Subgroups — #18090395

Order 4864.

962 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10597262	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926546	C₂	1	1	yes	maximal, characteristic
3	#14566223	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926312	C₂	1	1	yes	maximal, characteristic, complemented
5	#14563356	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561865	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#339	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	C₂×#10597262	—	2	2	no	—
13	C₂×#10597262	—	2	2	no	—
14	C₂×#10597262	—	2	2	no	—
15	#11926546	—	2	2	no	—
16	#11926546	C₄	1	4	yes	complemented
17	C₂×#10597273	—	2	1	no	—
18	C₂×#10597278	—	2	1	no	—
19	#11926450	—	2	1	no	—
20	#11926446	—	2	1	no	—
21	#11926421	—	2	2	no	—
22	#11926401	—	2	1	no	—
23	#11926401	—	2	1	no	—
24	C₂×C₁₉⋊#95	—	2	2	no	—
25	#11926312	—	2	2	no	—
26	#11926306	—	2	1	no	—
27	#11926306	—	2	1	no	—
28	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
31	C₁₉×#339	—	2	2	no	—
32	C₂³×C₄×C₁₉	—	2	1	no	—
33	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
34	C₂²×C₂²⋊D₁₉	—	2	1	no	—
35	C₂³×Dic₁₉	—	2	1	no	—
36	C₂³×Dic₁₉	D₄	1	2	yes	—
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	—	2	1	no	—
45	C₂×#64541	—	2	1	no	—
46	C₂×#64541	—	2	1	no	—
47	C₂×#64541	C₂×C₄	1	2	yes	—
48	C₂×#64541	D₄	1	2	yes	—
49	C₂²×D₇₆	D₄	1	1	yes	characteristic
50	C₂²×C₄×D₁₉	—	2	1	no	—
51	C₂²×Dic₃₈	D₄	1	1	yes	characteristic
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	C₂×C₄	1	2	yes	—
58	C₂²×C₈×C₁₉	—	2	1	no	—
59	C₁₉×#117	—	2	1	no	—
60	C₁₉×#117	—	2	1	no	—
61	C₁₉×#117	—	2	1	no	—
62	C₁₉×#117	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₄²×C₁₉	—	2	1	no	—
67	C₂×C₄²×C₁₉	—	2	1	no	—
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	D₄	1	2	yes	—
73	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
74	C₂×(C₂×D₁₉)⋊C₄	—	2	2	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	—	2	1	no	—
81	C₂×C₄⋊Dic₁₉	—	2	1	no	—
82	C₂×C₄⋊Dic₁₉	—	2	1	no	—
83	C₂×C₄⋊Dic₁₉	—	2	1	no	—
84	C₂×C₄⋊Dic₁₉	—	2	1	no	—
85	C₂×C₄⋊Dic₁₉	—	2	1	no	—
86	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
87	C₂×#64520	—	2	1	no	—
88	C₂×#64520	—	2	1	no	—
89	C₂×#64520	—	2	1	no	—
90	C₂×#64520	—	2	1	no	—
91	C₂×#64520	—	2	1	no	—
92	C₂×#64520	D₄	1	2	yes	—
93	C₂²×C₁₉⋊C₈	—	2	1	no	—
94	C₁₉⋊#95	—	2	2	no	—
95	C₁₉⋊#95	—	2	2	no	—
96	C₁₉⋊#95	—	4	4	no	—
