Group #18070762 — subgroups

Subgroups — #18070762

Order 4864.

874 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 874 conjugacy classes of subgroups — too many to draw. Only its 139 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	#14563397	C₂	1	2	yes	maximal, complemented
2	#14561456	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₉×#390	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
5	C₂×#10597260	—	2	2	no	—
6	#11926299	C₂²	1	4	yes	complemented
7	C₂³×D₄×C₁₉	C₄	1	1	yes	characteristic
8	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
9	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
10	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#390	—	2	2	no	—
12	C₁₉×#390	C₄	1	2	yes	—
13	C₁₉×#390	C₂²	1	2	yes	—
14	C₂⁵×C₁₉	—	2	1	no	—
15	C₂²×D₄×C₁₉	—	2	4	no	—
16	C₂²×D₄×C₁₉	—	2	1	no	—
17	C₂²×D₄×C₁₉	—	4	2	no	—
18	C₂²×D₄×C₁₉	—	4	2	no	—
19	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
20	C₂³×C₄×C₁₉	—	2	1	no	—
21	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	D₄	1	2	yes	—
23	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
24	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
25	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
26	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
27	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
28	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
29	C₂×C₄²×C₁₉	—	4	2	no	—
30	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₉	D₄	1	2	yes	—
32	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
33	C₂²×C₁₉⋊C₈	—	2	4	no	—
34	C₂²⋊(C₁₉⋊C₈)	—	2	8	no	—
35	#10597260	—	4	4	no	—
36	C₂⁴×C₁₉	—	2	4	no	—
37	C₂⁴×C₁₉	—	2	2	no	—
38	C₂⁴×C₁₉	—	4	4	no	—
39	C₂⁴×C₁₉	—	4	2	no	—
40	C₂⁴×C₁₉	—	4	2	no	—
41	C₂⁴×C₁₉	—	4	4	no	—
42	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
43	C₂×D₄×C₁₉	—	2	4	no	—
44	C₂×D₄×C₁₉	—	2	2	no	—
45	C₂×D₄×C₁₉	—	4	2	no	—
46	C₂×D₄×C₁₉	—	4	2	no	—
47	C₂×D₄×C₁₉	—	4	16	no	—
48	C₂×D₄×C₁₉	—	4	2	no	—
49	C₂×D₄×C₁₉	—	4	2	no	—
50	C₂×D₄×C₁₉	M₁₆	1	4	yes	—
51	C₂²×C₄×C₁₉	—	2	2	no	—
52	C₂²×C₄×C₁₉	—	2	2	no	—
53	C₂²×C₄×C₁₉	—	2	2	no	—
54	C₂²×C₄×C₁₉	—	2	4	no	—
55	C₂²×C₄×C₁₉	—	2	4	no	—
56	C₂²×C₄×C₁₉	—	2	2	no	—
57	C₂²×C₄×C₁₉	—	4	2	no	—
58	C₂²×C₄×C₁₉	—	4	4	no	—
59	C₂²×C₄×C₁₉	—	4	2	no	—
60	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
64	C₄⋊C₄×C₁₉	—	4	2	no	—
65	C₄⋊C₄×C₁₉	—	4	2	no	—
66	C₂²⋊C₄×C₁₉	—	4	8	no	—
67	C₂²⋊C₄×C₁₉	—	4	8	no	—
68	C₄²×C₁₉	—	2	4	no	—
69	C₄²×C₁₉	—	4	1	no	—
70	C₄²×C₁₉	—	4	1	no	—
71	C₂×C₁₉⋊C₈	—	2	8	no	—
72	C₂×C₁₉⋊C₈	—	4	4	no	—
73	C₂×C₁₉⋊C₈	—	4	4	no	—
74	#7626	—	19	1	no	maximal, Sylow
75	C₂³×C₁₉	—	2	1	no	—
76	C₂³×C₁₉	—	2	1	no	—
77	C₂³×C₁₉	—	2	2	no	—
78	C₂³×C₁₉	—	2	4	no	—
79	C₂³×C₁₉	—	4	8	no	—
80	C₂³×C₁₉	—	4	16	no	—
81	C₂³×C₁₉	—	4	2	no	—
