Subgroups — #18089290

Order 4864.

1242 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10597388	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926562	C₂	1	1	yes	maximal, characteristic
3	C₂²×#10597293	C₂	1	1	yes	maximal, characteristic, complemented
4	#14572079	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926314	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉⋊#338	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64541	C₂²	1	1	yes	characteristic
9	C₂×#10597388	—	2	2	no	—
10	C₂×#10597388	—	2	2	no	—
11	C₂×#10597388	—	2	2	no	—
12	C₂×#10597388	—	2	2	no	—
13	C₂×#10597388	—	2	2	no	—
14	C₂×#10597388	—	2	2	no	—
15	C₂²×#64528	C₄	1	2	yes	complemented
16	C₂²×#64527	C₄	1	2	yes	complemented
17	C₂²×#64520	C₂²	1	1	yes	characteristic
18	C₂²×#64520	C₂²	1	1	yes	characteristic
19	C₂²×#64520	C₂²	1	1	yes	characteristic
20	#11926562	—	2	2	no	—
21	#11926562	—	2	2	no	—
22	C₂×#10597262	—	2	2	no	—
23	C₂×#10597293	—	2	2	no	—
24	C₂×#10597293	—	2	2	no	—
25	C₂×#10597293	—	2	2	no	—
26	#11926512	—	2	2	no	—
27	#11926510	—	2	2	no	—
28	#11926507	—	2	2	no	—
29	#11926314	—	2	2	no	—
30	C₁₉⋊#338	—	2	2	no	—
31	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
32	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
34	C₁₉×#419	—	2	2	no	—
35	C₁₉×#419	—	2	2	no	—
36	C₂×C₁₉×#103	—	2	2	no	—
37	C₂²×Q₈×C₁₉	—	2	1	no	—
38	C₂²×Q₈×C₁₉	—	2	1	no	—
39	C₂²×Q₈×C₁₉	—	2	1	no	—
40	C₂²×Q₈×C₁₉	—	2	1	no	—
41	C₂²×Q₈×C₁₉	—	2	1	no	—
42	C₂²×Q₈×C₁₉	—	2	1	no	—
43	C₂²×Q₈×C₁₉	—	2	1	no	—
44	C₂²×Q₈×C₁₉	—	2	1	no	—
45	C₂²×Q₈×C₁₉	—	2	1	no	—
46	C₂²×Q₈×C₁₉	—	2	1	no	—
47	C₂²×Q₈×C₁₉	—	2	1	no	—
48	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
49	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
50	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
51	C₂³×C₄×C₁₉	—	2	1	no	—
52	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×C₂²⋊D₁₉	—	2	1	no	—
54	C₂×#64541	—	2	1	no	—
55	C₂×#64541	—	2	1	no	—
56	C₂×#64541	—	2	1	no	—
57	C₂×#64541	—	2	1	no	—
58	C₂×#64541	—	2	1	no	—
59	C₂×#64541	—	2	1	no	—
60	C₂×#64541	—	2	1	no	—
61	C₂×#64541	—	2	1	no	—
62	C₂×#64541	—	2	1	no	—
63	C₂×#64541	—	2	1	no	—
64	C₂×#64541	D₄	1	2	yes	—
65	C₂×#64541	D₄	1	2	yes	—
66	C₂²×D₇₆	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₄×D₁₉	—	2	1	no	—
68	C₂²×Dic₃₈	C₂×C₄	1	1	yes	characteristic
69	C₂×M₁₆×C₁₉	—	2	1	no	—
70	C₂×M₁₆×C₁₉	—	2	1	no	—
71	C₂×M₁₆×C₁₉	—	2	1	no	—
72	C₂×M₁₆×C₁₉	—	2	1	no	—
73	C₂×M₁₆×C₁₉	—	2	1	no	—
74	C₂×M₁₆×C₁₉	—	2	1	no	—
75	C₂²×C₈×C₁₉	D₄	1	2	yes	—
76	C₁₉×#117	—	2	1	no	—
77	C₁₉×#117	—	2	1	no	—
78	C₁₉×#117	—	2	1	no	—
79	C₁₉×#117	D₄	1	2	yes	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄²×C₁₉	—	2	1	no	—