97	#10597278	—	2	4	no	—
98	#10597273	—	2	4	no	—
99	#10597262	—	2	8	no	—
100	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂³×D₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	—	2	1	no	—
107	C₂²×C₄×C₁₉	—	4	1	no	—
108	C₂²×C₄×C₁₉	—	4	1	no	—
109	C₂²×C₄×C₁₉	—	4	1	no	—
110	C₂²×C₄×C₁₉	—	4	1	no	—
111	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
125	C₂×C₂²⋊D₁₉	—	2	2	no	—
126	C₂×C₂²⋊D₁₉	—	2	2	no	—
127	C₂×C₂²⋊D₁₉	—	4	1	no	—
128	C₂×C₂²⋊D₁₉	—	4	1	no	—
129	C₂×C₂²⋊D₁₉	—	4	1	no	—
130	C₂×C₂²⋊D₁₉	—	4	1	no	—
131	C₂²×Dic₁₉	—	2	1	no	—
132	C₂²×Dic₁₉	—	2	2	no	—
133	C₂²×Dic₁₉	—	2	2	no	—
134	C₂²×Dic₁₉	—	2	2	no	—
135	C₂²×Dic₁₉	—	2	2	no	—
136	C₂²×Dic₁₉	—	4	2	no	—
137	C₂²×Dic₁₉	—	4	2	no	—
138	C₂²×Dic₁₉	—	4	2	no	—
139	C₂²×Dic₁₉	—	4	2	no	—
140	C₂²×Dic₁₉	—	4	1	no	—
141	C₂²×Dic₁₉	—	4	1	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	—	2	2	no	—
150	#64541	—	4	1	no	—
151	#64541	—	4	1	no	—
152	#64541	—	4	1	no	—
153	#64541	—	4	1	no	—
154	#64541	—	4	1	no	—
155	#64541	—	4	1	no	—
156	#64541	—	4	1	no	—
157	#64541	—	4	1	no	—
158	C₂×D₇₆	—	2	1	no	—
159	C₂×D₇₆	—	2	1	no	—
160	C₂×D₇₆	—	2	1	no	—
161	C₂×D₇₆	—	2	1	no	—
162	C₂×D₇₆	—	2	1	no	—
163	C₂×D₇₆	C₂²⋊C₄	1	2	yes	—
164	C₂×C₄×D₁₉	—	2	2	no	—
165	C₂×C₄×D₁₉	—	2	2	no	—
166	C₂×C₄×D₁₉	—	4	1	no	—
167	C₂×C₄×D₁₉	—	4	1	no	—
168	C₂×C₄×D₁₉	—	4	1	no	—
169	C₂×C₄×D₁₉	—	4	1	no	—
170	C₂×Dic₃₈	—	2	1	no	—
171	C₂×Dic₃₈	—	2	1	no	—
172	C₂×Dic₃₈	—	2	1	no	—
173	C₂×Dic₃₈	—	2	1	no	—
174	C₂×Dic₃₈	—	2	1	no	—
175	C₂×Dic₃₈	C₂²⋊C₄	1	2	yes	—
176	M₁₆×C₁₉	—	2	2	no	—
177	M₁₆×C₁₉	—	2	2	no	—
178	M₁₆×C₁₉	—	4	1	no	—
179	M₁₆×C₁₉	—	4	1	no	—
180	C₂×C₈×C₁₉	—	2	2	no	—
181	C₂×C₈×C₁₉	—	4	1	no	—
182	C₂×C₈×C₁₉	—	4	1	no	—
183	C₄⋊C₄×C₁₉	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₂²⋊C₄×C₁₉	—	4	1	no	—
188	C₂²⋊C₄×C₁₉	—	4	1	no	—
189	C₄²×C₁₉	—	2	2	no	—
190	C₄²×C₁₉	—	2	2	no	—
191	C₄²×C₁₉	—	4	1	no	—
192	C₄²×C₁₉	—	4	1	no	—
193	C₄²×C₁₉	—	4	1	no	—
194	C₄²×C₁₉	—	4	1	no	—
195	(C₂×D₁₉)⋊C₄	—	8	2	no	—
196	(C₂×D₁₉)⋊C₄	—	8	2	no	—
197	C₄⋊Dic₁₉	—	2	2	no	—
198	C₄⋊Dic₁₉	—	2	2	no	—
199	C₄⋊Dic₁₉	—	4	1	no	—
200	C₄⋊Dic₁₉	—	4	1	no	—
201	C₄⋊Dic₁₉	—	4	1	no	—
202	C₄⋊Dic₁₉	—	4	1	no	—
203	C₄⋊Dic₁₉	—	4	1	no	—
204	C₄⋊Dic₁₉	—	4	1	no	—
205	#64520	—	2	2	no	—
206	#64520	—	2	2	no	—
207	#64520	—	4	1	no	—
208	#64520	—	4	1	no	—
209	C₂×C₁₉⋊C₈	—	2	2	no	—
210	C₂×C₁₉⋊C₈	—	4	1	no	—
211	C₂×C₁₉⋊C₈	—	4	1	no	—
212	#11195	—	19	1	no	maximal, Sylow
213	C₂³×C₁₉	—	2	1	no	—
