Subgroups — #18088123

Order 4864.

1250 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10597347	C₂	1	1	yes	maximal, characteristic
2	C₂²×#10597262	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926541	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926309	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926304	C₂	1	1	yes	maximal, characteristic, complemented
6	#14563331	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#336	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64541	C₂²	1	1	yes	characteristic
9	C₂×#10597347	—	2	2	no	—
10	C₂×#10597347	—	2	2	no	—
11	C₂×#10597347	—	2	2	no	—
12	C₂×#10597347	—	2	2	no	—
13	C₂×#10597347	—	2	2	no	—
14	C₂×#10597347	C₄	1	4	yes	complemented
15	C₂²×#64520	C₂²	1	1	yes	characteristic
16	C₂²×#64520	C₂²	1	1	yes	characteristic
17	C₂²×#64515	—	2	1	no	—
18	C₂²×C₈×D₁₉	—	2	1	no	—
19	C₂×#10597372	C₂²	1	1	yes	characteristic
20	C₂×#10597262	—	2	2	no	—
21	C₂×#10597262	—	2	2	no	—
22	C₂×#10597262	C₄	1	4	yes	complemented
23	#11926541	—	2	2	no	—
24	#11926541	—	2	2	no	—
25	C₂×#10597273	C₄	1	2	yes	complemented
26	C₂×#10597278	C₄	1	2	yes	complemented
27	#11926309	—	2	2	no	—
28	#11926304	—	2	2	no	—
29	#11926298	—	2	1	no	—
30	#11926298	—	2	1	no	—
31	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
32	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
34	C₁₉×#336	—	2	2	no	—
35	C₂³×C₄×C₁₉	—	2	1	no	—
36	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
37	C₂²×C₂²⋊D₁₉	—	2	1	no	—
38	C₂×#64541	—	2	1	no	—
39	C₂×#64541	—	2	1	no	—
40	C₂×#64541	—	2	1	no	—
41	C₂×#64541	—	2	1	no	—
42	C₂×#64541	—	2	1	no	—
43	C₂×#64541	—	2	1	no	—
44	C₂×#64541	C₂×C₄	1	2	yes	—
45	C₂×#64541	C₂×C₄	1	2	yes	—
46	C₂×#64541	D₄	1	2	yes	—
47	C₂×#64541	D₄	1	2	yes	—
48	C₂×#64541	D₄	1	2	yes	—
49	C₂×#64541	Q₈	1	2	yes	—
50	C₂²×D₇₆	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₄×D₁₉	—	2	1	no	—
52	C₂²×Dic₃₈	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₉	—	2	1	no	—
54	C₂²×C₈×C₁₉	—	2	1	no	—
55	C₂²×C₈×C₁₉	—	2	1	no	—
56	C₂²×C₈×C₁₉	—	2	1	no	—
57	C₂²×C₈×C₁₉	—	2	1	no	—
58	C₂²×C₈×C₁₉	—	2	1	no	—
59	C₂²×C₈×C₁₉	—	2	1	no	—
60	C₂²×C₈×C₁₉	—	2	1	no	—
61	C₂²×C₈×C₁₉	—	2	1	no	—
62	C₂²×C₈×C₁₉	—	2	1	no	—
63	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
64	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
65	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
66	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
67	C₂²×C₈×C₁₉	D₄	1	2	yes	—
68	C₂×C₄²×C₁₉	—	2	1	no	—
69	C₂×C₄²×C₁₉	—	2	1	no	—
70	C₂×C₄²×C₁₉	—	2	1	no	—
71	C₂×C₄²×C₁₉	—	2	1	no	—
72	C₂×C₄²×C₁₉	—	2	1	no	—
73	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
74	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
75	#10597372	—	2	1	no	—
76	#10597372	—	2	1	no	—
77	#10597372	—	2	1	no	—
78	#10597372	—	2	1	no	—
