Subgroups — #18090374

Order 4864.

866 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926546	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926546	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926510	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926312	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926312	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11926307	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#341	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64541	C₂²	1	1	yes	characteristic
9	C₂²×#64520	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
12	#11926546	—	2	2	no	—
13	#11926546	—	2	2	no	—
14	#11926546	—	2	2	no	—
15	#11926546	C₄	1	4	yes	complemented
16	C₂×#10597273	—	2	1	no	—
17	C₂×#10597273	—	2	1	no	—
18	C₂×#10597278	—	2	1	no	—
19	C₂×#10597278	—	2	1	no	—
20	#11926510	—	2	2	no	—
21	#11926510	—	2	2	no	—
22	C₂×(C₂×D₁₉)⋊C₈	—	2	2	no	—
23	#11926312	—	2	2	no	—
24	#11926312	—	2	2	no	—
25	#11926307	—	2	2	no	—
26	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
28	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#341	—	2	2	no	—
30	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂²×C₂²⋊D₁₉	—	2	1	no	—
32	C₂³×Dic₁₉	—	2	1	no	—
33	C₂³×Dic₁₉	—	2	1	no	—
34	C₂×#64541	—	2	1	no	—
35	C₂×#64541	—	2	1	no	—
36	C₂×#64541	—	2	1	no	—
37	C₂×#64541	—	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	D₄	1	2	yes	—
46	C₂²×D₇₆	D₄	1	1	yes	characteristic
47	C₂²×C₄×D₁₉	—	2	1	no	—
48	C₂²×Dic₃₈	D₄	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	C₂×M₁₆×C₁₉	—	2	1	no	—
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂×M₁₆×C₁₉	—	2	1	no	—
59	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
60	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
61	C₂²×C₈×C₁₉	—	2	1	no	—
62	C₂²×C₈×C₁₉	—	2	1	no	—
63	C₂²×C₈×C₁₉	—	2	1	no	—
64	C₂²×C₈×C₁₉	—	2	1	no	—
65	C₂²×C₈×C₁₉	—	2	1	no	—
66	C₂²×C₈×C₁₉	—	2	1	no	—
67	C₂²×C₈×C₁₉	—	2	1	no	—
68	C₂²×C₈×C₁₉	—	2	1	no	—
69	C₂²×C₈×C₁₉	D₄	1	2	yes	—
70	C₂×C₄⋊Dic₁₉	—	2	1	no	—
71	C₂×C₄⋊Dic₁₉	—	2	1	no	—
72	C₂×C₄⋊Dic₁₉	—	2	1	no	—
73	C₂×C₄⋊Dic₁₉	—	2	1	no	—
74	C₂×C₄⋊Dic₁₉	—	2	1	no	—
75	C₂×C₄⋊Dic₁₉	—	2	1	no	—
76	C₂×C₄⋊Dic₁₉	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
81	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
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	D₄	1	2	yes	—
88	C₂²×C₁₉⋊C₈	—	2	1	no	—
89	#10597278	—	2	4	no	—
90	#10597278	—	2	4	no	—
91	(C₂×D₁₉)⋊C₈	—	2	8	no	—
92	#10597273	—	2	4	no	—
93	#10597273	—	2	4	no	—
94	C₂⁴×C₁₉	#41	1	1	yes	characteristic
95	C₂³×D₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
110	C₂×C₂²⋊D₁₉	—	2	2	no	—
111	C₂×C₂²⋊D₁₉	—	2	2	no	—
112	C₂×C₂²⋊D₁₉	—	4	1	no	—