214	C₂³×C₁₉	—	2	1	no	—
215	C₂³×C₁₉	—	2	1	no	—
216	C₂³×C₁₉	—	2	1	no	—
217	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
218	C₂³×C₁₉	#120	1	1	yes	characteristic
219	C₂³×C₁₉	#121	1	1	yes	characteristic
220	C₂³×C₁₉	#121	1	1	yes	characteristic
221	C₂³×C₁₉	#121	1	1	yes	characteristic
222	C₂³×C₁₉	#123	1	1	yes	characteristic
223	C₂³×C₁₉	#124	1	1	yes	characteristic
224	C₂²×D₁₉	—	2	2	no	—
225	C₂²×D₁₉	—	4	1	no	—
226	C₂²×D₁₉	—	4	1	no	—
227	C₂²×D₁₉	—	4	1	no	—
228	C₂²×D₁₉	—	4	1	no	—
229	C₂²×D₁₉	—	4	1	no	—
230	C₂²×D₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	2	4	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	4	2	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
246	C₂×C₄×C₁₉	#117	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	#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	#121	1	1	yes	characteristic
256	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
257	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
258	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
259	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
260	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
261	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
262	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
263	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
264	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
265	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
266	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
267	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
268	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
269	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
270	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
271	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
272	C₂²⋊D₁₉	—	4	2	no	—
273	C₂²⋊D₁₉	—	4	2	no	—
274	C₂²⋊D₁₉	—	4	2	no	—
275	C₂²⋊D₁₉	—	4	2	no	—
276	C₂×Dic₁₉	—	2	2	no	—
277	C₂×Dic₁₉	—	4	1	no	—
278	C₂×Dic₁₉	—	4	1	no	—
279	C₂×Dic₁₉	—	4	4	no	—
280	C₂×Dic₁₉	—	4	4	no	—
281	C₂×Dic₁₉	—	4	2	no	—
282	C₂×Dic₁₉	—	4	2	no	—
283	C₂×Dic₁₉	—	4	2	no	—
284	C₂×Dic₁₉	—	4	2	no	—
285	C₂×Dic₁₉	—	8	2	no	—
286	C₂×Dic₁₉	—	8	1	no	—
287	C₂×Dic₁₉	—	8	1	no	—
288	C₂×Dic₁₉	—	8	2	no	—
289	D₇₆	—	2	2	no	—
290	D₇₆	—	2	2	no	—
291	D₇₆	—	4	1	no	—
292	D₇₆	—	4	1	no	—
293	C₄×D₁₉	—	4	2	no	—
294	C₄×D₁₉	—	4	2	no	—
295	C₄×D₁₉	—	4	2	no	—
296	C₄×D₁₉	—	4	2	no	—
