Subgroups — #18074575

Order 4864.

792 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563655	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#10597289	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562134	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562090	C₂	1	1	yes	maximal, characteristic, complemented
5	#14562060	C₂	1	1	yes	maximal, characteristic, complemented
6	#14562017	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3475	C₂	1	1	yes	maximal, characteristic
8	#11926597	C₂²	1	1	yes	characteristic
9	#11926568	C₂²	1	1	yes	characteristic
10	C₂×#10597294	—	2	1	no	—
11	C₂×#10597289	—	2	1	no	—
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
14	#11926306	—	2	1	no	—
15	#11926303	—	2	1	no	—
16	#11926281	—	2	2	no	—
17	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
18	Q₈⋊(C₁₉⋊C₈)	—	2	1	no	—
19	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
20	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
21	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
22	C₁₉×#556	C₄	1	1	yes	characteristic, complemented
23	C₁₉×#555	C₄	1	1	yes	characteristic, complemented
24	C₁₉×#554	C₄	1	1	yes	characteristic, complemented
25	C₁₉×#553	—	2	1	no	—
26	C₁₉×#552	—	2	1	no	—
27	C₁₉×#552	—	2	1	no	—
28	C₁₉×#551	—	2	2	no	—
29	C₁₉×#547	C₄	1	1	yes	characteristic, complemented
30	C₁₉×#546	—	2	1	no	—
31	C₁₉×#533	C₂²	1	1	yes	characteristic
32	C₁₉×#529	—	2	2	no	—
33	C₁₉×#529	—	2	1	no	—
34	C₁₉×#525	—	2	1	no	—
35	C₄×#41×C₁₉	—	2	1	no	—
36	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#117	—	2	1	no	—
39	C₂×#41×C₁₉	—	2	1	no	—
40	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₉	—	2	1	no	—
43	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
44	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
45	C₁₉×#126	—	2	2	no	—
46	C₁₉×#126	—	2	2	no	—
47	C₁₉×#126	—	2	2	no	—
48	C₁₉×#125	—	2	2	no	—
49	C₁₉×#125	—	2	1	no	—
50	C₁₉×#125	—	2	1	no	—
51	C₁₉×#124	—	2	2	no	—
52	C₁₉×#124	—	2	1	no	—
53	C₁₉×#123	—	2	2	no	—
54	C₁₉×#123	—	2	2	no	—
55	C₁₉×#123	—	2	2	no	—
56	C₁₉×#123	—	2	2	no	—
57	C₁₉×C₂²⋊Q₈	—	2	1	no	—
58	C₁₉×C₂²⋊Q₈	—	2	1	no	—
59	C₁₉×C₂²⋊Q₈	—	2	2	no	—
60	C₁₉×C₂²⋊Q₈	—	2	1	no	—
61	C₁₉×C₂²⋊Q₈	—	2	1	no	—
62	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
63	C₁₉×#121	—	2	2	no	—
64	C₁₉×#121	—	2	1	no	—
65	C₁₉×#121	—	2	1	no	—
66	C₁₉×#121	—	2	1	no	—
67	C₁₉×#120	—	2	2	no	—
68	C₄×Q₈×C₁₉	—	2	1	no	—
69	C₄×Q₈×C₁₉	—	2	1	no	—
70	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
71	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
72	C₄×Q₈×C₁₉	D₄	1	2	yes	—
73	C₄×D₄×C₁₉	—	2	2	no	—
74	C₄×D₄×C₁₉	—	2	2	no	—
75	C₄×D₄×C₁₉	—	2	2	no	—
76	C₄×D₄×C₁₉	—	2	1	no	—
77	C₄×D₄×C₁₉	—	2	1	no	—
78	C₄×D₄×C₁₉	—	2	1	no	—
79	C₄×D₄×C₁₉	—	2	1	no	—
80	C₄×D₄×C₁₉	—	2	1	no	—
81	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
82	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
83	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
84	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
85	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
86	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
87	C₁₉×#117	—	2	2	no	—
88	C₁₉×#117	—	2	2	no	—
89	C₁₉×#117	—	2	2	no	—
90	C₁₉×#117	—	2	1	no	—
91	C₁₉×#117	—	2	1	no	—
92	C₁₉×#117	—	2	1	no	—
93	C₁₉×#117	—	2	1	no	—
94	C₁₉×#117	—	2	1	no	—
95	C₁₉×#117	D₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₄²×C₁₉	—	2	2	no	—
