Group #18083505 — subgroups

Subgroups — #18083505

Order 4864.

636 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 103 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	#14574081	C₂	1	1	yes	maximal, characteristic, complemented
2	#14573635	C₂	1	2	yes	maximal, complemented
3	#14562033	C₂	1	2	yes	maximal, complemented
4	#14561466	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1955	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597350	—	2	2	no	—
7	#11927094	C₂²	1	2	yes	—
8	#11926938	—	2	2	no	—
9	#11926933	—	2	2	no	—
10	#11926857	—	2	2	no	—
11	#11926824	—	2	2	no	—
12	#11926739	—	2	2	no	—
13	#11926678	—	2	2	no	—
14	C₄×#64525	—	2	4	no	—
15	#11926597	C₂²	1	2	yes	—
16	#11926271	—	2	4	no	—
17	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
20	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
21	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₉	—	2	1	no	—
23	C₂×#64541	—	2	2	no	—
24	C₂²×C₈×C₁₉	—	2	1	no	—
25	C₂²×C₈×C₁₉	D₄	1	2	yes	—
26	C₄×D₄×C₁₉	—	2	2	no	—
27	C₄×D₄×C₁₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
30	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×#64525	—	2	4	no	—
32	#10597376	—	2	2	no	—
33	#10597376	—	2	2	no	—
34	C₂×Dic₇₆	—	2	2	no	—
35	#10597350	—	4	4	no	—
36	#10597350	—	4	4	no	—
37	C₂×D₁₅₂	—	2	2	no	—
38	C₂×#64516	—	2	4	no	—
39	#10597321	—	2	2	no	—
40	#10597320	D₄	1	2	yes	—
41	C₄×D₇₆	—	2	2	no	—
42	C₄×D₇₆	—	2	2	no	—
43	#10597315	D₄	1	2	yes	—
44	C₁₉×C₄⋊C₈	—	2	2	no	—
45	C₁₉×C₂²⋊C₈	—	4	4	no	—
46	C₁₉×#97	—	2	2	no	—
47	#10597289	—	2	4	no	—
48	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
49	#10597266	—	2	4	no	—
50	#10597264	—	2	4	no	—
51	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
52	C₄×C₁₉⋊C₈	D₄	1	4	yes	—
53	C₂⁴×C₁₉	—	2	1	no	—
54	C₂×D₄×C₁₉	—	2	2	no	—
55	C₂×D₄×C₁₉	—	4	2	no	—
56	C₂²×C₄×C₁₉	—	2	1	no	—
57	C₂²×C₄×C₁₉	—	4	1	no	—
58	C₂²×C₄×C₁₉	—	4	1	no	—
59	C₂²×C₄×C₁₉	—	4	2	no	—
60	C₂²×C₄×C₁₉	—	4	2	no	—
61	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
64	C₂×C₂²⋊D₁₉	—	4	2	no	—
65	#64541	—	4	4	no	—
