Subgroups — #18084888

Order 4864.

628 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926839	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11926835	C₂	1	1	yes	maximal, characteristic
3	#14568553	C₂	1	1	yes	maximal, characteristic
4	#14564437	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926273	C₂	1	1	yes	maximal, characteristic
6	#14561519	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597315	C₂²	1	1	yes	characteristic
9	C₂×#10597392	—	2	1	no	—
10	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
11	#11926839	—	2	2	no	—
12	#11926839	—	2	2	no	—
13	#11926835	—	2	2	no	—
14	#11926835	—	2	2	no	—
15	C₂×#10597264	—	2	1	no	—
16	C₂×#10597274	—	2	1	no	—
17	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×#10597273	—	2	2	no	—
19	C₂×#10597292	—	2	1	no	—
20	C₂×#10597278	—	2	1	no	—
21	#11926466	—	2	2	no	—
22	#11926446	—	2	1	no	—
23	#11926442	—	2	1	no	—
24	#11926414	C₂²	1	1	yes	characteristic
25	#11926401	—	2	1	no	—
26	#11926273	—	2	2	no	—
27	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×Q₈⋊C₈	—	2	2	no	—
31	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×D₇₆	D₄	1	1	yes	characteristic
33	C₂²×C₄×D₁₉	—	2	1	no	—
34	C₂²×Dic₃₈	—	2	1	no	—
35	C₂²×C₈×C₁₉	—	2	1	no	—
36	C₂²×C₈×C₁₉	—	2	1	no	—
37	C₄×Q₈×C₁₉	—	2	1	no	—
38	C₄×Q₈×C₁₉	—	2	1	no	—
39	C₄×Q₈×C₁₉	—	2	1	no	—
40	C₄×Q₈×C₁₉	—	2	1	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₉	—	2	1	no	—
44	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
45	#10597392	—	4	2	no	—
46	#10597392	—	4	2	no	—
47	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
48	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
49	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
50	C₂×C₄⋊Dic₁₉	—	2	1	no	—
51	C₂×C₄⋊Dic₁₉	—	2	1	no	—
52	C₂×C₄⋊Dic₁₉	—	2	1	no	—
53	C₂×C₄⋊Dic₁₉	—	2	1	no	—
54	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
55	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
56	C₂×Dic₁₉⋊C₄	—	2	2	no	—
57	C₂²×C₁₉⋊C₈	—	2	1	no	—
58	C₄×D₇₆	—	2	1	no	—
59	C₄×D₇₆	—	2	1	no	—
60	C₄×D₇₆	—	2	1	no	—
61	C₄×D₇₆	—	2	1	no	—
62	#10597315	—	2	1	no	—
63	#10597315	—	2	1	no	—
64	#10597315	—	2	1	no	—
65	#10597315	D₄	1	2	yes	—
66	C₁₉×C₄⋊C₈	—	2	1	no	—
67	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
68	C₄×C₈×C₁₉	—	2	1	no	—
69	C₄×C₈×C₁₉	—	2	1	no	—
70	#10597292	—	2	4	no	—
71	C₁₉⋊#95	—	2	2	no	—
72	#10597278	—	2	4	no	—
73	#10597274	—	2	4	no	—
74	#10597273	—	4	4	no	—
75	#10597264	—	2	4	no	—
76	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
77	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
78	C₂³×D₁₉	—	2	1	no	—
79	C₂×Q₈×C₁₉	—	2	1	no	—
80	C₂×Q₈×C₁₉	—	2	1	no	—
