Group #18081640 — subgroups

Subgroups — #18081640

Order 4864.

610 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 151 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	#14571992	C₂	1	1	yes	maximal, characteristic
2	#14563488	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11926292	C₂	1	2	yes	maximal, complemented
4	C₂×#11926287	C₂	1	2	yes	maximal
5	C₁₉×#1842	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597315	C₂²	1	1	yes	characteristic
7	C₂×#10597320	C₂²	1	1	yes	characteristic
8	C₂×#10597321	C₄	1	4	yes	—
9	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
10	C₂×#10597260	—	2	1	no	—
11	#11926446	—	2	1	no	—
12	#11926446	—	2	1	no	—
13	#11926446	—	2	2	no	—
14	#11926299	—	2	1	no	—
15	#11926292	—	2	4	no	—
16	#11926287	—	2	4	no	—
17	C₂×C₁₉×C₄⋊C₈	—	2	2	no	—
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
19	C₄³×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×D₇₆	—	2	1	no	—
21	C₂²×D₇₆	—	2	1	no	—
22	C₂²×D₇₆	C₂×C₄	1	2	yes	—
23	C₂²×Dic₃₈	C₂×C₄	1	2	yes	—
24	C₂²×C₈×C₁₉	—	2	2	no	—
25	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₉	D₄	1	2	yes	—
29	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	C₂×(C₂×D₁₉)⋊C₄	—	2	4	no	—
31	C₂×(C₂×D₁₉)⋊C₄	—	2	4	no	—
32	C₂×C₄⋊Dic₁₉	—	2	1	no	—
33	C₂×C₄⋊Dic₁₉	—	2	1	no	—
34	C₂²×C₁₉⋊C₈	—	2	2	no	—
35	#10597321	—	4	8	no	—
36	#10597320	—	2	2	no	—
37	#10597320	—	2	2	no	—
38	#10597315	—	2	2	no	—
39	#10597315	—	2	2	no	—
40	C₁₉×C₄⋊C₈	—	2	2	no	—
41	C₁₉×C₄⋊C₈	—	2	2	no	—
42	C₁₉×C₄⋊C₈	—	4	4	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
44	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
45	#10597260	—	4	2	no	—
46	C₂³×D₁₉	—	2	2	no	—
47	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
48	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
49	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂²×Dic₁₉	—	2	2	no	—
53	C₂×D₇₆	—	2	4	no	—
54	C₂×D₇₆	—	4	4	no	—
55	C₂×D₇₆	—	4	2	no	—
56	C₂×D₇₆	—	4	1	no	—
57	C₂×D₇₆	—	4	1	no	—
58	C₂×D₇₆	—	4	2	no	—
59	C₂×D₇₆	—	4	2	no	—
60	C₂×D₇₆	—	4	1	no	—
61	C₂×D₇₆	—	4	2	no	—
62	C₂×D₇₆	—	4	1	no	—
63	C₂×Dic₃₈	—	2	4	no	—
64	C₂×Dic₃₈	—	4	4	no	—
65	C₂×C₈×C₁₉	—	4	2	no	—
66	C₂×C₈×C₁₉	—	4	4	no	—
67	C₄²×C₁₉	—	2	4	no	—
68	C₄²×C₁₉	—	2	2	no	—
69	C₄²×C₁₉	—	2	1	no	—
70	C₄²×C₁₉	—	2	2	no	—
71	C₄²×C₁₉	—	2	2	no	—
72	C₄²×C₁₉	—	2	1	no	—
73	C₄²×C₁₉	C₂×D₄	1	2	yes	—
74	C₄²×C₁₉	#41	1	2	yes	—
75	(C₂×D₁₉)⋊C₄	—	4	8	no	—
76	(C₂×D₁₉)⋊C₄	—	4	8	no	—
77	C₄⋊Dic₁₉	—	4	2	no	—
78	C₄⋊Dic₁₉	—	4	1	no	—
79	C₄⋊Dic₁₉	—	4	1	no	—
80	C₂×C₁₉⋊C₈	—	2	4	no	—
81	C₂×C₁₉⋊C₈	—	4	2	no	—
82	C₂×C₁₉⋊C₈	—	4	2	no	—
83	#9707	—	19	1	no	maximal, Sylow
84	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×D₁₉	—	4	2	no	—
86	C₂²×D₁₉	—	4	4	no	—
87	C₂²×D₁₉	—	4	2	no	—
88	C₂²×D₁₉	—	4	4	no	—
89	C₂²×D₁₉	—	4	2	no	—
90	C₂×C₄×C₁₉	—	2	2	no	—