113	C₂×C₂²⋊D₁₉	—	4	1	no	—
114	C₂×C₂²⋊D₁₉	—	4	1	no	—
115	C₂×C₂²⋊D₁₉	—	4	1	no	—
116	C₂²×Dic₁₉	—	2	1	no	—
117	C₂²×Dic₁₉	—	2	2	no	—
118	C₂²×Dic₁₉	—	2	2	no	—
119	C₂²×Dic₁₉	—	4	1	no	—
120	C₂²×Dic₁₉	—	4	1	no	—
121	C₂²×Dic₁₉	—	4	1	no	—
122	C₂²×Dic₁₉	—	4	1	no	—
123	C₂²×Dic₁₉	—	8	1	no	—
124	C₂²×Dic₁₉	—	8	1	no	—
125	C₂²×Dic₁₉	—	8	1	no	—
126	C₂²×Dic₁₉	—	8	1	no	—
127	#64541	—	2	2	no	—
128	#64541	—	2	2	no	—
129	#64541	—	2	2	no	—
130	#64541	—	2	2	no	—
131	#64541	—	2	2	no	—
132	#64541	—	2	2	no	—
133	#64541	—	2	2	no	—
134	#64541	—	2	2	no	—
135	#64541	—	4	1	no	—
136	#64541	—	4	1	no	—
137	#64541	—	4	1	no	—
138	#64541	—	4	1	no	—
139	#64541	—	4	1	no	—
140	#64541	—	4	1	no	—
141	#64541	—	4	1	no	—
142	#64541	—	4	1	no	—
143	C₂×D₇₆	—	2	1	no	—
144	C₂×D₇₆	—	2	1	no	—
145	C₂×D₇₆	—	2	1	no	—
146	C₂×D₇₆	—	2	1	no	—
147	C₂×D₇₆	—	2	1	no	—
148	C₂×D₇₆	C₂²⋊C₄	1	2	yes	—
149	C₂×C₄×D₁₉	—	2	2	no	—
150	C₂×C₄×D₁₉	—	2	2	no	—
151	C₂×C₄×D₁₉	—	4	1	no	—
152	C₂×C₄×D₁₉	—	4	1	no	—
153	C₂×C₄×D₁₉	—	4	1	no	—
154	C₂×C₄×D₁₉	—	4	1	no	—
155	C₂×Dic₃₈	—	2	1	no	—
156	C₂×Dic₃₈	—	2	1	no	—
157	C₂×Dic₃₈	—	2	1	no	—
158	C₂×Dic₃₈	—	2	1	no	—
159	C₂×Dic₃₈	—	2	1	no	—
160	C₂×Dic₃₈	C₂²⋊C₄	1	2	yes	—
161	M₁₆×C₁₉	—	2	2	no	—
162	M₁₆×C₁₉	—	2	2	no	—
163	M₁₆×C₁₉	—	2	2	no	—
164	M₁₆×C₁₉	—	2	2	no	—
165	M₁₆×C₁₉	—	4	1	no	—
166	M₁₆×C₁₉	—	4	1	no	—
167	M₁₆×C₁₉	—	4	1	no	—
168	M₁₆×C₁₉	—	4	1	no	—
169	C₂×C₈×C₁₉	—	2	2	no	—
170	C₂×C₈×C₁₉	—	2	2	no	—
171	C₂×C₈×C₁₉	—	2	2	no	—
172	C₂×C₈×C₁₉	—	2	2	no	—
173	C₂×C₈×C₁₉	—	2	2	no	—
174	C₂×C₈×C₁₉	—	4	1	no	—
175	C₂×C₈×C₁₉	—	4	1	no	—
176	C₂×C₈×C₁₉	—	4	1	no	—
177	C₂×C₈×C₁₉	—	4	1	no	—
178	C₂×C₈×C₁₉	—	4	1	no	—
179	C₂×C₈×C₁₉	—	4	1	no	—
180	C₂×C₈×C₁₉	—	4	1	no	—
181	C₂×C₈×C₁₉	—	4	1	no	—
182	C₄⋊Dic₁₉	—	2	2	no	—
183	C₄⋊Dic₁₉	—	2	2	no	—
184	C₄⋊Dic₁₉	—	2	2	no	—
185	C₄⋊Dic₁₉	—	2	2	no	—
186	C₄⋊Dic₁₉	—	4	1	no	—
187	C₄⋊Dic₁₉	—	4	1	no	—
188	C₄⋊Dic₁₉	—	4	1	no	—
189	C₄⋊Dic₁₉	—	4	1	no	—
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	#11192	—	19	1	no	maximal, Sylow
198	C₂³×C₁₉	—	2	1	no	—
199	C₂³×C₁₉	—	2	1	no	—
200	C₂³×C₁₉	—	2	1	no	—
201	C₂³×C₁₉	—	2	1	no	—
202	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
203	C₂³×C₁₉	#121	1	1	yes	characteristic
204	C₂³×C₁₉	#123	1	1	yes	characteristic
205	C₂³×C₁₉	#123	1	1	yes	characteristic
206	C₂³×C₁₉	#124	1	1	yes	characteristic
207	C₂³×C₁₉	#126	1	1	yes	characteristic
208	C₂³×C₁₉	#126	1	1	yes	characteristic
209	C₂²×D₁₉	—	2	2	no	—
210	C₂²×D₁₉	—	4	1	no	—
211	C₂²×D₁₉	—	4	1	no	—
212	C₂²×D₁₉	—	4	1	no	—
213	C₂²×D₁₉	—	4	1	no	—
214	C₂²×D₁₉	—	4	1	no	—
215	C₂²×D₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
218	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
219	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