297	Dic₃₈	—	2	2	no	—
298	Dic₃₈	—	2	2	no	—
299	Dic₃₈	—	4	1	no	—
300	Dic₃₈	—	4	1	no	—
301	C₈×C₁₉	—	4	2	no	—
302	C₁₉⋊C₈	—	4	2	no	—
303	C₂²×#104	—	19	1	no	—
304	C₂×#417	—	19	1	no	—
305	#2311	—	19	1	no	—
306	C₂×#343	—	19	1	no	—
307	#1736	—	19	1	no	—
308	C₂×#339	D₁₉	1	1	yes	characteristic, complemented
309	C₄⋊#95	—	19	1	no	—
310	C₂²×C₁₉	—	2	1	no	—
311	C₂²×C₁₉	—	2	1	no	—
312	C₂²×C₁₉	—	2	1	no	—
313	C₂²×C₁₉	—	2	1	no	—
314	C₂²×C₁₉	—	2	1	no	—
315	C₂²×C₁₉	—	2	1	no	—
316	C₂²×C₁₉	—	2	1	no	—
317	C₂²×C₁₉	—	2	1	no	—
318	C₂²×C₁₉	—	2	1	no	—
319	C₂²×C₁₉	—	2	1	no	—
320	C₂²×C₁₉	—	2	1	no	—
321	C₂²×C₁₉	—	2	1	no	—
322	C₂²×C₁₉	#386	1	1	yes	characteristic
323	C₂²×C₁₉	#388	1	1	yes	characteristic
324	C₂²×C₁₉	#388	1	1	yes	characteristic
325	C₂²×C₁₉	#394	1	1	yes	characteristic
326	C₂²×C₁₉	#394	1	1	yes	characteristic
327	C₂²×C₁₉	#394	1	1	yes	characteristic
328	C₂²×C₁₉	#397	1	1	yes	characteristic
329	C₂²×C₁₉	#453	1	1	yes	characteristic
330	C₂²×C₁₉	#454	1	1	yes	characteristic
331	C₂²×C₁₉	#455	1	1	yes	characteristic
332	C₂²×C₁₉	#456	1	1	yes	characteristic
333	C₂×D₁₉	—	4	2	no	—
334	C₂×D₁₉	—	4	2	no	—
335	C₂×D₁₉	—	4	2	no	—
336	C₂×D₁₉	—	8	1	no	—
337	C₂×D₁₉	—	8	1	no	—
338	C₂×D₁₉	—	8	1	no	—
339	C₂×D₁₉	—	8	1	no	—
340	C₄×C₁₉	—	4	4	no	—
341	C₄×C₁₉	—	8	1	no	—
342	C₄×C₁₉	—	8	1	no	—
343	C₄×C₁₉	#381	1	1	yes	characteristic
344	C₄×C₁₉	#386	1	1	yes	characteristic
345	C₄×C₁₉	#388	1	1	yes	characteristic
346	C₄×C₁₉	#388	1	1	yes	characteristic
347	C₄×C₁₉	#394	1	1	yes	characteristic
348	C₄×C₁₉	#397	1	1	yes	characteristic
349	C₄×C₁₉	#397	1	1	yes	characteristic
350	C₄×C₁₉	#397	1	1	yes	characteristic
351	Dic₁₉	—	4	2	no	—
352	Dic₁₉	—	8	2	no	—
353	Dic₁₉	—	8	2	no	—
354	C₂²×#41	—	19	1	no	—
355	C₂²×M₁₆	—	19	1	no	—
356	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
357	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
358	C₂²×C₄⋊C₄	—	19	1	no	—
359	C₂²×C₄⋊C₄	—	19	1	no	—
360	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
361	C₂×#104	—	38	2	no	—
362	C₂×#104	—	38	2	no	—
363	C₂×#104	—	38	2	no	—
364	#417	—	19	4	no	—
365	#417	—	38	2	no	—
366	C₂×#103	—	38	1	no	—
367	C₂×#102	—	38	1	no	—
368	#391	—	38	1	no	—
369	#390	—	38	1	no	—
370	#386	—	38	2	no	—
371	#380	—	38	1	no	—
372	#380	—	38	1	no	—
373	C₂×#95	—	38	2	no	—
374	#343	—	38	2	no	—
375	#340	—	38	1	no	—
376	#340	—	38	1	no	—
377	#339	—	2	2	no	—
378	C₂×C₁₉	—	2	1	no	—
379	C₂×C₁₉	—	2	1	no	—
