Subgroups — #18088476

Order 4864.

746 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926580	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926580	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926502	C₂	1	1	yes	maximal, characteristic
4	#14563368	C₂	1	1	yes	maximal, characteristic
5	#14563367	C₂	1	1	yes	maximal, characteristic
6	#14563346	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1733	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×#10597372	C₂²	1	1	yes	characteristic
10	C₂×#10597372	C₂²	1	1	yes	characteristic
11	C₂×#10597372	C₂²	1	1	yes	characteristic
12	#11926580	—	2	2	no	—
13	#11926580	—	2	1	no	—
14	#11926580	—	2	1	no	—
15	#11926580	—	2	1	no	—
16	#11926580	—	2	1	no	—
17	#11926580	C₄	1	4	yes	complemented
18	C₂×#10597264	—	2	1	no	—
19	C₂×#10597264	C₄	1	2	yes	complemented
20	C₂×#10597265	—	2	1	no	—
21	C₂×#10597265	C₄	1	2	yes	complemented
22	#11926502	—	2	2	no	—
23	#11926502	C₄	1	4	yes	complemented
24	C₂×#10597272	—	2	1	no	—
25	C₂×C₈×Dic₁₉	—	2	1	no	—
26	#11926311	—	2	2	no	—
27	#11926310	—	2	2	no	—
28	#11926305	—	2	2	no	—
29	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
32	C₁₉×#339	—	2	2	no	—
33	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
34	C₂×M₁₆×C₁₉	—	2	1	no	—
35	C₂×M₁₆×C₁₉	—	2	1	no	—
36	C₂×M₁₆×C₁₉	—	2	1	no	—
37	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
38	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
39	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
40	C₂²×C₈×C₁₉	—	2	1	no	—
41	C₁₉×#117	—	2	1	no	—
42	C₁₉×#117	—	2	1	no	—
43	C₁₉×#117	—	2	1	no	—
44	C₁₉×#117	—	2	1	no	—
45	C₁₉×#117	—	2	1	no	—
46	C₁₉×#117	—	2	1	no	—
47	C₁₉×#117	—	2	1	no	—
48	C₁₉×#117	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄²×C₁₉	—	2	1	no	—
54	C₂×C₄²×C₁₉	—	2	1	no	—
55	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
56	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
57	C₂×C₂²⋊Dic₁₉	D₄	1	2	yes	—
58	#10597372	—	2	1	no	—
59	#10597372	—	2	1	no	—
60	#10597372	—	2	1	no	—
61	#10597372	—	2	1	no	—
62	#10597372	—	2	1	no	—
63	#10597372	—	2	1	no	—
64	#10597372	—	2	1	no	—
65	#10597372	—	2	1	no	—
66	#10597372	—	2	1	no	—
67	#10597372	C₂×C₄	1	2	yes	—
68	#10597372	C₂×C₄	1	2	yes	—
69	#10597372	Q₈	1	2	yes	—
70	C₂×C₄⋊Dic₁₉	—	2	1	no	—
71	C₂×C₄⋊Dic₁₉	—	2	1	no	—
72	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
73	C₂×C₄×Dic₁₉	—	2	1	no	—
74	C₂×C₄×Dic₁₉	—	2	1	no	—
75	C₂×C₄×Dic₁₉	—	2	1	no	—
76	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
79	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
80	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
81	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
82	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
83	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
84	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
85	C₂²×C₁₉⋊C₈	Q₈	1	2	yes	—
86	#10597272	—	2	4	no	—
87	C₈×Dic₁₉	—	2	4	no	—
88	#10597265	—	2	4	no	—
89	#10597265	—	2	2	no	—
90	#10597265	—	2	2	no	—
91	#10597264	—	2	4	no	—