82	C₂³×C₁₉	—	4	2	no	—
83	C₂³×C₁₉	—	4	4	no	—
84	C₂³×C₁₉	—	4	4	no	—
85	C₂³×C₁₉	—	8	4	no	—
86	C₂³×C₁₉	—	8	8	no	—
87	C₂³×C₁₉	—	8	4	no	—
88	C₂³×C₁₉	#100	1	2	yes	—
89	C₂³×C₁₉	#104	1	4	yes	—
90	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	D₄×C₁₉	—	4	4	no	—
92	D₄×C₁₉	—	4	8	no	—
93	D₄×C₁₉	—	4	4	no	—
94	C₂×C₄×C₁₉	—	2	8	no	—
95	C₂×C₄×C₁₉	—	2	1	no	—
96	C₂×C₄×C₁₉	—	2	2	no	—
97	C₂×C₄×C₁₉	—	2	1	no	—
98	C₂×C₄×C₁₉	—	2	1	no	—
99	C₂×C₄×C₁₉	—	2	1	no	—
100	C₂×C₄×C₁₉	—	2	2	no	—
101	C₂×C₄×C₁₉	—	2	2	no	—
102	C₂×C₄×C₁₉	—	2	2	no	—
103	C₂×C₄×C₁₉	—	2	2	no	—
104	C₂×C₄×C₁₉	—	4	8	no	—
105	C₂×C₄×C₁₉	—	4	2	no	—
106	C₂×C₄×C₁₉	—	4	4	no	—
107	C₂×C₄×C₁₉	—	8	4	no	—
108	C₂×C₄×C₁₉	#99	1	2	yes	—
109	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
110	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
111	C₁₉⋊C₈	—	4	8	no	—
112	C₂×#390	D₁₉	1	1	yes	characteristic
113	#1749	—	19	2	no	—
114	#1270	—	19	4	no	—
115	C₂²×C₁₉	—	2	2	no	—
116	C₂²×C₁₉	—	2	2	no	—
117	C₂²×C₁₉	—	2	4	no	—
118	C₂²×C₁₉	—	2	4	no	—
119	C₂²×C₁₉	—	4	4	no	—
120	C₂²×C₁₉	—	4	8	no	—
121	C₂²×C₁₉	—	8	16	no	—
122	C₂²×C₁₉	—	8	2	no	—
123	C₂²×C₁₉	—	8	4	no	—
124	C₂²×C₁₉	—	8	2	no	—
125	C₂²×C₁₉	#329	1	4	yes	—
126	C₂²×C₁₉	#407	1	1	yes	characteristic
127	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
128	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
129	C₂²×C₁₉	#418	1	2	yes	—
130	C₂²×C₁₉	C₂×#104	1	2	yes	—
131	C₄×C₁₉	—	2	2	no	—
132	C₄×C₁₉	—	2	2	no	—
133	C₄×C₁₉	—	2	4	no	—
134	C₄×C₁₉	—	4	2	no	—
135	C₄×C₁₉	—	8	2	no	—
136	C₂³×D₄	Dic₁₉	1	1	yes	characteristic
137	C₂²×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
138	C₂²×C₂²⋊C₄	—	2	2	no	—
139	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
140	C₂×C₂²⋊C₈	—	38	2	no	—
141	C₂×#97	—	38	2	no	—
142	#390	—	2	2	no	—
143	#390	Dic₁₉	1	2	yes	—
144	#390	C₂×D₁₉	1	2	yes	—
145	#336	—	19	4	no	—
146	C₂×C₁₉	—	2	4	no	—
147	C₂×C₁₉	—	8	4	no	—
148	C₂×C₁₉	#1462	1	1	yes	characteristic
149	C₂×C₁₉	#1490	1	2	yes	—
150	C₂×C₁₉	#1507	1	2	yes	—
151	C₂×C₁₉	C₂×#329	1	1	yes	characteristic
152	C₂×C₁₉	#1555	1	1	yes	characteristic
153	C₂⁵	—	2	1	no	—
154	C₂²×D₄	—	2	4	no	—
155	C₂²×D₄	—	2	1	no	—
156	C₂²×D₄	—	4	2	no	—
157	C₂²×D₄	—	4	2	no	—
158	C₂²×D₄	C₂×Dic₁₉	1	2	yes	—
159	C₂³×C₄	—	2	1	no	—
160	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
161	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
162	C₂²×C₈	—	38	4	no	—
163	C₂×C₄⋊C₄	—	2	1	no	—
164	C₂×C₄⋊C₄	—	4	2	no	—
165	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
166	C₂×C₂²⋊C₄	—	2	4	no	—
167	C₂×C₂²⋊C₄	—	2	4	no	—
168	C₂×C₂²⋊C₄	—	4	8	no	—
169	C₂×C₄²	—	4	2	no	—
170	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
171	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
172	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