91	C₂×C₄×C₁₉	—	2	2	no	—
92	C₂×C₄×C₁₉	—	2	2	no	—
93	C₂×C₄×C₁₉	—	2	2	no	—
94	C₂×C₄×C₁₉	—	2	2	no	—
95	C₂×C₄×C₁₉	—	2	2	no	—
96	C₂×C₄×C₁₉	#100	1	4	yes	—
97	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
98	C₂×C₄×C₁₉	#121	1	2	yes	—
99	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
100	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
101	C₂×C₄×C₁₉	#135	1	2	yes	—
102	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
103	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
104	C₂×C₄×C₁₉	#137	1	2	yes	—
105	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
106	C₂×Dic₁₉	—	4	2	no	—
107	C₂×Dic₁₉	—	4	4	no	—
108	D₇₆	—	8	4	no	—
109	D₇₆	—	8	2	no	—
110	D₇₆	—	8	2	no	—
111	D₇₆	—	8	2	no	—
112	D₇₆	—	8	1	no	—
113	D₇₆	—	8	1	no	—
114	Dic₃₈	—	8	4	no	—
115	C₈×C₁₉	—	8	2	no	—
116	C₁₉⋊C₈	—	4	4	no	—
117	#2858	—	19	1	no	—
118	#1842	D₁₉	1	1	yes	characteristic, complemented
119	#1767	—	19	1	no	—
120	C₂×#333	—	19	2	no	—
121	C₂×#331	—	19	2	no	—
122	C₂²×C₁₉	#390	1	1	yes	characteristic
123	C₂²×C₁₉	C₂×#100	1	2	yes	—
124	C₂²×C₁₉	#416	1	1	yes	characteristic
125	C₂²×C₁₉	#417	1	2	yes	—
126	C₂²×C₁₉	#417	1	1	yes	characteristic
127	C₂×D₁₉	—	8	4	no	—
128	C₂×D₁₉	—	8	4	no	—
129	C₂×D₁₉	—	8	2	no	—
130	C₂×D₁₉	—	8	2	no	—
131	C₂×D₁₉	—	8	2	no	—
132	C₄×C₁₉	—	2	4	no	—
133	C₄×C₁₉	—	2	2	no	—
134	C₄×C₁₉	—	4	2	no	—
135	C₄×C₁₉	#463	1	2	yes	—
136	C₄×C₁₉	#464	1	2	yes	—
137	C₄×C₁₉	#489	1	2	yes	—
138	C₄×C₁₉	#496	1	1	yes	characteristic
139	C₄×C₁₉	#497	1	1	yes	characteristic
140	Dic₁₉	—	8	2	no	—
141	C₂×C₄⋊Q₈	—	19	1	no	—
142	C₂×#127	—	19	1	no	—
143	C₂×#124	—	19	4	no	—
144	C₂×C₄⋊C₈	—	2	2	no	—
145	C₂×C₄⋊C₈	—	19	2	no	—
146	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
147	C₂×#97	—	38	1	no	—
148	#390	—	38	1	no	—
149	#390	—	38	1	no	—
150	#390	—	38	2	no	—
151	C₄³	C₂×D₁₉	1	1	yes	characteristic
152	#336	—	38	1	no	—
153	#333	—	38	4	no	—
154	#331	—	38	4	no	—
155	C₂×C₁₉	#1551	1	2	yes	—
156	C₂×C₁₉	#1560	1	2	yes	—
157	C₂×C₁₉	#1959	1	1	yes	characteristic
158	C₂×C₁₉	#1965	1	1	yes	characteristic
159	C₂×C₁₉	#1983	1	1	yes	characteristic
160	D₁₉	—	16	2	no	—
161	C₂²×Q₈	—	19	2	no	—
162	C₂²×D₄	—	19	2	no	—
163	C₂²×D₄	—	38	1	no	—
164	C₂²×D₄	—	38	1	no	—
165	C₂²×C₈	—	2	2	no	—
166	C₂²×C₈	—	38	2	no	—
167	C₄⋊Q₈	—	38	2	no	—
168	C₄⋊Q₈	—	38	2	no	—
169	#127	—	38	2	no	—
170	#127	—	38	2	no	—
171	#124	—	76	8	no	—
172	C₂×C₄⋊C₄	—	38	1	no	—
173	C₂×C₄⋊C₄	—	38	1	no	—
174	C₂×C₂²⋊C₄	—	38	4	no	—
175	C₂×C₂²⋊C₄	—	38	4	no	—
176	C₂×C₄²	C₄×D₁₉	1	2	yes	—
177	C₂×C₄²	D₇₆	1	1	yes	characteristic
178	C₂×C₄²	D₇₆	1	1	yes	characteristic
179	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
180	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
181	C₄⋊C₈	—	2	2	no	—
182	C₄⋊C₈	—	2	2	no	—
183	C₄⋊C₈	—	4	4	no	—
184	C₄⋊C₈	—	19	4	no	—
185	C₄⋊C₈	—	38	2	no	—
