Subgroups — #18088488

Order 4864.

714 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10597279	C₂	1	1	yes	maximal, characteristic
2	C₂²×#10597279	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926500	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926314	C₂	1	1	yes	maximal, characteristic
5	#14563362	C₂	1	1	yes	maximal, characteristic
6	#14563361	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#344	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂²×#64520	C₂²	1	1	yes	characteristic
10	C₂²×#64520	C₂²	1	1	yes	characteristic
11	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×#10597279	—	2	2	no	—
13	C₂×#10597279	—	2	2	no	—
14	C₂×#10597279	—	2	1	no	—
15	C₂×#10597279	—	2	1	no	—
16	C₂×#10597279	—	2	2	no	—
17	C₂×#10597279	C₄	1	4	yes	complemented
18	C₂×#10597279	C₄	1	4	yes	complemented
19	#11926500	—	2	2	no	—
20	#11926500	C₄	1	4	yes	—
21	C₂×#10597260	—	2	1	no	—
22	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
23	#11926314	—	2	2	no	—
24	#11926309	—	2	2	no	—
25	#11926308	—	2	2	no	—
26	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
29	C₁₉×#344	—	2	2	no	—
30	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
35	C₂×M₁₆×C₁₉	—	2	1	no	—
36	C₂×M₁₆×C₁₉	—	2	1	no	—
37	C₂×M₁₆×C₁₉	—	2	1	no	—
38	C₂×M₁₆×C₁₉	—	2	1	no	—
39	C₂×M₁₆×C₁₉	—	2	1	no	—
40	C₂×M₁₆×C₁₉	—	2	1	no	—
41	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
42	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
43	C₂²×C₈×C₁₉	—	2	1	no	—
44	C₂²×C₈×C₁₉	—	2	1	no	—
45	C₁₉×#117	—	2	1	no	—
46	C₁₉×#117	—	2	1	no	—
47	C₁₉×#117	C₂×C₄	1	2	yes	—
48	C₁₉×#117	D₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₂²⋊C₄×C₁₉	Q₈	1	2	yes	—
51	C₂×C₄²×C₁₉	—	2	1	no	—
52	C₂×#64520	—	2	1	no	—
53	C₂×#64520	—	2	1	no	—
54	C₂×#64520	—	2	1	no	—
55	C₂×#64520	—	2	1	no	—
56	C₂×#64520	—	2	1	no	—
57	C₂×#64520	—	2	1	no	—
58	C₂×#64520	—	2	1	no	—
59	C₂×#64520	—	2	1	no	—
60	C₂×#64520	—	2	1	no	—
61	C₂×#64520	—	2	1	no	—
62	C₂×#64520	—	2	1	no	—
63	C₂×#64520	—	2	1	no	—
64	C₂×#64520	—	2	1	no	—
65	C₂×#64520	C₂×C₄	1	2	yes	—
66	C₂×#64520	C₂×C₄	1	2	yes	—
67	C₂×#64520	C₂×C₄	1	2	yes	—
68	C₂×#64520	D₄	1	2	yes	—
69	C₂×#64520	Q₈	1	2	yes	—
70	C₂²×C₁₉⋊C₈	—	2	1	no	—
71	C₂²×C₁₉⋊C₈	—	2	1	no	—
72	C₂²×C₁₉⋊C₈	—	2	1	no	—
73	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
74	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
75	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
76	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
77	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
78	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
79	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
80	C₂²×C₁₉⋊C₈	Q₈	1	2	yes	—
81	#10597279	—	2	4	no	—
82	#10597279	—	2	4	no	—
83	#10597279	—	2	8	no	—
84	#10597260	—	2	4	no	—
85	C₄×C₁₉⋊C₈	—	2	4	no	—
86	C₂⁴×C₁₉	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×Q₈	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×C₄×C₁₉	#41	1	1	yes	characteristic
102	M₁₆×C₁₉	—	2	2	no	—
103	M₁₆×C₁₉	—	2	2	no	—
104	M₁₆×C₁₉	—	2	2	no	—
105	M₁₆×C₁₉	—	2	2	no	—
106	M₁₆×C₁₉	—	4	1	no	—
107	M₁₆×C₁₉	—	4	1	no	—
108	M₁₆×C₁₉	—	4	1	no	—
109	M₁₆×C₁₉	—	4	1	no	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	4	1	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₂×C₈×C₁₉	—	4	1	no	—
115	C₂×C₈×C₁₉	—	4	1	no	—
116	C₄⋊C₄×C₁₉	—	2	2	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₂²⋊C₄×C₁₉	—	2	2	no	—
119	C₂²⋊C₄×C₁₉	C₄⋊C₄	1	4	yes	—