81	C₂×Q₈×C₁₉	—	2	1	no	—
82	C₂×Q₈×C₁₉	—	2	1	no	—
83	C₂×Q₈×C₁₉	—	2	1	no	—
84	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	—
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	C₂×D₄	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×Dic₁₉	—	2	1	no	—
91	C₂²×Dic₁₉	—	2	2	no	—
92	C₂²×Dic₁₉	—	4	1	no	—
93	C₂×D₇₆	—	2	1	no	—
94	C₂×D₇₆	—	2	1	no	—
95	C₂×D₇₆	—	2	1	no	—
96	C₂×D₇₆	—	2	1	no	—
97	C₂×D₇₆	—	2	1	no	—
98	C₂×D₇₆	Q₁₆	1	2	yes	—
99	C₂×C₄×D₁₉	—	4	1	no	—
100	C₂×C₄×D₁₉	—	4	1	no	—
101	C₂×C₄×D₁₉	—	4	1	no	—
102	C₂×C₄×D₁₉	—	4	1	no	—
103	C₂×C₄×D₁₉	—	4	1	no	—
104	C₂×C₄×D₁₉	—	4	1	no	—
105	C₂×Dic₃₈	—	2	2	no	—
106	C₂×Dic₃₈	—	4	2	no	—
107	C₂×Dic₃₈	—	4	2	no	—
108	C₂×Dic₃₈	—	4	1	no	—
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	—	4	1	no	—
112	C₂×C₈×C₁₉	—	4	1	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₂×C₈×C₁₉	—	4	1	no	—
115	C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₄⋊C₄×C₁₉	—	2	1	no	—
117	C₄⋊C₄×C₁₉	—	4	1	no	—
118	C₄⋊C₄×C₁₉	—	4	1	no	—
119	C₄²×C₁₉	—	4	1	no	—
120	C₄²×C₁₉	—	4	1	no	—
121	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₁₉	#41	1	1	yes	characteristic
125	(C₂×D₁₉)⋊C₄	—	4	4	no	—
126	(C₂×D₁₉)⋊C₄	—	4	1	no	—
127	(C₂×D₁₉)⋊C₄	—	4	1	no	—
128	(C₂×D₁₉)⋊C₄	—	8	2	no	—
129	C₄⋊Dic₁₉	—	2	2	no	—
130	C₄⋊Dic₁₉	—	2	1	no	—
131	C₄⋊Dic₁₉	—	2	2	no	—
132	C₄⋊Dic₁₉	—	2	1	no	—
133	C₄⋊Dic₁₉	—	4	1	no	—
134	C₄⋊Dic₁₉	—	4	1	no	—
135	C₄⋊Dic₁₉	—	4	1	no	—
136	C₄⋊Dic₁₉	—	4	1	no	—
137	C₄⋊Dic₁₉	—	4	1	no	—
138	C₄⋊Dic₁₉	—	4	1	no	—
139	C₄⋊Dic₁₉	—	4	2	no	—
140	Dic₁₉⋊C₄	—	4	4	no	—
141	C₂×C₁₉⋊C₈	—	2	2	no	—
142	C₂×C₁₉⋊C₈	—	4	1	no	—
143	C₂×C₁₉⋊C₈	—	4	1	no	—
144	#10236	—	19	1	no	maximal, Sylow
145	C₂³×C₁₉	#120	1	1	yes	characteristic
146	C₂²×D₁₉	—	2	2	no	—
147	C₂²×D₁₉	—	4	1	no	—
148	C₂²×D₁₉	—	4	1	no	—
149	C₂²×D₁₉	—	4	1	no	—
150	C₂²×D₁₉	—	4	1	no	—
151	C₂²×D₁₉	—	4	1	no	—
152	C₂²×D₁₉	—	4	1	no	—
153	Q₈×C₁₉	—	2	2	no	—
154	Q₈×C₁₉	—	2	2	no	—
155	Q₈×C₁₉	—	4	1	no	—
156	Q₈×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
175	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
179	C₂×Dic₁₉	—	4	2	no	—
180	C₂×Dic₁₉	—	4	1	no	—
181	C₂×Dic₁₉	—	4	1	no	—
182	C₂×Dic₁₉	—	4	2	no	—
183	C₂×Dic₁₉	—	4	2	no	—
184	C₂×Dic₁₉	—	4	1	no	—
185	C₂×Dic₁₉	—	4	2	no	—
186	C₂×Dic₁₉	—	8	1	no	—
187	C₂×Dic₁₉	—	8	1	no	—
188	D₇₆	—	2	2	no	—
189	D₇₆	—	2	2	no	—
190	D₇₆	—	4	1	no	—
191	D₇₆	—	4	1	no	—
192	C₄×D₁₉	—	8	1	no	—
193	C₄×D₁₉	—	8	1	no	—
194	C₄×D₁₉	—	8	1	no	—
195	C₄×D₁₉	—	8	1	no	—
196	Dic₃₈	—	4	4	no	—
197	Dic₃₈	—	8	2	no	—
198	C₈×C₁₉	—	4	2	no	—
199	C₈×C₁₉	—	4	2	no	—
200	C₁₉⋊C₈	—	4	2	no	—
201	C₂×#477	—	19	1	no	—
202	C₂×#476	—	19	1	no	—
203	#2538	—	19	1	no	—
204	#1956	—	19	1	no	—