186	#97	—	76	2	no	—
187	C₁₉	#9707	1	1	yes	characteristic, complemented, Sylow
188	C₂⁴	—	38	2	no	—
189	C₂×Q₈	—	38	4	no	—
190	C₂×Q₈	—	76	4	no	—
191	C₂×D₄	—	38	4	no	—
192	C₂×D₄	—	76	4	no	—
193	C₂×D₄	—	76	2	no	—
194	C₂×D₄	—	76	1	no	—
195	C₂×D₄	—	76	2	no	—
196	C₂×D₄	—	76	1	no	—
197	C₂×D₄	—	76	2	no	—
198	C₂×D₄	—	76	2	no	—
199	C₂×D₄	—	76	1	no	—
200	C₂×D₄	—	76	1	no	—
201	C₂²×C₄	—	38	2	no	—
202	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
203	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
204	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
205	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
206	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
207	C₂×C₈	—	4	4	no	—
208	C₂×C₈	—	4	2	no	—
209	C₂×C₈	—	38	4	no	—
210	C₂×C₈	—	76	2	no	—
211	C₂×C₈	—	76	2	no	—
212	C₄⋊C₄	—	76	1	no	—
213	C₄⋊C₄	—	76	1	no	—
214	C₄⋊C₄	—	76	2	no	—
215	C₂²⋊C₄	—	76	8	no	—
216	C₂²⋊C₄	—	76	8	no	—
217	C₄²	—	2	2	no	—
218	C₄²	—	2	2	no	—
219	C₄²	—	2	4	no	—
220	C₄²	—	2	2	no	—
221	C₄²	—	2	1	no	—
222	C₄²	—	2	1	no	—
223	C₄²	D₄×D₁₉	1	2	yes	—
224	C₄²	#64545	1	2	yes	—
225	C₂³	—	76	2	no	—
226	C₂³	—	76	4	no	—
227	C₂³	—	76	2	no	—
228	C₂³	—	76	2	no	—
229	C₂³	—	76	4	no	—
230	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
231	Q₈	—	152	4	no	—
232	D₄	—	152	4	no	—
233	D₄	—	152	2	no	—
234	D₄	—	152	1	no	—
235	D₄	—	152	1	no	—
236	D₄	—	152	2	no	—
237	D₄	—	152	2	no	—
238	C₂×C₄	—	2	2	no	—
239	C₂×C₄	—	2	2	no	—
240	C₂×C₄	—	2	2	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	2	2	no	—
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	76	2	no	—
245	C₂×C₄	—	76	4	no	—
246	C₂×C₄	#10597280	1	4	yes	—
247	C₂×C₄	#10597339	1	2	yes	—
248	C₂×C₄	#10597341	1	2	yes	—
249	C₂×C₄	#10597350	1	2	yes	—
250	C₂×C₄	#10597354	1	1	yes	characteristic
251	C₂×C₄	#10597355	1	1	yes	characteristic
252	C₂×C₄	#10597378	1	2	yes	—
253	C₂×C₄	#10597386	1	1	yes	characteristic
254	C₂×C₄	#10597388	1	2	yes	—
255	C₂×C₄	#10597393	1	1	yes	characteristic
256	C₈	—	8	2	no	—
257	C₈	—	76	4	no	—
258	C₂²	—	152	4	no	—
259	C₂²	—	152	4	no	—
260	C₂²	—	152	2	no	—
261	C₂²	—	152	2	no	—
262	C₂²	—	152	2	no	—
263	C₂²	#11926445	1	1	yes	characteristic
264	C₂²	C₂×#10597280	1	2	yes	—
265	C₂²	#11926541	1	1	yes	characteristic
266	C₂²	#11926543	1	2	yes	—
267	C₂²	#11926546	1	1	yes	characteristic
268	C₄	—	2	4	no	—
269	C₄	—	2	2	no	—
270	C₄	—	4	2	no	—
271	C₄	—	152	2	no	—
272	C₄	#11926760	1	2	yes	—
273	C₄	#11926767	1	2	yes	—
274	C₄	#11926906	1	2	yes	—
275	C₄	#11926931	1	1	yes	characteristic
276	C₄	#11926936	1	1	yes	characteristic
277	C₂	—	304	2	no	—
278	C₂	#14562328	1	2	yes	—
279	C₂	#14562368	1	2	yes	—
280	C₂	#14564449	1	1	yes	characteristic
281	C₂	#14564474	1	1	yes	characteristic
282	C₂	#14564565	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14571992

