Group #18082132 — subgroups

Subgroups — #18082132

Order 4864.

410 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564625	C₂	1	1	yes	maximal, characteristic
2	#14564625	C₂	1	1	yes	maximal, characteristic
3	#14562394	C₂	1	1	yes	maximal, characteristic
4	#14562320	C₂	1	1	yes	maximal, characteristic
5	#14562316	C₂	1	1	yes	maximal, characteristic
6	C₈×#64520	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#487	C₂	1	1	yes	maximal, characteristic
8	#11926597	C₂²	1	1	yes	characteristic
9	#11926568	C₂²	1	1	yes	characteristic
10	#11926568	C₂²	1	1	yes	characteristic
11	C₄×#64520	C₂²	1	1	yes	characteristic
12	#11926313	—	2	2	no	—
13	#11926313	—	2	2	no	—
14	#11926297	—	2	2	no	—
15	#11926293	—	2	2	no	—
16	#11926290	—	2	2	no	—
17	#11926266	—	2	1	no	—
18	C₈×C₁₉⋊C₈	—	2	1	no	—
19	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₁₉×#487	—	2	2	no	—
22	C₁₉×#487	—	2	1	no	—
23	C₁₉×#487	—	2	1	no	—
24	C₂×C₁₉×#103	C₄	1	4	yes	—
25	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×Q₈×C₁₉	—	2	1	no	—
27	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
28	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
29	C₁₉×C₄⋊Q₈	—	2	1	no	—
30	C₁₉×C₄⋊Q₈	—	2	1	no	—
31	C₁₉×C₄⋊Q₈	—	2	1	no	—
32	C₁₉×C₄⋊Q₈	—	2	1	no	—
33	C₁₉×C₄⋊Q₈	—	2	1	no	—
34	C₁₉×C₄⋊Q₈	—	2	1	no	—
35	C₁₉×C₄⋊Q₈	—	2	1	no	—
36	C₁₉×C₄⋊Q₈	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
41	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
42	C₂×#64520	—	2	1	no	—
43	C₂×#64520	—	2	1	no	—
44	C₂×#64520	D₄	1	2	yes	—
45	C₁₉×#103	—	2	4	no	—
46	C₁₉×#103	—	2	4	no	—
47	C₄×C₈×C₁₉	D₄	1	2	yes	—
48	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
49	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
50	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
51	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
52	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
53	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
54	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
55	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
56	#10597260	—	2	1	no	—
57	C₄×C₁₉⋊C₈	—	2	1	no	—
58	C₄×C₁₉⋊C₈	—	2	1	no	—
59	C₂×Q₈×C₁₉	—	2	2	no	—
60	C₂×Q₈×C₁₉	—	2	2	no	—
61	C₂×Q₈×C₁₉	—	4	4	no	—
62	C₂×Q₈×C₁₉	—	4	1	no	—
63	C₂×Q₈×C₁₉	—	4	1	no	—
64	C₂×Q₈×C₁₉	—	8	2	no	—
65	C₂²×C₄×C₁₉	—	2	2	no	—
66	C₂²×C₄×C₁₉	—	2	2	no	—
67	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
70	C₂×C₈×C₁₉	—	4	2	no	—
71	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
72	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
73	C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₄⋊C₄×C₁₉	—	4	1	no	—
76	C₄⋊C₄×C₁₉	—	4	1	no	—
77	C₄⋊C₄×C₁₉	—	4	1	no	—
78	C₄⋊C₄×C₁₉	—	4	1	no	—
79	C₄⋊C₄×C₁₉	—	4	1	no	—
80	C₄⋊C₄×C₁₉	—	4	1	no	—
