Subgroups — #14577296

Order 2432.

1658 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597435	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#64541	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927215	C₂	1	2	yes	maximal, complemented
4	#11927203	C₂	1	2	yes	maximal, complemented
5	#11927190	C₂	1	2	yes	maximal, complemented
6	#11927186	C₂	1	4	yes	maximal, complemented
7	D₄×D₇₆	C₂	1	2	yes	maximal, complemented
8	#11927176	C₂	1	4	yes	maximal, complemented
9	#11927124	C₂	1	2	yes	maximal, complemented
10	#11927122	C₂	1	1	yes	maximal, characteristic, complemented
11	#11927113	C₂	1	1	yes	maximal, characteristic, complemented
12	#11927110	C₂	1	2	yes	maximal, complemented
13	#11927057	C₂	1	2	yes	maximal, complemented
14	C₂×#10597376	C₂	1	1	yes	maximal, characteristic, complemented
15	#121×D₁₉	C₂	1	2	yes	maximal, complemented
16	#11927024	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₉×#525	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
21	C₂²×C₂²⋊D₁₉	C₂²	1	2	yes	complemented
22	#10597435	—	2	8	no	—
23	C₂×#64545	C₂²	1	2	yes	complemented
24	C₂×D₄×D₁₉	C₂²	1	2	yes	complemented
25	C₂×D₄×D₁₉	C₂²	1	4	yes	complemented
26	C₂×D₄×D₁₉	C₂²	1	4	yes	complemented
27	C₂×#64541	—	2	8	no	—
28	C₂×#64541	C₂²	1	1	yes	characteristic
29	C₂×#64541	C₂²	1	2	yes	complemented
30	C₂×#64541	C₂²	1	1	yes	characteristic, complemented
31	C₂×#64541	C₂²	1	2	yes	complemented
32	C₂×#64541	C₂²	1	1	yes	characteristic, complemented
33	C₂×#64541	C₂²	1	1	yes	characteristic, complemented
34	C₂×#64541	C₂²	1	2	yes	complemented
35	C₂²×D₇₆	C₂²	1	1	yes	characteristic, complemented
36	C₂²×D₇₆	C₂²	1	1	yes	characteristic, complemented
37	C₂²×D₇₆	C₂²	1	2	yes	complemented
38	C₂²×C₄×D₁₉	C₂²	1	2	yes	complemented
39	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#123	C₂²	1	2	yes	complemented
41	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
44	C₁₉×#121	C₂²	1	1	yes	characteristic, complemented
45	C₁₉×#120	C₂²	1	2	yes	complemented
46	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
47	C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
48	C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
49	#10597392	C₂²	1	2	yes	complemented
50	#10597386	C₂²	1	4	yes	complemented
51	#10597385	C₂²	1	4	yes	complemented
52	#10597385	C₂²	1	4	yes	complemented
53	#10597384	C₂²	1	2	yes	complemented
54	#10597383	C₂²	1	4	yes	complemented
55	#10597376	C₂²	1	2	yes	complemented
56	#10597376	C₂²	1	2	yes	complemented
57	#10597376	C₂²	1	2	yes	complemented
58	#10597376	C₂²	1	2	yes	complemented
59	#10597376	C₂²	1	2	yes	complemented