205	C₂×Q₈⋊C₈	D₁₉	1	1	yes	characteristic, complemented
206	C₂×D₄⋊C₈	—	19	1	no	—
207	#1296	—	19	1	no	—
208	C₂²×C₁₉	#392	1	1	yes	characteristic
209	C₂²×C₁₉	#450	1	1	yes	characteristic
210	C₂²×C₁₉	#451	1	1	yes	characteristic
211	C₂²×C₁₉	#452	1	1	yes	characteristic
212	C₂²×C₁₉	#452	1	1	yes	characteristic
213	C₂²×C₁₉	#453	1	1	yes	characteristic
214	C₂²×C₁₉	#454	1	1	yes	characteristic
215	C₂×D₁₉	—	4	2	no	—
216	C₂×D₁₉	—	4	2	no	—
217	C₂×D₁₉	—	4	2	no	—
218	C₂×D₁₉	—	8	1	no	—
219	C₂×D₁₉	—	8	1	no	—
220	C₂×D₁₉	—	8	1	no	—
221	C₂×D₁₉	—	8	1	no	—
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	—	2	1	no	—
224	C₄×C₁₉	—	4	2	no	—
225	C₄×C₁₉	—	8	1	no	—
226	C₄×C₁₉	#448	1	1	yes	characteristic
227	C₄×C₁₉	#449	1	1	yes	characteristic
228	C₄×C₁₉	#451	1	1	yes	characteristic
229	C₄×C₁₉	#452	1	1	yes	characteristic
230	C₄×C₁₉	#465	1	1	yes	characteristic
231	C₄×C₁₉	#467	1	1	yes	characteristic
232	C₄×C₁₉	#468	1	1	yes	characteristic
233	C₄×C₁₉	#470	1	1	yes	characteristic
234	Dic₁₉	—	8	2	no	—
235	Dic₁₉	—	8	1	no	—
236	Dic₁₉	—	8	2	no	—
237	C₂×C₄⋊Q₈	—	19	1	no	—
238	C₂×C₂²⋊Q₈	—	38	1	no	—
239	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
240	C₂×C₄×D₄	—	19	1	no	—
241	#477	—	38	2	no	—
242	#477	—	38	2	no	—
243	#476	—	38	2	no	—
244	#476	—	38	2	no	—
245	C₂×#107	—	38	1	no	—
246	C₂×#106	—	38	1	no	—
247	C₂×C₄⋊C₈	—	19	1	no	—
248	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
249	C₂×#103	—	38	1	no	—
250	C₂×#103	—	38	2	no	—
251	C₂×#102	—	38	1	no	—
252	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
253	#396	—	38	2	no	—
254	#390	—	38	1	no	—
255	#389	—	38	1	no	—
256	#384	—	19	1	no	—
257	#380	—	38	1	no	—
258	Q₈⋊C₈	—	2	2	no	—
259	D₄⋊C₈	—	38	2	no	—
260	C₂×C₁₉	#1631	1	1	yes	characteristic
261	C₂×C₁₉	#1632	1	1	yes	characteristic
262	C₂×C₁₉	#1637	1	1	yes	characteristic
263	C₂×C₁₉	#1638	1	1	yes	characteristic
264	C₂×C₁₉	#2000	1	1	yes	characteristic
265	C₂×C₁₉	#2001	1	1	yes	characteristic
266	C₂×C₁₉	#2006	1	1	yes	characteristic
267	D₁₉	—	8	2	no	—
268	C₂²×Q₈	—	38	1	no	—
269	C₂²×Q₈	D₇₆	1	1	yes	characteristic
270	C₂²×D₄	—	19	1	no	—
271	C₂³×C₄	—	38	1	no	—
272	C₂²×C₈	—	2	1	no	—
273	C₂²×C₈	—	2	1	no	—
274	C₂²×C₈	—	38	1	no	—
275	C₄⋊Q₈	—	19	2	no	—
276	C₄⋊Q₈	—	38	1	no	—
277	C₄⋊Q₈	—	38	1	no	—
278	C₄⋊Q₈	—	38	1	no	—
279	C₂²⋊Q₈	—	76	2	no	—
280	C₂²⋊Q₈	—	76	2	no	—
281	C₄×Q₈	—	2	1	no	—
282	C₄×Q₈	—	2	1	no	—
283	C₄×Q₈	—	2	1	no	—
284	C₄×Q₈	—	2	1	no	—
285	C₄×D₄	—	38	1	no	—
286	C₄×D₄	—	38	1	no	—
287	C₄×D₄	—	38	1	no	—
288	C₄×D₄	—	38	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	19	1	no	—
291	C₂×C₄⋊C₄	—	19	2	no	—
292	C₂×C₄⋊C₄	—	38	1	no	—
293	C₂×C₄⋊C₄	—	38	1	no	—
294	C₂×C₄⋊C₄	—	38	2	no	—
