Subgroups — #18091332

Order 4864.

794 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14566038	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926305	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926304	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926303	C₂	1	1	yes	maximal, characteristic
5	#14563328	C₂	1	1	yes	maximal, characteristic
6	C₄×C₁₉⋊#95	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#339	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂×#10597372	C₂²	1	1	yes	characteristic
10	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	#11926413	C₄	1	2	yes	complemented
13	#11926409	C₄	1	2	yes	complemented
14	#11926402	—	2	2	no	—
15	C₄×Dic₁₉⋊C₄	—	2	2	no	—
16	C₂×C₁₉⋊#95	—	2	2	no	—
17	#11926305	—	2	2	no	—
18	#11926304	—	2	2	no	—
19	#11926303	—	2	2	no	—
20	#11926298	—	2	2	no	—
21	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#339	—	2	2	no	—
25	C₂³×C₄×C₁₉	—	2	1	no	—
26	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₂³×Dic₁₉	—	2	1	no	—
28	C₂³×Dic₁₉	D₄	1	2	yes	—
29	C₂×M₁₆×C₁₉	—	2	1	no	—
30	C₂×M₁₆×C₁₉	—	2	1	no	—
31	C₂×M₁₆×C₁₉	—	2	1	no	—
32	C₂×M₁₆×C₁₉	—	2	1	no	—
33	C₂×M₁₆×C₁₉	—	2	1	no	—
34	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
35	C₂²×C₈×C₁₉	—	2	1	no	—
36	C₁₉×#117	—	2	1	no	—
37	C₁₉×#117	—	2	1	no	—
38	C₁₉×#117	—	2	1	no	—
39	C₁₉×#117	—	2	1	no	—
40	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
41	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₄²×C₁₉	—	2	1	no	—
43	C₂×C₄²×C₁₉	—	2	1	no	—
44	C₂×C₄²×C₁₉	—	2	1	no	—
45	C₂×C₄²×C₁₉	—	2	1	no	—
46	C₂×C₄²×C₁₉	—	2	1	no	—
47	C₂×C₄²×C₁₉	—	2	1	no	—
48	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
49	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
50	#10597372	—	2	1	no	—
51	#10597372	—	2	1	no	—
52	#10597372	—	2	1	no	—
53	#10597372	—	2	1	no	—
54	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
55	C₂×Dic₁₉⋊C₄	—	2	2	no	—
56	C₂×Dic₁₉⋊C₄	—	2	2	no	—
57	C₂×C₄×Dic₁₉	—	2	1	no	—
58	C₂×C₄×Dic₁₉	—	2	1	no	—
59	C₂×C₄×Dic₁₉	—	2	1	no	—
60	C₂×C₄×Dic₁₉	—	2	1	no	—
61	C₂×C₄×Dic₁₉	—	2	1	no	—
62	C₂×C₄×Dic₁₉	—	2	1	no	—
63	C₂×C₄×Dic₁₉	—	2	1	no	—
64	C₂×C₄×Dic₁₉	—	2	1	no	—
65	C₂×C₄×Dic₁₉	—	2	1	no	—
66	C₂×C₄×Dic₁₉	—	2	1	no	—
67	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
70	C₂×C₄×Dic₁₉	Q₈	1	2	yes	—
71	C₂×#64520	—	2	1	no	—
72	C₂×#64520	—	2	1	no	—
73	C₂×#64520	—	2	1	no	—
74	C₂×#64520	—	2	1	no	—
75	C₂×#64520	—	2	1	no	—
76	C₂×#64520	D₄	1	2	yes	—
77	C₂²×C₁₉⋊C₈	—	2	1	no	—
78	C₁₉⋊#95	—	2	8	no	—
79	C₁₉⋊#95	—	2	4	no	—
80	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	—	2	4	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	4	2	no	—
85	C₂²×C₄×C₁₉	—	4	1	no	—
86	C₂²×C₄×C₁₉	—	4	1	no	—
87	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
101	C₂²×Dic₁₉	—	2	4	no	—
102	C₂²×Dic₁₉	—	2	2	no	—
103	C₂²×Dic₁₉	—	2	2	no	—
104	C₂²×Dic₁₉	—	2	2	no	—
105	C₂²×Dic₁₉	—	2	4	no	—