83	C₂×#64528	—	2	4	no	—
84	C₂×#64528	—	2	4	no	—
85	C₂×#64528	—	2	4	no	—
86	#10597388	—	2	8	no	—
87	#10597388	—	2	8	no	—
88	#10597388	—	2	8	no	—
89	#10597388	—	2	8	no	—
90	C₂×#64527	—	2	4	no	—
91	C₂×#64527	—	2	4	no	—
92	C₂×#64527	—	2	4	no	—
93	C₂×#64520	—	2	1	no	—
94	C₂×#64520	—	2	1	no	—
95	C₂×#64520	—	2	1	no	—
96	C₂×#64520	—	2	1	no	—
97	C₂×#64520	—	2	1	no	—
98	C₂×#64520	—	2	1	no	—
99	C₂×#64520	—	2	1	no	—
100	C₂×#64520	—	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	D₄	1	2	yes	—
108	C₂×#64520	D₄	1	2	yes	—
109	C₂×#64520	D₄	1	2	yes	—
110	C₂×#64520	D₄	1	2	yes	—
111	C₂²×C₁₉⋊C₈	—	2	1	no	—
112	C₂²×C₁₉⋊C₈	—	2	1	no	—
113	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
114	C₁₉×#103	—	2	8	no	—
115	#10597293	—	2	8	no	—
116	(C₂×D₁₉)⋊C₈	—	2	8	no	—
117	#10597262	—	2	8	no	—
118	C₂⁴×C₁₉	#41	1	1	yes	characteristic
119	C₂³×D₁₉	—	2	1	no	—
120	C₂×Q₈×C₁₉	—	2	2	no	—
121	C₂×Q₈×C₁₉	—	2	2	no	—
122	C₂×Q₈×C₁₉	—	2	2	no	—
123	C₂×Q₈×C₁₉	—	2	2	no	—
124	C₂×Q₈×C₁₉	—	2	2	no	—
125	C₂×Q₈×C₁₉	—	2	2	no	—
126	C₂×Q₈×C₁₉	—	2	2	no	—
127	C₂×Q₈×C₁₉	—	2	2	no	—
128	C₂×Q₈×C₁₉	—	2	2	no	—
129	C₂×Q₈×C₁₉	—	2	2	no	—
130	C₂×Q₈×C₁₉	—	2	2	no	—
131	C₂×Q₈×C₁₉	—	2	2	no	—
132	C₂×Q₈×C₁₉	—	2	2	no	—
133	C₂×Q₈×C₁₉	—	2	2	no	—
134	C₂×Q₈×C₁₉	—	2	2	no	—
135	C₂×Q₈×C₁₉	—	4	1	no	—
136	C₂×Q₈×C₁₉	—	4	1	no	—
137	C₂×Q₈×C₁₉	—	4	1	no	—
138	C₂×Q₈×C₁₉	—	4	1	no	—
139	C₂×Q₈×C₁₉	—	4	1	no	—
140	C₂×Q₈×C₁₉	—	4	1	no	—
141	C₂×Q₈×C₁₉	—	4	1	no	—
142	C₂×Q₈×C₁₉	—	4	1	no	—
143	C₂×Q₈×C₁₉	—	4	1	no	—
144	C₂×Q₈×C₁₉	—	4	1	no	—
145	C₂×Q₈×C₁₉	—	4	1	no	—
146	C₂×Q₈×C₁₉	—	4	1	no	—
147	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
148	C₂²×C₄×C₁₉	—	2	2	no	—
149	C₂²×C₄×C₁₉	—	2	2	no	—
150	C₂²×C₄×C₁₉	—	2	2	no	—
151	C₂²×C₄×C₁₉	—	4	1	no	—
152	C₂²×C₄×C₁₉	—	4	1	no	—
153	C₂²×C₄×C₁₉	—	4	1	no	—
154	C₂²×C₄×C₁₉	—	4	1	no	—
155	C₂²×C₄×C₁₉	—	4	1	no	—
156	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
170	C₂×C₂²⋊D₁₉	—	2	2	no	—
171	C₂×C₂²⋊D₁₉	—	2	2	no	—
172	C₂×C₂²⋊D₁₉	—	4	1	no	—
173	C₂×C₂²⋊D₁₉	—	4	1	no	—
174	C₂×C₂²⋊D₁₉	—	4	1	no	—
175	C₂×C₂²⋊D₁₉	—	4	1	no	—
176	C₂²×Dic₁₉	—	2	1	no	—
177	#64541	—	2	2	no	—
178	#64541	—	2	2	no	—
179	#64541	—	2	2	no	—
180	#64541	—	2	2	no	—
181	#64541	—	2	2	no	—
182	#64541	—	2	2	no	—
183	#64541	—	2	2	no	—
184	#64541	—	2	2	no	—
185	#64541	—	4	1	no	—
186	#64541	—	4	1	no	—
187	#64541	—	4	1	no	—
188	#64541	—	4	1	no	—
189	#64541	—	4	1	no	—
190	#64541	—	4	1	no	—
191	#64541	—	4	1	no	—
192	#64541	—	4	1	no	—
193	C₂×D₇₆	—	2	1	no	—
194	C₂×D₇₆	—	2	1	no	—
195	C₂×D₇₆	—	2	1	no	—
196	C₂×D₇₆	—	2	1	no	—
197	C₂×D₇₆	—	2	1	no	—
198	C₂×D₇₆	C₂²⋊C₄	1	2	yes	—
199	C₂×C₄×D₁₉	—	2	2	no	—