223	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
224	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
225	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
226	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
227	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
228	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
229	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
230	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
231	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
232	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
233	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
234	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
235	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
236	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
237	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
238	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
239	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
240	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
241	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
242	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
243	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
244	C₂²⋊D₁₉	—	4	2	no	—
245	C₂²⋊D₁₉	—	4	2	no	—
246	C₂²⋊D₁₉	—	4	2	no	—
247	C₂²⋊D₁₉	—	4	2	no	—
248	C₂×Dic₁₉	—	2	2	no	—
249	C₂×Dic₁₉	—	4	1	no	—
250	C₂×Dic₁₉	—	4	1	no	—
251	C₂×Dic₁₉	—	4	2	no	—
252	C₂×Dic₁₉	—	4	2	no	—
253	C₂×Dic₁₉	—	8	2	no	—
254	C₂×Dic₁₉	—	8	2	no	—
255	C₂×Dic₁₉	—	8	1	no	—
256	C₂×Dic₁₉	—	8	1	no	—
257	C₂×Dic₁₉	—	8	1	no	—
258	C₂×Dic₁₉	—	8	1	no	—
259	C₂×Dic₁₉	—	8	2	no	—
260	C₂×Dic₁₉	—	8	2	no	—
261	D₇₆	—	2	2	no	—
262	D₇₆	—	2	2	no	—
263	D₇₆	—	4	1	no	—
264	D₇₆	—	4	1	no	—
265	C₄×D₁₉	—	4	2	no	—
266	C₄×D₁₉	—	4	2	no	—
267	C₄×D₁₉	—	4	2	no	—
268	C₄×D₁₉	—	4	2	no	—
269	Dic₃₈	—	2	2	no	—
270	Dic₃₈	—	2	2	no	—
271	Dic₃₈	—	4	1	no	—
272	Dic₃₈	—	4	1	no	—
273	C₈×C₁₉	—	4	2	no	—
274	C₈×C₁₉	—	4	2	no	—
275	C₈×C₁₉	—	4	2	no	—
276	C₁₉⋊C₈	—	4	2	no	—
277	C₂×#417	—	19	1	no	—
278	C₂×#417	—	19	1	no	—
279	C₂×#408	—	19	1	no	—
280	C₂×#343	—	19	1	no	—
281	C₂×#343	—	19	1	no	—
282	C₂×#341	D₁₉	1	1	yes	characteristic, complemented
283	C₂×#340	—	19	1	no	—
284	C₂²×C₁₉	—	2	1	no	—
285	C₂²×C₁₉	—	2	1	no	—
286	C₂²×C₁₉	—	2	1	no	—
287	C₂²×C₁₉	—	2	1	no	—
288	C₂²×C₁₉	—	2	1	no	—
289	C₂²×C₁₉	—	2	1	no	—
290	C₂²×C₁₉	—	2	1	no	—
291	C₂²×C₁₉	—	2	1	no	—
292	C₂²×C₁₉	—	2	1	no	—
293	C₂²×C₁₉	—	2	1	no	—
294	C₂²×C₁₉	—	2	1	no	—
295	C₂²×C₁₉	—	2	1	no	—
296	C₂²×C₁₉	#386	1	1	yes	characteristic
297	C₂²×C₁₉	#388	1	1	yes	characteristic
298	C₂²×C₁₉	#388	1	1	yes	characteristic
299	C₂²×C₁₉	#394	1	1	yes	characteristic
300	C₂²×C₁₉	#397	1	1	yes	characteristic