60	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	complemented
61	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic, complemented
62	#10597370	C₂²	1	2	yes	complemented
63	#10597342	C₂²	1	4	yes	complemented
64	#10597341	C₂²	1	2	yes	complemented
65	#10597341	C₂²	1	2	yes	complemented
66	#10597341	C₂²	1	4	yes	complemented
67	#10597340	C₂²	1	4	yes	complemented
68	#10597339	C₂²	1	4	yes	complemented
69	#10597338	C₂²	1	2	yes	complemented
70	C₄⋊C₄×D₁₉	C₂²	1	2	yes	complemented
71	#10597331	C₂²	1	4	yes	complemented
72	#10597330	C₂²	1	4	yes	complemented
73	#10597330	C₂²	1	4	yes	complemented
74	#10597330	C₂²	1	4	yes	complemented
75	#10597328	C₂²	1	4	yes	complemented
76	#10597328	C₂²	1	4	yes	complemented
77	#10597328	C₂²	1	4	yes	complemented
78	(C₂²⋊D₁₉)⋊C₄	C₂²	1	4	yes	complemented
79	(C₂²⋊D₁₉)⋊C₄	C₂²	1	4	yes	complemented
80	C₂²⋊C₄×D₁₉	C₂²	1	4	yes	complemented
81	#10597321	C₂²	1	2	yes	complemented
82	#10597320	C₂²	1	2	yes	complemented
83	C₄×D₇₆	C₂²	1	2	yes	complemented
84	C₄×Dic₃₈	C₂²	1	2	yes	complemented
85	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
86	C₂³×D₁₉	C₂³	1	2	yes	—
87	C₂³×D₁₉	C₂³	1	4	yes	—
88	C₂³×D₁₉	C₂³	1	2	yes	—
89	#41×C₁₉	—	2	4	no	—
90	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×D₄×C₁₉	C₂³	1	2	yes	—
93	C₂×D₄×C₁₉	C₂³	1	2	yes	—
94	C₂×D₄×C₁₉	C₂³	1	2	yes	—
95	C₂²×C₄×C₁₉	—	2	4	no	—
96	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
101	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
103	C₂×C₂²⋊D₁₉	—	2	8	no	—
104	C₂×C₂²⋊D₁₉	—	4	4	no	—
105	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
106	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
107	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
108	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
109	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
110	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
111	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
112	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
113	C₂²×Dic₁₉	C₂³	1	2	yes	—
114	C₂²×Dic₁₉	C₂³	1	2	yes	—
115	#64545	—	2	8	no	—
116	D₄×D₁₉	—	2	16	no	—
117	D₄×D₁₉	—	2	8	no	—
118	D₄×D₁₉	—	4	8	no	—
119	#64541	—	2	4	no	—
120	#64541	—	2	8	no	—
121	#64541	—	2	4	no	—
122	#64541	—	2	8	no	—
123	#64541	—	2	4	no	—
124	#64541	—	2	8	no	—
125	#64541	D₄	1	8	yes	complemented
126	C₂×D₇₆	—	2	4	no	—
127	C₂×D₇₆	—	2	4	no	—
128	C₂×D₇₆	—	2	8	no	—
129	C₂×D₇₆	C₂³	1	2	yes	—
130	C₂×D₇₆	C₂³	1	1	yes	characteristic
131	C₂×D₇₆	C₂³	1	2	yes	—
132	C₂×D₇₆	C₂³	1	2	yes	—
133	C₂×D₇₆	C₂³	1	4	yes	—
134	C₂×D₇₆	C₂³	1	4	yes	—
135	C₂×D₇₆	C₂³	1	4	yes	—