200	C₂×C₄×D₁₉	—	2	2	no	—
201	C₂×C₄×D₁₉	—	4	1	no	—
202	C₂×C₄×D₁₉	—	4	1	no	—
203	C₂×C₄×D₁₉	—	4	1	no	—
204	C₂×C₄×D₁₉	—	4	1	no	—
205	C₂×Dic₃₈	—	2	1	no	—
206	C₂×Dic₃₈	—	2	1	no	—
207	C₂×Dic₃₈	—	2	1	no	—
208	C₂×Dic₃₈	—	2	1	no	—
209	C₂×Dic₃₈	—	2	1	no	—
210	C₂×Dic₃₈	C₂²⋊C₄	1	2	yes	—
211	M₁₆×C₁₉	—	4	1	no	—
212	M₁₆×C₁₉	—	4	1	no	—
213	M₁₆×C₁₉	—	4	1	no	—
214	M₁₆×C₁₉	—	4	1	no	—
215	C₂×C₈×C₁₉	—	2	2	no	—
216	C₂×C₈×C₁₉	—	2	2	no	—
217	C₂×C₈×C₁₉	—	2	2	no	—
218	C₄⋊C₄×C₁₉	—	2	2	no	—
219	C₄⋊C₄×C₁₉	—	4	1	no	—
220	C₂²⋊C₄×C₁₉	—	2	2	no	—
221	C₂²⋊C₄×C₁₉	—	4	1	no	—
222	C₄²×C₁₉	—	2	2	no	—
223	C₄²×C₁₉	—	4	1	no	—
224	#64528	—	2	16	no	—
225	#64527	—	2	16	no	—
226	#64520	—	2	2	no	—
227	#64520	—	2	2	no	—
228	#64520	—	2	2	no	—
229	#64520	—	2	2	no	—
230	#64520	—	2	2	no	—
231	#64520	—	2	2	no	—
232	#64520	—	2	2	no	—
233	#64520	—	2	2	no	—
234	#64520	—	4	1	no	—
235	#64520	—	4	1	no	—
236	#64520	—	4	1	no	—
237	#64520	—	4	1	no	—
238	C₂×C₁₉⋊C₈	—	2	2	no	—
239	C₂×C₁₉⋊C₈	—	2	2	no	—
240	C₂×C₁₉⋊C₈	—	2	2	no	—
241	C₂×C₁₉⋊C₈	—	2	2	no	—
242	C₂×C₁₉⋊C₈	—	4	1	no	—
243	C₂×C₁₉⋊C₈	—	4	1	no	—
244	C₂×C₁₉⋊C₈	—	4	1	no	—
245	C₂×C₁₉⋊C₈	—	4	1	no	—
246	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	4	yes	—
247	#11015	—	19	1	no	maximal, Sylow
248	C₂³×C₁₉	—	4	2	no	—
249	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
250	C₂³×C₁₉	#121	1	1	yes	characteristic
251	C₂³×C₁₉	#121	1	1	yes	characteristic
252	C₂³×C₁₉	#121	1	1	yes	characteristic
253	C₂³×C₁₉	#123	1	1	yes	characteristic
254	C₂³×C₁₉	#123	1	1	yes	characteristic
255	C₂³×C₁₉	#124	1	1	yes	characteristic
256	C₂²×D₁₉	—	2	2	no	—
257	C₂²×D₁₉	—	4	1	no	—
258	C₂²×D₁₉	—	4	1	no	—
259	C₂²×D₁₉	—	8	2	no	—
260	Q₈×C₁₉	—	2	4	no	—
261	Q₈×C₁₉	—	2	4	no	—
262	Q₈×C₁₉	—	4	2	no	—
263	Q₈×C₁₉	—	4	2	no	—
264	Q₈×C₁₉	—	4	2	no	—
265	Q₈×C₁₉	—	4	2	no	—
266	Q₈×C₁₉	—	4	2	no	—
267	Q₈×C₁₉	—	4	2	no	—
268	C₂×C₄×C₁₉	—	2	4	no	—
269	C₂×C₄×C₁₉	—	4	2	no	—
270	C₂×C₄×C₁₉	—	4	2	no	—
271	C₂×C₄×C₁₉	—	4	2	no	—
272	C₂×C₄×C₁₉	—	4	2	no	—
273	C₂×C₄×C₁₉	—	4	2	no	—
274	C₂×C₄×C₁₉	—	4	2	no	—
275	C₂×C₄×C₁₉	—	4	2	no	—
276	C₂×C₄×C₁₉	—	8	2	no	—
277	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
281	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
282	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
283	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
284	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
285	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
286	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
287	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
288	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
289	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