301	C₂²×C₁₉	#397	1	1	yes	characteristic
302	C₂²×C₁₉	#397	1	1	yes	characteristic
303	C₂²×C₁₉	#471	1	1	yes	characteristic
304	C₂²×C₁₉	#471	1	1	yes	characteristic
305	C₂²×C₁₉	#472	1	1	yes	characteristic
306	C₂²×C₁₉	#473	1	1	yes	characteristic
307	C₂×D₁₉	—	4	2	no	—
308	C₂×D₁₉	—	4	2	no	—
309	C₂×D₁₉	—	4	2	no	—
310	C₂×D₁₉	—	8	1	no	—
311	C₂×D₁₉	—	8	1	no	—
312	C₂×D₁₉	—	8	1	no	—
313	C₂×D₁₉	—	8	1	no	—
314	C₄×C₁₉	#381	1	1	yes	characteristic
315	C₄×C₁₉	#386	1	1	yes	characteristic
316	C₄×C₁₉	#388	1	1	yes	characteristic
317	C₄×C₁₉	#388	1	1	yes	characteristic
318	C₄×C₁₉	#394	1	1	yes	characteristic
319	C₄×C₁₉	#394	1	1	yes	characteristic
320	C₄×C₁₉	#394	1	1	yes	characteristic
321	C₄×C₁₉	#397	1	1	yes	characteristic
322	Dic₁₉	—	4	2	no	—
323	Dic₁₉	—	8	2	no	—
324	Dic₁₉	—	8	2	no	—
325	C₂²×#41	—	19	1	no	—
326	C₂²×M₁₆	—	19	1	no	—
327	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
328	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
329	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
330	C₂²×C₄⋊C₄	—	19	1	no	—
331	C₂²×C₄⋊C₄	—	19	1	no	—
332	#417	—	19	4	no	—
333	#417	—	38	2	no	—
334	#417	—	38	2	no	—
335	#417	—	38	2	no	—
336	C₂×#103	—	38	1	no	—
337	C₂×#103	—	38	1	no	—
338	C₂×#102	—	38	1	no	—
339	C₂×#102	—	38	1	no	—
340	#408	—	38	2	no	—
341	#408	—	38	2	no	—
342	C₂×C₂²⋊C₈	—	38	2	no	—
343	#343	—	38	2	no	—
344	#343	—	38	2	no	—
345	#341	—	2	2	no	—
346	#340	—	38	2	no	—
347	C₂×C₁₉	—	2	1	no	—
348	C₂×C₁₉	—	2	1	no	—
349	C₂×C₁₉	—	2	1	no	—
350	C₂×C₁₉	—	2	1	no	—
351	C₂×C₁₉	#1440	1	1	yes	characteristic
352	C₂×C₁₉	#1907	1	1	yes	characteristic
353	C₂×C₁₉	#1908	1	1	yes	characteristic
354	C₂×C₁₉	#2051	1	1	yes	characteristic
355	C₂×C₁₉	#2052	1	1	yes	characteristic
356	C₂×C₁₉	#2078	1	1	yes	characteristic
357	C₂×C₁₉	#2079	1	1	yes	characteristic
358	D₁₉	—	8	2	no	—
359	C₂×#41	—	19	2	no	—
360	C₂×#41	—	19	2	no	—
361	C₂×#41	—	38	1	no	—
362	C₂×#41	—	38	1	no	—
363	C₂×#41	—	38	1	no	—
364	C₂×#41	—	38	1	no	—
365	C₂×#41	—	38	1	no	—
366	C₂×#41	—	38	1	no	—
367	C₂×#41	—	38	1	no	—
368	C₂×#41	—	38	1	no	—
369	C₂×#41	—	38	1	no	—
370	C₂×#41	—	38	1	no	—
371	C₂²×Q₈	—	19	1	no	—
372	C₂²×D₄	—	19	1	no	—
373	C₂²×D₄	—	38	1	no	—
374	C₂³×C₄	—	38	1	no	—
375	C₂³×C₄	—	38	1	no	—
376	C₂³×C₄	—	38	1	no	—
377	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
378	C₂×M₁₆	—	2	1	no	—
379	C₂×M₁₆	—	2	1	no	—
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	—	2	1	no	—
384	C₂×M₁₆	—	2	1	no	—
385	C₂×M₁₆	—	2	1	no	—
386	C₂×M₁₆	—	2	1	no	—
387	C₂×M₁₆	—	2	1	no	—
388	C₂×M₁₆	—	19	2	no	—
389	C₂×M₁₆	—	38	1	no	—
390	C₂×M₁₆	—	38	1	no	—
391	C₂×M₁₆	—	38	1	no	—
392	C₂×M₁₆	—	38	1	no	—
393	C₂×M₁₆	—	38	1	no	—
394	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