81	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₄²×C₁₉	#41	1	1	yes	characteristic
85	#64520	—	2	2	no	—
86	#64520	—	4	2	no	—
87	#64520	—	4	2	no	—
88	#64520	Q₁₆	1	4	yes	—
89	C₂×C₁₉⋊C₈	—	2	2	no	—
90	C₂×C₁₉⋊C₈	—	2	2	no	—
91	C₂×C₁₉⋊C₈	—	4	1	no	—
92	C₂×C₁₉⋊C₈	—	4	1	no	—
93	#9795	—	19	1	no	maximal, Sylow
94	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
95	Q₈×C₁₉	—	4	4	no	—
96	Q₈×C₁₉	—	8	2	no	—
97	Q₈×C₁₉	—	8	2	no	—
98	Q₈×C₁₉	—	8	2	no	—
99	C₂×C₄×C₁₉	—	2	2	no	—
100	C₂×C₄×C₁₉	—	2	2	no	—
101	C₂×C₄×C₁₉	—	4	2	no	—
102	C₂×C₄×C₁₉	—	4	2	no	—
103	C₂×C₄×C₁₉	—	8	2	no	—
104	C₂×C₄×C₁₉	—	8	2	no	—
105	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
107	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
108	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
109	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
110	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
111	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
112	C₂×C₄×C₁₉	#135	1	2	yes	—
113	C₈×C₁₉	—	2	2	no	—
114	C₈×C₁₉	—	2	2	no	—
115	C₁₉⋊C₈	—	2	4	no	—
116	C₁₉⋊C₈	—	4	2	no	—
117	C₁₉⋊C₈	—	8	1	no	—
118	C₁₉⋊C₈	—	8	1	no	—
119	C₂×#487	D₁₉	1	1	yes	characteristic
120	#1997	—	19	1	no	—
121	#1997	—	19	1	no	—
122	#1567	—	19	1	no	—
123	#1549	—	19	1	no	—
124	#1548	—	19	1	no	—
125	C₈×M₁₆	—	19	1	no	—
126	C₂²×C₁₉	—	2	1	no	—
127	C₂²×C₁₉	—	2	1	no	—
128	C₂²×C₁₉	#390	1	1	yes	characteristic
129	C₂²×C₁₉	C₄×Q₁₆	1	2	yes	—
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	—	8	2	no	—
133	C₄×C₁₉	—	8	2	no	—
134	C₄×C₁₉	#413	1	2	yes	—
135	C₄×C₁₉	#467	1	2	yes	—
136	C₄×C₁₉	#471	1	2	yes	—
137	C₄×C₁₉	#494	1	1	yes	characteristic
138	C₄×C₁₉	#495	1	1	yes	characteristic
139	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
140	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
141	#487	—	2	1	no	—
142	#487	—	2	1	no	—
143	#487	—	2	2	no	—
144	#431	—	19	1	no	—
145	#423	—	19	1	no	—
146	#423	—	19	1	no	—
147	C₂×#103	Dic₁₉	1	4	yes	—
148	C₄×M₁₆	—	19	1	no	—
149	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
150	#343	—	38	2	no	—
151	#343	—	38	2	no	—
152	#335	—	38	2	no	—
153	#333	—	38	2	no	—
154	#332	—	38	2	no	—
155	#322	—	38	1	no	—
156	C₈²	—	38	1	no	—
157	C₂×C₁₉	—	2	2	no	—
158	C₂×C₁₉	#1967	1	1	yes	characteristic
159	C₂×C₁₉	#1969	1	1	yes	characteristic
160	C₂×C₁₉	#1977	1	1	yes	characteristic
161	C₂²×Q₈	—	2	1	no	—
162	C₂²×Q₈	C₂×Dic₁₉	1	2	yes	—
163	C₂×M₁₆	—	19	2	no	—
164	C₂×M₁₆	—	38	1	no	—
165	C₂×M₁₆	—	38	1	no	—
166	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
167	C₄⋊Q₈	—	2	1	no	—
168	C₄⋊Q₈	—	2	1	no	—
169	C₄⋊Q₈	—	2	1	no	—
170	C₄⋊Q₈	—	2	1	no	—
171	C₄⋊Q₈	—	2	1	no	—
172	C₄⋊Q₈	—	2	1	no	—
173	C₄⋊Q₈	—	2	1	no	—
174	C₄⋊Q₈	—	2	1	no	—
175	C₂×C₄⋊C₄	—	2	1	no	—
176	C₂×C₄⋊C₄	—	2	1	no	—
177	C₂×C₄⋊C₄	—	2	1	no	—
178	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