66	#64541	—	4	4	no	—
67	C₂×D₇₆	—	2	2	no	—
68	C₂×D₇₆	—	2	2	no	—
69	C₂×D₇₆	—	2	2	no	—
70	C₂×C₄×D₁₉	—	4	2	no	—
71	C₂×Dic₃₈	—	2	2	no	—
72	C₂×C₈×C₁₉	—	2	2	no	—
73	C₂×C₈×C₁₉	—	2	2	no	—
74	C₂×C₈×C₁₉	—	4	1	no	—
75	C₂×C₈×C₁₉	—	4	2	no	—
76	C₂×C₈×C₁₉	D₈	1	4	yes	complemented
77	C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₂²⋊C₄×C₁₉	—	4	2	no	—
79	C₄²×C₁₉	C₂×D₄	1	2	yes	—
80	C₄²×C₁₉	C₂×D₄	1	2	yes	—
81	#64525	—	4	8	no	—
82	(C₂×D₁₉)⋊C₄	—	4	2	no	—
83	(C₂×D₁₉)⋊C₄	—	4	2	no	—
84	C₄⋊Dic₁₉	—	2	2	no	—
85	C₄⋊Dic₁₉	—	2	2	no	—
86	C₂×C₁₉⋊C₈	—	2	4	no	—
87	Dic₇₆	—	4	4	no	—
88	D₁₅₂	—	4	4	no	—
89	#64516	—	4	8	no	—
90	#10032	—	19	1	no	maximal, Sylow
91	C₂³×C₁₉	—	2	2	no	—
92	C₂³×C₁₉	—	4	1	no	—
93	C₂³×C₁₉	—	4	2	no	—
94	C₂³×C₁₉	—	4	1	no	—
95	C₂³×C₁₉	—	4	2	no	—
96	C₂³×C₁₉	#121	1	1	yes	characteristic
97	C₂²×D₁₉	—	4	2	no	—
98	D₄×C₁₉	—	2	4	no	—
99	D₄×C₁₉	—	4	2	no	—
100	C₂×C₄×C₁₉	—	4	1	no	—
101	C₂×C₄×C₁₉	—	4	1	no	—
102	C₂×C₄×C₁₉	—	4	1	no	—
103	C₂×C₄×C₁₉	—	4	2	no	—
104	C₂×C₄×C₁₉	—	8	2	no	—
105	C₂×C₄×C₁₉	—	8	1	no	—
106	C₂×C₄×C₁₉	—	8	1	no	—
107	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
108	C₂×C₄×C₁₉	#120	1	2	yes	—
109	C₂×C₄×C₁₉	#121	1	2	yes	—
110	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
111	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
112	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
113	C₂²⋊D₁₉	—	8	4	no	—
114	C₂×Dic₁₉	—	4	2	no	—
115	D₇₆	—	4	4	no	—
116	D₇₆	—	4	4	no	—
117	D₇₆	—	4	4	no	—
118	C₄×D₁₉	—	8	2	no	—
119	C₄×D₁₉	—	8	2	no	—
120	Dic₃₈	—	4	4	no	—
121	C₈×C₁₉	—	2	4	no	—
122	C₈×C₁₉	—	8	1	no	—
123	C₁₉⋊C₈	—	4	4	no	—
124	#3150	—	19	1	no	—
125	#3100	—	19	2	no	—
126	#1955	D₁₉	1	1	yes	characteristic, complemented
127	#1480	—	19	2	no	—
128	#1275	—	19	1	no	—
129	C₂²×C₁₉	—	2	1	no	—
130	C₂²×C₁₉	—	2	1	no	—
131	C₂²×C₁₉	—	4	4	no	—
132	C₂²×C₁₉	—	4	2	no	—
133	C₂²×C₁₉	—	8	2	no	—
134	C₂²×C₁₉	—	8	1	no	—
135	C₂²×C₁₉	—	8	1	no	—
136	C₂²×C₁₉	#392	1	1	yes	characteristic
137	C₂²×C₁₉	#459	1	2	yes	—
138	C₂×D₁₉	—	8	2	no	—
139	C₂×D₁₉	—	8	2	no	—
140	C₂×D₁₉	—	8	2	no	—