290	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
291	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
292	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
293	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
294	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
295	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
296	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
297	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
298	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
299	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
300	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
301	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
302	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
303	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
304	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
305	C₂²⋊D₁₉	—	4	2	no	—
306	C₂²⋊D₁₉	—	4	2	no	—
307	C₂²⋊D₁₉	—	4	2	no	—
308	C₂²⋊D₁₉	—	4	2	no	—
309	C₂×Dic₁₉	—	2	2	no	—
310	C₂×Dic₁₉	—	4	1	no	—
311	C₂×Dic₁₉	—	4	1	no	—
312	D₇₆	—	2	2	no	—
313	D₇₆	—	2	2	no	—
314	D₇₆	—	4	1	no	—
315	D₇₆	—	4	1	no	—
316	C₄×D₁₉	—	4	2	no	—
317	C₄×D₁₉	—	4	2	no	—
318	C₄×D₁₉	—	4	2	no	—
319	C₄×D₁₉	—	4	2	no	—
320	Dic₃₈	—	2	2	no	—
321	Dic₃₈	—	2	2	no	—
322	Dic₃₈	—	4	1	no	—
323	Dic₃₈	—	4	1	no	—
324	C₈×C₁₉	—	4	2	no	—
325	C₁₉⋊C₈	—	2	4	no	—
326	C₁₉⋊C₈	—	4	2	no	—
327	C₁₉⋊C₈	—	4	2	no	—
328	C₂²×#137	—	19	1	no	—
329	C₂×#421	—	19	1	no	—
330	C₂×#419	D₁₉	1	1	yes	characteristic, complemented
331	C₂²×#101	—	19	1	no	—
332	#2879	—	19	1	no	—
333	C₂×#344	—	19	1	no	—
334	C₂×#338	—	19	1	no	—
335	C₂²×C₁₉	—	2	2	no	—
336	C₂²×C₁₉	—	2	2	no	—
337	C₂²×C₁₉	—	2	2	no	—
338	C₂²×C₁₉	—	4	1	no	—
339	C₂²×C₁₉	—	4	1	no	—
340	C₂²×C₁₉	—	4	1	no	—
341	C₂²×C₁₉	—	4	1	no	—
342	C₂²×C₁₉	#386	1	1	yes	characteristic
343	C₂²×C₁₉	#386	1	1	yes	characteristic
344	C₂²×C₁₉	#390	1	1	yes	characteristic
345	C₂²×C₁₉	#392	1	1	yes	characteristic
346	C₂²×C₁₉	#394	1	1	yes	characteristic
347	C₂²×C₁₉	#394	1	1	yes	characteristic
348	C₂²×C₁₉	#394	1	1	yes	characteristic
349	C₂×D₁₉	—	4	4	no	—
350	C₂×D₁₉	—	4	2	no	—
351	C₂×D₁₉	—	8	2	no	—
352	C₂×D₁₉	—	8	2	no	—
353	C₄×C₁₉	—	4	4	no	—
354	C₄×C₁₉	—	8	2	no	—
355	C₄×C₁₉	#379	1	1	yes	characteristic
356	C₄×C₁₉	#386	1	1	yes	characteristic
357	C₄×C₁₉	#386	1	1	yes	characteristic
358	C₄×C₁₉	#390	1	1	yes	characteristic
359	C₄×C₁₉	#392	1	1	yes	characteristic
360	C₄×C₁₉	#392	1	1	yes	characteristic
361	C₄×C₁₉	#392	1	1	yes	characteristic
362	C₄×C₁₉	#394	1	1	yes	characteristic
363	Dic₁₉	—	4	2	no	—
364	C₂²×#41	—	19	1	no	—
365	C₂³×Q₈	C₂×D₁₉	1	1	yes	characteristic
366	C₂×#137	—	38	2	no	—