380	C₂×C₁₉	—	2	1	no	—
381	C₂×C₁₉	—	2	1	no	—
382	C₂×C₁₉	#1440	1	1	yes	characteristic
383	C₂×C₁₉	#1882	1	1	yes	characteristic
384	C₂×C₁₉	#1883	1	1	yes	characteristic
385	C₂×C₁₉	#2037	1	1	yes	characteristic
386	C₂×C₁₉	#2038	1	1	yes	characteristic
387	C₂×C₁₉	#2039	1	1	yes	characteristic
388	C₂×C₁₉	#2040	1	1	yes	characteristic
389	D₁₉	—	8	2	no	—
390	C₂×#41	—	19	2	no	—
391	C₂×#41	—	19	2	no	—
392	C₂×#41	—	38	1	no	—
393	C₂×#41	—	38	1	no	—
394	C₂×#41	—	38	1	no	—
395	C₂×#41	—	38	1	no	—
396	C₂×#41	—	38	1	no	—
397	C₂×#41	—	38	1	no	—
398	C₂×#41	—	38	1	no	—
399	C₂×#41	—	38	1	no	—
400	C₂×#41	—	38	1	no	—
401	C₂×#41	—	38	1	no	—
402	C₂²×Q₈	—	19	1	no	—
403	C₂²×D₄	—	19	1	no	—
404	C₂²×D₄	—	38	1	no	—
405	C₂³×C₄	—	2	1	no	—
406	C₂³×C₄	—	19	2	no	—
407	C₂³×C₄	—	38	1	no	—
408	C₂³×C₄	—	38	1	no	—
409	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
410	C₂×M₁₆	—	2	1	no	—
411	C₂×M₁₆	—	2	1	no	—
412	C₂×M₁₆	—	2	1	no	—
413	C₂×M₁₆	—	2	1	no	—
414	C₂×M₁₆	—	2	1	no	—
415	C₂×M₁₆	—	19	2	no	—
416	C₂×M₁₆	—	38	1	no	—
417	C₂×M₁₆	—	38	1	no	—
418	C₂×M₁₆	—	38	1	no	—
419	C₂×M₁₆	—	38	1	no	—
420	C₂×M₁₆	—	38	1	no	—
421	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
422	C₂²×C₈	—	2	1	no	—
423	C₂²×C₈	—	38	1	no	—
424	#117	—	2	1	no	—
425	#117	—	2	1	no	—
426	#117	—	2	1	no	—
427	#117	—	2	1	no	—
428	C₂×C₄⋊C₄	—	19	2	no	—
429	C₂×C₄⋊C₄	—	38	1	no	—
430	C₂×C₄⋊C₄	—	38	1	no	—
431	C₂×C₄⋊C₄	—	38	1	no	—
432	C₂×C₄⋊C₄	—	38	1	no	—
433	C₂×C₄⋊C₄	—	38	1	no	—
434	C₂×C₄⋊C₄	—	38	1	no	—
435	C₂×C₄⋊C₄	—	38	1	no	—
436	C₂×C₄⋊C₄	—	38	1	no	—
437	C₂×C₄⋊C₄	—	38	1	no	—
438	C₂×C₄⋊C₄	—	38	1	no	—
439	C₂×C₄⋊C₄	—	38	1	no	—
440	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
441	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	38	2	no	—
444	C₂×C₂²⋊C₄	—	38	2	no	—
445	C₂×C₄²	—	2	1	no	—
446	C₂×C₄²	—	2	1	no	—
447	C₂×C₄²	—	2	1	no	—
448	C₂×C₄²	—	2	1	no	—
449	C₂×C₄²	—	2	1	no	—
450	C₂×C₄²	—	2	1	no	—
451	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
452	#104	—	38	8	no	—
453	#103	—	38	4	no	—
454	#102	—	38	4	no	—
455	#95	—	38	2	no	—
456	#95	—	38	2	no	—
457	#95	—	76	4	no	—
458	C₁₉	#11195	1	1	yes	characteristic, complemented, Sylow
459	C₂⁴	—	38	1	no	—
460	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
461	#41	—	38	2	no	—
462	#41	—	38	2	no	—
463	#41	—	38	2	no	—
464	#41	—	38	2	no	—
465	#41	—	38	2	no	—
466	#41	—	38	2	no	—
467	#41	—	38	2	no	—
468	#41	—	38	2	no	—
469	#41	—	76	1	no	—
