂×C₄	1	2	yes	—
73	#10597372	C₂×C₄	1	2	yes	—
74	#10597372	C₂×C₄	1	2	yes	—
75	#10597372	D₄	1	2	yes	—
76	#10597372	D₄	1	2	yes	—
77	C₂×C₄⋊Dic₁₉	—	2	1	no	—
78	C₂×C₄⋊Dic₁₉	—	2	1	no	—
79	C₂×C₄⋊Dic₁₉	—	2	1	no	—
80	C₂×C₄×Dic₁₉	—	2	1	no	—
81	C₂×C₄×Dic₁₉	—	2	1	no	—
82	C₂×C₄×Dic₁₉	—	2	4	no	—
83	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
84	C₂×#64520	—	2	1	no	—
85	C₂×#64520	—	2	1	no	—
86	C₂×#64520	—	2	1	no	—
87	C₂×#64520	—	2	1	no	—
88	C₂×#64520	—	2	1	no	—
89	C₂×#64520	C₂×C₄	1	2	yes	—
90	C₂²×C₁₉⋊C₈	—	2	1	no	—
91	C₁₉×#103	—	2	4	no	—
92	C₁₉×#102	—	2	4	no	—
93	#10597294	—	2	8	no	—
94	#10597291	—	2	8	no	—
95	C₁₉⋊#95	—	2	4	no	—
96	C₂⁴×C₁₉	—	2	1	no	—
97	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	2	no	—
105	#41×C₁₉	—	2	2	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	#41×C₁₉	—	4	1	no	—
113	#41×C₁₉	—	4	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	—	2	1	no	—
118	C₂×Q₈×C₁₉	—	2	1	no	—
119	C₂×Q₈×C₁₉	C₄²	1	2	yes	complemented
120	C₂×D₄×C₁₉	—	2	2	no	—
121	C₂×D₄×C₁₉	—	2	2	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	—	2	1	no	—
126	C₂×D₄×C₁₉	—	2	1	no	—
127	C₂×D₄×C₁₉	—	4	1	no	—
128	C₂×D₄×C₁₉	—	4	1	no	—
129	C₂×D₄×C₁₉	—	4	1	no	—
130	C₂×D₄×C₁₉	—	4	1	no	—
131	C₂×D₄×C₁₉	C₄²	1	2	yes	complemented
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	4	1	no	—
139	C₂²×C₄×C₁₉	—	4	1	no	—
140	C₂²×C₄×C₁₉	—	4	1	no	—
141	C₂²×C₄×C₁₉	—	4	1	no	—
142	C₂²×C₄×C₁₉	—	8	2	no	—
143	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	C₂×D₄	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×C₄×C₁₉	#41	1	1	yes	characteristic
157	C₂²×Dic₁₉	—	2	2	no	—
158	C₂²×Dic₁₉	—	2	2	no	—
159	C₂²×Dic₁₉	—	4	1	no	—
160	M₁₆×C₁₉	—	4	1	no	—
161	M₁₆×C₁₉	—	4	1	no	—
162	M₁₆×C₁₉	—	4	1	no	—
163	M₁₆×C₁₉	—	4	1	no	—
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₂×C₈×C₁₉	—	2	2	no	—
166	C₂×C₈×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	2	2	no	—
170	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
171	C₂²⋊Dic₁₉	—	2	2	no	—
172	C₂²⋊Dic₁₉	—	2	2	no	—
173	C₂²⋊Dic₁₉	—	2	2	no	—
174	C₂²⋊Dic₁₉	—	2	2	no	—
175	C₂²⋊Dic₁₉	—	4	1	no	—
176	C₂²⋊Dic₁₉	C₂²⋊C₄	1	4	yes	—
177	C₄⋊Dic₁₉	—	2	2	no	—
178	C₄⋊Dic₁₉	—	2	2	no	—
179	C₄⋊Dic₁₉	—	2	2	no	—
180	C₄⋊Dic₁₉	—	2	2	no	—
181	C₄⋊Dic₁₉	—	2	2	no	—
182	C₄⋊Dic₁₉	—	4	1	no	—
183	C₄×Dic₁₉	—	2	2	no	—
184	C₄×Dic₁₉	—	2	2	no	—
185	C₄×Dic₁₉	—	2	2	no	—
186	C₄×Dic₁₉	—	2	2	no	—
187	C₄×Dic₁₉	—	4	1	no	—
188	C₄×Dic₁₉	—	8	4	no	—
189	C₄×Dic₁₉	C₂²⋊C₄	1	4	yes	—
190	#64520	—	2	2	no	—
191	#64520	—	2	2	no	—
192	#64520	—	4	1	no	—
193	#64520	—	4	1	no	—
194	C₂×C₁₉⋊C₈	—	2	2	no	—
195	C₂×C₁₉⋊C₈	—	4	1	no	—
196	C₂×C₁₉⋊C₈	—	4	1	no	—
197	#10954	—	19	1	no	maximal, Sylow
198	C₂³×C₁₉	—	2	2	no	—
199	C₂³×C₁₉	—	4	1	no	—
200	C₂³×C₁₉	—	4	1	no	—
201	C₂³×C₁₉	—	4	1	no	—
202	C₂³×C₁₉	—	4	1	no	—
203	C₂³×C₁₉	—	8	1	no	—
204	C₂³×C₁₉	—	8	1	no	—
205	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
207	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
208	C₂³×C₁₉	#120	1	1	yes	characteristic
209	C₂³×C₁₉	#121	1	1	yes	characteristic
210	C₂³×C₁₉	#121	1	1	yes	characteristic
211	C₂³×C₁₉	#123	1	1	yes	characteristic
212	Q₈×C₁₉	—	2	2	no	—
213	Q₈×C₁₉	—	2	2	no	—