295	C₂×C₄⋊C₄	—	38	1	no	—
296	C₂×C₄⋊C₄	—	38	1	no	—
297	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	—	38	2	no	—
299	C₂×C₂²⋊C₄	—	38	1	no	—
300	C₂×C₂²⋊C₄	—	38	2	no	—
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
303	#107	—	38	4	no	—
304	#106	—	38	4	no	—
305	C₄⋊C₈	—	2	1	no	—
306	C₄⋊C₈	—	19	2	no	—
307	C₄⋊C₈	—	38	1	no	—
308	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
309	#103	—	38	4	no	—
310	#103	—	76	4	no	—
311	#102	—	38	4	no	—
312	C₄×C₈	—	2	1	no	—
313	C₄×C₈	—	2	1	no	—
314	#95	—	38	2	no	—
315	C₁₉	#10236	1	1	yes	characteristic, complemented, Sylow
316	C₂⁴	—	38	1	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	38	2	no	—
323	C₂×Q₈	—	76	2	no	—
324	C₂×Q₈	—	76	2	no	—
325	C₂×Q₈	—	76	1	no	—
326	C₂×Q₈	#64516	1	2	yes	—
327	C₂×D₄	—	19	2	no	—
328	C₂×D₄	—	38	1	no	—
329	C₂×D₄	—	38	1	no	—
330	C₂×D₄	—	38	1	no	—
331	C₂×D₄	—	38	1	no	—
332	C₂×D₄	—	38	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	38	1	no	—
336	C₂²×C₄	—	38	2	no	—
337	C₂²×C₄	—	76	1	no	—
338	C₂²×C₄	—	76	1	no	—
339	C₂²×C₄	—	76	1	no	—
340	C₂²×C₄	—	76	1	no	—
341	C₂²×C₄	—	76	1	no	—
342	C₂²×C₄	—	76	1	no	—
343	C₂²×C₄	—	76	1	no	—
344	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
345	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
346	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	4	1	no	—
352	C₂×C₈	—	4	1	no	—
353	C₂×C₈	—	38	2	no	—
354	C₂×C₈	—	76	1	no	—
355	C₂×C₈	—	76	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	4	1	no	—
359	C₄⋊C₄	—	4	1	no	—
360	C₄⋊C₄	—	38	2	no	—
361	C₄⋊C₄	—	38	1	no	—
362	C₄⋊C₄	—	38	2	no	—
363	C₄⋊C₄	—	38	1	no	—
364	C₄⋊C₄	—	76	2	no	—
365	C₄⋊C₄	—	76	4	no	—
366	C₄⋊C₄	—	76	1	no	—
367	C₄⋊C₄	—	76	1	no	—
368	C₄⋊C₄	—	76	1	no	—
369	C₄⋊C₄	—	76	1	no	—
370	C₄⋊C₄	—	76	1	no	—
371	C₄⋊C₄	—	76	1	no	—
372	C₂²⋊C₄	—	76	4	no	—
373	C₂²⋊C₄	—	76	1	no	—
374	C₂²⋊C₄	—	76	1	no	—
375	C₂²⋊C₄	—	152	2	no	—
376	C₄²	—	4	1	no	—
377	C₄²	—	4	1	no	—
378	C₄²	#64541	1	1	yes	characteristic
379	C₄²	D₄×D₁₉	1	1	yes	characteristic
380	C₄²	D₄×D₁₉	1	1	yes	characteristic
381	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
382	C₂³	—	38	2	no	—
383	C₂³	—	76	1	no	—
384	C₂³	—	76	1	no	—
385	C₂³	—	76	1	no	—
386	C₂³	—	76	1	no	—
387	C₂³	—	76	1	no	—
388	C₂³	—	76	1	no	—
389	C₂³	#10597328	1	1	yes	characteristic
390	Q₈	—	2	2	no	—
391	Q₈	—	2	2	no	—
392	Q₈	—	4	1	no	—
393	Q₈	—	4	1	no	—
394	Q₈	—	76	4	no	—
395	Q₈	—	152	2	no	—
396	D₄	—	38	2	no	—
397	D₄	—	38	2	no	—
398	D₄	—	76	1	no	—
399	D₄	—	76	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	76	2	no	—
409	C₂×C₄	—	76	1	no	—
410	C₂×C₄	—	76	1	no	—
411	C₂×C₄	—	76	1	no	—
412	C₂×C₄	—	76	2	no	—
413	C₂×C₄	—	76	2	no	—