79	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
80	C₂×C₄×Dic₁₉	—	2	1	no	—
81	C₂×#64520	—	2	1	no	—
82	C₂×#64520	—	2	1	no	—
83	C₂×#64520	—	2	1	no	—
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	C₂×#64520	C₂×C₄	1	2	yes	—
91	C₂×#64520	D₄	1	2	yes	—
92	C₂×#64520	D₄	1	2	yes	—
93	C₂²×C₁₉⋊C₈	—	2	1	no	—
94	C₂²×C₁₉⋊C₈	—	2	1	no	—
95	#10597347	—	2	8	no	—
96	#10597347	—	2	8	no	—
97	#10597347	—	2	8	no	—
98	#10597347	—	2	8	no	—
99	C₂×#64515	—	2	4	no	—
100	C₂×#64515	—	2	4	no	—
101	C₂×#64515	—	2	4	no	—
102	C₂×C₈×D₁₉	—	2	4	no	—
103	C₂×C₈×D₁₉	—	2	4	no	—
104	C₂×C₈×D₁₉	—	2	4	no	—
105	#10597278	—	2	4	no	—
106	#10597273	—	2	4	no	—
107	#10597262	—	2	8	no	—
108	C₂⁴×C₁₉	#41	1	1	yes	characteristic
109	C₂³×D₁₉	—	2	1	no	—
110	C₂²×C₄×C₁₉	—	2	4	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	4	2	no	—
113	C₂²×C₄×C₁₉	—	4	1	no	—
114	C₂²×C₄×C₁₉	—	4	1	no	—
115	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
129	C₂×C₂²⋊D₁₉	—	2	2	no	—
130	C₂×C₂²⋊D₁₉	—	2	2	no	—
131	C₂×C₂²⋊D₁₉	—	2	2	no	—
132	C₂×C₂²⋊D₁₉	—	2	2	no	—
133	C₂×C₂²⋊D₁₉	—	2	2	no	—
134	C₂×C₂²⋊D₁₉	—	2	2	no	—
135	C₂²×Dic₁₉	—	2	1	no	—
136	C₂²×Dic₁₉	—	2	2	no	—
137	#64541	—	2	2	no	—
138	#64541	—	2	2	no	—
139	#64541	—	2	2	no	—
140	#64541	—	2	2	no	—
141	#64541	—	2	2	no	—
142	#64541	—	2	2	no	—
143	#64541	—	2	2	no	—
144	#64541	—	2	2	no	—
145	#64541	—	2	2	no	—
146	#64541	—	2	2	no	—
147	#64541	—	2	2	no	—
148	#64541	—	2	2	no	—
149	#64541	C₂²⋊C₄	1	4	yes	—
150	#64541	C₂²⋊C₄	1	4	yes	—
151	#64541	C₄⋊C₄	1	4	yes	—
152	#64541	C₄⋊C₄	1	4	yes	—
153	C₂×D₇₆	—	2	1	no	—
154	C₂×D₇₆	—	2	1	no	—
155	C₂×D₇₆	—	2	1	no	—
156	C₂×D₇₆	C₄²	1	2	yes	—
157	C₂×D₇₆	C₂²⋊C₄	1	2	yes	—
158	C₂×D₇₆	C₄⋊C₄	1	2	yes	—
159	C₂×C₄×D₁₉	—	2	2	no	—
160	C₂×C₄×D₁₉	—	2	2	no	—
161	C₂×C₄×D₁₉	—	2	2	no	—
162	C₂×C₄×D₁₉	—	2	2	no	—
163	C₂×C₄×D₁₉	—	2	2	no	—
164	C₂×C₄×D₁₉	—	2	2	no	—
165	C₂×Dic₃₈	—	2	1	no	—
166	C₂×Dic₃₈	—	2	1	no	—
167	C₂×Dic₃₈	—	2	1	no	—
168	C₂×Dic₃₈	C₄²	1	2	yes	—
169	C₂×Dic₃₈	C₂²⋊C₄	1	2	yes	—
170	C₂×Dic₃₈	C₄⋊C₄	1	2	yes	—
171	C₂×C₈×C₁₉	—	2	2	no	—
172	C₂×C₈×C₁₉	—	2	2	no	—
173	C₂×C₈×C₁₉	—	2	1	no	—
174	C₂×C₈×C₁₉	—	2	1	no	—
175	C₂×C₈×C₁₉	—	2	1	no	—
176	C₂×C₈×C₁₉	—	2	1	no	—
177	C₂×C₈×C₁₉	—	2	2	no	—
178	C₂×C₈×C₁₉	—	2	2	no	—
179	C₂×C₈×C₁₉	—	2	2	no	—
180	C₂×C₈×C₁₉	—	2	2	no	—
181	C₂×C₈×C₁₉	—	2	2	no	—
182	C₂×C₈×C₁₉	—	4	1	no	—
183	C₂×C₈×C₁₉	—	4	1	no	—
184	C₂×C₈×C₁₉	—	4	1	no	—
185	C₂×C₈×C₁₉	—	4	1	no	—
186	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
187	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
188	C₄²×C₁₉	—	2	2	no	—
189	C₄²×C₁₉	—	2	2	no	—
190	C₄²×C₁₉	—	4	1	no	—
191	C₄²×C₁₉	—	4	1	no	—
192	C₂²⋊Dic₁₉	—	4	1	no	—
193	C₂²⋊Dic₁₉	—	4	1	no	—
194	C₄⋊Dic₁₉	—	2	2	no	—
195	C₄⋊Dic₁₉	—	2	2	no	—
196	C₄×Dic₁₉	—	4	1	no	—
197	C₄×Dic₁₉	—	4	1	no	—
198	#64520	—	2	2	no	—
199	#64520	—	2	2	no	—