92	#10597264	—	2	2	no	—
93	#10597264	—	2	2	no	—
94	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	4	1	no	—
97	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×Q₈	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	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
111	C₂²×Dic₁₉	—	2	2	no	—
112	C₂²×Dic₁₉	—	2	2	no	—
113	C₂²×Dic₁₉	—	4	1	no	—
114	M₁₆×C₁₉	—	2	2	no	—
115	M₁₆×C₁₉	—	2	2	no	—
116	M₁₆×C₁₉	—	2	2	no	—
117	M₁₆×C₁₉	C₄⋊C₄	1	4	yes	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	2	2	no	—
121	C₄⋊C₄×C₁₉	—	2	2	no	—
122	C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₄⋊C₄×C₁₉	—	2	2	no	—
124	C₄⋊C₄×C₁₉	—	4	1	no	—
125	C₂²⋊C₄×C₁₉	—	2	2	no	—
126	C₂²⋊C₄×C₁₉	—	4	1	no	—
127	C₂²⋊C₄×C₁₉	—	4	1	no	—
128	C₂²⋊C₄×C₁₉	—	4	1	no	—
129	C₄²×C₁₉	—	2	2	no	—
130	C₄²×C₁₉	—	4	1	no	—
131	C₄²×C₁₉	—	4	1	no	—
132	C₄²×C₁₉	—	4	1	no	—
133	C₂²⋊Dic₁₉	—	2	2	no	—
134	C₂²⋊Dic₁₉	—	2	2	no	—
135	C₂²⋊Dic₁₉	—	4	1	no	—
136	C₂²⋊Dic₁₉	—	4	1	no	—
137	C₂²⋊Dic₁₉	—	4	1	no	—
138	C₂²⋊Dic₁₉	C₄⋊C₄	1	4	yes	—
139	C₄⋊Dic₁₉	—	2	2	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	—	2	2	no	—
146	C₄×Dic₁₉	—	2	2	no	—
147	C₄×Dic₁₉	—	2	2	no	—
148	C₄×Dic₁₉	—	4	1	no	—
149	C₄×Dic₁₉	—	4	1	no	—
150	C₄×Dic₁₉	—	4	1	no	—
151	C₂×C₁₉⋊C₈	C₄²	1	2	yes	—
152	C₂×C₁₉⋊C₈	C₄²	1	2	yes	—
153	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
154	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
157	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
160	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
161	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
162	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
163	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
164	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
165	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
166	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
167	#10871	—	19	1	no	maximal, Sylow
168	C₂³×C₁₉	—	4	2	no	—
169	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
171	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
172	C₂³×C₁₉	#121	1	1	yes	characteristic
173	C₂³×C₁₉	#121	1	1	yes	characteristic
174	C₂³×C₁₉	#127	1	1	yes	characteristic
175	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	8	2	no	—
179	C₂×C₄×C₁₉	—	8	2	no	—
180	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
202	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
204	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
205	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
206	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
207	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
208	C₂×Dic₁₉	—	2	4	no	—
209	C₂×Dic₁₉	—	4	4	no	—
210	C₂×Dic₁₉	—	4	2	no	—
211	C₂×Dic₁₉	—	4	2	no	—
212	C₂×Dic₁₉	—	8	2	no	—
213	C₂×Dic₁₉	—	8	2	no	—
214	C₈×C₁₉	—	2	4	no	—
215	C₁₉⋊C₈	#95	1	2	yes	—
216	C₁₉⋊C₈	#95	1	2	yes	—
217	C₁₉⋊C₈	#95	1	2	yes	—
218	C₁₉⋊C₈	#95	1	2	yes	—
219	C₂×#427	—	19	1	no	—
220	C₂×#427	—	19	1	no	—
221	C₂×#405	—	19	1	no	—
222	#1740	—	19	1	no	—
223	#1740	—	19	1	no	—