106	C₂²×Dic₁₉	—	2	2	no	—
107	C₂²×Dic₁₉	—	4	2	no	—
108	C₂²×Dic₁₉	—	4	2	no	—
109	C₂²×Dic₁₉	—	4	1	no	—
110	C₂²×Dic₁₉	—	4	1	no	—
111	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
112	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
113	M₁₆×C₁₉	—	2	2	no	—
114	M₁₆×C₁₉	—	2	2	no	—
115	M₁₆×C₁₉	—	4	1	no	—
116	M₁₆×C₁₉	—	4	1	no	—
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	—	4	1	no	—
119	C₂×C₈×C₁₉	—	4	1	no	—
120	C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₄⋊C₄×C₁₉	—	2	2	no	—
122	C₂²⋊C₄×C₁₉	—	4	1	no	—
123	C₂²⋊C₄×C₁₉	—	4	1	no	—
124	C₄²×C₁₉	—	2	2	no	—
125	C₄²×C₁₉	—	2	2	no	—
126	C₄²×C₁₉	—	4	1	no	—
127	C₄²×C₁₉	—	4	1	no	—
128	C₄²×C₁₉	—	4	1	no	—
129	C₄²×C₁₉	—	4	1	no	—
130	C₂²⋊Dic₁₉	—	4	1	no	—
131	C₂²⋊Dic₁₉	—	4	1	no	—
132	C₄⋊Dic₁₉	—	2	2	no	—
133	C₄⋊Dic₁₉	—	2	2	no	—
134	Dic₁₉⋊C₄	—	4	4	no	—
135	Dic₁₉⋊C₄	—	4	4	no	—
136	C₄×Dic₁₉	—	2	1	no	—
137	C₄×Dic₁₉	—	2	1	no	—
138	C₄×Dic₁₉	—	2	1	no	—
139	C₄×Dic₁₉	—	2	1	no	—
140	C₄×Dic₁₉	—	2	2	no	—
141	C₄×Dic₁₉	—	2	2	no	—
142	C₄×Dic₁₉	—	2	2	no	—
143	C₄×Dic₁₉	—	2	2	no	—
144	C₄×Dic₁₉	—	4	1	no	—
145	C₄×Dic₁₉	—	4	1	no	—
146	C₄×Dic₁₉	—	4	1	no	—
147	C₄×Dic₁₉	—	4	1	no	—
148	#64520	—	2	2	no	—
149	#64520	—	2	2	no	—
150	#64520	—	4	1	no	—
151	#64520	—	4	1	no	—
152	C₂×C₁₉⋊C₈	—	2	2	no	—
153	C₂×C₁₉⋊C₈	—	4	1	no	—
154	C₂×C₁₉⋊C₈	—	4	1	no	—
155	#11359	—	19	1	no	maximal, Sylow
156	C₂³×C₁₉	—	2	2	no	—
157	C₂³×C₁₉	—	2	2	no	—
158	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
160	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
161	C₂³×C₁₉	#123	1	1	yes	characteristic
162	C₂³×C₁₉	#123	1	1	yes	characteristic
163	C₂³×C₁₉	#124	1	1	yes	characteristic
164	C₂³×C₁₉	#127	1	1	yes	characteristic
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	4	4	no	—
167	C₂×C₄×C₁₉	—	4	4	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
191	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
192	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
193	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
194	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
195	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
199	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
201	C₂×Dic₁₉	—	2	2	no	—
202	C₂×Dic₁₉	—	2	2	no	—
203	C₂×Dic₁₉	—	2	4	no	—
204	C₂×Dic₁₉	—	2	2	no	—
205	C₂×Dic₁₉	—	2	2	no	—
206	C₂×Dic₁₉	—	2	2	no	—
207	C₂×Dic₁₉	—	4	4	no	—
208	C₂×Dic₁₉	—	4	4	no	—
209	C₂×Dic₁₉	—	4	4	no	—
210	C₂×Dic₁₉	—	4	4	no	—
211	C₂×Dic₁₉	—	4	2	no	—
212	C₂×Dic₁₉	—	4	2	no	—
213	C₂×Dic₁₉	—	4	2	no	—
214	C₂×Dic₁₉	—	4	2	no	—
215	C₂×Dic₁₉	—	4	2	no	—
216	C₂×Dic₁₉	#104	1	4	yes	—
217	C₈×C₁₉	—	4	2	no	—
218	C₁₉⋊C₈	—	4	2	no	—
219	#2285	—	19	1	no	—
220	C₂×#339	—	19	1	no	—
221	C₂×#339	—	19	1	no	—
222	C₂×#339	—	19	1	no	—
223	C₂×#339	D₁₉	1	1	yes	characteristic
224	#1728	—	19	1	no	—
225	C₄×#95	—	19	1	no	—
226	C₂²×C₁₉	—	2	2	no	—
227	C₂²×C₁₉	—	2	2	no	—
228	C₂²×C₁₉	—	2	2	no	—
229	C₂²×C₁₉	—	2	2	no	—