395	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
396	C₂²×C₈	—	2	1	no	—
397	C₂²×C₈	—	2	1	no	—
398	C₂²×C₈	—	2	1	no	—
399	C₂²×C₈	—	2	1	no	—
400	C₂²×C₈	—	2	1	no	—
401	C₂²×C₈	—	2	1	no	—
402	C₂²×C₈	—	2	1	no	—
403	C₂²×C₈	—	2	1	no	—
404	C₂²×C₈	—	38	1	no	—
405	C₂²×C₈	D₇₆	1	2	yes	—
406	C₂×C₄⋊C₄	—	19	2	no	—
407	C₂×C₄⋊C₄	—	19	2	no	—
408	C₂×C₄⋊C₄	—	38	1	no	—
409	C₂×C₄⋊C₄	—	38	1	no	—
410	C₂×C₄⋊C₄	—	38	1	no	—
411	C₂×C₄⋊C₄	—	38	1	no	—
412	C₂×C₄⋊C₄	—	38	1	no	—
413	C₂×C₄⋊C₄	—	38	1	no	—
414	C₂×C₄⋊C₄	—	38	1	no	—
415	C₂×C₄⋊C₄	—	38	1	no	—
416	C₂×C₄⋊C₄	—	38	1	no	—
417	C₂×C₄⋊C₄	—	38	1	no	—
418	#103	—	38	4	no	—
419	#103	—	38	4	no	—
420	#102	—	38	4	no	—
421	#102	—	38	4	no	—
422	C₂²⋊C₈	—	38	8	no	—
423	C₁₉	#11192	1	1	yes	characteristic, complemented, Sylow
424	C₂⁴	—	38	1	no	—
425	C₂⁴	#64545	1	1	yes	characteristic
426	#41	—	38	2	no	—
427	#41	—	38	2	no	—
428	#41	—	38	2	no	—
429	#41	—	38	2	no	—
430	#41	—	38	2	no	—
431	#41	—	38	2	no	—
432	#41	—	38	2	no	—
433	#41	—	38	2	no	—
434	#41	—	76	1	no	—
435	#41	—	76	1	no	—
436	#41	—	76	1	no	—
437	#41	—	76	1	no	—
438	#41	—	76	1	no	—
439	#41	—	76	1	no	—
440	#41	—	76	1	no	—
441	#41	—	76	1	no	—
442	C₂×Q₈	—	19	2	no	—
443	C₂×Q₈	—	38	1	no	—
444	C₂×Q₈	—	38	1	no	—
445	C₂×Q₈	—	38	1	no	—
446	C₂×Q₈	—	38	1	no	—
447	C₂×Q₈	—	38	1	no	—
448	C₂×D₄	—	19	2	no	—
449	C₂×D₄	—	38	2	no	—
450	C₂×D₄	—	38	2	no	—
451	C₂×D₄	—	38	1	no	—
452	C₂×D₄	—	38	1	no	—
453	C₂×D₄	—	38	1	no	—
454	C₂×D₄	—	38	1	no	—
455	C₂×D₄	—	38	1	no	—
456	C₂×D₄	—	76	1	no	—
457	C₂×D₄	—	76	1	no	—
458	C₂×D₄	—	76	1	no	—
459	C₂×D₄	—	76	1	no	—
460	C₂²×C₄	—	38	1	no	—
461	C₂²×C₄	—	38	2	no	—
462	C₂²×C₄	—	38	2	no	—
463	C₂²×C₄	—	38	2	no	—
464	C₂²×C₄	—	38	2	no	—
465	C₂²×C₄	—	76	1	no	—
466	C₂²×C₄	—	76	1	no	—
467	C₂²×C₄	—	76	1	no	—
468	C₂²×C₄	—	76	1	no	—
469	C₂²×C₄	—	76	1	no	—
470	C₂²×C₄	—	76	1	no	—
471	C₂²×C₄	—	76	1	no	—
472	C₂²×C₄	—	76	1	no	—
473	C₂²×C₄	—	152	1	no	—
474	C₂²×C₄	—	152	1	no	—
475	C₂²×C₄	—	152	1	no	—
476	C₂²×C₄	—	152	1	no	—
477	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
479	C₂²×C₄	#64541	1	1	yes	characteristic
480	C₂²×C₄	#64541	1	1	yes	characteristic
481	C₂²×C₄	#64541	1	1	yes	characteristic
482	C₂²×C₄	#64541	1	1	yes	characteristic
483	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
484	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
485	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
486	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
487	C₂²×C₄	#64543	1	1	yes	characteristic
488	C₂²×C₄	#64543	1	1	yes	characteristic
489	C₂²×C₄	#64545	1	1	yes	characteristic
490	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
491	M₁₆	—	2	2	no	—
492	M₁₆	—	2	2	no	—
493	M₁₆	—	2	2	no	—