367	C₂×#137	—	38	2	no	—
368	C₂×#137	—	38	2	no	—
369	C₂×#137	—	38	2	no	—
370	C₂×#137	—	38	2	no	—
371	C₂×#137	—	38	2	no	—
372	C₂²×Q₁₆	—	19	2	no	—
373	C₂²×SD₁₆	—	19	2	no	—
374	C₂²×M₁₆	—	19	1	no	—
375	C₂²×M₁₆	—	19	1	no	—
376	C₂²×M₁₆	—	19	1	no	—
377	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
378	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
379	#421	—	38	2	no	—
380	#421	—	38	2	no	—
381	C₂×#104	—	38	2	no	—
382	#419	—	2	2	no	—
383	#419	—	2	2	no	—
384	C₂×#103	—	2	2	no	—
385	C₂×#101	—	38	2	no	—
386	C₂×#101	—	38	2	no	—
387	C₂×#101	—	38	2	no	—
388	#408	—	38	2	no	—
389	#408	—	38	2	no	—
390	#407	—	38	2	no	—
391	#344	—	38	2	no	—
392	#338	—	38	2	no	—
393	C₂×C₁₉	—	2	1	no	—
394	C₂×C₁₉	—	2	1	no	—
395	C₂×C₁₉	—	2	1	no	—
396	C₂×C₁₉	—	2	1	no	—
397	C₂×C₁₉	—	2	1	no	—
398	C₂×C₁₉	—	2	1	no	—
399	C₂×C₁₉	#1438	1	1	yes	characteristic
400	C₂×C₁₉	#1902	1	2	yes	—
401	D₁₉	—	8	2	no	—
402	C₂×#41	—	19	2	no	—
403	C₂×#41	—	19	2	no	—
404	C₂×#41	—	38	1	no	—
405	C₂×#41	—	38	1	no	—
406	C₂×#41	—	38	1	no	—
407	C₂×#41	—	38	1	no	—
408	C₂×#41	—	38	1	no	—
409	C₂×#41	—	38	1	no	—
410	C₂×#41	—	38	1	no	—
411	C₂×#41	—	38	1	no	—
412	C₂×#41	—	38	1	no	—
413	C₂×#41	—	38	1	no	—
414	C₂²×Q₈	—	2	1	no	—
415	C₂²×Q₈	—	2	1	no	—
416	C₂²×Q₈	—	2	1	no	—
417	C₂²×Q₈	—	2	1	no	—
418	C₂²×Q₈	—	2	1	no	—
419	C₂²×Q₈	—	2	1	no	—
420	C₂²×Q₈	—	2	1	no	—
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	—	19	1	no	—
426	C₂²×Q₈	C₄×D₁₉	1	2	yes	—
427	C₂²×Q₈	D₇₆	1	2	yes	—
428	C₂²×Q₈	C₂²⋊D₁₉	1	2	yes	—
429	C₂²×D₄	—	19	1	no	—
430	C₂²×D₄	—	38	1	no	—
431	C₂³×C₄	—	2	1	no	—
432	C₂³×C₄	—	38	1	no	—
433	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
434	#137	—	38	8	no	—
435	#137	—	38	8	no	—
436	#137	—	38	8	no	—
437	#137	—	38	8	no	—
438	C₂×Q₁₆	—	38	4	no	—
439	C₂×Q₁₆	—	38	4	no	—
440	C₂×Q₁₆	—	38	4	no	—
441	C₂×SD₁₆	—	38	4	no	—
442	C₂×SD₁₆	—	38	4	no	—
443	C₂×SD₁₆	—	38	4	no	—
444	C₂×M₁₆	—	2	1	no	—
445	C₂×M₁₆	—	2	1	no	—
446	C₂×M₁₆	—	2	1	no	—
447	C₂×M₁₆	—	2	1	no	—
448	C₂×M₁₆	—	2	1	no	—
449	C₂×M₁₆	—	2	1	no	—
450	C₂×M₁₆	—	19	2	no	—
451	C₂×M₁₆	—	19	2	no	—
452	C₂×M₁₆	—	19	2	no	—
453	C₂×M₁₆	—	19	2	no	—
454	C₂×M₁₆	—	38	1	no	—
455	C₂×M₁₆	—	38	1	no	—
456	C₂×M₁₆	—	38	1	no	—
457	C₂×M₁₆	—	38	1	no	—
458	C₂×M₁₆	—	38	1	no	—
459	C₂×M₁₆	—	38	1	no	—
460	C₂×M₁₆	—	38	1	no	—
461	C₂×M₁₆	—	38	1	no	—
462	C₂×M₁₆	—	38	1	no	—
463	C₂×M₁₆	—	38	1	no	—
464	C₂×M₁₆	—	38	1	no	—
465	C₂×M₁₆	—	38	1	no	—
466	C₂×M₁₆	—	38	1	no	—
467	C₂×M₁₆	—	38	1	no	—
468	C₂²×C₈	—	19	2	no	—
469	C₂²×C₈	—	38	1	no	—
470	C₂²×C₈	—	38	1	no	—
471	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
472	#117	—	2	1	no	—
473	#117	—	2	1	no	—
474	#117	—	2	1	no	—