179	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
180	C₄⋊C₈	—	19	2	no	—
181	C₄⋊C₈	—	38	1	no	—
182	C₄⋊C₈	—	38	1	no	—
183	C₄⋊C₈	—	38	1	no	—
184	C₄⋊C₈	—	38	1	no	—
185	#103	—	2	4	no	—
186	#103	—	2	4	no	—
187	C₂²⋊C₈	—	38	1	no	—
188	#97	—	38	1	no	—
189	C₄×C₈	—	38	1	no	—
190	C₄×C₈	—	38	1	no	—
191	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
192	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
193	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
194	C₁₉	#9795	1	1	yes	characteristic, complemented, Sylow
195	C₂×Q₈	—	2	2	no	—
196	C₂×Q₈	—	2	2	no	—
197	C₂×Q₈	—	4	4	no	—
198	C₂×Q₈	—	4	1	no	—
199	C₂×Q₈	—	4	1	no	—
200	C₂×Q₈	—	8	2	no	—
201	C₂²×C₄	—	2	2	no	—
202	C₂²×C₄	—	2	2	no	—
203	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
204	C₂²×C₄	#64543	1	1	yes	characteristic
205	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
206	M₁₆	—	19	4	no	—
207	M₁₆	—	38	2	no	—
208	M₁₆	—	76	2	no	—
209	M₁₆	—	76	2	no	—
210	C₂×C₈	—	4	2	no	—
211	C₂×C₈	—	38	2	no	—
212	C₂×C₈	—	38	2	no	—
213	C₂×C₈	—	76	1	no	—
214	C₂×C₈	—	76	1	no	—
215	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
216	C₂×C₈	C₂²⋊Dic₁₉	1	2	yes	—
217	C₄⋊C₄	—	2	2	no	—
218	C₄⋊C₄	—	2	2	no	—
219	C₄⋊C₄	—	4	1	no	—
220	C₄⋊C₄	—	4	1	no	—
221	C₄⋊C₄	—	4	1	no	—
222	C₄⋊C₄	—	4	1	no	—
223	C₄⋊C₄	—	4	1	no	—
224	C₄⋊C₄	—	4	1	no	—
225	C₄²	D₄×D₁₉	1	1	yes	characteristic
226	C₄²	#64543	1	1	yes	characteristic
227	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
228	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
229	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
230	Q₈	—	4	4	no	—
231	Q₈	—	8	2	no	—
232	Q₈	—	8	2	no	—
233	Q₈	—	8	2	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	4	2	no	—
237	C₂×C₄	—	4	2	no	—
238	C₂×C₄	—	8	2	no	—
239	C₂×C₄	—	8	2	no	—
240	C₂×C₄	Q₁₆×D₁₉	1	2	yes	—
241	C₂×C₄	#10597365	1	2	yes	—
242	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
243	C₂×C₄	#10597382	1	1	yes	characteristic
244	C₂×C₄	#10597384	1	1	yes	characteristic
245	C₂×C₄	#10597384	1	1	yes	characteristic
246	C₂×C₄	#10597386	1	1	yes	characteristic
247	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
248	C₈	—	2	2	no	—
249	C₈	—	2	2	no	—
250	C₈	—	38	4	no	—
251	C₈	—	76	2	no	—
252	C₈	—	152	1	no	—
253	C₈	—	152	1	no	—
254	C₂²	—	2	1	no	—
255	C₂²	—	2	1	no	—
256	C₂²	#11926447	1	1	yes	characteristic
257	C₂²	Q₁₆×Dic₁₉	1	2	yes	—
258	C₄	—	2	1	no	—
259	C₄	—	2	1	no	—
260	C₄	—	8	2	no	—
261	C₄	—	8	2	no	—
262	C₄	#11926528	1	2	yes	—
263	C₄	#11926782	1	2	yes	—
264	C₄	#11926804	1	2	yes	—
265	C₄	#11926922	1	1	yes	characteristic
266	C₄	#11926929	1	1	yes	characteristic
267	C₂	—	2	2	no	—
268	C₂	#14564485	1	1	yes	characteristic
269	C₂	#14564497	1	1	yes	characteristic
270	C₂	#14564540	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14564625