136	C₂×D₇₆	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₁₉	—	2	8	no	—
138	C₂×C₄×D₁₉	C₂³	1	2	yes	—
139	C₂×C₄×D₁₉	C₂³	1	2	yes	—
140	C₂×C₄×D₁₉	C₂³	1	2	yes	—
141	C₂×C₄×D₁₉	C₂³	1	4	yes	—
142	C₂×C₄×D₁₉	C₂³	1	4	yes	—
143	C₂×C₄×D₁₉	C₂³	1	2	yes	—
144	C₂×Dic₃₈	—	2	4	no	—
145	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
146	C₂×Dic₃₈	C₂³	1	2	yes	—
147	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
148	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
149	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
150	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
151	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
152	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
153	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
154	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
155	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
156	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
157	C₄²×C₁₉	C₂³	1	2	yes	—
158	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
159	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
160	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
161	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
162	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
163	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
164	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
165	C₄⋊Dic₁₉	C₂³	1	2	yes	—
166	C₄⋊Dic₁₉	C₂³	1	2	yes	—
167	Dic₁₉⋊C₄	C₂³	1	4	yes	—
168	Dic₁₉⋊C₄	C₂³	1	4	yes	—
169	C₄×Dic₁₉	C₂³	1	4	yes	—
170	C₂³×C₁₉	—	2	2	no	—
171	C₂³×C₁₉	—	2	2	no	—
172	C₂³×C₁₉	—	4	1	no	—
173	C₂³×C₁₉	C₂⁴	1	2	yes	—
174	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
175	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
176	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
177	C₂²×D₁₉	—	2	4	no	—
178	C₂²×D₁₉	—	2	4	no	—
179	C₂²×D₁₉	—	2	4	no	—
180	C₂²×D₁₉	—	2	8	no	—
181	C₂²×D₁₉	—	4	2	no	—
182	C₂²×D₁₉	—	4	4	no	—
183	C₂²×D₁₉	—	4	2	no	—
184	C₂²×D₁₉	—	4	4	no	—
185	C₂²×D₁₉	—	4	2	no	—
186	C₂²×D₁₉	C₂⁴	1	4	yes	—
187	C₂²×D₁₉	C₂⁴	1	2	yes	—
188	C₂²×D₁₉	C₂⁴	1	2	yes	—
189	Q₈×C₁₉	—	2	2	no	—
190	D₄×C₁₉	—	2	4	no	—
191	D₄×C₁₉	—	2	4	no	—
192	D₄×C₁₉	—	2	2	no	—
193	D₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	4	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	complemented
201	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
202	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
203	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
204	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