475	#117	C₂²⋊D₁₉	1	2	yes	—
476	C₂×C₄⋊C₄	—	2	1	no	—
477	C₂×C₂²⋊C₄	—	2	1	no	—
478	C₂×C₄²	—	2	1	no	—
479	#104	—	38	8	no	—
480	#103	—	2	8	no	—
481	#101	—	38	8	no	—
482	C₂²⋊C₈	—	38	8	no	—
483	C₁₉	#11015	1	1	yes	characteristic, complemented, Sylow
484	C₂⁴	—	38	1	no	—
485	C₂⁴	#64543	1	1	yes	characteristic
486	#41	—	38	2	no	—
487	#41	—	38	2	no	—
488	#41	—	38	2	no	—
489	#41	—	38	2	no	—
490	#41	—	38	2	no	—
491	#41	—	38	2	no	—
492	#41	—	38	2	no	—
493	#41	—	38	2	no	—
494	#41	—	76	1	no	—
495	#41	—	76	1	no	—
496	#41	—	76	1	no	—
497	#41	—	76	1	no	—
498	#41	—	76	1	no	—
499	#41	—	76	1	no	—
500	#41	—	76	1	no	—
501	#41	—	76	1	no	—
502	C₂×Q₈	—	2	2	no	—
503	C₂×Q₈	—	2	2	no	—
504	C₂×Q₈	—	2	2	no	—
505	C₂×Q₈	—	2	2	no	—
506	C₂×Q₈	—	2	2	no	—
507	C₂×Q₈	—	2	2	no	—
508	C₂×Q₈	—	2	2	no	—
509	C₂×Q₈	—	2	2	no	—
510	C₂×Q₈	—	2	2	no	—
511	C₂×Q₈	—	2	2	no	—
512	C₂×Q₈	—	2	2	no	—
513	C₂×Q₈	—	2	2	no	—
514	C₂×Q₈	—	2	2	no	—
515	C₂×Q₈	—	2	2	no	—
516	C₂×Q₈	—	2	2	no	—
517	C₂×Q₈	—	4	1	no	—
518	C₂×Q₈	—	4	1	no	—
519	C₂×Q₈	—	4	1	no	—
520	C₂×Q₈	—	4	1	no	—
521	C₂×Q₈	—	4	1	no	—
522	C₂×Q₈	—	4	1	no	—
523	C₂×Q₈	—	4	1	no	—
524	C₂×Q₈	—	4	1	no	—
525	C₂×Q₈	—	4	1	no	—
526	C₂×Q₈	—	4	1	no	—
527	C₂×Q₈	—	4	1	no	—
528	C₂×Q₈	—	4	1	no	—
529	C₂×Q₈	—	19	2	no	—
530	C₂×Q₈	—	38	1	no	—
531	C₂×Q₈	—	38	1	no	—
532	C₂×Q₈	—	38	1	no	—
533	C₂×Q₈	—	38	1	no	—
534	C₂×Q₈	—	38	1	no	—
535	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
536	C₂×D₄	—	19	2	no	—
537	C₂×D₄	—	38	2	no	—
538	C₂×D₄	—	38	2	no	—
539	C₂×D₄	—	38	1	no	—
540	C₂×D₄	—	38	1	no	—
541	C₂×D₄	—	38	1	no	—
542	C₂×D₄	—	38	1	no	—
543	C₂×D₄	—	38	1	no	—
544	C₂×D₄	—	76	1	no	—
545	C₂×D₄	—	76	1	no	—
546	C₂×D₄	—	76	1	no	—
547	C₂×D₄	—	76	1	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	4	1	no	—
552	C₂²×C₄	—	4	1	no	—
553	C₂²×C₄	—	4	1	no	—
554	C₂²×C₄	—	4	1	no	—
555	C₂²×C₄	—	4	1	no	—
556	C₂²×C₄	—	38	1	no	—
557	C₂²×C₄	—	38	2	no	—
558	C₂²×C₄	—	38	2	no	—
559	C₂²×C₄	—	76	1	no	—
560	C₂²×C₄	—	76	1	no	—
561	C₂²×C₄	—	76	1	no	—
562	C₂²×C₄	—	76	1	no	—
563	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
564	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
565	C₂²×C₄	#64541	1	1	yes	characteristic
566	C₂²×C₄	#64541	1	1	yes	characteristic
567	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
568	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
569	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
570	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
571	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
572	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
573	C₂²×C₄	#64543	1	1	yes	characteristic
574	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