141	C₄×C₁₉	—	2	2	no	—
142	C₄×C₁₉	—	2	2	no	—
143	C₄×C₁₉	—	8	1	no	—
144	C₄×C₁₉	#447	1	2	yes	—
145	C₄×C₁₉	#493	1	1	yes	characteristic
146	C₄×C₁₉	#496	1	1	yes	characteristic
147	Dic₁₉	—	8	2	no	—
148	C₂×#135	—	38	2	no	—
149	#532	—	19	2	no	—
150	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
151	#497	—	38	2	no	—
152	#496	—	38	2	no	—
153	#480	—	38	2	no	—
154	#474	—	38	2	no	—
155	#459	—	38	2	no	—
156	#447	—	38	2	no	—
157	C₄×D₈	—	38	4	no	—
158	#431	—	19	2	no	—
159	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
160	C₂×C₂²⋊C₈	—	2	2	no	—
161	C₂×#97	C₂×D₁₉	1	1	yes	characteristic
162	D₄⋊C₈	—	38	4	no	—
163	C₂×C₁₉	—	2	2	no	—
164	C₂×C₁₉	—	8	2	no	—
165	C₂×C₁₉	#2010	1	1	yes	characteristic
166	C₂×C₁₉	#2011	1	1	yes	characteristic
167	C₂×C₁₉	#2017	1	1	yes	characteristic
168	D₁₉	—	16	2	no	—
169	C₂×#41	—	38	2	no	—
170	C₂²×D₄	D₇₆	1	1	yes	characteristic
171	C₂³×C₄	—	2	1	no	—
172	#135	—	76	4	no	—
173	#135	—	76	4	no	—
174	C₂×Q₁₆	—	38	2	no	—
175	C₂×SD₁₆	—	38	4	no	—
176	C₂×D₈	—	38	2	no	—
177	C₂×D₈	—	38	4	no	—
178	C₂²×C₈	—	2	1	no	—
179	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
180	C₄⋊Q₈	—	19	2	no	—
181	#127	—	19	2	no	—
182	#124	—	38	2	no	—
183	#121	—	38	2	no	—
184	#121	—	38	2	no	—
185	C₄×D₄	—	2	2	no	—
186	C₄×D₄	—	2	2	no	—
187	C₄×D₄	—	38	2	no	—
188	C₄×D₄	—	38	2	no	—
189	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
190	C₂×C₂²⋊C₄	—	2	1	no	—
191	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
192	#107	—	38	4	no	—
193	C₄⋊C₈	—	2	2	no	—
194	C₄⋊C₈	—	38	2	no	—
195	#102	—	38	4	no	—
196	#102	—	38	4	no	—
197	C₂²⋊C₈	—	4	4	no	—
198	C₂²⋊C₈	—	38	2	no	—
199	#97	—	2	2	no	—
200	C₄×C₈	—	19	4	no	—
201	C₁₉	#10032	1	1	yes	characteristic, complemented, Sylow
202	C₂⁴	—	2	1	no	—
203	#41	—	76	4	no	—
204	#41	—	76	4	no	—
205	C₂×Q₈	—	38	2	no	—
206	C₂×D₄	—	2	2	no	—
207	C₂×D₄	—	4	2	no	—
208	C₂×D₄	—	38	2	no	—
209	C₂×D₄	—	38	2	no	—
210	C₂×D₄	—	38	2	no	—
211	C₂×D₄	—	76	2	no	—
212	C₂²×C₄	—	2	1	no	—
213	C₂²×C₄	—	4	2	no	—
214	C₂²×C₄	—	4	1	no	—
215	C₂²×C₄	—	4	1	no	—
216	C₂²×C₄	—	4	2	no	—
217	C₂²×C₄	—	76	2	no	—