214	Q₈×C₁₉	—	4	1	no	—
215	Q₈×C₁₉	—	4	1	no	—
216	D₄×C₁₉	—	2	2	no	—
217	D₄×C₁₉	—	2	2	no	—
218	D₄×C₁₉	—	4	2	no	—
219	D₄×C₁₉	—	4	2	no	—
220	D₄×C₁₉	—	4	2	no	—
221	D₄×C₁₉	—	4	2	no	—
222	D₄×C₁₉	—	4	1	no	—
223	D₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	2	4	no	—
226	C₂×C₄×C₁₉	—	4	4	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	2	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	8	2	no	—
234	C₂×C₄×C₁₉	—	8	2	no	—
235	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
239	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
240	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₄×D₄	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	C₄×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
250	C₂×C₄×C₁₉	C₄×D₄	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	#124	1	1	yes	characteristic
258	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
259	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
260	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
261	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
262	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
263	C₂×Dic₁₉	—	2	4	no	—
264	C₂×Dic₁₉	—	2	4	no	—
265	C₂×Dic₁₉	—	4	2	no	—
266	C₂×Dic₁₉	—	4	2	no	—
267	C₂×Dic₁₉	—	4	2	no	—
268	C₂×Dic₁₉	—	4	2	no	—
269	C₂×Dic₁₉	—	4	2	no	—
270	C₂×Dic₁₉	—	8	1	no	—
271	C₂×Dic₁₉	—	8	1	no	—
272	C₈×C₁₉	—	4	2	no	—
273	C₁₉⋊C₈	—	4	2	no	—
274	C₂×#421	—	19	1	no	—
275	C₂×#417	D₁₉	1	1	yes	characteristic
276	C₂×#410	—	19	1	no	—
277	#2274	—	19	1	no	—
278	C₂×#344	—	19	1	no	—
279	#1736	—	19	1	no	—
280	C₂×H(3,ℤ/4)	—	19	1	no	—
281	C₂²×C₁₉	—	2	1	no	—
282	C₂²×C₁₉	—	2	1	no	—
283	C₂²×C₁₉	—	2	1	no	—
284	C₂²×C₁₉	—	2	1	no	—
285	C₂²×C₁₉	—	2	1	no	—
286	C₂²×C₁₉	—	2	1	no	—
287	C₂²×C₁₉	—	4	1	no	—
288	C₂²×C₁₉	—	4	1	no	—
289	C₂²×C₁₉	—	4	1	no	—
290	C₂²×C₁₉	—	4	1	no	—
291	C₂²×C₁₉	—	4	2	no	—
292	C₂²×C₁₉	—	8	2	no	—
293	C₂²×C₁₉	—	8	2	no	—
294	C₂²×C₁₉	—	8	1	no	—
295	C₂²×C₁₉	—	8	1	no	—
296	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
297	C₂²×C₁₉	#386	1	1	yes	characteristic
298	C₂²×C₁₉	#386	1	1	yes	characteristic
299	C₂²×C₁₉	#386	1	1	yes	characteristic
300	C₂²×C₁₉	#388	1	1	yes	characteristic
301	C₂²×C₁₉	#388	1	1	yes	characteristic
302	C₂²×C₁₉	#390	1	1	yes	characteristic
303	C₄×C₁₉	—	4	4	no	—
304	C₄×C₁₉	—	4	2	no	—
305	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
306	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
307	C₄×C₁₉	#388	1	1	yes	characteristic
308	C₄×C₁₉	#388	1	1	yes	characteristic
309	C₄×C₁₉	#388	1	1	yes	characteristic
310	C₄×C₁₉	#388	1	1	yes	characteristic
311	C₄×C₁₉	#390	1	1	yes	characteristic
312	C₄×C₁₉	#390	1	1	yes	characteristic
313	Dic₁₉	—	4	4	no	—
314	Dic₁₉	—	4	4	no	—
315	Dic₁₉	—	8	2	no	—
316	C₂²×#41	C₂×D₁₉	1	1	yes	characteristic
317	C₂²×M₁₆	—	19	1	no	—
318	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
319	C₂×#117	—	19	1	no	—
320	C₂×#117	—	19	1	no	—
321	C₂×#117	—	19	1	no	—
322	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
323	#421	—	19	4	no	—
324	#421	—	38	2	no	—
325	C₂×#104	—	38	2	no	—
326	#417	—	2	2	no	—
327	#417	—	2	2	no	—
328	C₂×#103	Dic₁₉	1	2	yes	complemented
329	C₂×#102	Dic₁₉	1	2	yes	complemented