575	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
576	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
577	Q₁₆	—	38	16	no	—
578	SD₁₆	—	38	16	no	—
579	M₁₆	—	4	1	no	—
580	M₁₆	—	4	1	no	—
581	M₁₆	—	4	1	no	—
582	M₁₆	—	4	1	no	—
583	M₁₆	—	38	2	no	—
584	M₁₆	—	38	2	no	—
585	M₁₆	—	38	2	no	—
586	M₁₆	—	38	2	no	—
587	M₁₆	—	38	2	no	—
588	M₁₆	—	38	2	no	—
589	M₁₆	—	38	2	no	—
590	M₁₆	—	38	2	no	—
591	M₁₆	—	76	1	no	—
592	M₁₆	—	76	1	no	—
593	M₁₆	—	76	1	no	—
594	M₁₆	—	76	1	no	—
595	C₂×C₈	—	2	2	no	—
596	C₂×C₈	—	2	2	no	—
597	C₂×C₈	—	2	2	no	—
598	C₂×C₈	—	19	4	no	—
599	C₂×C₈	—	38	2	no	—
600	C₂×C₈	—	38	2	no	—
601	C₂×C₈	—	38	2	no	—
602	C₂×C₈	—	38	2	no	—
603	C₂×C₈	—	76	1	no	—
604	C₂×C₈	—	76	1	no	—
605	C₂×C₈	—	76	1	no	—
606	C₂×C₈	—	76	1	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	4	1	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	4	1	no	—
611	C₄²	—	2	2	no	—
612	C₄²	—	4	1	no	—
613	C₂³	—	4	2	no	—
614	C₂³	—	38	2	no	—
615	C₂³	—	76	1	no	—
616	C₂³	—	76	1	no	—
617	C₂³	—	152	2	no	—
618	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
619	C₂³	#10597329	1	1	yes	characteristic
620	C₂³	#10597331	1	1	yes	characteristic
621	C₂³	#10597332	1	1	yes	characteristic
622	C₂³	#10597384	1	1	yes	characteristic
623	C₂³	#10597385	1	1	yes	characteristic
624	C₂³	#10597385	1	1	yes	characteristic
625	Q₈	—	2	4	no	—
626	Q₈	—	2	4	no	—
627	Q₈	—	4	2	no	—
628	Q₈	—	4	2	no	—
629	Q₈	—	4	2	no	—
630	Q₈	—	4	2	no	—
631	Q₈	—	4	2	no	—
632	Q₈	—	4	2	no	—
633	Q₈	—	38	2	no	—
634	Q₈	—	38	2	no	—
635	Q₈	—	76	1	no	—
636	Q₈	—	76	1	no	—
637	D₄	—	38	2	no	—
638	D₄	—	38	2	no	—
639	D₄	—	76	2	no	—
640	D₄	—	76	2	no	—
641	D₄	—	76	2	no	—
642	D₄	—	76	2	no	—
643	D₄	—	76	1	no	—
644	D₄	—	76	1	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	4	2	no	—
647	C₂×C₄	—	4	2	no	—
648	C₂×C₄	—	4	2	no	—
649	C₂×C₄	—	4	2	no	—
650	C₂×C₄	—	4	2	no	—
651	C₂×C₄	—	4	2	no	—
652	C₂×C₄	—	4	2	no	—
653	C₂×C₄	—	8	2	no	—
654	C₂×C₄	—	38	2	no	—
655	C₂×C₄	—	76	1	no	—
656	C₂×C₄	—	76	1	no	—
657	C₂×C₄	—	76	2	no	—
658	C₂×C₄	—	76	2	no	—
659	C₂×C₄	—	76	2	no	—
660	C₂×C₄	—	76	2	no	—
661	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
662	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
663	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
664	C₂×C₄	#10597328	1	1	yes	characteristic
665	C₂×C₄	#10597328	1	1	yes	characteristic
666	C₂×C₄	#10597328	1	1	yes	characteristic
667	C₂×C₄	#10597329	1	1	yes	characteristic
668	C₂×C₄	#10597330	1	1	yes	characteristic
669	C₂×C₄	#10597330	1	1	yes	characteristic
670	C₂×C₄	#10597330	1	1	yes	characteristic
671	C₂×C₄	#10597330	1	1	yes	characteristic