200	#64520	—	2	2	no	—
201	#64520	—	2	2	no	—
202	#64520	—	2	2	no	—
203	#64520	—	4	1	no	—
204	#64520	—	4	1	no	—
205	#64520	C₂²⋊C₄	1	4	yes	—
206	C₂×C₁₉⋊C₈	—	2	2	no	—
207	C₂×C₁₉⋊C₈	—	2	2	no	—
208	C₂×C₁₉⋊C₈	—	2	2	no	—
209	C₂×C₁₉⋊C₈	—	2	2	no	—
210	C₂×C₁₉⋊C₈	—	4	1	no	—
211	C₂×C₁₉⋊C₈	—	4	1	no	—
212	#64515	—	2	16	no	—
213	C₈×D₁₉	—	2	16	no	—
214	#10791	—	19	1	no	maximal, Sylow
215	C₂³×C₁₉	—	2	2	no	—
216	C₂³×C₁₉	—	2	2	no	—
217	C₂³×C₁₉	#117	1	1	yes	characteristic
218	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
219	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
220	C₂³×C₁₉	#121	1	1	yes	characteristic
221	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
222	C₂³×C₁₉	#123	1	1	yes	characteristic
223	C₂³×C₁₉	#123	1	1	yes	characteristic
224	C₂²×D₁₉	—	2	2	no	—
225	C₂²×D₁₉	—	2	2	no	—
226	C₂²×D₁₉	—	2	2	no	—
227	C₂²×D₁₉	—	4	2	no	—
228	C₂²×D₁₉	—	4	2	no	—
229	C₂×C₄×C₁₉	—	2	4	no	—
230	C₂×C₄×C₁₉	—	4	4	no	—
231	C₂×C₄×C₁₉	—	4	4	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	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	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₁₉	#117	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	#120	1	1	yes	characteristic
251	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
252	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
253	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
254	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
255	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
256	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
257	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
258	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
260	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
261	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
262	C₂²⋊D₁₉	—	2	4	no	—
263	C₂²⋊D₁₉	—	2	4	no	—
264	C₂²⋊D₁₉	—	2	4	no	—
265	C₂²⋊D₁₉	—	2	4	no	—
266	C₂×Dic₁₉	—	2	2	no	—
267	C₂×Dic₁₉	—	2	2	no	—
268	C₂×Dic₁₉	—	2	2	no	—
269	C₂×Dic₁₉	—	4	2	no	—
270	C₂×Dic₁₉	—	4	2	no	—
271	C₂×Dic₁₉	—	4	2	no	—
272	D₇₆	—	2	2	no	—
273	D₇₆	—	2	2	no	—
274	D₇₆	—	2	2	no	—
275	D₇₆	#95	1	4	yes	—
276	C₄×D₁₉	—	2	4	no	—
277	C₄×D₁₉	—	2	4	no	—
278	C₄×D₁₉	—	2	4	no	—
279	C₄×D₁₉	—	2	4	no	—
280	Dic₃₈	—	2	2	no	—
281	Dic₃₈	—	2	2	no	—
282	Dic₃₈	—	2	2	no	—
283	Dic₃₈	#95	1	4	yes	—
284	C₈×C₁₉	—	2	2	no	—
285	C₈×C₁₉	—	2	2	no	—
286	C₈×C₁₉	—	4	2	no	—
287	C₁₉⋊C₈	—	2	4	no	—
288	C₁₉⋊C₈	—	4	2	no	—
289	C₂²×#131	—	19	1	no	—
290	C₂²×#104	—	19	1	no	—
291	C₂×#416	—	19	1	no	—
292	C₂×#341	—	19	1	no	—
293	C₂×#339	—	19	1	no	—
294	#1729	—	19	1	no	—
295	C₂×#336	D₁₉	1	1	yes	characteristic, complemented
296	C₂²×C₁₉	—	2	2	no	—
297	C₂²×C₁₉	—	2	2	no	—
298	C₂²×C₁₉	—	2	2	no	—
299	C₂²×C₁₉	—	2	2	no	—
300	C₂²×C₁₉	—	2	1	no	—
301	C₂²×C₁₉	—	2	1	no	—
302	C₂²×C₁₉	—	2	1	no	—