470	#41	—	76	1	no	—
471	#41	—	76	1	no	—
472	#41	—	76	1	no	—
473	#41	—	76	1	no	—
474	#41	—	76	1	no	—
475	#41	—	76	1	no	—
476	#41	—	76	1	no	—
477	C₂×Q₈	—	19	2	no	—
478	C₂×Q₈	—	38	1	no	—
479	C₂×Q₈	—	38	1	no	—
480	C₂×Q₈	—	38	1	no	—
481	C₂×Q₈	—	38	1	no	—
482	C₂×Q₈	—	38	1	no	—
483	C₂×D₄	—	19	2	no	—
484	C₂×D₄	—	38	2	no	—
485	C₂×D₄	—	38	2	no	—
486	C₂×D₄	—	38	1	no	—
487	C₂×D₄	—	38	1	no	—
488	C₂×D₄	—	38	1	no	—
489	C₂×D₄	—	38	1	no	—
490	C₂×D₄	—	38	1	no	—
491	C₂×D₄	—	76	1	no	—
492	C₂×D₄	—	76	1	no	—
493	C₂×D₄	—	76	1	no	—
494	C₂×D₄	—	76	1	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	4	1	no	—
501	C₂²×C₄	—	4	1	no	—
502	C₂²×C₄	—	4	1	no	—
503	C₂²×C₄	—	4	1	no	—
504	C₂²×C₄	—	38	1	no	—
505	C₂²×C₄	—	38	2	no	—
506	C₂²×C₄	—	38	2	no	—
507	C₂²×C₄	—	38	2	no	—
508	C₂²×C₄	—	38	2	no	—
509	C₂²×C₄	—	38	2	no	—
510	C₂²×C₄	—	38	2	no	—
511	C₂²×C₄	—	76	1	no	—
512	C₂²×C₄	—	76	1	no	—
513	C₂²×C₄	—	76	1	no	—
514	C₂²×C₄	—	76	1	no	—
515	C₂²×C₄	—	76	2	no	—
516	C₂²×C₄	—	76	2	no	—
517	C₂²×C₄	—	76	2	no	—
518	C₂²×C₄	—	76	2	no	—
519	C₂²×C₄	—	76	1	no	—
520	C₂²×C₄	—	76	1	no	—
521	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
522	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
523	C₂²×C₄	#64541	1	1	yes	characteristic
524	C₂²×C₄	#64541	1	1	yes	characteristic
525	C₂²×C₄	#64541	1	1	yes	characteristic
526	C₂²×C₄	#64541	1	1	yes	characteristic
527	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
528	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
529	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
530	C₂²×C₄	#64543	1	1	yes	characteristic
531	C₂²×C₄	#64543	1	1	yes	characteristic
532	C₂²×C₄	#64545	1	1	yes	characteristic
533	C₂²×C₄	#64545	1	1	yes	characteristic
534	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
535	M₁₆	—	2	2	no	—
536	M₁₆	—	2	2	no	—
537	M₁₆	—	4	1	no	—
538	M₁₆	—	4	1	no	—
539	M₁₆	—	38	2	no	—
540	M₁₆	—	38	2	no	—
541	M₁₆	—	76	1	no	—
542	M₁₆	—	76	1	no	—
543	C₂×C₈	—	2	2	no	—
544	C₂×C₈	—	4	1	no	—
545	C₂×C₈	—	4	1	no	—
546	C₂×C₈	—	38	2	no	—
547	C₂×C₈	—	76	1	no	—
548	C₂×C₈	—	76	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	38	2	no	—
554	C₄⋊C₄	—	38	2	no	—
555	C₄⋊C₄	—	76	1	no	—
556	C₄⋊C₄	—	76	1	no	—
557	C₄⋊C₄	—	76	1	no	—
558	C₄⋊C₄	—	76	1	no	—
559	C₄⋊C₄	—	76	1	no	—
560	C₄⋊C₄	—	76	1	no	—
561	C₂²⋊C₄	—	4	1	no	—
562	C₂²⋊C₄	—	4	1	no	—
563	C₂²⋊C₄	—	152	2	no	—
564	C₂²⋊C₄	—	152	2	no	—
565	C₄²	—	2	2	no	—