120	C₄²×C₁₉	—	2	2	no	—
121	C₄²×C₁₉	—	2	2	no	—
122	#64520	—	2	2	no	—
123	#64520	—	2	2	no	—
124	#64520	—	2	2	no	—
125	#64520	—	2	2	no	—
126	#64520	—	2	2	no	—
127	#64520	—	2	2	no	—
128	#64520	—	2	2	no	—
129	#64520	—	4	1	no	—
130	#64520	—	4	1	no	—
131	#64520	—	4	1	no	—
132	#64520	—	4	1	no	—
133	#64520	C₄⋊C₄	1	4	yes	—
134	C₂×C₁₉⋊C₈	—	2	2	no	—
135	C₂×C₁₉⋊C₈	—	2	2	no	—
136	C₂×C₁₉⋊C₈	—	2	2	no	—
137	C₂×C₁₉⋊C₈	—	2	2	no	—
138	C₂×C₁₉⋊C₈	—	2	2	no	—
139	C₂×C₁₉⋊C₈	—	4	1	no	—
140	C₂×C₁₉⋊C₈	—	4	1	no	—
141	C₂×C₁₉⋊C₈	—	4	1	no	—
142	C₂×C₁₉⋊C₈	—	4	1	no	—
143	C₂×C₁₉⋊C₈	C₄²	1	4	yes	—
144	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
145	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
146	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
147	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
148	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	4	yes	—
149	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
150	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
151	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
152	C₂×C₁₉⋊C₈	C₄⋊C₄	1	4	yes	—
153	#10873	—	19	1	no	maximal, Sylow
154	C₂³×C₁₉	—	4	2	no	—
155	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
157	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
158	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
159	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
160	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
161	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
162	C₂×C₄×C₁₉	—	2	4	no	—
163	C₂×C₄×C₁₉	—	4	4	no	—
164	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₄×D₄	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×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
192	C₈×C₁₉	—	4	2	no	—
193	C₈×C₁₉	—	4	2	no	—
194	C₁₉⋊C₈	—	2	4	no	—
195	C₁₉⋊C₈	—	4	2	no	—
196	C₁₉⋊C₈	—	4	2	no	—
197	C₁₉⋊C₈	#95	1	4	yes	—
198	C₁₉⋊C₈	#95	1	4	yes	—
199	C₂²×#108	—	19	1	no	—
200	C₂²×#108	—	19	1	no	—
201	C₂×#405	—	19	1	no	—
202	C₂×#344	—	19	1	no	—
203	C₂×#344	D₁₉	1	1	yes	characteristic
204	#1738	—	19	1	no	—
205	#1738	—	19	1	no	—
206	C₂²×C₁₉	—	2	2	no	—
207	C₂²×C₁₉	—	2	2	no	—
208	C₂²×C₁₉	—	2	2	no	—
209	C₂²×C₁₉	—	4	1	no	—
210	C₂²×C₁₉	—	4	1	no	—
211	C₂²×C₁₉	—	4	1	no	—
212	C₂²×C₁₉	—	4	1	no	—
213	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
214	C₂²×C₁₉	#380	1	1	yes	characteristic
215	C₂²×C₁₉	#384	1	1	yes	characteristic
216	C₂²×C₁₉	#389	1	1	yes	characteristic
217	C₂²×C₁₉	#389	1	1	yes	characteristic
218	C₂²×C₁₉	#391	1	1	yes	characteristic
219	C₂²×C₁₉	#391	1	1	yes	characteristic
220	C₄×C₁₉	—	4	4	no	—
221	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
222	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
223	C₄×C₁₉	#380	1	1	yes	characteristic
224	C₄×C₁₉	#382	1	1	yes	characteristic
225	C₄×C₁₉	#389	1	1	yes	characteristic
226	C₄×C₁₉	#389	1	1	yes	characteristic
227	C₄×C₁₉	#390	1	1	yes	characteristic
228	C₄×C₁₉	#390	1	1	yes	characteristic
229	C₂²×M₁₆	—	19	1	no	—
230	C₂²×M₁₆	—	19	1	no	—
231	C₂²×M₁₆	—	19	1	no	—
232	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
233	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
234	C₂³×C₈	—	19	1	no	—
235	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
236	C₂×#108	—	19	4	no	—
237	C₂×#108	—	19	4	no	—
238	C₂×#108	—	38	1	no	—
239	C₂×#108	—	38	1	no	—
240	C₂×#108	—	38	2	no	—
241	C₂×#108	—	38	2	no	—
242	C₂×#108	—	38	2	no	—
243	#405	—	19	4	no	—
244	#405	—	38	2	no	—
245	C₂×#97	—	38	1	no	—