230	C₂²×C₁₉	—	2	1	no	—
231	C₂²×C₁₉	—	2	1	no	—
232	C₂²×C₁₉	—	2	1	no	—
233	C₂²×C₁₉	—	2	1	no	—
234	C₂²×C₁₉	#381	1	1	yes	characteristic
235	C₂²×C₁₉	#390	1	1	yes	characteristic
236	C₂²×C₁₉	#391	1	1	yes	characteristic
237	C₂²×C₁₉	#399	1	1	yes	characteristic
238	C₂²×C₁₉	#399	1	1	yes	characteristic
239	C₂²×C₁₉	#400	1	1	yes	characteristic
240	C₂²×C₁₉	#400	1	1	yes	characteristic
241	C₂²×C₁₉	C₂×#104	1	2	yes	—
242	C₂²×C₁₉	#421	1	2	yes	—
243	C₄×C₁₉	—	4	4	no	—
244	C₄×C₁₉	—	8	2	no	—
245	C₄×C₁₉	#387	1	1	yes	characteristic
246	C₄×C₁₉	#387	1	1	yes	characteristic
247	C₄×C₁₉	#387	1	1	yes	characteristic
248	C₄×C₁₉	#387	1	1	yes	characteristic
249	C₄×C₁₉	#397	1	1	yes	characteristic
250	C₄×C₁₉	#397	1	1	yes	characteristic
251	C₄×C₁₉	#398	1	1	yes	characteristic
252	C₄×C₁₉	#398	1	1	yes	characteristic
253	Dic₁₉	—	2	4	no	—
254	Dic₁₉	—	4	4	no	—
255	Dic₁₉	—	4	2	no	—
256	Dic₁₉	—	8	2	no	—
257	C₂²×M₁₆	—	19	1	no	—
258	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
259	C₂×#117	—	19	1	no	—
260	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
261	C₂²×C₄²	—	19	1	no	—
262	C₂²×C₄²	—	19	1	no	—
263	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
264	#384	—	19	2	no	—
265	#382	—	19	2	no	—
266	#380	—	38	2	no	—
267	C₄×C₄⋊C₄	—	38	2	no	—
268	C₂×#95	—	38	2	no	—
269	#339	—	2	2	no	—
270	#339	—	38	2	no	—
271	#339	—	38	2	no	—
272	#339	—	38	2	no	—
273	#336	—	38	2	no	—
274	C₂×C₁₉	—	2	1	no	—
275	C₂×C₁₉	—	2	1	no	—
276	C₂×C₁₉	—	2	1	no	—
277	C₂×C₁₉	—	2	1	no	—
278	C₂×C₁₉	#1445	1	1	yes	characteristic
279	C₂×C₁₉	#1826	1	2	yes	—
280	C₂×C₁₉	#1980	1	2	yes	—
281	C₂×C₁₉	#1994	1	1	yes	characteristic
282	C₂×C₁₉	#1995	1	1	yes	characteristic
283	C₂³×C₄	—	2	1	no	—
284	C₂³×C₄	—	19	2	no	—
285	C₂³×C₄	—	38	1	no	—
286	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
287	C₂×M₁₆	—	2	1	no	—
288	C₂×M₁₆	—	2	1	no	—
289	C₂×M₁₆	—	2	1	no	—
290	C₂×M₁₆	—	2	1	no	—
291	C₂×M₁₆	—	2	1	no	—
292	C₂×M₁₆	—	19	2	no	—
293	C₂×M₁₆	—	38	1	no	—
294	C₂×M₁₆	—	38	1	no	—
295	C₂×M₁₆	—	38	1	no	—
296	C₂×M₁₆	—	38	1	no	—
297	C₂×M₁₆	—	38	1	no	—
298	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
299	C₂²×C₈	—	2	1	no	—
300	C₂²×C₈	—	38	1	no	—
301	#117	—	2	1	no	—
302	#117	—	2	1	no	—
303	#117	—	2	1	no	—
304	#117	—	2	1	no	—
305	#117	—	38	1	no	—
306	#117	—	38	1	no	—
307	#117	—	38	1	no	—
308	#117	—	38	1	no	—
309	C₂×C₄⋊C₄	—	19	2	no	—
310	C₂×C₄⋊C₄	—	38	2	no	—
311	C₂×C₄⋊C₄	—	38	2	no	—
312	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₂²⋊C₄	—	38	1	no	—
315	C₂×C₄²	—	2	1	no	—
316	C₂×C₄²	—	2	1	no	—
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	—	2	1	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	—	2	1	no	—
321	C₂×C₄²	—	19	1	no	—
322	C₂×C₄²	—	19	1	no	—
323	C₂×C₄²	—	19	2	no	—
324	C₂×C₄²	—	19	2	no	—
325	C₂×C₄²	—	38	1	no	—
326	C₂×C₄²	—	38	1	no	—
327	C₂×C₄²	—	38	1	no	—
328	C₂×C₄²	—	38	1	no	—
329	C₂×C₄²	—	38	1	no	—
330	C₂×C₄²	—	38	1	no	—