566	C₄²	—	2	2	no	—
567	C₄²	—	4	1	no	—
568	C₄²	—	4	1	no	—
569	C₄²	—	4	1	no	—
570	C₄²	—	4	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	38	2	no	—
576	C₂³	—	76	1	no	—
577	C₂³	—	76	1	no	—
578	C₂³	—	76	1	no	—
579	C₂³	—	76	1	no	—
580	C₂³	—	76	1	no	—
581	C₂³	—	76	1	no	—
582	C₂³	#10597328	1	1	yes	characteristic
583	C₂³	#10597330	1	1	yes	characteristic
584	C₂³	#10597330	1	1	yes	characteristic
585	C₂³	#10597331	1	1	yes	characteristic
586	C₂³	#10597339	1	1	yes	characteristic
587	C₂³	#10597340	1	1	yes	characteristic
588	C₂³	#10597385	1	1	yes	characteristic
589	Q₈	—	38	2	no	—
590	Q₈	—	38	2	no	—
591	Q₈	—	76	1	no	—
592	Q₈	—	76	1	no	—
593	D₄	—	38	2	no	—
594	D₄	—	38	2	no	—
595	D₄	—	76	2	no	—
596	D₄	—	76	2	no	—
597	D₄	—	76	2	no	—
598	D₄	—	76	2	no	—
599	D₄	—	76	1	no	—
600	D₄	—	76	1	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	2	no	—
605	C₂×C₄	—	4	2	no	—
606	C₂×C₄	—	4	2	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	38	2	no	—
615	C₂×C₄	—	76	1	no	—
616	C₂×C₄	—	76	1	no	—
617	C₂×C₄	—	76	2	no	—
618	C₂×C₄	—	76	2	no	—
619	C₂×C₄	—	76	2	no	—
620	C₂×C₄	—	76	2	no	—
621	C₂×C₄	—	76	4	no	—
622	C₂×C₄	—	76	4	no	—
623	C₂×C₄	—	76	2	no	—
624	C₂×C₄	—	76	2	no	—
625	C₂×C₄	—	76	2	no	—
626	C₂×C₄	—	76	2	no	—
627	C₂×C₄	—	152	2	no	—
628	C₂×C₄	—	152	1	no	—
629	C₂×C₄	—	152	1	no	—
630	C₂×C₄	—	152	2	no	—
631	C₂×C₄	#10597318	1	1	yes	characteristic
632	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
633	C₂×C₄	#10597321	1	1	yes	characteristic
634	C₂×C₄	#10597322	1	1	yes	characteristic
635	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
636	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
637	C₂×C₄	#10597329	1	1	yes	characteristic
638	C₂×C₄	#10597329	1	1	yes	characteristic
639	C₂×C₄	#10597329	1	1	yes	characteristic
640	C₂×C₄	#10597330	1	1	yes	characteristic
641	C₂×C₄	#10597331	1	1	yes	characteristic
642	C₂×C₄	#10597332	1	1	yes	characteristic
643	C₂×C₄	#10597338	1	1	yes	characteristic
644	C₂×C₄	#10597340	1	1	yes	characteristic
645	C₂×C₄	#10597340	1	1	yes	characteristic
646	C₂×C₄	#10597340	1	1	yes	characteristic
647	C₂×C₄	#10597340	1	1	yes	characteristic
648	C₂×C₄	#10597341	1	1	yes	characteristic
649	C₂×C₄	#10597341	1	1	yes	characteristic
650	C₂×C₄	#10597344	1	1	yes	characteristic
651	C₂×C₄	#10597344	1	1	yes	characteristic
652	C₂×C₄	#10597344	1	1	yes	characteristic
653	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