C₂

yes

maximal, characteristic

#14563488

C₂

yes

maximal, characteristic, complemented

C₂×#11926292

C₂

yes

maximal, complemented

C₂×#11926287

C₂

yes

maximal

C₁₉×#1842

C₂

yes

maximal, characteristic, complemented

C₂×#10597315

C₂²

yes

characteristic

C₂×#10597320

C₂²

yes

characteristic

C₂×#10597321

C₄

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

—

—

—

—

—

—

—

C₂×C₁₉×C₄⋊C₈

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₂²×D₇₆

—

C₂²×D₇₆

—

C₂²×D₇₆

C₂×C₄

yes

—

C₂²×Dic₃₈

C₂×C₄

yes

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

—

—

—

—

—

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

#10597260

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9707

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#100

yes

—

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#124

yes

characteristic

100

C₂×C₄×C₁₉

#127

yes

characteristic

101

C₂×C₄×C₁₉

#135

yes

—

102

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

103

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

characteristic

104

C₂×C₄×C₁₉

#137

yes

—

105

C₂×C₄×C₁₉

#137

yes

characteristic

106

C₂×Dic₁₉

—

107

C₂×Dic₁₉

—

108

D₇₆

—

109

D₇₆

—

110

D₇₆

—

111

D₇₆

—

112

D₇₆

—

113

D₇₆

—

114

Dic₃₈

—

115

C₈×C₁₉

—

116

C₁₉⋊C₈

—

117

#2858

—

118

#1842

D₁₉

yes

characteristic, complemented

119

#1767

—

120

C₂×#333

—

121

C₂×#331

—

122

C₂²×C₁₉

#390

yes

characteristic

123

C₂²×C₁₉

C₂×#100

yes

—

124

C₂²×C₁₉

#416

yes

characteristic

125

C₂²×C₁₉

#417

yes

—

126

C₂²×C₁₉

#417

yes

characteristic

127

C₂×D₁₉

—

128

C₂×D₁₉

—

129

C₂×D₁₉

—

130

C₂×D₁₉

—

131

C₂×D₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

—

135

C₄×C₁₉

#463

yes

—

136

C₄×C₁₉

#464

yes

—

137

C₄×C₁₉

#489

yes

—

138

C₄×C₁₉

#496

yes

characteristic

139

C₄×C₁₉

#497

yes

characteristic

140

Dic₁₉

—

141

C₂×C₄⋊Q₈

—

142

C₂×#127

—

143

C₂×#124

—

144

C₂×C₄⋊C₈

—

145

C₂×C₄⋊C₈

—

146

C₂×C₄⋊C₈

C₂×D₁₉

yes

—

147

C₂×#97

—

148

#390

—

149

#390

—

150

#390

—

151

C₄³

C₂×D₁₉

yes

characteristic

152

#336

—

153

#333

—

154

#331

—

155

C₂×C₁₉

#1551

yes

—

156

C₂×C₁₉

#1560

yes

—

157

C₂×C₁₉

#1959

yes

characteristic

158

C₂×C₁₉

#1965

yes

characteristic

159

C₂×C₁₉

#1983

yes

characteristic

160

D₁₉

—

161

C₂²×Q₈

—

162

C₂²×D₄

—

163

C₂²×D₄

—

164

C₂²×D₄

—

165

C₂²×C₈

—

166

C₂²×C₈

—

167

C₄⋊Q₈

—

168

C₄⋊Q₈

—

169

#127

—

170

#127

—

171

#124

—

172

C₂×C₄⋊C₄

—

173

C₂×C₄⋊C₄

—

174

C₂×C₂²⋊C₄

—

175

C₂×C₂²⋊C₄

—

176

C₂×C₄²

C₄×D₁₉

yes

—

177

C₂×C₄²

D₇₆

yes

characteristic

178

C₂×C₄²

D₇₆

yes

characteristic

179

C₂×C₄²

C₂²⋊D₁₉

yes

—

180

C₂×C₄²

C₂²×D₁₉

yes

characteristic

181

C₄⋊C₈

—

182

C₄⋊C₈

—

183

C₄⋊C₈

—

184

C₄⋊C₈

—

185

C₄⋊C₈

—

186

#97

—

187

C₁₉

#9707

yes

characteristic, complemented, Sylow

188

C₂⁴

—

189

C₂×Q₈

—

190

C₂×Q₈

—

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂×D₄

—

194

C₂×D₄

—

195

C₂×D₄

—

196