331	C₂×C₄²	—	38	1	no	—
332	C₂×C₄²	—	38	1	no	—
333	C₂×C₄²	—	38	1	no	—
334	C₂×C₄²	—	38	1	no	—
335	C₂×C₄²	Dic₃₈	1	2	yes	—
336	#95	—	38	4	no	—
337	#95	—	38	8	no	—
338	C₁₉	#11359	1	1	yes	characteristic, complemented, Sylow
339	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	—	19	2	no	—
347	C₂²×C₄	—	19	2	no	—
348	C₂²×C₄	—	38	4	no	—
349	C₂²×C₄	—	38	4	no	—
350	C₂²×C₄	—	38	2	no	—
351	C₂²×C₄	—	38	2	no	—
352	C₂²×C₄	—	38	2	no	—
353	C₂²×C₄	—	38	2	no	—
354	C₂²×C₄	—	76	2	no	—
355	C₂²×C₄	—	76	2	no	—
356	C₂²×C₄	—	76	1	no	—
357	C₂²×C₄	—	76	1	no	—
358	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
359	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
360	C₂²×C₄	#64541	1	1	yes	characteristic
361	C₂²×C₄	#64541	1	1	yes	characteristic
362	C₂²×C₄	#64541	1	1	yes	characteristic
363	C₂²×C₄	#64541	1	1	yes	characteristic
364	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
365	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
366	C₂²×C₄	#64543	1	1	yes	characteristic
367	C₂²×C₄	#64543	1	1	yes	characteristic
368	C₂²×C₄	#64543	1	1	yes	characteristic
369	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
370	C₂²×C₄	#64545	1	1	yes	characteristic
371	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
372	M₁₆	—	2	2	no	—
373	M₁₆	—	2	2	no	—
374	M₁₆	—	4	1	no	—
375	M₁₆	—	4	1	no	—
376	M₁₆	—	38	2	no	—
377	M₁₆	—	38	2	no	—
378	M₁₆	—	76	1	no	—
379	M₁₆	—	76	1	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	4	1	no	—
382	C₂×C₈	—	4	1	no	—
383	C₂×C₈	—	38	2	no	—
384	C₂×C₈	—	76	1	no	—
385	C₂×C₈	—	76	1	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	38	2	no	—
389	C₄⋊C₄	—	38	2	no	—
390	C₄⋊C₄	—	76	4	no	—
391	C₄⋊C₄	—	76	4	no	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₂²⋊C₄	—	4	1	no	—
394	C₂²⋊C₄	—	76	1	no	—
395	C₂²⋊C₄	—	76	1	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	4	1	no	—
399	C₄²	—	4	1	no	—
400	C₄²	—	4	1	no	—
401	C₄²	—	4	1	no	—
402	C₄²	—	38	1	no	—
403	C₄²	—	38	1	no	—
404	C₄²	—	38	2	no	—
405	C₄²	—	38	1	no	—
406	C₄²	—	38	1	no	—
407	C₄²	—	38	2	no	—
408	C₄²	—	38	2	no	—
409	C₄²	—	38	2	no	—
410	C₄²	—	76	1	no	—
411	C₄²	—	76	1	no	—
412	C₄²	—	76	1	no	—
413	C₄²	—	76	1	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	#10597324	1	1	yes	characteristic
417	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
418	C₂³	#10597329	1	1	yes	characteristic
419	C₂³	#10597331	1	1	yes	characteristic
420	C₂³	#10597340	1	1	yes	characteristic
421	C₂³	#10597342	1	1	yes	characteristic
422	C₂³	#10597386	1	1	yes	characteristic
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	19	4	no	—
432	C₂×C₄	—	38	2	no	—
433	C₂×C₄	—	38	2	no	—
434	C₂×C₄	—	38	4	no	—
435	C₂×C₄	—	38	2	no	—
436	C₂×C₄	—	38	2	no	—
437	C₂×C₄	—	38	2	no	—
438	C₂×C₄	—	76	4	no	—
439	C₂×C₄	—	76	4	no	—
440	C₂×C₄	—	76	2	no	—
441	C₂×C₄	—	76	4	no	—
442	C₂×C₄	—	76	4	no	—
443	C₂×C₄	—	76	2	no	—
444	C₂×C₄	—	76	2	no	—
445	C₂×C₄	—	76	2	no	—