102	C₂×C₄²×C₁₉	—	2	1	no	—
103	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊Dic₁₉	—	2	1	no	—
105	C₂×C₄×Dic₁₉	—	2	1	no	—
106	C₂×#64520	—	2	1	no	—
107	C₂²×C₁₉⋊C₈	—	2	1	no	—
108	#10597294	—	4	2	no	—
109	#10597289	—	2	4	no	—
110	C₁₉⋊#95	—	2	1	no	—
111	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
112	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
113	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
114	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
115	C₄×C₁₉⋊C₈	—	2	1	no	—
116	C₄×C₁₉⋊C₈	—	2	1	no	—
117	C₄×C₁₉⋊C₈	—	2	1	no	—
118	C₂⁴×C₁₉	—	2	1	no	—
119	#41×C₁₉	—	2	1	no	—
120	#41×C₁₉	—	2	1	no	—
121	#41×C₁₉	—	2	1	no	—
122	#41×C₁₉	—	2	1	no	—
123	#41×C₁₉	—	4	2	no	—
124	#41×C₁₉	—	4	2	no	—
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
127	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	2	1	no	—
131	C₂×D₄×C₁₉	—	2	2	no	—
132	C₂×D₄×C₁₉	—	2	1	no	—
133	C₂×D₄×C₁₉	—	4	1	no	—
134	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
135	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
136	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	1	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	2	1	no	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	4	1	no	—
148	C₂²×C₄×C₁₉	—	4	1	no	—
149	C₂²×C₄×C₁₉	—	4	1	no	—
150	C₂²×C₄×C₁₉	—	4	1	no	—
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×Dic₁₉	—	4	1	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	2	1	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
168	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
169	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
170	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
171	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
172	C₂²⋊C₄×C₁₉	—	2	2	no	—
173	C₂²⋊C₄×C₁₉	—	2	2	no	—
174	C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₉	—	2	2	no	—
176	C₂²⋊C₄×C₁₉	—	2	2	no	—
177	C₂²⋊C₄×C₁₉	—	2	2	no	—
178	C₂²⋊C₄×C₁₉	—	2	1	no	—
179	C₂²⋊C₄×C₁₉	—	2	2	no	—
180	C₂²⋊C₄×C₁₉	—	2	1	no	—
181	C₂²⋊C₄×C₁₉	—	2	1	no	—
182	C₂²⋊C₄×C₁₉	—	2	1	no	—
183	C₂²⋊C₄×C₁₉	—	2	1	no	—
184	C₂²⋊C₄×C₁₉	—	2	1	no	—
185	C₂²⋊C₄×C₁₉	—	2	1	no	—
186	C₄²×C₁₉	—	2	2	no	—
187	C₄²×C₁₉	—	2	2	no	—
188	C₄²×C₁₉	—	2	1	no	—
189	C₄²×C₁₉	—	2	1	no	—
190	C₄²×C₁₉	—	2	2	no	—
191	C₄²×C₁₉	—	2	1	no	—
192	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
193	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₄⋊Dic₁₉	—	2	2	no	—
197	C₄⋊Dic₁₉	—	4	1	no	—
198	C₄×Dic₁₉	—	4	1	no	—
199	C₄×Dic₁₉	—	4	1	no	—
200	#64520	—	4	1	no	—
201	#64520	—	4	1	no	—
202	C₂×C₁₉⋊C₈	—	2	2	no	—
203	C₂×C₁₉⋊C₈	—	4	1	no	—
204	C₂×C₁₉⋊C₈	—	4	1	no	—
205	C₂×C₁₉⋊C₈	—	4	1	no	—
206	C₂×C₁₉⋊C₈	—	4	1	no	—
207	#8438	—	19	1	no	maximal, Sylow
208	C₂³×C₁₉	—	2	1	no	—
209	C₂³×C₁₉	—	2	1	no	—
210	C₂³×C₁₉	—	2	1	no	—
211	C₂³×C₁₉	—	4	2	no	—
212	C₂³×C₁₉	—	4	1	no	—
213	C₂³×C₁₉	—	4	1	no	—
214	C₂³×C₁₉	—	8	1	no	—
215	C₂³×C₁₉	#120	1	1	yes	characteristic
216	Q₈×C₁₉	—	2	1	no	—
217	Q₈×C₁₉	—	2	1	no	—
218	Q₈×C₁₉	—	4	2	no	—
219	Q₈×C₁₉	—	4	1	no	—
220	Q₈×C₁₉	—	4	1	no	—
221	D₄×C₁₉	—	2	1	no	—
222	D₄×C₁₉	—	2	1	no	—
223	D₄×C₁₉	—	2	1	no	—
224	D₄×C₁₉	—	2	1	no	—
225	D₄×C₁₉	—	2	1	no	—
226	D₄×C₁₉	—	4	2	no	—
227	D₄×C₁₉	—	4	4	no	—
228	D₄×C₁₉	—	4	1	no	—
229	D₄×C₁₉	—	4	1	no	—
230	D₄×C₁₉	—	8	2	no	—
231	D₄×C₁₉	#104	1	2	yes	complemented