C₂×D₄

—

197

C₂×D₄

—

198

C₂×D₄

—

199

C₂×D₄

—

200

C₂×D₄

—

201

C₂²×C₄

—

202

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

203

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

204

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

205

C₂²×C₄

C₂×D₇₆

yes

characteristic

206

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

207

C₂×C₈

—

208

C₂×C₈

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

214

C₄⋊C₄

—

215

C₂²⋊C₄

—

216

C₂²⋊C₄

—

217

C₄²

—

218

C₄²

—

219

C₄²

—

220

C₄²

—

221

C₄²

—

222

C₄²

—

223

C₄²

D₄×D₁₉

yes

—

224

C₄²

#64545

yes

—

225

C₂³

—

226

C₂³

—

227

C₂³

—

228

C₂³

—

229

C₂³

—

230

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

231

Q₈

—

152

—

232

D₄

—

152

—

233

D₄

—

152

—

234

D₄

—

152

—

235

D₄

—

152

—

236

D₄

—

152

—

237

D₄

—

152

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

246

C₂×C₄

#10597280

yes

—

247

C₂×C₄

#10597339

yes

—

248

C₂×C₄

#10597341

yes

—

249

C₂×C₄

#10597350

yes

—

250

C₂×C₄

#10597354

yes

characteristic

251

C₂×C₄

#10597355

yes

characteristic

252

C₂×C₄

#10597378

yes

—

253

C₂×C₄

#10597386

yes

characteristic

254

C₂×C₄

#10597388

yes

—

255

C₂×C₄

#10597393

yes

characteristic

256

C₈

—

257

C₈

—

258

C₂²

—

152

—

259

C₂²

—

152

—

260

C₂²

—

152

—

261

C₂²

—

152

—

262

C₂²

—

152

—

263

C₂²

#11926445

yes

characteristic

264

C₂²

C₂×#10597280

yes

—

265

C₂²

#11926541

yes

characteristic

266

C₂²

#11926543

yes

—

267

C₂²

#11926546

yes

characteristic

268

C₄

—

269

C₄

—

270

C₄

—

271

C₄

—

152

—

272

C₄

#11926760

yes

—

273

C₄

#11926767

yes

—

274

C₄

#11926906

yes

—

275

C₄

#11926931

yes

characteristic

276

C₄

#11926936

yes

characteristic

277

C₂

—

304

—

278

C₂

#14562328

yes

—

279

C₂

#14562368

yes

—

280

C₂

#14564449

yes

characteristic

281

C₂

#14564474

yes

characteristic

282

C₂

#14564565

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1842	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂×#10597320	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1842	D₁₉
hypocenter	C₁₉	#9707
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1842

subgroup

G/H

center

C₂³

C₂×(C₂×D₁₉)⋊C₄

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1842

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂×#10597320

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1842

N	H ≅ G/N	type
2. #14563488	C₂	semidirect
3. C₂×#11926292	C₂	semidirect
5. C₁₉×#1842	C₂	semidirect
118. #1842	D₁₉	semidirect
187. C₁₉	#9707	semidirect

H ≅ G/N

type

2. #14563488

C₂

semidirect

3. C₂×#11926292

C₂

semidirect

5. C₁₉×#1842

C₂

semidirect

118. #1842

D₁₉

semidirect

187. C₁₉

#9707

semidirect

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

subgroup	index
#14571992	2
#14563488	2
C₂×#11926292	2
C₂×#11926287	2
C₁₉×#1842	2
#9707	19

subgroup

index

C₁₉×#1842

Subgroups — #18081640

Conjugacy classes of subgroups

Complements

Maximal subgroups