303	C₂²×C₁₉	—	2	1	no	—
304	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
305	C₂²×C₁₉	#380	1	1	yes	characteristic
306	C₂²×C₁₉	#381	1	1	yes	characteristic
307	C₂²×C₁₉	#385	1	1	yes	characteristic
308	C₂²×C₁₉	#385	1	1	yes	characteristic
309	C₂²×C₁₉	#386	1	1	yes	characteristic
310	C₂²×C₁₉	#386	1	1	yes	characteristic
311	C₂²×C₁₉	#443	1	2	yes	—
312	C₂²×C₁₉	#444	1	2	yes	—
313	C₂×D₁₉	—	2	4	no	—
314	C₂×D₁₉	—	4	4	no	—
315	C₂×D₁₉	—	4	4	no	—
316	C₂×D₁₉	—	4	2	no	—
317	C₂×D₁₉	—	4	2	no	—
318	C₄×C₁₉	—	4	4	no	—
319	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
320	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
321	C₄×C₁₉	#379	1	1	yes	characteristic
322	C₄×C₁₉	#380	1	1	yes	characteristic
323	C₄×C₁₉	#385	1	1	yes	characteristic
324	C₄×C₁₉	#385	1	1	yes	characteristic
325	C₄×C₁₉	#386	1	1	yes	characteristic
326	C₄×C₁₉	#386	1	1	yes	characteristic
327	Dic₁₉	—	2	4	no	—
328	Dic₁₉	—	8	2	no	—
329	C₂²×#41	—	19	1	no	—
330	C₂×#131	—	19	4	no	—
331	C₂×#131	—	38	2	no	—
332	C₂×#131	—	38	2	no	—
333	C₂×#131	—	38	2	no	—
334	C₂×#131	—	38	2	no	—
335	C₂×#131	—	38	2	no	—
336	C₂²×M₁₆	—	19	1	no	—
337	C₂²×M₁₆	—	19	1	no	—
338	C₂²×M₁₆	—	38	1	no	—
339	C₂³×C₈	—	38	1	no	—
340	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
341	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
342	C₂×#117	—	19	1	no	—
343	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
344	C₂×#104	—	19	4	no	—
345	C₂×#104	—	38	2	no	—
346	C₂×#104	—	38	2	no	—
347	#416	—	38	2	no	—
348	#416	—	38	2	no	—
349	C₂×#103	—	19	2	no	—
350	C₂×#102	—	19	2	no	—
351	#341	—	38	2	no	—
352	#339	—	38	2	no	—
353	#336	—	2	2	no	—
354	#336	—	38	1	no	—
355	#336	—	38	1	no	—
356	C₂×C₁₉	—	2	1	no	—
357	C₂×C₁₉	—	2	1	no	—
358	C₂×C₁₉	—	2	1	no	—
359	C₂×C₁₉	—	2	1	no	—
360	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
361	C₂×C₁₉	#1764	1	1	yes	characteristic
362	C₂×C₁₉	#1765	1	1	yes	characteristic
363	C₂×C₁₉	#1866	1	2	yes	—
364	C₂×C₁₉	#1876	1	2	yes	—
365	D₁₉	—	4	4	no	—
366	C₂×#41	—	19	2	no	—
367	C₂×#41	—	19	2	no	—
368	C₂×#41	—	19	2	no	—
369	C₂×#41	—	19	2	no	—
370	C₂×#41	—	19	2	no	—
371	C₂×#41	—	19	2	no	—
372	C₂×#41	—	38	1	no	—
373	C₂×#41	—	38	1	no	—
374	C₂×#41	—	38	1	no	—
375	C₂×#41	—	38	1	no	—
376	C₂×#41	—	38	1	no	—
377	C₂×#41	—	38	1	no	—
378	C₂²×Q₈	—	19	1	no	—
379	C₂²×D₄	—	19	1	no	—
380	C₂²×D₄	—	38	1	no	—
381	C₂³×C₄	—	2	1	no	—
382	C₂³×C₄	—	38	1	no	—
383	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
384	#131	—	38	8	no	—
385	#131	—	38	8	no	—
386	#131	—	38	8	no	—
387	#131	—	38	8	no	—
388	C₂×M₁₆	—	19	2	no	—
389	C₂×M₁₆	—	19	2	no	—
390	C₂×M₁₆	—	19	2	no	—
391	C₂×M₁₆	—	19	2	no	—
392	C₂×M₁₆	—	38	4	no	—
393	C₂×M₁₆	—	38	4	no	—
394	C₂×M₁₆	—	38	1	no	—
395	C₂×M₁₆	—	38	1	no	—
396	C₂×M₁₆	—	38	1	no	—
397	C₂×M₁₆	—	38	1	no	—
398	C₂×M₁₆	—	38	4	no	—
399	C₂×M₁₆	—	38	1	no	—