205	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
206	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
207	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
208	C₂²⋊D₁₉	—	2	4	no	—
209	C₂²⋊D₁₉	—	2	8	no	—
210	C₂²⋊D₁₉	—	2	4	no	—
211	C₂²⋊D₁₉	—	2	4	no	—
212	C₂²⋊D₁₉	—	2	8	no	—
213	C₂²⋊D₁₉	—	4	4	no	—
214	C₂²⋊D₁₉	—	4	4	no	—
215	C₂²⋊D₁₉	C₂×D₄	1	8	yes	complemented
216	C₂×Dic₁₉	—	2	4	no	—
217	C₂×Dic₁₉	—	4	2	no	—
218	C₂×Dic₁₉	C₂⁴	1	4	yes	—
219	C₂×Dic₁₉	C₂⁴	1	2	yes	—
220	C₂×Dic₁₉	C₂⁴	1	2	yes	—
221	D₇₆	—	2	4	no	—
222	D₇₆	—	2	8	no	—
223	D₇₆	—	2	4	no	—
224	D₇₆	—	2	2	no	—
225	D₇₆	—	2	4	no	—
226	D₇₆	—	4	4	no	—
227	D₇₆	—	4	4	no	—
228	D₇₆	C₂×D₄	1	4	yes	complemented
229	C₄×D₁₉	—	2	4	no	—
230	C₄×D₁₉	—	2	4	no	—
231	C₄×D₁₉	—	2	4	no	—
232	C₄×D₁₉	—	2	8	no	—
233	C₄×D₁₉	—	4	4	no	—
234	C₄×D₁₉	C₂×D₄	1	8	yes	complemented
235	Dic₃₈	—	2	2	no	—
236	Dic₃₈	—	2	4	no	—
237	Dic₃₈	C₂×D₄	1	4	yes	complemented
238	#3488	—	19	1	no	maximal, Sylow
239	C₂²×C₁₉	—	2	1	no	—
240	C₂²×C₁₉	—	2	1	no	—
241	C₂²×C₁₉	—	2	1	no	—
242	C₂²×C₁₉	—	2	1	no	—
243	C₂²×C₁₉	—	2	1	no	—
244	C₂²×C₁₉	—	2	2	no	—
245	C₂²×C₁₉	—	2	1	no	—
246	C₂²×C₁₉	—	2	2	no	—
247	C₂²×C₁₉	—	2	1	no	—
248	C₂²×C₁₉	—	2	2	no	—
249	C₂²×C₁₉	—	4	4	no	—
250	C₂²×C₁₉	C₂²×D₄	1	2	yes	—
251	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	complemented
252	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
253	C₂×D₁₉	—	2	2	no	—
254	C₂×D₁₉	—	2	2	no	—
255	C₂×D₁₉	—	2	2	no	—
256	C₂×D₁₉	—	2	4	no	—
257	C₂×D₁₉	—	2	2	no	—
258	C₂×D₁₉	—	2	4	no	—
259	C₂×D₁₉	—	2	2	no	—
260	C₂×D₁₉	—	2	4	no	—
261	C₂×D₁₉	—	4	8	no	—
262	C₂×D₁₉	—	8	8	no	—
263	C₂×D₁₉	—	8	4	no	—
264	C₂×D₁₉	C₂²×D₄	1	4	yes	—
265	C₄×C₁₉	—	2	1	no	—
266	C₄×C₁₉	—	2	1	no	—
267	C₄×C₁₉	—	2	2	no	—
268	C₄×C₁₉	—	2	2	no	—
269	C₄×C₁₉	—	2	2	no	—
270	C₄×C₁₉	C₂²×D₄	1	2	yes	—
271	C₄×C₁₉	C₂²×D₄	1	2	yes	—
272	Dic₁₉	—	2	2	no	—
273	Dic₁₉	—	2	4	no	—
274	Dic₁₉	C₂²×D₄	1	4	yes	—
275	C₂×H(5,𝔽₂)	—	19	1	no	—
276	C₂²×#41	—	19	1	no	—
277	#550	—	19	2	no	—
278	#548	—	19	2	no	—
279	#546	—	19	4	no	—
280	#546	—	19	2	no	—
281	D₄²	—	19	4	no	—
282	D₄²	—	19	2	no	—
283	#537	—	19	1	no	—
284	#537	—	19	2	no	—
285	#535	—	19	2	no	—
286	#535	—	19	1	no	—
287	#525	—	19	2	no	—
288	#525	D₁₉	1	1	yes	characteristic, complemented
289	C₂×#121	—	19	1	no	—
290	C₂×#121	—	19	2	no	—
291	#520	—	19	1	no	—
292	C₂×C₁₉	—	2	2	no	—
293	C₂×C₁₉	—	2	2	no	—
294	C₂×C₁₉	—	4	2	no	—
295	C₂×C₁₉	—	4	1	no	—
296	C₂×C₁₉	C₂³×D₄	1	1	yes	characteristic
297	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
298	C₂×C₁₉	#585	1	1	yes	characteristic
299	D₁₉	—	2	4	no	—
300	D₁₉	—	4	2	no	—
301	D₁₉	—	4	4	no	—
302	H(5,𝔽₂)	—	38	8	no	—
