Subgroups — #18087899

Order 4864.

1190 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11927311	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926511	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926314	C₂	1	2	yes	maximal, complemented
4	#14563332	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#410	C₂	1	1	yes	maximal, characteristic
6	#11927311	—	2	4	no	—
7	#11927311	—	2	2	no	—
8	#11927311	C₄	1	4	yes	complemented
9	C₂×#10597394	—	2	4	no	—
10	C₂²×#64520	—	2	2	no	—
11	C₂²×#64520	C₂²	1	1	yes	characteristic
12	C₂²×#64520	C₂²	1	2	yes	—
13	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	#11926511	—	2	2	no	—
15	#11926511	C₄	1	4	yes	complemented
16	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
17	#11926314	—	2	4	no	—
18	#11926299	—	2	4	no	—
19	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#117	C₂²	1	2	yes	—
21	C₁₉×#410	—	2	2	no	—
22	C₁₉×#410	—	2	2	no	—
23	C₂×C₁₉×#99	C₄	1	4	yes	—
24	C₂×#41×C₁₉	—	2	2	no	—
25	C₂×#41×C₁₉	—	2	2	no	—
26	C₂×#41×C₁₉	—	2	2	no	—
27	C₂×#41×C₁₉	—	2	2	no	—
28	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
29	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
30	C₂×#41×C₁₉	D₄	1	2	yes	—
31	C₂×#41×C₁₉	D₄	1	2	yes	—
32	C₂²×Q₈×C₁₉	Q₈	1	1	yes	characteristic
33	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
34	C₂²×D₄×C₁₉	Q₈	1	1	yes	characteristic
35	C₂³×C₄×C₁₉	D₄	1	2	yes	—
36	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
37	C₁₉×#117	—	2	2	no	—
38	C₁₉×#117	—	2	2	no	—
39	C₁₉×#117	—	2	2	no	—
40	C₁₉×#117	—	2	2	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
42	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
43	C₂×C₄²×C₁₉	—	2	2	no	—
44	#10597394	—	2	16	no	—
45	#10597394	—	2	16	no	—
46	C₂×#64520	—	2	4	no	—
47	C₂×#64520	—	2	8	no	—
48	C₂×#64520	—	2	8	no	—
49	C₂×#64520	—	2	2	no	—
50	C₂×#64520	—	2	2	no	—
51	C₂×#64520	—	2	2	no	—
52	C₂×#64520	—	2	2	no	—
53	C₂×#64520	—	2	1	no	—
54	C₂×#64520	—	2	2	no	—
55	C₂×#64520	—	2	2	no	—
56	C₂×#64520	C₂×C₄	1	2	yes	—
57	C₂×#64520	C₂×C₄	1	4	yes	—
58	C₂×#64520	D₄	1	4	yes	—
59	C₂²×C₁₉⋊C₈	—	2	4	no	—
60	C₂²×C₁₉⋊C₈	—	2	2	no	—
61	C₂²×C₁₉⋊C₈	—	2	1	no	—
62	C₂²×C₁₉⋊C₈	—	2	1	no	—
63	C₂²×C₁₉⋊C₈	—	2	1	no	—
64	C₂²×C₁₉⋊C₈	—	2	2	no	—
65	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
66	C₂²×C₁₉⋊C₈	D₄	1	4	yes	—
67	C₁₉×#99	—	2	8	no	—
68	C₂²⋊(C₁₉⋊C₈)	—	2	8	no	—
69	C₂⁴×C₁₉	C₄⋊C₄	1	2	yes	—
70	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
71	#41×C₁₉	—	2	4	no	—
72	#41×C₁₉	—	2	4	no	—
73	#41×C₁₉	—	2	4	no	—
74	#41×C₁₉	—	2	4	no	—
75	#41×C₁₉	—	2	4	no	—
76	#41×C₁₉	—	2	4	no	—
77	#41×C₁₉	—	2	4	no	—
78	#41×C₁₉	—	2	4	no	—
79	C₂×Q₈×C₁₉	—	2	2	no	—
80	C₂×Q₈×C₁₉	—	2	2	no	—
81	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
82	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
83	C₂×D₄×C₁₉	—	2	4	no	—
84	C₂×D₄×C₁₉	—	2	4	no	—
85	C₂×D₄×C₁₉	—	2	2	no	—
86	C₂×D₄×C₁₉	—	2	2	no	—
87	C₂×D₄×C₁₉	C₄²	1	4	yes	—
88	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
89	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
90	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	4	no	—