224	#1733	—	19	1	no	—
225	#1733	D₁₉	1	1	yes	characteristic
226	C₂²×C₁₉	—	2	2	no	—
227	C₂²×C₁₉	—	2	2	no	—
228	C₂²×C₁₉	—	2	2	no	—
229	C₂²×C₁₉	—	4	1	no	—
230	C₂²×C₁₉	—	4	1	no	—
231	C₂²×C₁₉	—	4	1	no	—
232	C₂²×C₁₉	—	4	1	no	—
233	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
234	C₂²×C₁₉	#380	1	1	yes	characteristic
235	C₂²×C₁₉	#384	1	1	yes	characteristic
236	C₂²×C₁₉	#389	1	1	yes	characteristic
237	C₂²×C₁₉	#389	1	1	yes	characteristic
238	C₂²×C₁₉	#390	1	1	yes	characteristic
239	C₂²×C₁₉	#390	1	1	yes	characteristic
240	C₄×C₁₉	—	8	2	no	—
241	C₄×C₁₉	—	8	2	no	—
242	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
243	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
244	C₄×C₁₉	#380	1	1	yes	characteristic
245	C₄×C₁₉	#382	1	1	yes	characteristic
246	C₄×C₁₉	#389	1	1	yes	characteristic
247	C₄×C₁₉	#389	1	1	yes	characteristic
248	C₄×C₁₉	#391	1	1	yes	characteristic
249	C₄×C₁₉	#391	1	1	yes	characteristic
250	Dic₁₉	—	4	4	no	—
251	Dic₁₉	—	8	2	no	—
252	Dic₁₉	—	8	2	no	—
253	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
254	C₂³×C₈	—	19	1	no	—
255	C₂×#117	—	19	1	no	—
256	C₂×#117	—	19	1	no	—
257	C₂×#117	—	19	1	no	—
258	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
259	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
260	#427	—	19	4	no	—
261	#427	—	38	1	no	—
262	#427	—	38	1	no	—
263	#427	—	38	1	no	—
264	#427	—	38	1	no	—
265	#427	—	38	2	no	—
266	C₂×#107	—	19	2	no	—
267	C₂×#107	—	38	1	no	—
268	C₂×#106	—	19	2	no	—
269	C₂×#106	—	38	1	no	—
270	#405	—	19	4	no	—
271	#405	—	38	2	no	—
272	C₂×#97	—	38	1	no	—
273	C₂×C₄×C₈	—	38	1	no	—
274	#342	—	38	2	no	—
275	#342	—	38	2	no	—
276	#339	—	2	2	no	—
277	#339	—	38	2	no	—
278	C₂×C₁₉	—	2	1	no	—
279	C₂×C₁₉	—	2	1	no	—
280	C₂×C₁₉	—	2	1	no	—
281	C₂×C₁₉	—	2	1	no	—
282	C₂×C₁₉	—	2	1	no	—
283	C₂×C₁₉	—	2	1	no	—
284	C₂×C₁₉	C₄⋊#95	1	1	yes	characteristic
285	C₂×C₁₉	#1976	1	2	yes	—
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	Dic₃₈	1	2	yes	—
291	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
292	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	—	19	2	no	—
295	C₂²×C₈	—	19	1	no	—
296	C₂²×C₈	—	19	1	no	—
297	C₂²×C₈	—	19	2	no	—
298	C₂²×C₈	—	19	1	no	—
299	C₂²×C₈	—	19	1	no	—
300	C₂²×C₈	—	19	2	no	—
301	C₂²×C₈	—	19	1	no	—
302	C₂²×C₈	—	19	1	no	—
303	C₂²×C₈	—	19	2	no	—
304	#117	—	2	1	no	—
305	#117	—	2	1	no	—
306	#117	—	2	1	no	—
307	#117	—	2	1	no	—
308	#117	—	2	1	no	—
309	#117	—	2	1	no	—
310	#117	—	2	1	no	—
311	#117	—	19	2	no	—
312	#117	—	19	2	no	—
313	#117	—	19	2	no	—
314	#117	—	38	1	no	—
315	#117	—	38	1	no	—
316	#117	—	38	1	no	—
317	#117	—	38	1	no	—
318	#117	—	38	1	no	—
319	#117	—	38	1	no	—
320	#117	—	38	1	no	—
321	#117	—	38	1	no	—
322	#117	—	38	1	no	—
323	#117	C₄×D₁₉	1	2	yes	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	19	2	no	—
326	C₂×C₄⋊C₄	—	38	1	no	—
327	C₂×C₄⋊C₄	—	38	1	no	—
328	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	19	2	no	—
332	C₂×C₂²⋊C₄	—	38	1	no	—
333	C₂×C₂²⋊C₄	—	38	1	no	—
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	—	2	1	no	—