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	2	2	no	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	2	2	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	4	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	4	1	no	—
256	C₂×C₄×C₁₉	—	4	1	no	—
257	C₂×C₄×C₁₉	—	8	1	no	—
258	C₂×C₄×C₁₉	—	8	2	no	—
259	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
263	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
264	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
265	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
266	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
267	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
268	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
269	C₂×Dic₁₉	—	4	2	no	—
270	C₂×Dic₁₉	—	8	1	no	—
271	C₂×Dic₁₉	—	8	1	no	—
272	C₁₉⋊C₈	—	4	2	no	—
273	C₁₉⋊C₈	—	8	1	no	—
274	C₁₉⋊C₈	—	8	1	no	—
275	#3475	D₁₉	1	1	yes	characteristic
276	#1806	—	19	1	no	—
277	C₄×#102	—	19	1	no	—
278	#1503	—	19	1	no	—
279	#1493	—	19	1	no	—
280	#1486	—	19	1	no	—
281	#1476	—	19	1	no	—
282	C₂²×C₁₉	—	2	1	no	—
283	C₂²×C₁₉	—	2	1	no	—
284	C₂²×C₁₉	—	2	2	no	—
285	C₂²×C₁₉	—	4	1	no	—
286	C₂²×C₁₉	—	4	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	1	no	—
292	C₂²×C₁₉	—	4	1	no	—
293	C₂²×C₁₉	—	8	2	no	—
294	C₂²×C₁₉	—	8	2	no	—
295	C₂²×C₁₉	#379	1	1	yes	characteristic
296	C₂²×C₁₉	#449	1	1	yes	characteristic
297	C₂²×C₁₉	#452	1	1	yes	characteristic
298	C₄×C₁₉	—	2	1	no	—
299	C₄×C₁₉	—	2	1	no	—
300	C₄×C₁₉	—	2	1	no	—
301	C₄×C₁₉	—	4	1	no	—
302	C₄×C₁₉	—	4	2	no	—
303	C₄×C₁₉	—	4	1	no	—
304	C₄×C₁₉	—	4	1	no	—
305	C₄×C₁₉	—	4	1	no	—
306	C₄×C₁₉	—	4	1	no	—
307	C₄×C₁₉	—	4	2	no	—
308	C₄×C₁₉	#416	1	1	yes	characteristic
309	C₄×C₁₉	#417	1	1	yes	characteristic
310	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
311	C₄×C₁₉	#421	1	1	yes	characteristic
312	C₄×C₁₉	#449	1	1	yes	characteristic
313	C₄×C₁₉	#452	1	1	yes	characteristic
314	Dic₁₉	—	8	2	no	—
315	#556	Dic₁₉	1	1	yes	characteristic, complemented
316	#555	Dic₁₉	1	1	yes	characteristic, complemented
317	#554	Dic₁₉	1	1	yes	characteristic, complemented
318	#553	—	2	1	no	—
319	#552	—	2	1	no	—
320	#552	—	2	1	no	—
321	#551	—	2	2	no	—
322	#547	Dic₁₉	1	1	yes	characteristic, complemented
323	#546	—	2	1	no	—
324	#533	C₂×D₁₉	1	1	yes	characteristic
325	#529	—	2	2	no	—
326	#529	—	2	1	no	—
327	#525	—	2	1	no	—
328	C₄×#41	—	2	1	no	—
329	C₄×#41	C₂×D₁₉	1	1	yes	characteristic
330	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
331	C₂×#117	—	2	1	no	—
332	#431	—	19	1	no	—
333	#423	—	19	1	no	—
334	C₂×#104	—	38	1	no	—
335	C₂×#102	—	38	1	no	—
336	C₂×C₄×C₈	—	19	1	no	—
337	C₄×C₄⋊C₄	—	19	1	no	—
338	#340	—	38	1	no	—
339	#339	—	38	1	no	—
340	#328	—	38	2	no	—
341	Q₈⋊C₈	—	38	1	no	—
342	Q₈⋊C₈	—	38	2	no	—
343	D₄⋊C₈	—	38	1	no	—
344	D₄⋊C₈	—	38	1	no	—
345	D₄⋊C₈	—	38	1	no	—
346	C₂×C₁₉	—	2	1	no	—
347	C₂×C₁₉	—	2	1	no	—
348	C₂×C₁₉	—	4	2	no	—
349	C₂×C₁₉	—	8	1	no	—
350	C₂×C₁₉	—	8	1	no	—
351	C₂×C₁₉	#1788	1	1	yes	characteristic
352	C₂×C₁₉	#1789	1	1	yes	characteristic
353	C₂×C₁₉	#1794	1	1	yes	characteristic
354	C₂×#41	—	2	1	no	—
355	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
356	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
357	C₂³×C₄	—	2	1	no	—
358	C₂×M₁₆	—	38	1	no	—
359	C₂²×C₈	—	38	1	no	—
360	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
361	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
362	#126	—	2	2	no	—
363	#126	—	2	2	no	—