672	C₂×C₄	#10597331	1	1	yes	characteristic
673	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
674	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
675	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
676	C₂×C₄	#10597375	1	1	yes	characteristic
677	C₂×C₄	#10597376	1	1	yes	characteristic
678	C₂×C₄	#10597376	1	1	yes	characteristic
679	C₂×C₄	#10597383	1	1	yes	characteristic
680	C₂×C₄	#10597383	1	1	yes	characteristic
681	C₂×C₄	#10597383	1	1	yes	characteristic
682	C₂×C₄	#10597383	1	1	yes	characteristic
683	C₂×C₄	#10597384	1	1	yes	characteristic
684	C₂×C₄	#10597385	1	1	yes	characteristic
685	C₂×C₄	#10597385	1	1	yes	characteristic
686	C₂×C₄	#10597386	1	1	yes	characteristic
687	C₂×C₄	#10597386	1	1	yes	characteristic
688	C₂×C₄	#10597399	1	1	yes	characteristic
689	C₈	—	4	2	no	—
690	C₈	—	38	4	no	—
691	C₈	—	76	2	no	—
692	C₈	—	76	2	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	76	4	no	—
701	C₂²	—	76	2	no	—
702	C₂²	—	152	2	no	—
703	C₂²	—	152	2	no	—
704	C₂²	#11926420	1	1	yes	characteristic
705	C₂²	#11926421	1	1	yes	characteristic
706	C₂²	#11926444	1	1	yes	characteristic
707	C₂²	#11926452	1	1	yes	characteristic
708	C₂²	#11926459	1	1	yes	characteristic
709	C₂²	#11926460	1	1	yes	characteristic
710	C₂²	#11926460	1	1	yes	characteristic
711	C₄	—	4	4	no	—
712	C₄	—	8	2	no	—
713	C₄	—	76	2	no	—
714	C₄	#11926399	1	1	yes	characteristic
715	C₄	#11926420	1	1	yes	characteristic
716	C₄	#11926423	1	1	yes	characteristic
717	C₄	#11926444	1	1	yes	characteristic
718	C₄	#11926452	1	1	yes	characteristic
719	C₄	#11926453	1	1	yes	characteristic
720	C₄	#11926453	1	1	yes	characteristic
721	C₄	#11926459	1	1	yes	characteristic
722	C₂	—	2	1	no	—
723	C₂	—	2	1	no	—
724	C₂	—	2	1	no	—
725	C₂	—	2	1	no	—
726	C₂	—	2	1	no	—
727	C₂	—	2	1	no	—
728	C₂	—	152	2	no	—
729	C₂	#14561874	1	1	yes	characteristic
730	C₂	#14564105	1	2	yes	—

	subgroup	G/H
center	C₂²	#11926420
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#419	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂²×#64541	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#419	D₁₉
hypocenter	C₁₉	#11015
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#419

Complements

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

N	H ≅ G/N	type
3. C₂²×#10597293	C₂	semidirect
5. C₂×#11926314	C₂	semidirect
6. C₂×C₁₉⋊#338	C₂	semidirect
7. C₂×C₁₉×#419	C₂	semidirect
15. C₂²×#64528	C₄	semidirect
16. C₂²×#64527	C₄	semidirect
330. C₂×#419	D₁₉	semidirect
483. C₁₉	#11015	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10597388	2
C₂×#11926562	2
C₂²×#10597293	2
#14572079	2
C₂×#11926314	2
C₂×C₁₉⋊#338	2
C₂×C₁₉×#419	2
#11015	19