336	C₂×C₄²	—	38	1	no	—
337	C₂×C₄²	—	38	1	no	—
338	C₂×C₄²	—	38	1	no	—
339	#107	—	38	2	no	—
340	#107	—	38	2	no	—
341	#107	—	38	4	no	—
342	#106	—	38	2	no	—
343	#106	—	38	2	no	—
344	#106	—	38	4	no	—
345	#97	—	38	4	no	—
346	C₄×C₈	—	38	4	no	—
347	C₁₉	#10871	1	1	yes	characteristic, complemented, Sylow
348	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	4	1	no	—
351	C₂²×C₄	—	38	2	no	—
352	C₂²×C₄	—	38	2	no	—
353	C₂²×C₄	—	76	1	no	—
354	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
355	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
356	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
357	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
358	C₂²×C₄	#64541	1	1	yes	characteristic
359	C₂²×C₄	#64541	1	1	yes	characteristic
360	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
361	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
362	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
363	C₂²×C₄	#64543	1	1	yes	characteristic
364	C₂²×C₄	#64543	1	1	yes	characteristic
365	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
366	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
368	M₁₆	—	2	2	no	—
369	M₁₆	—	2	2	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	Dic₁₉⋊C₄	1	4	yes	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	19	2	no	—
376	C₂×C₈	—	19	2	no	—
377	C₂×C₈	—	19	2	no	—
378	C₂×C₈	—	19	2	no	—
379	C₂×C₈	—	19	1	no	—
380	C₂×C₈	—	19	1	no	—
381	C₂×C₈	—	19	2	no	—
382	C₂×C₈	—	19	1	no	—
383	C₂×C₈	—	19	1	no	—
384	C₂×C₈	—	19	2	no	—
385	C₂×C₈	—	19	2	no	—
386	C₂×C₈	—	19	2	no	—
387	C₂×C₈	—	19	2	no	—
388	C₂×C₈	—	19	2	no	—
389	C₂×C₈	—	19	2	no	—
390	C₂×C₈	—	19	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	4	1	no	—
395	C₄⋊C₄	—	38	2	no	—
396	C₄⋊C₄	—	38	2	no	—
397	C₄⋊C₄	—	38	2	no	—
398	C₄⋊C₄	—	38	2	no	—
399	C₄⋊C₄	—	38	2	no	—
400	C₄⋊C₄	—	76	1	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	4	1	no	—
403	C₂²⋊C₄	—	4	1	no	—
404	C₂²⋊C₄	—	4	1	no	—
405	C₂²⋊C₄	—	19	4	no	—
406	C₂²⋊C₄	—	38	2	no	—
407	C₂²⋊C₄	—	38	2	no	—
408	C₂²⋊C₄	—	76	1	no	—
409	C₂²⋊C₄	—	76	1	no	—
410	C₂²⋊C₄	—	76	1	no	—
411	C₄²	—	2	2	no	—
412	C₄²	—	4	1	no	—
413	C₄²	—	4	1	no	—
414	C₄²	—	4	1	no	—
415	C₄²	—	38	2	no	—
416	C₄²	—	38	2	no	—
417	C₄²	—	38	2	no	—
418	C₄²	—	76	1	no	—
419	C₄²	—	76	1	no	—
420	C₄²	—	76	1	no	—
421	C₂³	—	4	2	no	—
422	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
423	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
424	C₂³	#10597330	1	1	yes	characteristic
425	C₂³	#10597330	1	1	yes	characteristic
426	C₂³	#10597334	1	1	yes	characteristic
427	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
428	C₂³	#10597386	1	1	yes	characteristic
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	8	2	no	—
432	C₂×C₄	—	8	2	no	—
433	C₂×C₄	—	38	4	no	—
434	C₂×C₄	—	76	4	no	—
435	C₂×C₄	—	76	2	no	—
436	C₂×C₄	—	76	2	no	—
437	C₂×C₄	—	152	2	no	—
438	C₂×C₄	—	152	2	no	—
439	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
440	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