C₂

yes

maximal, characteristic

#14564625

C₂

yes

maximal, characteristic

#14562394

C₂

yes

maximal, characteristic

#14562320

C₂

yes

maximal, characteristic

#14562316

C₂

yes

maximal, characteristic

C₈×#64520

C₂

yes

maximal, characteristic

C₂×C₁₉×#487

C₂

yes

maximal, characteristic

#11926597

C₂²

yes

characteristic

#11926568

C₂²

yes

characteristic

#11926568

C₂²

yes

characteristic

C₄×#64520

C₂²

yes

—

—

—

—

—

—

C₈×C₁₉⋊C₈

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#487

—

C₁₉×#487

—

C₁₉×#487

—

C₂×C₁₉×#103

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

D₄

yes

—

C₁₉×#103

—

C₁₉×#103

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

—

—

—

Q₁₆

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9795

—

maximal, Sylow

C₂³×C₁₉

C₄×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

100

C₂×C₄×C₁₉

—

101

C₂×C₄×C₁₉

—

102

C₂×C₄×C₁₉

—

103

C₂×C₄×C₁₉

—

104

C₂×C₄×C₁₉

—

105

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

106

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

107

C₂×C₄×C₁₉

#121

yes

characteristic

108

C₂×C₄×C₁₉

#121

yes

characteristic

109

C₂×C₄×C₁₉

#124

yes

characteristic

110

C₂×C₄×C₁₉

#127

yes

characteristic

111

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

112

C₂×C₄×C₁₉

#135

yes

—

113

C₈×C₁₉

—

114

C₈×C₁₉

—

115

C₁₉⋊C₈

—

116

C₁₉⋊C₈

—

117

C₁₉⋊C₈

—

118

C₁₉⋊C₈

—

119

C₂×#487

D₁₉

yes

characteristic

120

#1997

—

121

#1997

—

122

#1567

—

123

#1549

—

124

#1548

—

125

C₈×M₁₆

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

—

128

C₂²×C₁₉

#390

yes

characteristic

129

C₂²×C₁₉

C₄×Q₁₆

yes

—

130

C₄×C₁₉

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

#413

yes

—

135

C₄×C₁₉

#467

yes

—

136

C₄×C₁₉

#471

yes

—

137

C₄×C₁₉

#494

yes

characteristic

138

C₄×C₁₉

#495

yes

characteristic

139

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

140

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

141

#487

—

142

#487

—

143

#487

—

144

#431

—

145

#423

—

146

#423

—

147

C₂×#103

Dic₁₉

yes

—

148

C₄×M₁₆

—

149

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

150

#343

—

151

#343

—

152

#335

—

153

#333

—

154

#332

—

155

#322

—

156

C₈²

—

157

C₂×C₁₉

—

158

C₂×C₁₉

#1967

yes

characteristic

159

C₂×C₁₉

#1969

yes

characteristic

160

C₂×C₁₉

#1977

yes

characteristic

161

C₂²×Q₈

—

162

C₂²×Q₈

C₂×Dic₁₉

yes

—

163

C₂×M₁₆

—

164

C₂×M₁₆

—

165

C₂×M₁₆

—

166

C₂²×C₈

C₂×Dic₁₉

yes

—

167

C₄⋊Q₈

—

168

C₄⋊Q₈

—

169

C₄⋊Q₈

—

170

C₄⋊Q₈

—

171

C₄⋊Q₈

—

172

C₄⋊Q₈

—

173

C₄⋊Q₈

—

174

C₄⋊Q₈

—

175

C₂×C₄⋊C₄

—

176

C₂×C₄⋊C₄

—

177

C₂×C₄⋊C₄

—

178

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

179

C₂×C₄²

C₂²×D₁₉

yes

characteristic

180

C₄⋊C₈

—

181

C₄⋊C₈

—

182

C₄⋊C₈

—

183

C₄⋊C₈

—