414	C₂×C₄	—	76	2	no	—
415	C₂×C₄	—	152	1	no	—
416	C₂×C₄	—	152	1	no	—
417	C₂×C₄	—	152	1	no	—
418	C₂×C₄	—	152	1	no	—
419	C₂×C₄	—	152	1	no	—
420	C₂×C₄	—	152	1	no	—
421	C₂×C₄	#10597328	1	1	yes	characteristic
422	C₂×C₄	#10597330	1	1	yes	characteristic
423	C₂×C₄	#10597330	1	1	yes	characteristic
424	C₂×C₄	C₂×#64516	1	1	yes	characteristic
425	C₂×C₄	#10597350	1	1	yes	characteristic
426	C₂×C₄	#10597354	1	1	yes	characteristic
427	C₂×C₄	#10597355	1	1	yes	characteristic
428	C₂×C₄	#10597361	1	1	yes	characteristic
429	C₂×C₄	#10597362	1	1	yes	characteristic
430	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
431	C₂×C₄	#10597364	1	1	yes	characteristic
432	C₂×C₄	#10597376	1	1	yes	characteristic
433	C₂×C₄	#10597383	1	1	yes	characteristic
434	C₂×C₄	#10597386	1	1	yes	characteristic
435	C₈	—	4	2	no	—
436	C₈	—	4	2	no	—
437	C₈	—	76	2	no	—
438	C₂²	—	76	2	no	—
439	C₂²	—	76	2	no	—
440	C₂²	—	76	2	no	—
441	C₂²	—	152	1	no	—
442	C₂²	—	152	1	no	—
443	C₂²	—	152	1	no	—
444	C₂²	—	152	1	no	—
445	C₂²	#11926453	1	1	yes	characteristic
446	C₂²	#11926697	1	1	yes	characteristic
447	C₂²	#11926701	1	1	yes	characteristic
448	C₂²	#11926708	1	1	yes	characteristic
449	C₂²	#11926709	1	1	yes	characteristic
450	C₂²	#11926713	1	1	yes	characteristic
451	C₂²	#11926718	1	1	yes	characteristic
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	4	2	no	—
455	C₄	—	8	1	no	—
456	C₄	—	152	1	no	—
457	C₄	—	152	2	no	—
458	C₄	—	152	2	no	—
459	C₄	#11926685	1	1	yes	characteristic
460	C₄	#11926691	1	1	yes	characteristic
461	C₄	#11926698	1	1	yes	characteristic
462	C₄	#11926703	1	1	yes	characteristic
463	C₄	#11926773	1	1	yes	characteristic
464	C₄	#11926784	1	1	yes	characteristic
465	C₄	#11926790	1	1	yes	characteristic
466	C₄	#11926801	1	1	yes	characteristic
467	C₂	—	152	2	no	—
468	C₂	#14562764	1	1	yes	characteristic
469	C₂	#14562772	1	1	yes	characteristic
470	C₂	#14562802	1	1	yes	characteristic
471	C₂	#14562810	1	1	yes	characteristic
472	C₂	#14564640	1	1	yes	characteristic
473	C₂	#14564644	1	1	yes	characteristic
474	C₂	#14564678	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597328
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×Q₈⋊C₈	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂²×D₇₆	D₄
hypercenter	C₂×Q₈⋊C₈	D₁₉
hypocenter	C₁₉	#10236
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#11926839	C₂	semidirect
4. #14564437	C₂	semidirect
6. #14561519	C₂	semidirect
7. C₂×C₁₉×Q₈⋊C₈	C₂	semidirect
205. C₂×Q₈⋊C₈	D₁₉	semidirect
315. C₁₉	#10236	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926839	2
C₂×#11926835	2
#14568553	2
#14564437	2
C₂×#11926273	2
#14561519	2
C₂×C₁₉×Q₈⋊C₈	2
#10236	19