218	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
219	C₂²×C₄	#64541	1	1	yes	characteristic
220	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
221	Q₁₆	—	76	4	no	—
222	SD₁₆	—	76	8	no	—
223	D₈	—	76	4	no	—
224	D₈	—	76	8	no	—
225	C₂×C₈	—	2	2	no	—
226	C₂×C₈	—	2	2	no	—
227	C₂×C₈	—	4	2	no	—
228	C₂×C₈	—	4	1	no	—
229	C₂×C₈	—	38	4	no	—
230	C₂×C₈	#64525	1	4	yes	complemented
231	C₄⋊C₄	—	2	2	no	—
232	C₄⋊C₄	—	38	2	no	—
233	C₄⋊C₄	—	38	2	no	—
234	C₂²⋊C₄	—	4	2	no	—
235	C₂²⋊C₄	—	76	2	no	—
236	C₂²⋊C₄	—	76	2	no	—
237	C₄²	D₄×D₁₉	1	2	yes	—
238	C₄²	D₄×D₁₉	1	2	yes	—
239	C₂³	—	2	2	no	—
240	C₂³	—	4	1	no	—
241	C₂³	—	4	2	no	—
242	C₂³	—	4	1	no	—
243	C₂³	—	4	2	no	—
244	C₂³	—	76	2	no	—
245	C₂³	#10597376	1	1	yes	characteristic
246	Q₈	—	76	4	no	—
247	D₄	—	2	4	no	—
248	D₄	—	4	2	no	—
249	D₄	—	76	4	no	—
250	D₄	—	76	4	no	—
251	D₄	—	76	4	no	—
252	D₄	—	152	4	no	—
253	C₂×C₄	—	4	1	no	—
254	C₂×C₄	—	4	1	no	—
255	C₂×C₄	—	4	1	no	—
256	C₂×C₄	—	4	2	no	—
257	C₂×C₄	—	8	1	no	—
258	C₂×C₄	—	8	2	no	—
259	C₂×C₄	—	8	1	no	—
260	C₂×C₄	—	76	2	no	—
261	C₂×C₄	—	152	2	no	—
262	C₂×C₄	—	152	2	no	—
263	C₂×C₄	#10597328	1	2	yes	—
264	C₂×C₄	#10597330	1	2	yes	—
265	C₂×C₄	C₂×#64525	1	2	yes	—
266	C₂×C₄	#10597383	1	1	yes	characteristic
267	C₂×C₄	#10597386	1	1	yes	characteristic
268	C₂×C₄	#10597395	1	2	yes	—
269	C₈	—	2	4	no	—
270	C₈	—	8	1	no	—
271	C₈	—	76	4	no	—
272	C₂²	—	2	1	no	—
273	C₂²	—	2	1	no	—
274	C₂²	—	4	4	no	—
275	C₂²	—	4	2	no	—
276	C₂²	—	8	2	no	—
277	C₂²	—	8	1	no	—
278	C₂²	—	8	1	no	—
279	C₂²	—	152	2	no	—
280	C₂²	—	152	2	no	—
281	C₂²	—	152	2	no	—
282	C₂²	#11926453	1	1	yes	characteristic
283	C₂²	#11926739	1	2	yes	—
284	C₄	—	2	2	no	—
285	C₄	—	2	2	no	—
286	C₄	—	8	1	no	—
287	C₄	—	152	2	no	—
288	C₄	#11926677	1	2	yes	—
289	C₄	#11926920	1	1	yes	characteristic
290	C₄	#11926934	1	1	yes	characteristic
291	C₂	—	2	2	no	—
292	C₂	—	8	2	no	—
293	C₂	—	304	2	no	—
294	C₂	#14564702	1	1	yes	characteristic
295	C₂	#14564705	1	1	yes	characteristic
296	C₂	#14564739	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574081