400	C₂×M₁₆	—	38	1	no	—
401	C₂×M₁₆	—	38	1	no	—
402	C₂×M₁₆	—	38	1	no	—
403	C₂²×C₈	—	2	1	no	—
404	C₂²×C₈	—	2	1	no	—
405	C₂²×C₈	—	2	1	no	—
406	C₂²×C₈	—	2	1	no	—
407	C₂²×C₈	—	2	1	no	—
408	C₂²×C₈	—	2	1	no	—
409	C₂²×C₈	—	2	1	no	—
410	C₂²×C₈	—	2	1	no	—
411	C₂²×C₈	—	2	1	no	—
412	C₂²×C₈	—	2	1	no	—
413	C₂²×C₈	—	38	4	no	—
414	C₂²×C₈	—	38	4	no	—
415	C₂²×C₈	—	38	1	no	—
416	C₂²×C₈	—	38	4	no	—
417	C₂²×C₈	—	38	1	no	—
418	C₂²×C₈	C₄×D₁₉	1	2	yes	—
419	C₂²×C₈	C₄×D₁₉	1	2	yes	—
420	C₂²×C₈	D₇₆	1	1	yes	characteristic
421	C₂²×C₈	D₇₆	1	1	yes	characteristic
422	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
423	#117	—	38	1	no	—
424	#117	—	38	1	no	—
425	#117	—	38	1	no	—
426	#117	—	38	1	no	—
427	C₂×C₄⋊C₄	—	19	2	no	—
428	C₂×C₂²⋊C₄	—	38	1	no	—
429	C₂×C₄²	—	2	1	no	—
430	C₂×C₄²	—	2	1	no	—
431	C₂×C₄²	—	2	1	no	—
432	C₂×C₄²	—	2	1	no	—
433	C₂×C₄²	—	2	1	no	—
434	C₂×C₄²	—	38	1	no	—
435	C₂×C₄²	C₄×D₁₉	1	2	yes	—
436	#104	—	38	8	no	—
437	#103	—	38	4	no	—
438	#102	—	38	4	no	—
439	C₁₉	#10791	1	1	yes	characteristic, complemented, Sylow
440	C₂⁴	—	38	1	no	—
441	C₂⁴	#64541	1	1	yes	characteristic
442	#41	—	19	4	no	—
443	#41	—	19	4	no	—
444	#41	—	19	4	no	—
445	#41	—	19	4	no	—
446	#41	—	38	2	no	—
447	#41	—	38	2	no	—
448	#41	—	38	2	no	—
449	#41	—	38	2	no	—
450	#41	—	38	2	no	—
451	#41	—	38	2	no	—
452	#41	—	38	2	no	—
453	#41	—	38	2	no	—
454	#41	—	38	2	no	—
455	#41	—	38	2	no	—
456	#41	—	38	2	no	—
457	#41	—	38	2	no	—
458	C₂×Q₈	—	19	2	no	—
459	C₂×Q₈	—	19	2	no	—
460	C₂×Q₈	—	19	2	no	—
461	C₂×Q₈	—	38	1	no	—
462	C₂×Q₈	—	38	1	no	—
463	C₂×Q₈	—	38	1	no	—
464	C₂×D₄	—	19	2	no	—
465	C₂×D₄	—	19	2	no	—
466	C₂×D₄	—	19	2	no	—
467	C₂×D₄	—	38	2	no	—
468	C₂×D₄	—	38	2	no	—
469	C₂×D₄	—	38	2	no	—
470	C₂×D₄	—	38	2	no	—
471	C₂×D₄	—	38	2	no	—
472	C₂×D₄	—	38	2	no	—
473	C₂×D₄	—	38	1	no	—
474	C₂×D₄	—	38	1	no	—
475	C₂×D₄	—	38	1	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	4	2	no	—
479	C₂²×C₄	—	4	1	no	—
480	C₂²×C₄	—	4	1	no	—
481	C₂²×C₄	—	38	1	no	—
482	C₂²×C₄	—	38	2	no	—
483	C₂²×C₄	—	38	2	no	—
484	C₂²×C₄	—	38	2	no	—
485	C₂²×C₄	—	38	2	no	—
486	C₂²×C₄	—	38	2	no	—
487	C₂²×C₄	—	38	2	no	—
488	C₂²×C₄	—	38	2	no	—
489	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
490	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
491	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
492	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
493	C₂²×C₄	#64541	1	1	yes	characteristic
494	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
495	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
496	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
497	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
498	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
499	C₂²×C₄	#64543	1	1	yes	characteristic
500	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