246	C₂×C₄×C₈	—	38	1	no	—
247	#344	—	2	2	no	—
248	#344	—	38	2	no	—
249	#341	—	38	2	no	—
250	#341	—	38	2	no	—
251	C₂×C₁₉	—	2	1	no	—
252	C₂×C₁₉	—	2	1	no	—
253	C₂×C₁₉	—	2	1	no	—
254	C₂×C₁₉	—	2	1	no	—
255	C₂×C₁₉	—	2	1	no	—
256	C₂×C₁₉	—	2	1	no	—
257	C₂×C₁₉	C₄⋊#95	1	1	yes	characteristic
258	C₂×C₁₉	#1953	1	2	yes	—
259	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	2	1	no	—
262	C₂×M₁₆	—	2	1	no	—
263	C₂×M₁₆	—	2	1	no	—
264	C₂×M₁₆	—	2	1	no	—
265	C₂×M₁₆	—	2	1	no	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂×M₁₆	—	2	1	no	—
268	C₂×M₁₆	—	2	1	no	—
269	C₂×M₁₆	—	2	1	no	—
270	C₂×M₁₆	—	19	2	no	—
271	C₂×M₁₆	—	19	2	no	—
272	C₂×M₁₆	—	19	2	no	—
273	C₂×M₁₆	—	19	2	no	—
274	C₂×M₁₆	—	19	2	no	—
275	C₂×M₁₆	—	38	1	no	—
276	C₂×M₁₆	—	38	1	no	—
277	C₂×M₁₆	—	38	1	no	—
278	C₂×M₁₆	—	38	1	no	—
279	C₂×M₁₆	—	38	1	no	—
280	C₂×M₁₆	—	38	1	no	—
281	C₂×M₁₆	—	38	1	no	—
282	C₂×M₁₆	—	38	1	no	—
283	C₂×M₁₆	—	38	1	no	—
284	C₂×M₁₆	—	38	1	no	—
285	C₂×M₁₆	—	38	1	no	—
286	C₂×M₁₆	—	38	1	no	—
287	C₂×M₁₆	—	38	1	no	—
288	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
289	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
290	C₂²×C₈	—	2	1	no	—
291	C₂²×C₈	—	2	1	no	—
292	C₂²×C₈	—	19	2	no	—
293	C₂²×C₈	—	19	2	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	2	no	—
299	C₂²×C₈	—	19	2	no	—
300	C₂²×C₈	—	38	1	no	—
301	C₂²×C₈	—	38	1	no	—
302	C₂²×C₈	—	38	1	no	—
303	#117	—	2	1	no	—
304	#117	—	2	1	no	—
305	#117	C₄×D₁₉	1	2	yes	—
306	#117	C₂²⋊D₁₉	1	2	yes	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₂²⋊C₄	Dic₃₈	1	2	yes	—
309	C₂×C₄²	—	2	1	no	—
310	#108	—	38	4	no	—
311	#108	—	38	4	no	—
312	#108	—	38	8	no	—
313	#97	—	38	4	no	—
314	C₄×C₈	—	38	4	no	—
315	C₁₉	#10873	1	1	yes	characteristic, complemented, Sylow
316	C₂⁴	C₂×Dic₃₈	1	1	yes	characteristic
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
319	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
321	C₂²×C₄	#64541	1	1	yes	characteristic
322	C₂²×C₄	#64541	1	1	yes	characteristic
323	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
324	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
325	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
326	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
327	C₂²×C₄	#64543	1	1	yes	characteristic
328	C₂²×C₄	#64543	1	1	yes	characteristic
329	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
330	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
331	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
332	M₁₆	—	2	2	no	—
333	M₁₆	—	2	2	no	—
334	M₁₆	—	2	2	no	—
335	M₁₆	—	2	2	no	—
336	M₁₆	—	4	1	no	—
337	M₁₆	—	4	1	no	—
338	M₁₆	—	4	1	no	—
339	M₁₆	—	4	1	no	—
340	M₁₆	—	19	4	no	—
341	M₁₆	—	38	2	no	—
342	M₁₆	—	38	2	no	—
343	M₁₆	—	38	2	no	—
344	M₁₆	—	38	2	no	—
345	M₁₆	—	38	2	no	—
346	M₁₆	—	38	2	no	—
347	M₁₆	—	38	2	no	—
348	M₁₆	—	76	1	no	—
349	M₁₆	—	76	1	no	—
350	M₁₆	—	76	1	no	—
351	M₁₆	—	76	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	4	1	no	—
355	C₂×C₈	—	4	1	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	—	19	4	no	—
359	C₂×C₈	—	19	2	no	—
360	C₂×C₈	—	19	2	no	—
361	C₂×C₈	—	19	2	no	—
362	C₂×C₈	—	19	2	no	—
363	C₂×C₈	—	19	4	no	—
364	C₂×C₈	—	19	4	no	—
365	C₂×C₈	—	19	2	no	—
366	C₂×C₈	—	19	2	no	—
367	C₂×C₈	—	19	4	no	—
368	C₂×C₈	—	38	2	no	—
369	C₂×C₈	—	38	2	no	—
370	C₂×C₈	—	38	2	no	—
371	C₂×C₈	—	38	2	no	—
372	C₂×C₈	—	38	2	no	—
373	C₂×C₈	—	76	1	no	—
374	C₂×C₈	—	76	1	no	—
375	C₂×C₈	—	76	1	no	—