96	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
97	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
98	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
99	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	#41	1	2	yes	—
108	C₂²×C₄×C₁₉	#41	1	2	yes	—
109	C₄⋊C₄×C₁₉	—	4	2	no	—
110	C₄⋊C₄×C₁₉	—	4	2	no	—
111	C₂²⋊C₄×C₁₉	—	2	4	no	—
112	C₂²⋊C₄×C₁₉	—	2	4	no	—
113	C₄²×C₁₉	—	4	2	no	—
114	C₄²×C₁₉	—	4	2	no	—
115	#64520	—	2	16	no	—
116	#64520	—	2	4	no	—
117	#64520	—	2	4	no	—
118	#64520	—	2	4	no	—
119	#64520	—	2	4	no	—
120	#64520	—	2	4	no	—
121	#64520	—	4	2	no	—
122	C₂×C₁₉⋊C₈	—	2	16	no	—
123	C₂×C₁₉⋊C₈	—	2	4	no	—
124	C₂×C₁₉⋊C₈	—	2	4	no	—
125	C₂×C₁₉⋊C₈	—	2	2	no	—
126	C₂×C₁₉⋊C₈	—	2	2	no	—
127	C₂×C₁₉⋊C₈	—	2	4	no	—
128	C₂×C₁₉⋊C₈	—	4	1	no	—
129	C₂×C₁₉⋊C₈	—	4	1	no	—
130	C₂×C₁₉⋊C₈	—	4	2	no	—
131	C₂×C₁₉⋊C₈	—	4	1	no	—
132	C₂×C₁₉⋊C₈	—	4	1	no	—
133	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	8	yes	—
134	#10748	—	19	1	no	maximal, Sylow
135	C₂³×C₁₉	—	2	2	no	—
136	C₂³×C₁₉	—	2	2	no	—
137	C₂³×C₁₉	—	4	2	no	—
138	C₂³×C₁₉	—	4	4	no	—
139	C₂³×C₁₉	#95	1	4	yes	—
140	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
141	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂³×C₁₉	C₄×D₄	1	2	yes	—
144	C₂³×C₁₉	C₄×D₄	1	2	yes	—
145	Q₈×C₁₉	—	2	4	no	—
146	Q₈×C₁₉	—	2	4	no	—
147	D₄×C₁₉	—	2	8	no	—
148	D₄×C₁₉	—	2	8	no	—
149	D₄×C₁₉	—	2	4	no	—
150	D₄×C₁₉	—	2	4	no	—
151	C₂×C₄×C₁₉	—	2	2	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	4	no	—
154	C₂×C₄×C₁₉	—	2	4	no	—
155	C₂×C₄×C₁₉	—	2	4	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	4	8	no	—
158	C₂×C₄×C₁₉	—	4	4	no	—
159	C₂×C₄×C₁₉	#95	1	4	yes	—
160	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#117	1	2	yes	—
166	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
168	C₂×C₄×C₁₉	#120	1	2	yes	—
169	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#121	1	2	yes	—
172	C₂×C₄×C₁₉	#121	1	2	yes	—
173	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
174	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
175	C₂×C₄×C₁₉	#123	1	2	yes	—
176	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
178	C₁₉⋊C₈	—	2	8	no	—
179	C₁₉⋊C₈	—	4	2	no	—
180	C₁₉⋊C₈	—	4	2	no	—
181	C₂×#568	—	19	1	no	—
182	C₂×#410	D₁₉	1	1	yes	characteristic
183	C₂×#408	—	19	1	no	—
184	C₂×#344	—	19	2	no	—
185	#1729	—	19	2	no	—
186	C₂²×C₁₉	—	2	4	no	—
187	C₂²×C₁₉	—	2	2	no	—
188	C₂²×C₁₉	—	2	4	no	—
189	C₂²×C₁₉	—	4	1	no	—
190	C₂²×C₁₉	—	4	1	no	—
191	C₂²×C₁₉	—	4	2	no	—
192	C₂²×C₁₉	—	4	4	no	—
193	C₂²×C₁₉	—	4	4	no	—
194	C₂²×C₁₉	—	8	2	no	—
195	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
196	C₂²×C₁₉	C₄×C₂²⋊C₄	1	2	yes	—
197	C₂²×C₁₉	#385	1	1	yes	characteristic
198	C₂²×C₁₉	#385	1	1	yes	characteristic
199	C₂²×C₁₉	#386	1	2	yes	—
200	C₄×C₁₉	—	2	4	no	—
201	C₄×C₁₉	—	8	4	no	—
202	C₄×C₁₉	#379	1	1	yes	characteristic
203	C₄×C₁₉	#380	1	2	yes	—
204	C₄×C₁₉	#381	1	1	yes	characteristic
205	C₄×C₁₉	#385	1	2	yes	—
206	C₄×C₁₉	#386	1	1	yes	characteristic
207	C₄×C₁₉	#386	1	1	yes	characteristic
208	C₂²×#41	C₂×D₁₉	1	1	yes	characteristic
209	#568	—	19	4	no	—
210	#568	—	38	4	no	—
211	#568	—	38	2	no	—