303	C₂×#41	—	19	2	no	—
304	C₂×#41	—	19	1	no	—
305	C₂×#41	—	19	2	no	—
306	C₂×#41	—	19	1	no	—
307	C₂×#41	—	19	1	no	—
308	C₂×#41	—	19	2	no	—
309	C₂×#41	—	19	2	no	—
310	C₂×#41	—	19	1	no	—
311	C₂×#41	—	38	8	no	—
312	C₂×#41	C₂×D₁₉	1	1	yes	characteristic, complemented
313	C₂²×Q₈	—	19	1	no	—
314	C₂²×D₄	—	19	2	no	—
315	C₂²×D₄	—	19	2	no	—
316	C₂²×D₄	—	19	2	no	—
317	C₂²×D₄	—	19	4	no	—
318	C₂²×D₄	—	19	4	no	—
319	C₂²×D₄	—	19	1	no	—
320	C₂²×D₄	—	19	1	no	—
321	C₂²×D₄	—	19	2	no	—
322	C₂³×C₄	—	19	2	no	—
323	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
324	#127	—	19	4	no	—
325	#127	—	19	2	no	—
326	#124	—	19	4	no	—
327	#124	—	19	2	no	—
328	#123	—	19	4	no	—
329	#123	C₂×D₁₉	1	2	yes	complemented
330	C₂²⋊Q₈	—	19	2	no	—
331	C₂²⋊Q₈	—	19	2	no	—
332	C₂²⋊Q₈	—	19	4	no	—
333	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
334	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
335	#121	—	19	2	no	—
336	#121	—	19	4	no	—
337	#121	—	19	4	no	—
338	#121	—	19	2	no	—
339	#121	—	19	2	no	—
340	#121	—	19	2	no	—
341	#121	—	19	2	no	—
342	#121	—	19	2	no	—
343	#121	—	19	2	no	—
344	#121	—	19	2	no	—
345	#121	—	19	4	no	—
346	#121	—	19	4	no	—
347	#121	—	19	4	no	—
348	#121	—	19	4	no	—
349	#121	C₂×D₁₉	1	1	yes	characteristic, complemented
350	#121	C₂×D₁₉	1	1	yes	characteristic, complemented
351	#120	—	19	4	no	—
352	#120	—	19	4	no	—
353	#120	—	19	4	no	—
354	#120	—	19	4	no	—
355	#120	C₂×D₁₉	1	2	yes	complemented
356	C₄×Q₈	—	19	2	no	—
357	C₄×D₄	—	19	4	no	—
358	C₄×D₄	—	19	4	no	—
359	C₄×D₄	—	19	4	no	—
360	C₄×D₄	—	19	2	no	—
361	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
362	C₄×D₄	C₂×D₁₉	1	2	yes	complemented
363	#117	—	19	2	no	—
364	#117	C₂×D₁₉	1	1	yes	characteristic, complemented
365	C₂×C₄⋊C₄	—	19	1	no	—
366	C₂×C₄⋊C₄	—	19	2	no	—
367	C₂×C₂²⋊C₄	—	19	2	no	—
368	C₂×C₂²⋊C₄	—	19	4	no	—
369	C₁₉	#3488	1	1	yes	characteristic, complemented, Sylow
370	C₂⁴	—	19	2	no	—
371	C₂⁴	—	19	4	no	—
372	C₂⁴	—	19	2	no	—
373	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
374	#41	—	2	4	no	—
375	#41	—	19	8	no	—
376	#41	—	38	8	no	—
377	#41	—	38	8	no	—
378	#41	—	38	4	no	—
379	#41	—	38	4	no	—
380	#41	—	38	8	no	—
381	#41	—	38	8	no	—
382	#41	—	38	4	no	—
383	C₂×Q₈	—	19	1	no	—
384	C₂×Q₈	—	19	2	no	—
385	C₂×Q₈	—	19	1	no	—
386	C₂×Q₈	—	38	4	no	—
387	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
388	C₂×D₄	—	19	2	no	—
389	C₂×D₄	—	19	4	no	—
390	C₂×D₄	—	19	2	no	—
391	C₂×D₄	—	19	2	no	—
392	C₂×D₄	—	19	4	no	—
393	C₂×D₄	—	19	2	no	—
394	C₂×D₄	—	19	4	no	—
395	C₂×D₄	—	19	4	no	—
396	C₂×D₄	—	19	1	no	—
397	C₂×D₄	—	19	2	no	—
398	C₂×D₄	—	19	4	no	—