654	C₂×C₄	#10597375	1	1	yes	characteristic
655	C₂×C₄	#10597376	1	1	yes	characteristic
656	C₂×C₄	#10597383	1	1	yes	characteristic
657	C₂×C₄	#10597384	1	1	yes	characteristic
658	C₂×C₄	#10597393	1	1	yes	characteristic
659	C₈	—	4	2	no	—
660	C₈	—	76	2	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	76	2	no	—
674	C₂²	—	76	2	no	—
675	C₂²	—	76	2	no	—
676	C₂²	—	152	1	no	—
677	C₂²	—	152	1	no	—
678	C₂²	—	152	1	no	—
679	C₂²	—	152	1	no	—
680	C₂²	#11926422	1	1	yes	characteristic
681	C₂²	#11926433	1	1	yes	characteristic
682	C₂²	#11926434	1	1	yes	characteristic
683	C₂²	#11926459	1	1	yes	characteristic
684	C₂²	#11926460	1	1	yes	characteristic
685	C₂²	#11926462	1	1	yes	characteristic
686	C₂²	#11926473	1	1	yes	characteristic
687	C₂²	#11926713	1	1	yes	characteristic
688	C₂²	#11926718	1	1	yes	characteristic
689	C₂²	#11926723	1	1	yes	characteristic
690	C₂²	#11926728	1	1	yes	characteristic
691	C₄	—	4	4	no	—
692	C₄	—	8	1	no	—
693	C₄	—	8	1	no	—
694	C₄	—	76	2	no	—
695	C₄	—	152	2	no	—
696	C₄	—	152	2	no	—
697	C₄	#11926406	1	1	yes	characteristic
698	C₄	#11926420	1	1	yes	characteristic
699	C₄	#11926435	1	1	yes	characteristic
700	C₄	#11926436	1	1	yes	characteristic
701	C₄	#11926461	1	1	yes	characteristic
702	C₄	#11926470	1	1	yes	characteristic
703	C₄	#11926471	1	1	yes	characteristic
704	C₄	#11926473	1	1	yes	characteristic
705	C₂	—	2	1	no	—
706	C₂	—	2	1	no	—
707	C₂	—	2	1	no	—
708	C₂	—	2	1	no	—
709	C₂	—	152	2	no	—
710	C₂	#14561883	1	1	yes	characteristic
711	C₂	#14564005	1	1	yes	characteristic
712	C₂	#14564012	1	1	yes	characteristic
713	C₂	#14564848	1	1	yes	characteristic
714	C₂	#14564855	1	1	yes	characteristic
715	C₂	#14564858	1	1	yes	characteristic
716	C₂	#14564863	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597328
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#339	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂²×#64541	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#339	D₁₉
hypocenter	C₁₉	#11195
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
4. C₂×#11926312	C₂	semidirect
5. #14563356	C₂	semidirect
6. #14561865	C₂	semidirect
7. C₂×C₁₉×#339	C₂	semidirect
16. #11926546	C₄	semidirect
308. C₂×#339	D₁₉	semidirect
458. C₁₉	#11195	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10597262	2
C₂×#11926546	2
#14566223	2
C₂×#11926312	2
#14563356	2
#14561865	2
C₂×C₁₉×#339	2
#11195	19