330	#410	—	19	4	no	—
331	#410	—	38	2	no	—
332	C₂×#99	—	38	2	no	—
333	C₄×C₄⋊C₄	—	38	2	no	—
334	C₄×C₄⋊C₄	—	38	2	no	—
335	C₄×C₂²⋊C₄	—	38	2	no	—
336	#344	—	38	2	no	—
337	#340	—	38	2	no	—
338	H(3,ℤ/4)	—	38	2	no	—
339	C₂×C₁₉	—	2	1	no	—
340	C₂×C₁₉	—	2	1	no	—
341	C₂×C₁₉	—	2	1	no	—
342	C₂×C₁₉	—	2	1	no	—
343	C₂×C₁₉	—	2	1	no	—
344	C₂×C₁₉	—	2	1	no	—
345	C₂×C₁₉	—	8	2	no	—
346	C₂×C₁₉	#1437	1	1	yes	characteristic
347	C₂×C₁₉	#1904	1	1	yes	characteristic
348	C₂×C₁₉	#1905	1	1	yes	characteristic
349	C₂×#41	—	2	1	no	—
350	C₂×#41	—	2	1	no	—
351	C₂×#41	—	2	1	no	—
352	C₂×#41	—	2	1	no	—
353	C₂×#41	—	2	1	no	—
354	C₂×#41	—	2	1	no	—
355	C₂×#41	—	2	1	no	—
356	C₂×#41	—	2	1	no	—
357	C₂×#41	—	2	1	no	—
358	C₂×#41	—	2	1	no	—
359	C₂×#41	C₄×D₁₉	1	2	yes	—
360	C₂×#41	C₄×D₁₉	1	2	yes	—
361	C₂²×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
362	C₂²×D₄	—	2	1	no	—
363	C₂²×D₄	C₂×Dic₁₉	1	1	yes	characteristic
364	C₂³×C₄	—	2	1	no	—
365	C₂³×C₄	—	2	1	no	—
366	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
367	C₂×M₁₆	—	2	1	no	—
368	C₂×M₁₆	—	2	1	no	—
369	C₂×M₁₆	—	2	1	no	—
370	C₂×M₁₆	—	2	1	no	—
371	C₂×M₁₆	—	2	1	no	—
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	19	2	no	—
374	C₂×M₁₆	—	38	1	no	—
375	C₂×M₁₆	—	38	1	no	—
376	C₂×M₁₆	—	38	1	no	—
377	C₂×M₁₆	—	38	1	no	—
378	C₂×M₁₆	—	38	1	no	—
379	C₂²×C₈	—	38	1	no	—
380	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
381	#117	—	19	2	no	—
382	#117	—	19	2	no	—
383	#117	—	19	2	no	—
384	#117	—	19	2	no	—
385	#117	—	19	2	no	—
386	#117	—	38	1	no	—
387	#117	—	38	1	no	—
388	#117	—	38	1	no	—
389	#117	—	38	1	no	—
390	#117	—	38	1	no	—
391	#117	—	38	1	no	—
392	#117	—	38	1	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	38	1	no	—
397	C₂×C₄⋊C₄	—	38	1	no	—
398	C₂×C₄⋊C₄	—	38	1	no	—
399	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
400	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
401	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
402	C₂×C₂²⋊C₄	—	19	2	no	—
403	C₂×C₂²⋊C₄	—	38	1	no	—
404	C₂×C₂²⋊C₄	—	38	1	no	—
405	C₂×C₄²	—	19	2	no	—
406	C₂×C₄²	—	38	1	no	—
407	C₂×C₄²	—	38	1	no	—
408	C₂×C₄²	—	38	4	no	—
409	#104	—	38	8	no	—
410	#103	—	2	4	no	—
411	#102	—	2	4	no	—
412	#99	—	38	8	no	—
413	#95	—	38	4	no	—
414	C₁₉	#10954	1	1	yes	characteristic, complemented, Sylow
415	C₂⁴	—	2	1	no	—
416	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
417	#41	—	2	2	no	—
418	#41	—	2	2	no	—
419	#41	—	2	2	no	—
420	#41	—	2	2	no	—
421	#41	—	2	2	no	—
422	#41	—	2	2	no	—
423	#41	—	2	2	no	—
424	#41	—	2	2	no	—
425	#41	—	4	1	no	—
426	#41	—	4	1	no	—
427	#41	—	4	1	no	—
428	#41	—	4	1	no	—
429	#41	—	4	1	no	—
430	#41	—	4	1	no	—
431	#41	—	4	1	no	—
432	#41	—	4	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	C₄×Dic₁₉	1	2	yes	complemented
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	4	1	no	—
447	C₂×D₄	—	4	1	no	—
448	C₂×D₄	—	4	1	no	—
449	C₂×D₄	—	4	1	no	—
450	C₂×D₄	C₄×Dic₁₉	1	2	yes	complemented
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	4	1	no	—
458	C₂²×C₄	—	4	1	no	—
459	C₂²×C₄	—	4	1	no	—
460	C₂²×C₄	—	4	1	no	—
461	C₂²×C₄	—	8	2	no	—
462	C₂²×C₄	—	38	2	no	—
463	C₂²×C₄	—	38	2	no	—
464	C₂²×C₄	—	76	1	no	—