501	C₂²×C₄	#64545	1	1	yes	characteristic
502	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
503	M₁₆	—	19	4	no	—
504	M₁₆	—	38	16	no	—
505	M₁₆	—	38	2	no	—
506	M₁₆	—	38	2	no	—
507	M₁₆	—	38	2	no	—
508	M₁₆	—	38	2	no	—
509	M₁₆	—	38	2	no	—
510	M₁₆	—	76	1	no	—
511	M₁₆	—	76	1	no	—
512	C₂×C₈	—	2	2	no	—
513	C₂×C₈	—	2	2	no	—
514	C₂×C₈	—	2	2	no	—
515	C₂×C₈	—	2	2	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	2	no	—
521	C₂×C₈	—	2	2	no	—
522	C₂×C₈	—	2	2	no	—
523	C₂×C₈	—	4	1	no	—
524	C₂×C₈	—	4	1	no	—
525	C₂×C₈	—	4	1	no	—
526	C₂×C₈	—	4	1	no	—
527	C₂×C₈	—	38	16	no	—
528	C₂×C₈	—	38	2	no	—
529	C₂×C₈	—	38	2	no	—
530	C₂×C₈	—	38	2	no	—
531	C₂×C₈	—	38	2	no	—
532	C₂×C₈	—	76	1	no	—
533	C₂×C₈	—	76	1	no	—
534	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
535	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
536	C₄⋊C₄	—	38	2	no	—
537	C₄⋊C₄	—	38	2	no	—
538	C₂²⋊C₄	—	76	1	no	—
539	C₂²⋊C₄	—	76	1	no	—
540	C₄²	—	2	2	no	—
541	C₄²	—	2	2	no	—
542	C₄²	—	4	1	no	—
543	C₄²	—	4	1	no	—
544	C₄²	—	76	1	no	—
545	C₄²	—	76	1	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	38	2	no	—
549	C₂³	—	38	2	no	—
550	C₂³	—	38	2	no	—
551	C₂³	—	76	2	no	—
552	C₂³	—	76	2	no	—
553	C₂³	#10597318	1	1	yes	characteristic
554	C₂³	C₄×D₇₆	1	1	yes	characteristic
555	C₂³	#10597329	1	1	yes	characteristic
556	C₂³	#10597330	1	1	yes	characteristic
557	C₂³	#10597340	1	1	yes	characteristic
558	C₂³	#10597342	1	1	yes	characteristic
559	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
560	Q₈	—	19	4	no	—
561	Q₈	—	38	2	no	—
562	Q₈	—	38	2	no	—
563	Q₈	—	38	2	no	—
564	D₄	—	19	4	no	—
565	D₄	—	38	4	no	—
566	D₄	—	38	4	no	—
567	D₄	—	38	4	no	—
568	D₄	—	38	4	no	—
569	D₄	—	38	2	no	—
570	D₄	—	38	2	no	—
571	D₄	—	38	2	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	4	4	no	—
574	C₂×C₄	—	4	4	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	38	2	no	—
578	C₂×C₄	—	38	2	no	—
579	C₂×C₄	—	38	2	no	—
580	C₂×C₄	—	38	4	no	—
581	C₂×C₄	—	38	4	no	—
582	C₂×C₄	—	38	4	no	—
583	C₂×C₄	—	38	4	no	—
584	C₂×C₄	—	76	2	no	—
585	C₂×C₄	—	76	2	no	—
586	C₂×C₄	—	76	2	no	—
587	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
588	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
589	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
590	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
591	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
592	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
593	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
594	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
595	C₂×C₄	#10597328	1	1	yes	characteristic
596	C₂×C₄	#10597328	1	1	yes	characteristic
597	C₂×C₄	#10597329	1	1	yes	characteristic
598	C₂×C₄	#10597330	1	1	yes	characteristic
599	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