212	C₂×#131	—	38	4	no	—
213	C₂²×M₁₆	—	19	2	no	—
214	C₂²×M₁₆	—	19	1	no	—
215	C₂²×M₁₆	—	38	2	no	—
216	C₂³×C₈	—	19	1	no	—
217	C₂×#117	C₂×D₁₉	1	2	yes	—
218	#410	—	2	2	no	—
219	#410	—	2	2	no	—
220	C₂×#99	Dic₁₉	1	4	yes	—
221	#408	—	19	4	no	—
222	#408	—	38	2	no	—
223	C₂×C₂²⋊C₈	—	38	2	no	—
224	#344	—	38	4	no	—
225	#336	—	38	4	no	—
226	C₂×C₁₉	—	2	2	no	—
227	C₂×C₁₉	—	2	1	no	—
228	C₂×C₁₉	—	2	1	no	—
229	C₂×C₁₉	—	2	2	no	—
230	C₂×C₁₉	—	4	4	no	—
231	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
232	C₂×C₁₉	#1868	1	2	yes	—
233	C₂×#41	—	2	2	no	—
234	C₂×#41	—	2	2	no	—
235	C₂×#41	—	2	2	no	—
236	C₂×#41	—	2	2	no	—
237	C₂×#41	C₄×D₁₉	1	2	yes	—
238	C₂×#41	C₄×D₁₉	1	2	yes	—
239	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
240	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
241	C₂²×Q₈	Dic₃₈	1	1	yes	characteristic
242	C₂²×D₄	Dic₃₈	1	1	yes	characteristic
243	C₂²×D₄	C₂×Dic₁₉	1	2	yes	—
244	C₂³×C₄	D₇₆	1	2	yes	—
245	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
246	#131	—	38	16	no	—
247	#131	—	38	16	no	—
248	C₂×M₁₆	—	19	4	no	—
249	C₂×M₁₆	—	19	4	no	—
250	C₂×M₁₆	—	19	2	no	—
251	C₂×M₁₆	—	38	4	no	—
252	C₂×M₁₆	—	38	8	no	—
253	C₂×M₁₆	—	38	8	no	—
254	C₂×M₁₆	—	38	2	no	—
255	C₂×M₁₆	—	38	2	no	—
256	C₂×M₁₆	—	38	2	no	—
257	C₂×M₁₆	—	38	2	no	—
258	C₂×M₁₆	—	38	1	no	—
259	C₂×M₁₆	—	38	2	no	—
260	C₂×M₁₆	—	38	2	no	—
261	C₂²×C₈	—	19	4	no	—
262	C₂²×C₈	—	19	2	no	—
263	C₂²×C₈	—	38	4	no	—
264	C₂²×C₈	—	38	1	no	—
265	C₂²×C₈	—	38	1	no	—
266	C₂²×C₈	—	38	2	no	—
267	C₂²×C₈	—	38	2	no	—
268	C₂²×C₈	—	38	1	no	—
269	#117	—	2	2	no	—
270	#117	—	2	2	no	—
271	#117	—	2	2	no	—
272	#117	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	4	yes	—
275	C₂×C₄²	—	2	2	no	—
276	#99	—	2	8	no	—
277	C₂²⋊C₈	—	38	8	no	—
278	C₁₉	#10748	1	1	yes	characteristic, complemented, Sylow
279	C₂⁴	C₄⋊Dic₁₉	1	2	yes	—
280	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
281	#41	—	2	4	no	—
282	#41	—	2	4	no	—
283	#41	—	2	4	no	—
284	#41	—	2	4	no	—
285	#41	—	2	4	no	—
286	#41	—	2	4	no	—
287	#41	—	2	4	no	—
288	#41	—	2	4	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	Dic₁₉⋊C₄	1	2	yes	—
292	C₂×Q₈	Dic₁₉⋊C₄	1	2	yes	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	2	4	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	C₄×Dic₁₉	1	4	yes	—
298	C₂×D₄	Dic₁₉⋊C₄	1	2	yes	—
299	C₂×D₄	Dic₁₉⋊C₄	1	2	yes	—
300	C₂×D₄	C₂²⋊Dic₁₉	1	4	yes	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	C₄⋊Dic₁₉	1	2	yes	—
307	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
308	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
309	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
313	C₂²×C₄	D₄×D₁₉	1	2	yes	—
314	C₂²×C₄	D₄×D₁₉	1	2	yes	—
315	C₂²×C₄	#64543	1	2	yes	—
316	C₂²×C₄	#64543	1	2	yes	—
317	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
318	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
319	M₁₆	—	38	16	no	—
320	M₁₆	—	38	4	no	—
321	M₁₆	—	38	4	no	—
322	M₁₆	—	38	4	no	—
323	M₁₆	—	38	4	no	—
324	M₁₆	—	38	4	no	—
325	M₁₆	—	76	2	no	—
326	C₂×C₈	—	19	8	no	—
327	C₂×C₈	—	38	16	no	—
328	C₂×C₈	—	38	4	no	—
329	C₂×C₈	—	38	4	no	—
330	C₂×C₈	—	38	4	no	—