399	C₂×D₄	—	19	2	no	—
400	C₂×D₄	—	19	2	no	—
401	C₂×D₄	—	19	1	no	—
402	C₂×D₄	—	19	4	no	—
403	C₂×D₄	—	19	4	no	—
404	C₂×D₄	—	38	4	no	—
405	C₂×D₄	—	38	8	no	—
406	C₂×D₄	—	38	8	no	—
407	C₂×D₄	—	38	16	no	—
408	C₂×D₄	—	38	8	no	—
409	C₂×D₄	—	38	4	no	—
410	C₂×D₄	—	76	8	no	—
411	C₂×D₄	—	76	4	no	—
412	C₂×D₄	C₂²×D₁₉	1	2	yes	—
413	C₂×D₄	C₂²×D₁₉	1	2	yes	—
414	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
415	C₂×D₄	C₂²×D₁₉	1	2	yes	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	19	2	no	—
418	C₂²×C₄	—	19	2	no	—
419	C₂²×C₄	—	19	2	no	—
420	C₂²×C₄	—	19	2	no	—
421	C₂²×C₄	—	19	2	no	—
422	C₂²×C₄	—	19	4	no	—
423	C₂²×C₄	—	19	2	no	—
424	C₂²×C₄	—	19	4	no	—
425	C₂²×C₄	—	38	8	no	—
426	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
427	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
428	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
429	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
430	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
431	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
432	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
433	C₄⋊C₄	—	19	4	no	—
434	C₄⋊C₄	—	19	4	no	—
435	C₄⋊C₄	—	19	2	no	—
436	C₄⋊C₄	—	19	2	no	—
437	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
438	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
439	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
440	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
441	C₂²⋊C₄	—	19	4	no	—
442	C₂²⋊C₄	—	19	4	no	—
443	C₂²⋊C₄	—	19	4	no	—
444	C₂²⋊C₄	—	19	4	no	—
445	C₂²⋊C₄	—	19	4	no	—
446	C₂²⋊C₄	—	19	4	no	—
447	C₂²⋊C₄	—	19	4	no	—
448	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
449	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
450	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
451	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
452	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
453	C₄²	—	19	4	no	—
454	C₄²	C₂²×D₁₉	1	2	yes	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	19	2	no	—
459	C₂³	—	19	4	no	—
460	C₂³	—	19	2	no	—
461	C₂³	—	38	4	no	—
462	C₂³	—	38	8	no	—
463	C₂³	—	38	4	no	—
464	C₂³	—	38	4	no	—
465	C₂³	—	76	2	no	—
466	C₂³	—	76	2	no	—
467	C₂³	—	76	4	no	—
468	C₂³	—	76	2	no	—
469	C₂³	—	76	4	no	—
470	C₂³	C₂³×D₁₉	1	2	yes	—
471	C₂³	C₂³×D₁₉	1	1	yes	characteristic
472	C₂³	C₂³×D₁₉	1	1	yes	characteristic
473	C₂³	C₂³×D₁₉	1	1	yes	characteristic
474	Q₈	—	2	2	no	—
475	Q₈	—	19	4	no	—
476	Q₈	—	38	4	no	—
477	Q₈	—	38	2	no	—
478	D₄	—	2	4	no	—
479	D₄	—	2	4	no	—
480	D₄	—	2	2	no	—
481	D₄	—	4	2	no	—
482	D₄	—	19	8	no	—
483	D₄	—	19	4	no	—
484	D₄	—	38	8	no	—