465	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
466	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
467	C₂²×C₄	#64541	1	1	yes	characteristic
468	C₂²×C₄	#64541	1	1	yes	characteristic
469	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
470	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
471	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
472	C₂²×C₄	#64543	1	1	yes	characteristic
473	C₂²×C₄	#64543	1	1	yes	characteristic
474	C₂²×C₄	#64543	1	1	yes	characteristic
475	C₂²×C₄	#64543	1	1	yes	characteristic
476	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
477	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
478	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
479	M₁₆	—	4	1	no	—
480	M₁₆	—	4	1	no	—
481	M₁₆	—	4	1	no	—
482	M₁₆	—	4	1	no	—
483	M₁₆	—	38	2	no	—
484	M₁₆	—	38	2	no	—
485	M₁₆	—	76	1	no	—
486	M₁₆	—	76	1	no	—
487	C₂×C₈	—	2	2	no	—
488	C₂×C₈	—	2	2	no	—
489	C₂×C₈	—	2	2	no	—
490	C₂×C₈	—	38	2	no	—
491	C₂×C₈	—	76	1	no	—
492	C₂×C₈	—	76	1	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	38	2	no	—
497	C₄⋊C₄	—	38	2	no	—
498	C₄⋊C₄	—	38	2	no	—
499	C₄⋊C₄	—	38	2	no	—
500	C₄⋊C₄	—	38	2	no	—
501	C₄⋊C₄	—	76	1	no	—
502	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
503	C₂²⋊C₄	—	19	4	no	—
504	C₂²⋊C₄	—	38	2	no	—
505	C₂²⋊C₄	—	38	2	no	—
506	C₂²⋊C₄	—	38	2	no	—
507	C₂²⋊C₄	—	38	2	no	—
508	C₂²⋊C₄	—	76	1	no	—
509	C₄²	—	19	4	no	—
510	C₄²	—	38	2	no	—
511	C₄²	—	38	2	no	—
512	C₄²	—	38	2	no	—
513	C₄²	—	38	2	no	—
514	C₄²	—	76	1	no	—
515	C₄²	—	152	4	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	4	1	no	—
518	C₂³	—	4	1	no	—
519	C₂³	—	4	1	no	—
520	C₂³	—	4	1	no	—
521	C₂³	—	8	1	no	—
522	C₂³	—	8	1	no	—
523	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
524	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
525	C₂³	#10597329	1	1	yes	characteristic
526	C₂³	#10597330	1	1	yes	characteristic
527	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
528	C₂³	#10597383	1	1	yes	characteristic
529	C₂³	#10597385	1	1	yes	characteristic
530	Q₈	—	2	2	no	—
531	Q₈	—	2	2	no	—
532	Q₈	—	4	1	no	—
533	Q₈	—	4	1	no	—
534	D₄	—	2	2	no	—
535	D₄	—	2	2	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	2	no	—
540	D₄	—	4	1	no	—
541	D₄	—	4	1	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	4	4	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	8	2	no	—
552	C₂×C₄	—	8	2	no	—
553	C₂×C₄	—	38	4	no	—
554	C₂×C₄	—	38	4	no	—
555	C₂×C₄	—	76	2	no	—
556	C₂×C₄	—	76	2	no	—
557	C₂×C₄	—	76	2	no	—
558	C₂×C₄	—	76	2	no	—
559	C₂×C₄	—	76	2	no	—
560	C₂×C₄	—	152	1	no	—
561	C₂×C₄	—	152	1	no	—
562	C₂×C₄	#10597323	1	1	yes	characteristic
563	C₂×C₄	#10597323	1	1	yes	characteristic
564	C₂×C₄	#10597325	1	1	yes	characteristic
565	C₂×C₄	#10597325	1	1	yes	characteristic
566	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
567	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
568	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
569	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
570	C₂×C₄	#10597329	1	1	yes	characteristic
571	C₂×C₄	#10597330	1	1	yes	characteristic
572	C₂×C₄	#10597331	1	1	yes	characteristic