494	M₁₆	—	2	2	no	—
495	M₁₆	—	4	1	no	—
496	M₁₆	—	4	1	no	—
497	M₁₆	—	4	1	no	—
498	M₁₆	—	4	1	no	—
499	M₁₆	—	38	2	no	—
500	M₁₆	—	38	2	no	—
501	M₁₆	—	76	1	no	—
502	M₁₆	—	76	1	no	—
503	C₂×C₈	—	2	2	no	—
504	C₂×C₈	—	2	2	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	2	2	no	—
507	C₂×C₈	—	2	2	no	—
508	C₂×C₈	—	4	1	no	—
509	C₂×C₈	—	4	1	no	—
510	C₂×C₈	—	4	1	no	—
511	C₂×C₈	—	4	1	no	—
512	C₂×C₈	—	4	1	no	—
513	C₂×C₈	—	4	1	no	—
514	C₂×C₈	—	4	1	no	—
515	C₂×C₈	—	4	1	no	—
516	C₂×C₈	—	38	2	no	—
517	C₂×C₈	—	76	1	no	—
518	C₂×C₈	—	76	1	no	—
519	C₄⋊C₄	—	38	2	no	—
520	C₄⋊C₄	—	38	2	no	—
521	C₄⋊C₄	—	38	2	no	—
522	C₄⋊C₄	—	38	2	no	—
523	C₄⋊C₄	—	76	1	no	—
524	C₄⋊C₄	—	76	1	no	—
525	C₄⋊C₄	—	76	1	no	—
526	C₄⋊C₄	—	76	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	38	2	no	—
532	C₂³	—	76	1	no	—
533	C₂³	—	76	1	no	—
534	C₂³	—	76	1	no	—
535	C₂³	—	76	1	no	—
536	C₂³	—	76	1	no	—
537	C₂³	—	76	1	no	—
538	C₂³	#10597339	1	1	yes	characteristic
539	C₂³	#10597340	1	1	yes	characteristic
540	C₂³	#10597340	1	1	yes	characteristic
541	C₂³	#10597341	1	1	yes	characteristic
542	C₂³	#10597344	1	1	yes	characteristic
543	C₂³	#10597344	1	1	yes	characteristic
544	C₂³	#10597393	1	1	yes	characteristic
545	Q₈	—	38	2	no	—
546	Q₈	—	38	2	no	—
547	Q₈	—	76	1	no	—
548	Q₈	—	76	1	no	—
549	D₄	—	38	2	no	—
550	D₄	—	38	2	no	—
551	D₄	—	76	2	no	—
552	D₄	—	76	2	no	—
553	D₄	—	76	2	no	—
554	D₄	—	76	2	no	—
555	D₄	—	76	1	no	—
556	D₄	—	76	1	no	—
557	C₂×C₄	—	38	2	no	—
558	C₂×C₄	—	76	1	no	—
559	C₂×C₄	—	76	1	no	—
560	C₂×C₄	—	76	2	no	—
561	C₂×C₄	—	76	2	no	—
562	C₂×C₄	—	76	2	no	—
563	C₂×C₄	—	76	2	no	—
564	C₂×C₄	—	76	2	no	—
565	C₂×C₄	—	76	2	no	—
566	C₂×C₄	—	152	2	no	—
567	C₂×C₄	—	152	2	no	—
568	C₂×C₄	—	152	1	no	—
569	C₂×C₄	—	152	1	no	—
570	C₂×C₄	—	152	1	no	—
571	C₂×C₄	—	152	1	no	—
572	C₂×C₄	—	152	2	no	—
573	C₂×C₄	—	152	2	no	—
574	C₂×C₄	#10597318	1	1	yes	characteristic
575	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
576	C₂×C₄	#10597321	1	1	yes	characteristic
577	C₂×C₄	#10597322	1	1	yes	characteristic
578	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
579	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
580	C₂×C₄	#10597328	1	1	yes	characteristic
581	C₂×C₄	#10597329	1	1	yes	characteristic
582	C₂×C₄	#10597329	1	1	yes	characteristic
583	C₂×C₄	#10597329	1	1	yes	characteristic
584	C₂×C₄	#10597330	1	1	yes	characteristic
585	C₂×C₄	#10597330	1	1	yes	characteristic
586	C₂×C₄	#10597330	1	1	yes	characteristic
587	C₂×C₄	#10597331	1	1	yes	characteristic
588	C₂×C₄	#10597331	1	1	yes	characteristic
589	C₂×C₄	#10597332	1	1	yes	characteristic
590	C₂×C₄	#10597338	1	1	yes	characteristic
591	C₂×C₄	#10597340	1	1	yes	characteristic
592	C₂×C₄	#10597340	1	1	yes	characteristic