364	#126	—	2	2	no	—
365	#125	—	2	2	no	—
366	#125	—	2	1	no	—
367	#125	—	2	1	no	—
368	#124	—	2	2	no	—
369	#124	—	2	1	no	—
370	#123	—	2	2	no	—
371	#123	—	2	2	no	—
372	#123	—	2	2	no	—
373	#123	—	2	2	no	—
374	C₂²⋊Q₈	—	2	1	no	—
375	C₂²⋊Q₈	—	2	1	no	—
376	C₂²⋊Q₈	—	2	2	no	—
377	C₂²⋊Q₈	—	2	1	no	—
378	C₂²⋊Q₈	—	2	1	no	—
379	C₂²⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
380	#121	—	2	2	no	—
381	#121	—	2	1	no	—
382	#121	—	2	1	no	—
383	#121	—	2	1	no	—
384	#120	—	2	2	no	—
385	C₄×Q₈	—	2	1	no	—
386	C₄×Q₈	—	2	1	no	—
387	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
388	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
389	C₄×Q₈	C₂²⋊D₁₉	1	2	yes	—
390	C₄×D₄	—	2	2	no	—
391	C₄×D₄	—	2	2	no	—
392	C₄×D₄	—	2	2	no	—
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	—	2	1	no	—
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
399	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
400	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
401	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
402	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
403	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
404	#117	—	2	2	no	—
405	#117	—	2	2	no	—
406	#117	—	2	2	no	—
407	#117	—	2	1	no	—
408	#117	—	2	1	no	—
409	#117	—	2	1	no	—
410	#117	—	2	1	no	—
411	#117	—	2	1	no	—
412	#117	C₂²⋊D₁₉	1	1	yes	characteristic
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	38	1	no	—
416	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
417	C₂×C₂²⋊C₄	—	2	2	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₄²	—	2	2	no	—
420	C₂×C₄²	—	2	1	no	—
421	C₂×C₄²	—	38	1	no	—
422	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
423	C₄⋊C₈	—	38	1	no	—
424	C₄⋊C₈	—	38	1	no	—
425	C₄⋊C₈	—	38	1	no	—
426	#104	—	76	2	no	—
427	#102	—	38	4	no	—
428	C₂²⋊C₈	—	38	1	no	—
429	C₄×C₈	—	38	1	no	—
430	C₄×C₈	—	38	1	no	—
431	C₄×C₈	—	38	1	no	—
432	#95	—	38	1	no	—
433	C₁₉	#8438	1	1	yes	characteristic, complemented, Sylow
434	C₂⁴	—	2	1	no	—
435	#41	—	2	1	no	—
436	#41	—	2	1	no	—
437	#41	—	2	1	no	—
438	#41	—	2	1	no	—
439	#41	—	4	2	no	—
440	#41	—	4	2	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
443	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	4	1	no	—
450	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
451	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
452	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	4	1	no	—
464	C₂²×C₄	—	4	1	no	—
465	C₂²×C₄	—	4	1	no	—
466	C₂²×C₄	—	4	1	no	—
467	C₂²×C₄	—	76	1	no	—
468	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
469	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
470	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
471	M₁₆	—	76	1	no	—
472	M₁₆	—	76	1	no	—
473	C₂×C₈	—	38	2	no	—
474	C₂×C₈	—	76	1	no	—
475	C₂×C₈	—	76	1	no	—
476	C₂×C₈	—	76	1	no	—
477	C₂×C₈	—	76	1	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	38	2	no	—
491	C₄⋊C₄	—	76	1	no	—
492	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
493	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
494	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
495	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
496	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	2	no	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	2	1	no	—
510	C₂²⋊C₄	—	2	1	no	—
511	C₄²	—	2	2	no	—
512	C₄²	—	2	2	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	2	2	no	—