446	C₂×C₄	—	76	2	no	—
447	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
448	C₂×C₄	#10597316	1	1	yes	characteristic
449	C₂×C₄	#10597318	1	1	yes	characteristic
450	C₂×C₄	#10597322	1	1	yes	characteristic
451	C₂×C₄	#10597324	1	1	yes	characteristic
452	C₂×C₄	#10597325	1	1	yes	characteristic
453	C₂×C₄	#10597325	1	1	yes	characteristic
454	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
455	C₂×C₄	#10597329	1	1	yes	characteristic
456	C₂×C₄	#10597329	1	1	yes	characteristic
457	C₂×C₄	#10597330	1	1	yes	characteristic
458	C₂×C₄	#10597331	1	1	yes	characteristic
459	C₂×C₄	#10597333	1	1	yes	characteristic
460	C₂×C₄	#10597334	1	1	yes	characteristic
461	C₂×C₄	#10597335	1	1	yes	characteristic
462	C₂×C₄	#10597335	1	1	yes	characteristic
463	C₂×C₄	#10597336	1	1	yes	characteristic
464	C₂×C₄	#10597338	1	1	yes	characteristic
465	C₂×C₄	#10597340	1	1	yes	characteristic
466	C₂×C₄	#10597340	1	1	yes	characteristic
467	C₂×C₄	#10597342	1	1	yes	characteristic
468	C₂×C₄	#10597344	1	1	yes	characteristic
469	C₂×C₄	#10597370	1	1	yes	characteristic
470	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
471	C₂×C₄	#10597375	1	1	yes	characteristic
472	C₂×C₄	#10597381	1	1	yes	characteristic
473	C₂×C₄	#10597385	1	1	yes	characteristic
474	C₂×C₄	#10597392	1	1	yes	characteristic
475	C₈	—	4	2	no	—
476	C₈	—	76	2	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	#11926406	1	1	yes	characteristic
486	C₂²	#11926444	1	1	yes	characteristic
487	C₂²	#11926448	1	1	yes	characteristic
488	C₂²	#11926479	1	1	yes	characteristic
489	C₂²	#11926480	1	1	yes	characteristic
490	C₂²	#11926485	1	1	yes	characteristic
491	C₂²	#11926486	1	1	yes	characteristic
492	C₂²	#104×D₁₉	1	2	yes	—
493	C₂²	#11926559	1	2	yes	—
494	C₄	—	4	4	no	—
495	C₄	—	8	2	no	—
496	C₄	—	38	4	no	—
497	C₄	—	76	4	no	—
498	C₄	—	76	2	no	—
499	C₄	—	152	2	no	—
500	C₄	#11926425	1	1	yes	characteristic
501	C₄	#11926426	1	1	yes	characteristic
502	C₄	#11926428	1	1	yes	characteristic
503	C₄	#11926431	1	1	yes	characteristic
504	C₄	#11926472	1	1	yes	characteristic
505	C₄	#11926473	1	1	yes	characteristic
506	C₄	#11926477	1	1	yes	characteristic
507	C₄	#11926478	1	1	yes	characteristic
508	C₂	—	2	1	no	—
509	C₂	—	2	1	no	—
510	C₂	—	2	1	no	—
511	C₂	—	2	1	no	—
512	C₂	#14561901	1	1	yes	characteristic
513	C₂	#14563733	1	2	yes	—
514	C₂	#14564552	1	2	yes	—
515	C₂	#14564610	1	1	yes	characteristic
516	C₂	#14564614	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#339	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#339	D₁₉
hypocenter	C₁₉	#11359
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
12. #11926413	C₄	semidirect
13. #11926409	C₄	semidirect
338. C₁₉	#11359	semidirect

Maximal subgroups

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

subgroup	index
#14566038	2
C₂×#11926305	2
C₂×#11926304	2
C₂×#11926303	2
#14563328	2
C₄×C₁₉⋊#95	2
C₂×C₁₉×#339	2
#11359	19