593	C₂×C₄	#10597340	1	1	yes	characteristic
594	C₂×C₄	#10597341	1	1	yes	characteristic
595	C₂×C₄	#10597344	1	1	yes	characteristic
596	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
597	C₂×C₄	#10597375	1	1	yes	characteristic
598	C₂×C₄	#10597376	1	1	yes	characteristic
599	C₂×C₄	#10597383	1	1	yes	characteristic
600	C₂×C₄	#10597384	1	1	yes	characteristic
601	C₂×C₄	#10597385	1	1	yes	characteristic
602	C₈	—	4	2	no	—
603	C₈	—	4	2	no	—
604	C₈	—	4	2	no	—
605	C₈	—	76	2	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	1	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	76	2	no	—
619	C₂²	—	76	2	no	—
620	C₂²	—	76	2	no	—
621	C₂²	—	152	1	no	—
622	C₂²	—	152	1	no	—
623	C₂²	—	152	1	no	—
624	C₂²	—	152	1	no	—
625	C₂²	#11926422	1	1	yes	characteristic
626	C₂²	#11926433	1	1	yes	characteristic
627	C₂²	#11926434	1	1	yes	characteristic
628	C₂²	#11926461	1	1	yes	characteristic
629	C₂²	#11926470	1	1	yes	characteristic
630	C₂²	#11926471	1	1	yes	characteristic
631	C₂²	#11926473	1	1	yes	characteristic
632	C₂²	#11926808	1	1	yes	characteristic
633	C₂²	#11926808	1	1	yes	characteristic
634	C₂²	#11926815	1	1	yes	characteristic
635	C₂²	#11926820	1	1	yes	characteristic
636	C₄	—	76	2	no	—
637	C₄	—	152	2	no	—
638	C₄	—	152	2	no	—
639	C₄	#11926406	1	1	yes	characteristic
640	C₄	#11926420	1	1	yes	characteristic
641	C₄	#11926435	1	1	yes	characteristic
642	C₄	#11926436	1	1	yes	characteristic
643	C₄	#11926459	1	1	yes	characteristic
644	C₄	#11926460	1	1	yes	characteristic
645	C₄	#11926462	1	1	yes	characteristic
646	C₄	#11926473	1	1	yes	characteristic
647	C₂	—	2	1	no	—
648	C₂	—	2	1	no	—
649	C₂	—	2	1	no	—
650	C₂	—	2	1	no	—
651	C₂	—	152	2	no	—
652	C₂	#14561883	1	1	yes	characteristic
653	C₂	#14564142	1	1	yes	characteristic
654	C₂	#14564149	1	1	yes	characteristic
655	C₂	#14564929	1	1	yes	characteristic
656	C₂	#14564936	1	1	yes	characteristic
657	C₂	#14565077	1	1	yes	characteristic
658	C₂	#14565082	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597341
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#341	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂²×#64541	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#341	D₁₉
hypocenter	C₁₉	#11192
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#341

Complements

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

N	H ≅ G/N	type
4. C₂×#11926312	C₂	semidirect
5. C₂×#11926312	C₂	semidirect
6. C₂×#11926307	C₂	semidirect
7. C₂×C₁₉×#341	C₂	semidirect
15. #11926546	C₄	semidirect
282. C₂×#341	D₁₉	semidirect
423. C₁₉	#11192	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926546	2
C₂×#11926510	2
C₂×#11926312	2
C₂×#11926307	2
C₂×C₁₉×#341	2
#11192	19