485	D₄	—	38	4	no	—
486	D₄	—	38	8	no	—
487	D₄	—	38	4	no	—
488	D₄	—	38	4	no	—
489	D₄	—	38	4	no	—
490	D₄	—	38	8	no	—
491	D₄	—	38	4	no	—
492	D₄	—	38	4	no	—
493	D₄	—	38	2	no	—
494	D₄	—	76	4	no	—
495	D₄	—	76	4	no	—
496	D₄	—	76	4	no	—
497	D₄	—	76	4	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	19	2	no	—
505	C₂×C₄	—	19	8	no	—
506	C₂×C₄	—	19	4	no	—
507	C₂×C₄	—	19	2	no	—
508	C₂×C₄	—	38	4	no	—
509	C₂×C₄	—	38	8	no	—
510	C₂×C₄	—	38	4	no	—
511	C₂×C₄	—	38	4	no	—
512	C₂×C₄	—	38	4	no	—
513	C₂×C₄	—	76	4	no	—
514	C₂×C₄	—	76	2	no	—
515	C₂×C₄	D₄×D₁₉	1	4	yes	complemented
516	C₂×C₄	C₂³×D₁₉	1	2	yes	—
517	C₂×C₄	C₂³×D₁₉	1	2	yes	—
518	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
519	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
520	C₂×C₄	C₂³×D₁₉	1	2	yes	—
521	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
522	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	4	4	no	—
534	C₂²	—	19	4	no	—
535	C₂²	—	38	2	no	—
536	C₂²	—	38	2	no	—
537	C₂²	—	38	2	no	—
538	C₂²	—	38	4	no	—
539	C₂²	—	38	4	no	—
540	C₂²	—	38	2	no	—
541	C₂²	—	38	2	no	—
542	C₂²	—	38	4	no	—
543	C₂²	—	76	8	no	—
544	C₂²	—	152	4	no	—
545	C₂²	—	152	8	no	—
546	C₂²	C₂×D₄×D₁₉	1	2	yes	—
547	C₂²	#10597435	1	2	yes	complemented
548	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	2	no	—
552	C₄	—	2	2	no	—
553	C₄	—	2	2	no	—
554	C₄	—	19	4	no	—
555	C₄	—	38	2	no	—
556	C₄	—	38	4	no	—
557	C₄	C₂×D₄×D₁₉	1	2	yes	—
558	C₄	C₂×D₄×D₁₉	1	2	yes	—
559	C₂	—	2	2	no	—
560	C₂	—	2	2	no	—
561	C₂	—	4	1	no	—
562	C₂	—	4	2	no	—
563	C₂	—	38	4	no	—
564	C₂	—	76	2	no	—
565	C₂	—	76	4	no	—
566	C₂	C₂²×D₄×D₁₉	1	1	yes	characteristic
567	C₂	C₂×#10597435	1	1	yes	characteristic
568	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#525	C₂
hypercenter	#525	D₁₉
hypocenter	C₁₉	#3488
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. C₂×#10597435	C₂	semidirect
2. C₂²×#64541	C₂	semidirect
3. #11927215	C₂	semidirect
4. #11927203	C₂	semidirect
5. #11927190	C₂	semidirect
6. #11927186	C₂	semidirect
7. D₄×D₇₆	C₂	semidirect
8. #11927176	C₂	semidirect
9. #11927124	C₂	semidirect
10. #11927122	C₂	semidirect
11. #11927113	C₂	semidirect
12. #11927110	C₂	semidirect
13. #11927057	C₂	semidirect
14. C₂×#10597376	C₂	semidirect
15. #121×D₁₉	C₂	semidirect
16. #11927024	C₂	semidirect
17. C₁₉×#525	C₂	semidirect
18. C₂×#41×C₁₉	C₂²	semidirect
19. C₂³×C₄×C₁₉	C₂²	semidirect
20. C₂²×C₂²⋊D₁₉	C₂²	semidirect
21. C₂²×C₂²⋊D₁₉	C₂²	semidirect
23. C₂×#64545	C₂²	semidirect
24. C₂×D₄×D₁₉	C₂²	semidirect
25. C₂×D₄×D₁₉	C₂²	semidirect
26. C₂×D₄×D₁₉	C₂²	semidirect
29. C₂×#64541	C₂²	semidirect
30. C₂×#64541	C₂²	semidirect