517	C₄²	—	76	1	no	—
518	C₄²	—	76	1	no	—
519	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
520	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
521	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
522	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
523	C₂³	—	2	1	no	—
524	C₂³	—	2	1	no	—
525	C₂³	—	2	1	no	—
526	C₂³	—	4	2	no	—
527	C₂³	—	4	1	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	8	1	no	—
530	C₂³	#10597399	1	1	yes	characteristic
531	Q₈	—	2	1	no	—
532	Q₈	—	2	1	no	—
533	Q₈	—	4	2	no	—
534	Q₈	—	4	1	no	—
535	Q₈	—	4	1	no	—
536	D₄	—	2	1	no	—
537	D₄	—	2	1	no	—
538	D₄	—	2	1	no	—
539	D₄	—	2	1	no	—
540	D₄	—	2	1	no	—
541	D₄	—	4	2	no	—
542	D₄	—	4	4	no	—
543	D₄	—	4	1	no	—
544	D₄	—	4	1	no	—
545	D₄	—	8	2	no	—
546	D₄	#10597294	1	2	yes	complemented
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	8	1	no	—
573	C₂×C₄	—	8	2	no	—
574	C₂×C₄	—	76	2	no	—
575	C₂×C₄	—	152	1	no	—
576	C₂×C₄	—	152	1	no	—
577	C₂×C₄	#10597395	1	1	yes	characteristic
578	C₂×C₄	#10597396	1	1	yes	characteristic
579	C₂×C₄	#10597396	1	1	yes	characteristic
580	C₂×C₄	#10597397	1	1	yes	characteristic
581	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
582	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
583	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
584	C₂×C₄	#10597399	1	1	yes	characteristic
585	C₂×C₄	#10597399	1	1	yes	characteristic
586	C₂×C₄	#10597399	1	1	yes	characteristic
587	C₈	—	76	2	no	—
588	C₈	—	152	1	no	—
589	C₈	—	152	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	8	2	no	—
602	C₂²	—	8	2	no	—
603	C₂²	#11926400	1	1	yes	characteristic
604	C₂²	#11926689	1	1	yes	characteristic
605	C₂²	#11926706	1	1	yes	characteristic
606	C₄	—	2	1	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	4	1	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	2	no	—
616	C₄	—	152	2	no	—
617	C₄	#11926540	1	1	yes	characteristic
618	C₄	#11926545	1	1	yes	characteristic
619	C₄	C₂×#10597294	1	1	yes	characteristic
620	C₄	#11926561	1	1	yes	characteristic
621	C₄	#11926689	1	1	yes	characteristic
622	C₄	#11926706	1	1	yes	characteristic
623	C₂	—	2	1	no	—
624	C₂	—	2	1	no	—
625	C₂	—	4	2	no	—
626	C₂	—	8	1	no	—
627	C₂	—	8	1	no	—
628	C₂	#14563575	1	1	yes	characteristic
629	C₂	#14563579	1	1	yes	characteristic
630	C₂	#14563599	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597399
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3475	C₂
socle	C₂²×C₁₉	#379
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3475	D₁₉
hypocenter	C₁₉	#8438
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3475

Complements

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

N	H ≅ G/N	type
1. #14563655	C₂	semidirect
2. C₄×#10597289	C₂	semidirect
3. #14562134	C₂	semidirect
4. #14562090	C₂	semidirect
5. #14562060	C₂	semidirect
6. #14562017	C₂	semidirect
22. C₁₉×#556	C₄	semidirect
23. C₁₉×#555	C₄	semidirect
24. C₁₉×#554	C₄	semidirect
29. C₁₉×#547	C₄	semidirect
231. D₄×C₁₉	#104	semidirect
315. #556	Dic₁₉	semidirect
316. #555	Dic₁₉	semidirect
317. #554	Dic₁₉	semidirect
322. #547	Dic₁₉	semidirect
433. C₁₉	#8438	semidirect
546. D₄	#10597294	semidirect

Maximal subgroups

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

subgroup	index
#14563655	2
C₄×#10597289	2
#14562134	2
#14562090	2
#14562060	2
#14562017	2
C₁₉×#3475	2
#8438	19