331	C₂×C₈	—	38	2	no	—
332	C₂×C₈	—	38	2	no	—
333	C₂×C₈	—	76	2	no	—
334	C₂×C₈	—	76	1	no	—
335	C₂×C₈	—	76	1	no	—
336	C₂×C₈	—	76	1	no	—
337	C₂×C₈	—	76	1	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	—	4	2	no	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₄²	—	4	2	no	—
343	C₄²	—	4	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	4	no	—
348	C₂³	C₁₉⋊#95	1	4	yes	—
349	C₂³	C₂×C₄×Dic₁₉	1	1	yes	characteristic
350	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
351	C₂³	D₄×Dic₁₉	1	2	yes	—
352	C₂³	D₄×Dic₁₉	1	2	yes	—
353	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
354	Q₈	—	2	4	no	—
355	Q₈	—	2	4	no	—
356	D₄	—	2	8	no	—
357	D₄	—	2	8	no	—
358	D₄	—	2	4	no	—
359	D₄	—	2	4	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	4	8	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	C₁₉⋊#95	1	4	yes	—
369	C₂×C₄	#10597323	1	2	yes	—
370	C₂×C₄	#10597324	1	2	yes	—
371	C₂×C₄	#10597324	1	2	yes	—
372	C₂×C₄	C₂²⋊C₄×D₁₉	1	2	yes	—
373	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
374	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
375	C₂×C₄	#10597328	1	1	yes	characteristic
376	C₂×C₄	#10597328	1	1	yes	characteristic
377	C₂×C₄	#10597332	1	1	yes	characteristic
378	C₂×C₄	#10597332	1	1	yes	characteristic
379	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
380	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
381	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
382	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
383	C₂×C₄	#10597381	1	2	yes	—
384	C₂×C₄	#10597383	1	2	yes	—
385	C₂×C₄	#10597385	1	2	yes	—
386	C₂×C₄	#10597385	1	2	yes	—
387	C₈	—	38	8	no	—
388	C₈	—	76	2	no	—
389	C₈	—	76	2	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	4	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	4	4	no	—
398	C₂²	—	8	2	no	—
399	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
400	C₂²	C₂²⋊C₄×Dic₁₉	1	2	yes	—
401	C₂²	#11926419	1	1	yes	characteristic
402	C₂²	#11926419	1	1	yes	characteristic
403	C₂²	#11926424	1	2	yes	—
404	C₄	—	2	4	no	—
405	C₄	—	8	4	no	—
406	C₄	#11926399	1	1	yes	characteristic
407	C₄	#11926402	1	2	yes	—
408	C₄	#11926405	1	1	yes	characteristic
409	C₄	#11926416	1	2	yes	—
410	C₄	#11926421	1	1	yes	characteristic
411	C₄	#11926421	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	2	1	no	—
414	C₂	—	2	1	no	—
415	C₂	—	2	2	no	—
416	C₂	—	4	4	no	—
417	C₂	#14561857	1	1	yes	characteristic
418	C₂	#14563923	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10597328
commutator	C₂³×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#410	C₂
socle	C₂²×C₁₉	#385
prime radical	C₂²×#41×C₁₉	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#410	D₁₉
hypocenter	C₁₉	#10748
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#410

Complements

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

N	H ≅ G/N	type
3. C₂×#11926314	C₂	semidirect
4. #14563332	C₂	semidirect
8. #11927311	C₄	semidirect
15. #11926511	C₄	semidirect
278. C₁₉	#10748	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11927311	2
C₂×#11926511	2
C₂×#11926314	2
#14563332	2
C₂×C₁₉×#410	2
#10748	19