573	C₂×C₄	#10597331	1	1	yes	characteristic
574	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
575	C₂×C₄	#10597372	1	1	yes	characteristic
576	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
577	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
578	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
579	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
580	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
581	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
582	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
583	C₂×C₄	#10597381	1	1	yes	characteristic
584	C₂×C₄	#10597382	1	1	yes	characteristic
585	C₂×C₄	#10597384	1	1	yes	characteristic
586	C₂×C₄	#10597384	1	1	yes	characteristic
587	C₂×C₄	#10597385	1	1	yes	characteristic
588	C₂×C₄	#10597386	1	1	yes	characteristic
589	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
590	C₈	—	4	2	no	—
591	C₈	—	76	2	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	1	no	—
597	C₂²	—	2	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	2	no	—
603	C₂²	—	8	2	no	—
604	C₂²	—	8	2	no	—
605	C₂²	—	8	1	no	—
606	C₂²	—	8	1	no	—
607	C₂²	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
608	C₂²	#11926420	1	1	yes	characteristic
609	C₂²	#11926420	1	1	yes	characteristic
610	C₂²	#11926424	1	1	yes	characteristic
611	C₂²	#11926437	1	1	yes	characteristic
612	C₂²	#11926438	1	1	yes	characteristic
613	C₂²	#11926444	1	1	yes	characteristic
614	C₄	—	4	4	no	—
615	C₄	—	4	2	no	—
616	C₄	—	76	4	no	—
617	C₄	—	76	4	no	—
618	C₄	—	152	2	no	—
619	C₄	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
620	C₄	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
621	C₄	#11926432	1	1	yes	characteristic
622	C₄	#11926432	1	1	yes	characteristic
623	C₄	#11926437	1	1	yes	characteristic
624	C₄	#11926438	1	1	yes	characteristic
625	C₄	#11926444	1	1	yes	characteristic
626	C₄	#11926447	1	1	yes	characteristic
627	C₂	—	2	1	no	—
628	C₂	—	2	1	no	—
629	C₂	—	2	1	no	—
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	2	1	no	—
633	C₂	—	8	2	no	—
634	C₂	#14561872	1	1	yes	characteristic
635	C₂	#14564124	1	1	yes	characteristic
636	C₂	#14564131	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926424
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#417	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂²×#41×C₁₉	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#417	D₁₉
hypocenter	C₁₉	#10954
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#417

Complements

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

N	H ≅ G/N	type
3. #14565992	C₂	semidirect
4. C₂×#11926315	C₂	semidirect
5. #14563354	C₂	semidirect
6. C₂×#11926301	C₂	semidirect
13. #11926561	C₄	semidirect
16. #11926518	C₄	semidirect
29. C₂×C₁₉×#103	C₄	semidirect
30. C₂×C₁₉×#102	C₄	semidirect
119. C₂×Q₈×C₁₉	C₄²	semidirect
131. C₂×D₄×C₁₉	C₄²	semidirect
328. C₂×#103	Dic₁₉	semidirect
329. C₂×#102	Dic₁₉	semidirect
414. C₁₉	#10954	semidirect
438. C₂×Q₈	C₄×Dic₁₉	semidirect
450. C₂×D₄	C₄×Dic₁₉	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×#11926518	2
#14565992	2
C₂×#11926315	2
#14563354	2
C₂×#11926301	2
C₂×C₁₉×#417	2
#10954	19