C₂

yes

maximal, characteristic, complemented

#14573635

C₂

yes

maximal, complemented

#14562033

C₂

yes

maximal, complemented

#14561466

C₂

yes

maximal, characteristic, complemented

C₁₉×#1955

C₂

yes

maximal, characteristic, complemented

C₂×#10597350

—

#11927094

C₂²

yes

—

—

—

—

—

—

—

—

C₂²

yes

—

#11926271

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

—

C₂×C₁₉×#97

C₂²

yes

characteristic

C₂²×D₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

—

C₂×#64541

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

C₂×Dic₇₆

—

#10597350

—

#10597350

—

C₂×D₁₅₂

—

C₂×#64516

—

#10597321

—

#10597320

D₄

yes

—

C₄×D₇₆

—

C₄×D₇₆

—

#10597315

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

#10597289

—

C₂²⋊(C₁₉⋊C₈)

—

#10597266

—

#10597264

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂×C₂²⋊D₁₉

—

#64541

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

complemented

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

#64525

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

D₁₅₂

—

#64516

—

#10032

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#121

yes

characteristic

C₂²×D₁₉

—

D₄×C₁₉

—

D₄×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

#120

yes

characteristic

108

C₂×C₄×C₁₉

#120

yes

—

109

C₂×C₄×C₁₉

#121

yes

—

110

C₂×C₄×C₁₉

#127

yes

characteristic

111

C₂×C₄×C₁₉

C₂×D₈

yes

—

112

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

113

C₂²⋊D₁₉

—

114

C₂×Dic₁₉

—

115

D₇₆

—

116

D₇₆

—

117

D₇₆

—

118

C₄×D₁₉

—

119

C₄×D₁₉

—

120

Dic₃₈

—

121

C₈×C₁₉

—

122

C₈×C₁₉

—

123

C₁₉⋊C₈

—

124

#3150

—

125

#3100

—

126

#1955

D₁₉

yes

characteristic, complemented

127

#1480

—

128

#1275

—

129

C₂²×C₁₉

—

130

C₂²×C₁₉

—

131

C₂²×C₁₉

—

132

C₂²×C₁₉

—

133

C₂²×C₁₉

—

134

C₂²×C₁₉

—

135

C₂²×C₁₉

—

136

C₂²×C₁₉

#392

yes

characteristic

137

C₂²×C₁₉

#459

yes

—

138

C₂×D₁₉

—

139

C₂×D₁₉

—

140

C₂×D₁₉

—

141

C₄×C₁₉

—

142

C₄×C₁₉

—

143

C₄×C₁₉

—

144

C₄×C₁₉

#447

yes

—

145

C₄×C₁₉

#493

yes

characteristic

146

C₄×C₁₉

#496

yes

characteristic

147

Dic₁₉

—

148

C₂×#135

—

149

#532

—

150

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

151

#497

—

152

#496

—

153

#480

—

154

#474

—

155

#459

—

156

#447

—

157

C₄×D₈

—

158

#431

—

159

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

160

C₂×C₂²⋊C₈

—

161

C₂×#97

C₂×D₁₉

yes

characteristic

162

D₄⋊C₈

—

163

C₂×C₁₉

—

164

C₂×C₁₉

—

165

C₂×C₁₉

#2010

yes

characteristic

166

C₂×C₁₉

#2011

yes

characteristic

167

C₂×C₁₉

#2017

yes

characteristic

168

D₁₉

—

169

C₂×#41

—

170

C₂²×D₄

D₇₆

yes

characteristic

171

C₂³×C₄

—

172

#135

—

173

#135

—

174

C₂×Q₁₆

—

175

C₂×SD₁₆

—

176

C₂×D₈

—

177

C₂×D₈

—

178

C₂²×C₈

—

179

C₂²×C₈

C₂²⋊D₁₉

yes

—

180

C₄⋊Q₈

—

181

#127

—

182

#124

—

183

#121

—

184

#121

—

185

C₄×D₄

—

186

C₄×D₄

—

187

C₄×D₄

—

188

C₄×D₄

—

189

C₂×C₄⋊C₄

D₇₆

yes

characteristic

190

C₂×C₂²⋊C₄

—

191

C₂×C₄²

C₂²×D₁₉

yes

characteristic

192

#107

—

193

C₄⋊C₈

—

194