31. C₂×#64541	C₂²	semidirect
32. C₂×#64541	C₂²	semidirect
33. C₂×#64541	C₂²	semidirect
34. C₂×#64541	C₂²	semidirect
35. C₂²×D₇₆	C₂²	semidirect
36. C₂²×D₇₆	C₂²	semidirect
37. C₂²×D₇₆	C₂²	semidirect
38. C₂²×C₄×D₁₉	C₂²	semidirect
39. C₂²×Dic₃₈	C₂²	semidirect
40. C₁₉×#123	C₂²	semidirect
41. C₁₉×C₂²⋊Q₈	C₂²	semidirect
42. C₁₉×C₂²⋊Q₈	C₂²	semidirect
43. C₁₉×#121	C₂²	semidirect
44. C₁₉×#121	C₂²	semidirect
45. C₁₉×#120	C₂²	semidirect
46. C₄×D₄×C₁₉	C₂²	semidirect
47. C₄×D₄×C₁₉	C₂²	semidirect
48. C₁₉×#117	C₂²	semidirect
49. #10597392	C₂²	semidirect
50. #10597386	C₂²	semidirect
51. #10597385	C₂²	semidirect
52. #10597385	C₂²	semidirect
53. #10597384	C₂²	semidirect
54. #10597383	C₂²	semidirect
55. #10597376	C₂²	semidirect
56. #10597376	C₂²	semidirect
57. #10597376	C₂²	semidirect
58. #10597376	C₂²	semidirect
59. #10597376	C₂²	semidirect
60. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
61. C₂×C₄⋊Dic₁₉	C₂²	semidirect
62. #10597370	C₂²	semidirect
63. #10597342	C₂²	semidirect
64. #10597341	C₂²	semidirect
65. #10597341	C₂²	semidirect
66. #10597341	C₂²	semidirect
67. #10597340	C₂²	semidirect
68. #10597339	C₂²	semidirect
69. #10597338	C₂²	semidirect
70. C₄⋊C₄×D₁₉	C₂²	semidirect
71. #10597331	C₂²	semidirect
72. #10597330	C₂²	semidirect
73. #10597330	C₂²	semidirect
74. #10597330	C₂²	semidirect
75. #10597328	C₂²	semidirect
76. #10597328	C₂²	semidirect
77. #10597328	C₂²	semidirect
78. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
79. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
80. C₂²⋊C₄×D₁₉	C₂²	semidirect
81. #10597321	C₂²	semidirect
82. #10597320	C₂²	semidirect
83. C₄×D₇₆	C₂²	semidirect
84. C₄×Dic₃₈	C₂²	semidirect
125. #64541	D₄	semidirect
200. C₂×C₄×C₁₉	C₂×D₄	semidirect
215. C₂²⋊D₁₉	C₂×D₄	semidirect
228. D₇₆	C₂×D₄	semidirect
234. C₄×D₁₉	C₂×D₄	semidirect
237. Dic₃₈	C₂×D₄	semidirect
251. C₂²×C₁₉	H(5,𝔽₂)	semidirect
288. #525	D₁₉	semidirect
312. C₂×#41	C₂×D₁₉	semidirect
323. C₂³×C₄	C₂×D₁₉	semidirect
329. #123	C₂×D₁₉	semidirect
333. C₂²⋊Q₈	C₂×D₁₉	semidirect
334. C₂²⋊Q₈	C₂×D₁₉	semidirect
349. #121	C₂×D₁₉	semidirect
350. #121	C₂×D₁₉	semidirect
355. #120	C₂×D₁₉	semidirect
361. C₄×D₄	C₂×D₁₉	semidirect
362. C₄×D₄	C₂×D₁₉	semidirect
364. #117	C₂×D₁₉	semidirect
369. C₁₉	#3488	semidirect
515. C₂×C₄	D₄×D₁₉	semidirect
547. C₂²	#10597435	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597435	2
C₂²×#64541	2
#11927215	2
#11927203	2
#11927190	2
#11927186	2
D₄×D₇₆	2
#11927176	2
#11927124	2
#11927122	2
#11927113	2
#11927110	2
#11927057	2
C₂×#10597376	2
#121×D₁₉	2
#11927024	2
C₁₉×#525	2
#3488	19