184

C₄⋊C₈

—

185

#103

—

186

#103

—

187

C₂²⋊C₈

—

188

#97

—

189

C₄×C₈

—

190

C₄×C₈

—

191

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

192

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

193

C₄×C₈

C₂²⋊D₁₉

yes

—

194

C₁₉

#9795

yes

characteristic, complemented, Sylow

195

C₂×Q₈

—

196

C₂×Q₈

—

197

C₂×Q₈

—

198

C₂×Q₈

—

199

C₂×Q₈

—

200

C₂×Q₈

—

201

C₂²×C₄

—

202

C₂²×C₄

—

203

C₂²×C₄

D₄×D₁₉

yes

characteristic

204

C₂²×C₄

#64543

yes

characteristic

205

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

206

M₁₆

—

207

M₁₆

—

208

M₁₆

—

209

M₁₆

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

C₂²⋊Dic₁₉

yes

—

216

C₂×C₈

C₂²⋊Dic₁₉

yes

—

217

C₄⋊C₄

—

218

C₄⋊C₄

—

219

C₄⋊C₄

—

220

C₄⋊C₄

—

221

C₄⋊C₄

—

222

C₄⋊C₄

—

223

C₄⋊C₄

—

224

C₄⋊C₄

—

225

C₄²

D₄×D₁₉

yes

characteristic

226

C₄²

#64543

yes

characteristic

227

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

228

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

229

C₂³

D₄×Dic₁₉

yes

characteristic

230

Q₈

—

231

Q₈

—

232

Q₈

—

233

Q₈

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

Q₁₆×D₁₉

yes

—

241

C₂×C₄

#10597365

yes

—

242

C₂×C₄

D₄×Dic₁₉

yes

characteristic

243

C₂×C₄

#10597382

yes

characteristic

244

C₂×C₄

#10597384

yes

characteristic

245

C₂×C₄

#10597384

yes

characteristic

246

C₂×C₄

#10597386

yes

characteristic

247

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

248

C₈

—

249

C₈

—

250

C₈

—

251

C₈

—

252

C₈

—

152

—

253

C₈

—

152

—

254

C₂²

—

255

C₂²

—

256

C₂²

#11926447

yes

characteristic

257

C₂²

Q₁₆×Dic₁₉

yes

—

258

C₄

—

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

#11926528

yes

—

263

C₄

#11926782

yes

—

264

C₄

#11926804

yes

—

265

C₄

#11926922

yes

characteristic

266

C₄

#11926929

yes

characteristic

267

C₂

—

268

C₂

#14564485

yes

characteristic

269

C₂

#14564497

yes

characteristic

270

C₂

#14564540

yes

characteristic

	subgroup	G/H
center	C₂²	#11926447
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#487	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂³×C₁₉	C₄×D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#487	D₁₉
hypocenter	C₁₉	#9795
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#487

subgroup

G/H

center

C₂²

#11926447

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#487

C₂

socle

C₂²×C₁₉

#390

prime radical

C₂³×C₁₉

C₄×D₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#487

N	H ≅ G/N	type
194. C₁₉	#9795	semidirect

H ≅ G/N

type

194. C₁₉

#9795

semidirect

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

subgroup	index
#14564625	2
#14562394	2
#14562320	2
#14562316	2
C₈×#64520	2
C₂×C₁₉×#487	2
#9795	19

subgroup

index

C₂×C₁₉×#487

Subgroups — #18082132

Conjugacy classes of subgroups

Complements

Maximal subgroups