C₄⋊C₈

—

195

#102

—

196

#102

—

197

C₂²⋊C₈

—

198

C₂²⋊C₈

—

199

#97

—

200

C₄×C₈

—

201

C₁₉

#10032

yes

characteristic, complemented, Sylow

202

C₂⁴

—

203

#41

—

204

#41

—

205

C₂×Q₈

—

206

C₂×D₄

—

207

C₂×D₄

—

208

C₂×D₄

—

209

C₂×D₄

—

210

C₂×D₄

—

211

C₂×D₄

—

212

C₂²×C₄

—

213

C₂²×C₄

—

214

C₂²×C₄

—

215

C₂²×C₄

—

216

C₂²×C₄

—

217

C₂²×C₄

—

218

C₂²×C₄

C₂×D₇₆

yes

characteristic

219

C₂²×C₄

#64541

yes

characteristic

220

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

221

Q₁₆

—

222

SD₁₆

—

223

D₈

—

224

D₈

—

225

C₂×C₈

—

226

C₂×C₈

—

227

C₂×C₈

—

228

C₂×C₈

—

229

C₂×C₈

—

230

C₂×C₈

#64525

yes

complemented

231

C₄⋊C₄

—

232

C₄⋊C₄

—

233

C₄⋊C₄

—

234

C₂²⋊C₄

—

235

C₂²⋊C₄

—

236

C₂²⋊C₄

—

237

C₄²

D₄×D₁₉

yes

—

238

C₄²

D₄×D₁₉

yes

—

239

C₂³

—

240

C₂³

—

241

C₂³

—

242

C₂³

—

243

C₂³

—

244

C₂³

—

245

C₂³

#10597376

yes

characteristic

246

Q₈

—

247

D₄

—

248

D₄

—

249

D₄

—

250

D₄

—

251

D₄

—

252

D₄

—

152

—

253

C₂×C₄

—

254

C₂×C₄

—

255

C₂×C₄

—

256

C₂×C₄

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

261

C₂×C₄

—

152

—

262

C₂×C₄

—

152

—

263

C₂×C₄

#10597328

yes

—

264

C₂×C₄

#10597330

yes

—

265

C₂×C₄

C₂×#64525

yes

—

266

C₂×C₄

#10597383

yes

characteristic

267

C₂×C₄

#10597386

yes

characteristic

268

C₂×C₄

#10597395

yes

—

269

C₈

—

270

C₈

—

271

C₈

—

272

C₂²

—

273

C₂²

—

274

C₂²

—

275

C₂²

—

276

C₂²

—

277

C₂²

—

278

C₂²

—

279

C₂²

—

152

—

280

C₂²

—

152

—

281

C₂²

—

152

—

282

C₂²

#11926453

yes

characteristic

283

C₂²

#11926739

yes

—

284

C₄

—

285

C₄

—

286

C₄

—

287

C₄

—

152

—

288

C₄

#11926677

yes

—

289

C₄

#11926920

yes

characteristic

290

C₄

#11926934

yes

characteristic

291

C₂

—

292

C₂

—

293

C₂

—

304

—

294

C₂

#14564702

yes

characteristic

295

C₂

#14564705

yes

characteristic

296

C₂

#14564739

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1955	C₂
socle	C₂²×C₁₉	#392
hypercenter	#1955	D₁₉
hypocenter	C₁₉	#10032
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1955

subgroup

G/H

center

C₂×C₄

#10597386

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1955

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1955

N	H ≅ G/N	type
1. #14574081	C₂	semidirect
2. #14573635	C₂	semidirect
3. #14562033	C₂	semidirect
4. #14561466	C₂	semidirect
5. C₁₉×#1955	C₂	semidirect
76. C₂×C₈×C₁₉	D₈	semidirect
126. #1955	D₁₉	semidirect
201. C₁₉	#10032	semidirect
230. C₂×C₈	#64525	semidirect

H ≅ G/N

type

1. #14574081

C₂

semidirect

2. #14573635

C₂

semidirect

3. #14562033

C₂

semidirect

4. #14561466

C₂

semidirect

5. C₁₉×#1955

C₂

semidirect

76. C₂×C₈×C₁₉

D₈

semidirect

126. #1955

D₁₉

semidirect

201. C₁₉

#10032

semidirect

230. C₂×C₈

#64525

semidirect

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

subgroup	index
#14574081	2
#14573635	2
#14562033	2
#14561466	2
C₁₉×#1955	2
#10032	19

subgroup

index

C₁₉×#1955

Subgroups — #18083505

Conjugacy classes of subgroups

Complements

Maximal subgroups