441	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
442	C₂×C₄	#10597318	1	1	yes	characteristic
443	C₂×C₄	#10597323	1	1	yes	characteristic
444	C₂×C₄	#10597324	1	1	yes	characteristic
445	C₂×C₄	#10597324	1	1	yes	characteristic
446	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
447	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
448	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
449	C₂×C₄	#10597331	1	1	yes	characteristic
450	C₂×C₄	#10597331	1	1	yes	characteristic
451	C₂×C₄	#10597333	1	1	yes	characteristic
452	C₂×C₄	#10597333	1	1	yes	characteristic
453	C₂×C₄	#10597334	1	1	yes	characteristic
454	C₂×C₄	#10597335	1	1	yes	characteristic
455	C₂×C₄	#10597335	1	1	yes	characteristic
456	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
457	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
458	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
459	C₂×C₄	#10597342	1	1	yes	characteristic
460	C₂×C₄	#10597342	1	1	yes	characteristic
461	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
462	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
463	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
464	C₂×C₄	#10597385	1	1	yes	characteristic
465	C₂×C₄	#10597385	1	1	yes	characteristic
466	C₂×C₄	#10597390	1	1	yes	characteristic
467	C₈	—	2	4	no	—
468	C₈	—	19	2	no	—
469	C₈	—	19	2	no	—
470	C₈	—	19	2	no	—
471	C₈	—	19	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	1	no	—
477	C₂²	—	4	1	no	—
478	C₂²	—	4	1	no	—
479	C₂²	#11926395	1	1	yes	characteristic
480	C₂²	#11926403	1	1	yes	characteristic
481	C₂²	#11926413	1	1	yes	characteristic
482	C₂²	#11926441	1	1	yes	characteristic
483	C₂²	#11926441	1	1	yes	characteristic
484	C₂²	#11926444	1	1	yes	characteristic
485	C₂²	#11926444	1	1	yes	characteristic
486	C₄	—	8	2	no	—
487	C₄	—	8	2	no	—
488	C₄	—	76	4	no	—
489	C₄	—	152	2	no	—
490	C₄	—	152	2	no	—
491	C₄	#95×D₁₉	1	1	yes	characteristic
492	C₄	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
493	C₄	#11926402	1	1	yes	characteristic
494	C₄	#11926408	1	1	yes	characteristic
495	C₄	#11926439	1	1	yes	characteristic
496	C₄	#11926439	1	1	yes	characteristic
497	C₄	#11926448	1	1	yes	characteristic
498	C₄	#11926448	1	1	yes	characteristic
499	C₂	—	2	1	no	—
500	C₂	—	2	1	no	—
501	C₂	—	2	1	no	—
502	C₂	—	2	1	no	—
503	C₂	—	2	1	no	—
504	C₂	—	2	1	no	—
505	C₂	Dic₁₉⋊#95	1	1	yes	characteristic
506	C₂	#14564532	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10597385
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1733	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1733	D₁₉
hypocenter	C₁₉	#10871
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1733

Complements

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

N	H ≅ G/N	type
17. #11926580	C₄	semidirect
19. C₂×#10597264	C₄	semidirect
21. C₂×#10597265	C₄	semidirect
23. #11926502	C₄	semidirect
347. C₁₉	#10871	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926580	2
C₂×#11926502	2
#14563368	2
#14563367	2
#14563346	2
C₁₉×#1733	2
#10871	19