600	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
601	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
602	C₂×C₄	#10597338	1	1	yes	characteristic
603	C₂×C₄	#10597339	1	1	yes	characteristic
604	C₂×C₄	#10597339	1	1	yes	characteristic
605	C₂×C₄	#10597340	1	1	yes	characteristic
606	C₂×C₄	#10597341	1	1	yes	characteristic
607	C₂×C₄	#10597342	1	1	yes	characteristic
608	C₂×C₄	#10597343	1	1	yes	characteristic
609	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
610	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
611	C₂×C₄	#10597383	1	1	yes	characteristic
612	C₂×C₄	#10597383	1	1	yes	characteristic
613	C₂×C₄	#10597384	1	1	yes	characteristic
614	C₂×C₄	#10597392	1	1	yes	characteristic
615	C₈	—	2	2	no	—
616	C₈	—	2	2	no	—
617	C₈	—	4	2	no	—
618	C₈	—	38	4	no	—
619	C₈	—	76	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	38	4	no	—
629	C₂²	—	76	4	no	—
630	C₂²	—	76	4	no	—
631	C₂²	—	76	2	no	—
632	C₂²	—	76	2	no	—
633	C₂²	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
634	C₂²	#11926403	1	1	yes	characteristic
635	C₂²	#11926406	1	1	yes	characteristic
636	C₂²	#11926415	1	1	yes	characteristic
637	C₂²	#11926418	1	1	yes	characteristic
638	C₂²	#11926420	1	1	yes	characteristic
639	C₂²	#11926422	1	1	yes	characteristic
640	C₂²	#11926662	1	2	yes	—
641	C₂²	#11926667	1	2	yes	—
642	C₄	—	4	4	no	—
643	C₄	—	38	4	no	—
644	C₄	—	152	2	no	—
645	C₄	#95×D₁₉	1	1	yes	characteristic
646	C₄	#11926391	1	1	yes	characteristic
647	C₄	#11926399	1	1	yes	characteristic
648	C₄	#11926401	1	1	yes	characteristic
649	C₄	#11926415	1	1	yes	characteristic
650	C₄	#11926418	1	1	yes	characteristic
651	C₄	#11926420	1	1	yes	characteristic
652	C₄	#11926422	1	1	yes	characteristic
653	C₂	—	2	1	no	—
654	C₂	—	2	1	no	—
655	C₂	—	2	1	no	—
656	C₂	—	2	1	no	—
657	C₂	—	76	4	no	—
658	C₂	(C₂×D₁₉)⋊#95	1	1	yes	characteristic
659	C₂	#14563472	1	1	yes	characteristic
660	C₂	#14563479	1	1	yes	characteristic
661	C₂	#14563913	1	2	yes	—
662	C₂	#14563961	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₇₆
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#336	C₂
socle	C₂³×C₁₉	C₄×D₄
prime radical	C₂²×#64541	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#336	D₁₉
hypocenter	C₁₉	#10791
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₈ ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
4. C₂×#11926309	C₂	semidirect
5. C₂×#11926304	C₂	semidirect
6. #14563331	C₂	semidirect
7. C₂×C₁₉×#336	C₂	semidirect
14. C₂×#10597347	C₄	semidirect
22. C₂×#10597262	C₄	semidirect
25. C₂×#10597273	C₄	semidirect
26. C₂×#10597278	C₄	semidirect
295. C₂×#336	D₁₉	semidirect
439. C₁₉	#10791	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10597347	2
C₂²×#10597262	2
C₂×#11926541	2
C₂×#11926309	2
C₂×#11926304	2
#14563331	2
C₂×C₁₉×#336	2
#10791	19