376	C₂×C₈	—	76	1	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	Dic₁₉⋊C₄	1	4	yes	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₂³	—	4	2	no	—
384	C₂³	C₄×Dic₃₈	1	1	yes	characteristic
385	C₂³	C₄×Dic₃₈	1	1	yes	characteristic
386	C₂³	#10597324	1	1	yes	characteristic
387	C₂³	#10597324	1	1	yes	characteristic
388	C₂³	#10597334	1	1	yes	characteristic
389	C₂³	#10597334	1	1	yes	characteristic
390	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	C₄²×D₁₉	1	1	yes	characteristic
394	C₂×C₄	#10597318	1	1	yes	characteristic
395	C₂×C₄	#10597323	1	1	yes	characteristic
396	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
397	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
398	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
399	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
400	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
401	C₂×C₄	#10597330	1	1	yes	characteristic
402	C₂×C₄	#10597330	1	1	yes	characteristic
403	C₂×C₄	#10597331	1	1	yes	characteristic
404	C₂×C₄	#10597331	1	1	yes	characteristic
405	C₂×C₄	#10597333	1	1	yes	characteristic
406	C₂×C₄	#10597333	1	1	yes	characteristic
407	C₂×C₄	#10597335	1	1	yes	characteristic
408	C₂×C₄	#10597335	1	1	yes	characteristic
409	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
410	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
411	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
412	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
413	C₂×C₄	#10597342	1	1	yes	characteristic
414	C₂×C₄	#10597342	1	1	yes	characteristic
415	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
416	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
417	C₂×C₄	#10597385	1	1	yes	characteristic
418	C₂×C₄	#10597385	1	1	yes	characteristic
419	C₂×C₄	#10597386	1	1	yes	characteristic
420	C₂×C₄	#10597390	1	1	yes	characteristic
421	C₈	—	4	2	no	—
422	C₈	—	4	2	no	—
423	C₈	—	19	4	no	—
424	C₈	—	19	4	no	—
425	C₈	—	38	4	no	—
426	C₈	—	76	2	no	—
427	C₈	—	76	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	4	1	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
436	C₂²	#11926402	1	1	yes	characteristic
437	C₂²	#11926413	1	1	yes	characteristic
438	C₂²	#11926441	1	1	yes	characteristic
439	C₂²	#11926441	1	1	yes	characteristic
440	C₂²	#11926448	1	1	yes	characteristic
441	C₂²	#11926448	1	1	yes	characteristic
442	C₄	—	4	4	no	—
443	C₄	#95×D₁₉	1	1	yes	characteristic
444	C₄	#11926395	1	1	yes	characteristic
445	C₄	#11926403	1	1	yes	characteristic
446	C₄	#11926408	1	1	yes	characteristic
447	C₄	#11926439	1	1	yes	characteristic
448	C₄	#11926439	1	1	yes	characteristic
449	C₄	#11926444	1	1	yes	characteristic
450	C₄	#11926444	1	1	yes	characteristic
451	C₂	—	2	1	no	—
452	C₂	—	2	1	no	—
453	C₂	—	2	1	no	—
454	C₂	—	2	1	no	—
455	C₂	—	2	1	no	—
456	C₂	—	2	1	no	—
457	C₂	Dic₁₉⋊#95	1	1	yes	characteristic
458	C₂	#14564424	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10597330
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#344	C₂
socle	C₂²×C₁₉	#389
prime radical	C₂⁴×C₁₉	C₂×Q₈
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#344	D₁₉
hypocenter	C₁₉	#10873
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#344

Complements

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

N	H ≅ G/N	type
17. C₂×#10597279	C₄	semidirect
18. C₂×#10597279	C₄	semidirect
315. C₁₉	#10873	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#10597279	2
C₂×#11926500	2
C₂×#11926314	2
#14563362	2
#14563361	2
C₂×C₁₉×#344	2
#10873	19