173	C₂²⋊C₈	—	38	8	no	—
174	#97	—	76	4	no	—
175	C₁₉	#7626	1	1	yes	characteristic, complemented, Sylow
176	C₂⁴	—	2	4	no	—
177	C₂⁴	—	2	2	no	—
178	C₂⁴	—	4	4	no	—
179	C₂⁴	—	4	2	no	—
180	C₂⁴	—	4	2	no	—
181	C₂⁴	—	4	4	no	—
182	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
183	C₂×D₄	—	2	4	no	—
184	C₂×D₄	—	2	2	no	—
185	C₂×D₄	—	4	2	no	—
186	C₂×D₄	—	4	2	no	—
187	C₂×D₄	—	4	16	no	—
188	C₂×D₄	—	4	2	no	—
189	C₂×D₄	—	4	2	no	—
190	C₂×D₄	#64520	1	4	yes	—
191	C₂²×C₄	—	2	2	no	—
192	C₂²×C₄	—	2	2	no	—
193	C₂²×C₄	—	2	2	no	—
194	C₂²×C₄	—	2	4	no	—
195	C₂²×C₄	—	2	4	no	—
196	C₂²×C₄	—	2	2	no	—
197	C₂²×C₄	—	4	2	no	—
198	C₂²×C₄	—	4	4	no	—
199	C₂²×C₄	—	4	2	no	—
200	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
201	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
202	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
203	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
204	C₂×C₈	—	38	8	no	—
205	C₂×C₈	—	76	4	no	—
206	C₂×C₈	—	76	4	no	—
207	C₄⋊C₄	—	4	2	no	—
208	C₄⋊C₄	—	4	2	no	—
209	C₂²⋊C₄	—	4	8	no	—
210	C₂²⋊C₄	—	4	8	no	—
211	C₄²	—	2	4	no	—
212	C₄²	—	4	1	no	—
213	C₄²	—	4	1	no	—
214	C₂³	—	2	2	no	—
215	C₂³	—	2	1	no	—
216	C₂³	—	2	1	no	—
217	C₂³	—	2	4	no	—
218	C₂³	—	4	8	no	—
219	C₂³	—	4	16	no	—
220	C₂³	—	4	4	no	—
221	C₂³	—	4	4	no	—
222	C₂³	—	4	2	no	—
223	C₂³	—	4	2	no	—
224	C₂³	—	8	4	no	—
225	C₂³	—	8	8	no	—
226	C₂³	—	8	4	no	—
227	C₂³	#10597290	1	2	yes	—
228	C₂³	#10597294	1	4	yes	—
229	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
230	D₄	—	4	4	no	—
231	D₄	—	4	8	no	—
232	D₄	—	4	4	no	—
233	C₂×C₄	—	2	8	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	1	no	—
236	C₂×C₄	—	2	2	no	—
237	C₂×C₄	—	2	1	no	—
238	C₂×C₄	—	2	1	no	—
239	C₂×C₄	—	2	1	no	—
240	C₂×C₄	—	2	2	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	2	2	no	—
243	C₂×C₄	—	4	8	no	—
244	C₂×C₄	—	4	4	no	—
245	C₂×C₄	—	4	2	no	—
246	C₂×C₄	—	8	4	no	—
247	C₂×C₄	#10597291	1	2	yes	—
248	C₂×C₄	C₂×#64520	1	2	yes	—
249	C₂×C₄	#10597378	1	4	yes	—
250	C₈	—	76	8	no	—
251	C₂²	—	2	4	no	—
252	C₂²	—	2	2	no	—
253	C₂²	—	2	4	no	—
254	C₂²	—	2	2	no	—
255	C₂²	—	4	8	no	—
256	C₂²	—	4	4	no	—
257	C₂²	—	8	16	no	—
258	C₂²	—	8	2	no	—
259	C₂²	—	8	4	no	—
260	C₂²	—	8	2	no	—
261	C₂²	#11926284	1	4	yes	—
262	C₂²	#11926508	1	1	yes	characteristic
263	C₂²	C₂×#10597291	1	1	yes	characteristic
264	C₂²	C₂×#10597290	1	1	yes	characteristic
265	C₂²	#11926549	1	2	yes	—
266	C₂²	C₂×#10597294	1	2	yes	—
267	C₄	—	2	4	no	—
268	C₄	—	2	2	no	—
269	C₄	—	2	2	no	—
270	C₄	—	4	2	no	—
271	C₄	—	8	2	no	—
272	C₂	—	2	4	no	—
273	C₂	—	8	4	no	—
274	C₂	#14561962	1	1	yes	characteristic
275	C₂	#14562078	1	2	yes	—
276	C₂	#14562151	1	2	yes	—
277	C₂	C₂×#11926284	1	1	yes	characteristic
278	C₂	#14562349	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563397

C₂

yes

maximal, complemented

#14561456

C₂

yes

maximal, complemented

C₂×C₁₉×#390

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×#10597260

—

#11926299

C₂²

yes

complemented

C₂³×D₄×C₁₉

C₄

yes

characteristic

C₂²×C₄⋊C₄×C₁₉

C₄

yes

characteristic

C₂²×C₂²⋊C₄×C₁₉

—

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₁₉×#390

—

C₁₉×#390

C₄

yes

—

C₁₉×#390

C₂²

yes

—

C₂⁵×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

#10597260

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

M₁₆

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7626

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#100

yes

—

C₂³×C₁₉

#104

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×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

—

106

C₂×C₄×C₁₉

—

107

C₂×C₄×C₁₉

—

108

C₂×C₄×C₁₉

#99

yes

—

109

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

110

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

111

C₁₉⋊C₈

—

112

C₂×#390

D₁₉

yes

characteristic

113

#1749

—

114

#1270

—

115

C₂²×C₁₉

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

#329

yes

—

126

C₂²×C₁₉

#407

yes

characteristic

127

C₂²×C₁₉

C₂×#99

yes

characteristic

128

C₂²×C₁₉

C₂×#100

yes

characteristic

129

C₂²×C₁₉

#418

yes

—

130

C₂²×C₁₉

C₂×#104

yes

—

131

C₄×C₁₉

—

132

C₄×C₁₉

—

133

C₄×C₁₉

—

134

C₄×C₁₉

—

135

C₄×C₁₉

—

136

C₂³×D₄

Dic₁₉

yes

characteristic

137

C₂²×C₄⋊C₄

Dic₁₉

yes

characteristic

138

C₂²×C₂²⋊C₄

—

139

C₂²×C₄²

C₂×D₁₉

yes

characteristic

140

C₂×C₂²⋊C₈

—

141

C₂×#97

—

142

#390

—

143

#390

Dic₁₉

yes

—

144

#390

C₂×D₁₉

yes

—

145

#336

—

146

C₂×C₁₉

—

147

C₂×C₁₉

—

148

C₂×C₁₉

#1462

yes

characteristic

149

C₂×C₁₉

#1490

yes

—

150

C₂×C₁₉

#1507

yes

—

151

C₂×C₁₉

C₂×#329

yes

characteristic

152

C₂×C₁₉

#1555

yes

characteristic

153

C₂⁵

—

154

C₂²×D₄

—

155

C₂²×D₄

—

156

C₂²×D₄

—

157

C₂²×D₄

—

158

C₂²×D₄

C₂×Dic₁₉

yes

—

159

C₂³×C₄

—

160

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

161

C₂³×C₄

C₂²⋊D₁₉

yes

—

162

C₂²×C₈

—

163

C₂×C₄⋊C₄

—

164

C₂×C₄⋊C₄

—

165

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

166

C₂×C₂²⋊C₄

—

167

C₂×C₂²⋊C₄

—

168

C₂×C₂²⋊C₄

—

169

C₂×C₄²

—

170

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

171

C₂×C₄²

C₂²⋊D₁₉

yes

—

172

C₂×C₄²

C₂²×D₁₉

yes

characteristic

173

C₂²⋊C₈

—

174

#97

—

175

C₁₉

#7626

yes

characteristic, complemented, Sylow

176

C₂⁴

—

177

C₂⁴

—

178

C₂⁴

—

179

C₂⁴

—

180

C₂⁴

—

181

C₂⁴

—

182

C₂⁴

C₂²⋊Dic₁₉

yes

characteristic

183

C₂×D₄

—

184

C₂×D₄

—

185

C₂×D₄

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

#64520

yes

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

—

197

C₂²×C₄

—

198

C₂²×C₄

—

199

C₂²×C₄

—

200

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

201

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

202

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

203

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₂²⋊C₄

—

210

C₂²⋊C₄

—

211

C₄²

—

212

C₄²

—

213

C₄²

—

214

C₂³

—

215

C₂³

—

216

C₂³

—

217

C₂³

—

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

—

223

C₂³

—

224

C₂³

—

225

C₂³

—

226

C₂³

—

227

C₂³

#10597290

yes

—

228

C₂³

#10597294

yes

—

229

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

230

D₄

—

231

D₄

—

232

D₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

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

—

247

C₂×C₄

#10597291

yes

—

248

C₂×C₄

C₂×#64520

yes

—

249

C₂×C₄

#10597378

yes

—

250

C₈

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

—

256

C₂²

—

257

C₂²

—

258

C₂²

—

259

C₂²

—

260

C₂²

—

261

C₂²

#11926284

yes

—

262

C₂²

#11926508

yes

characteristic

263

C₂²

C₂×#10597291

yes

characteristic

264

C₂²

C₂×#10597290

yes

characteristic

265

C₂²

#11926549

yes

—

266

C₂²

C₂×#10597294

yes

—

267

C₄

—

268

C₄

—

269

C₄

—

270

C₄

—

271

C₄

—

272

C₂

—

273

C₂

—

274

C₂

#14561962

yes

characteristic

275

C₂

#14562078

yes

—

276

C₂

#14562151

yes

—

277

C₂

C₂×#11926284

yes

characteristic

278

C₂

#14562349

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#390	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×D₄×C₁₉	C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#390	D₁₉
hypocenter	C₁₉	#7626
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#390

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#390

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂³×D₄×C₁₉

C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#390

N	H ≅ G/N	type
1. #14563397	C₂	semidirect
2. #14561456	C₂	semidirect
6. #11926299	C₂²	semidirect
175. C₁₉	#7626	semidirect

H ≅ G/N

type

1. #14563397

C₂

semidirect

2. #14561456

C₂

semidirect

6. #11926299

C₂²

semidirect

175. C₁₉

#7626

semidirect

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

subgroup	index
#14563397	2
#14561456	2
C₂×C₁₉×#390	2
#7626	19

subgroup

index

#14563397

#14561456

C₂×C₁₉×#390

#7626

Subgroups — #18070762

Conjugacy classes of subgroups

Complements

Maximal subgroups