Subgroups — Dic₃×#3994 #14296647

Order 1920.

560 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91223	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#3994	C₂	1	1	yes	maximal, characteristic
3	Dic₃×C₄⋊AGL(1,𝔽₅)	C₂	1	2	yes	maximal
4	C₈×D₅×Dic₃	C₂	1	1	yes	maximal, characteristic
5	#11746529	C₂	1	2	yes	maximal
6	C₄×#3994	—	3	1	no	maximal, Hall
7	C₂×C₄⋊ΓL(1,𝔽₁₆)	C₂²	1	2	yes	—
8	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
9	C₂×Dic₃×AGL(1,𝔽₅)	—	2	2	no	—
10	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
11	C₄×D₅×Dic₃	C₂²	1	1	yes	characteristic
12	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
13	#91223	C₄	1	4	yes	complemented
14	C₃×#3994	C₄	1	4	yes	complemented
15	(C₂×AGL(1,𝔽₅))⋊Dic₃	—	2	2	no	—
16	C₈×Dic₁₅	C₄	1	1	yes	characteristic, complemented
17	C₅×C₈×Dic₃	C₄	1	1	yes	characteristic, complemented
18	#90951	C₄	1	1	yes	characteristic, complemented
19	Dic₃×#168	C₄	1	1	yes	characteristic, complemented
20	Dic₃×#107	—	5	1	no	maximal, Hall
21	C₂×#3994	—	3	1	no	—
22	C₂×#3994	D₃	1	1	yes	characteristic
23	C₄×C₄⋊AGL(1,𝔽₅)	—	3	2	no	—
24	C₄×C₈×D₅	—	3	1	no	—
25	#64893	—	3	2	no	—
26	C₂²×ΓL(1,𝔽₁₆)	—	2	2	no	—
27	C₂²×C₃×AGL(1,𝔽₅)	—	2	2	no	—
28	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
29	C₂×D₅×Dic₃	D₄	1	1	yes	characteristic
30	C₂×D₅×Dic₃	D₄	1	1	yes	characteristic
31	C₄⋊ΓL(1,𝔽₁₆)	—	2	2	no	—
32	C₄⋊ΓL(1,𝔽₁₆)	C₂×C₄	1	4	yes	—
33	C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
34	C₃×C₄⋊AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
35	Dic₃×AGL(1,𝔽₅)	—	4	4	no	—
36	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
37	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
38	C₂×C₃⋊#168	C₂×C₄	1	1	yes	characteristic
39	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
42	C₃×C₈×D₅	C₂×C₄	1	2	yes	—
43	C₃×C₈×D₅	C₂×C₄	1	2	yes	—
44	Dic₃×Dic₅	Q₈	1	1	yes	characteristic
45	Dic₃×Dic₅	Q₈	1	1	yes	characteristic
46	D₅×C₃⋊C₈	—	2	1	no	—
47	D₅×C₃⋊C₈	—	2	1	no	—
48	C₂×C₃×#107	—	5	1	no	—
49	C₂×#818	—	5	1	no	—
50	C₂×C₈×Dic₃	—	5	1	no	—
51	Dic₃×C₄⋊C₄	—	5	2	no	—
52	#4529	—	5	2	no	—
53	C₂×C₄⋊AGL(1,𝔽₅)	—	3	2	no	—
54	C₂×C₄⋊AGL(1,𝔽₅)	C₂×D₃	1	2	yes	—
55	C₂×C₄×AGL(1,𝔽₅)	—	6	2	no	—
56	C₂×C₈×D₅	—	3	1	no	—
57	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
58	C₄²×D₅	—	3	1	no	—
59	(C₂×AGL(1,𝔽₅))⋊C₄	—	6	2	no	—
60	#3994	—	3	4	no	—
61	#3994	Dic₃	1	4	yes	direct product factor
62	C₄×C₅×C₈	—	3	1	no	—
63	C₈×Dic₅	—	3	1	no	—
64	C₈×Dic₅	—	3	1	no	—
65	C₄×#168	—	3	1	no	—
66	C₄×#107	—	15	1	no	Sylow
67	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
68	C₂×ΓL(1,𝔽₁₆)	—	2	4	no	—
69	C₂×ΓL(1,𝔽₁₆)	—	4	2	no	—
70	C₂×ΓL(1,𝔽₁₆)	—	4	2	no	—
71	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
72	C₂×C₃×AGL(1,𝔽₅)	—	4	2	no	—
73	C₂×C₃×AGL(1,𝔽₅)	—	4	2	no	—
74	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
75	C₂×Dic₁₅	C₄⋊C₄	1	1	yes	characteristic
76	C₂×Dic₁₅	C₄⋊C₄	1	1	yes	characteristic
77	C₂×C₅×Dic₃	C₄⋊C₄	1	1	yes	characteristic
78	C₂×C₅×Dic₃	C₄⋊C₄	1	1	yes	characteristic
79	C₂×C₃×Dic₅	C₂×Q₈	1	1	yes	characteristic
80	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
81	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
82	C₃×C₄×D₅	#41	1	1	yes	characteristic
83	C₃×C₄×D₅	#41	1	1	yes	characteristic
84	D₅×Dic₃	—	2	1	no	—
85	D₅×Dic₃	—	2	1	no	—
86	D₅×Dic₃	D₈	1	2	yes	—
87	D₅×Dic₃	Q₁₆	1	2	yes	—
88	C₃×C₅×C₈	C₄²	1	2	yes	complemented
89	C₃⋊#168	—	2	1	no	—
90	C₃×#168	C₄²	1	2	yes	complemented
91	C₅×C₃⋊C₈	—	2	1	no	—
92	C₂²×C₃×C₈	—	5	1	no	—
93	C₂×C₃×C₄⋊C₄	—	5	2	no	—
94	C₂×C₄⋊Dic₃	—	5	2	no	—
95	C₂×C₄×Dic₃	—	5	1	no	—
96	C₂×C₄×Dic₃	—	10	2	no	—
97	C₂²×C₃⋊C₈	—	5	1	no	—
98	C₃×#107	—	5	4	no	—
99	C₃⋊#95	—	10	2	no	—
100	#818	—	5	4	no	—
101	C₈×Dic₃	—	5	1	no	—
102	C₈×Dic₃	—	5	1	no	—
103	C₈×Dic₃	—	5	1	no	—
104	C₈×Dic₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
105	C₂²×AGL(1,𝔽₅)	—	2	2	no	—
106	C₂²×AGL(1,𝔽₅)	—	6	2	no	—
107	C₂×C₄×D₅	—	3	1	no	—
108	C₂×C₄×D₅	—	3	1	no	—
109	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
110	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
111	C₄⋊AGL(1,𝔽₅)	—	3	4	no	—
112	C₄⋊AGL(1,𝔽₅)	—	6	2	no	—
113	C₄⋊AGL(1,𝔽₅)	C₂×Dic₃	1	4	yes	—
114	C₄×AGL(1,𝔽₅)	—	12	4	no	—
115	C₂×C₅×C₈	—	3	1	no	—
116	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
117	C₄²×C₅	—	3	1	no	—
118	C₄×Dic₅	—	3	1	no	—
119	C₄×Dic₅	—	3	1	no	—
120	C₄×Dic₅	—	3	1	no	—
121	C₂×#168	—	3	1	no	—
122	C₂×#168	C₄×D₃	1	1	yes	characteristic
123	C₈×D₅	—	6	1	no	—
124	C₈×D₅	—	6	1	no	—
125	C₈×D₅	C₄×D₃	1	2	yes	—
126	C₈×D₅	C₂×Dic₃	1	2	yes	—
127	C₂×#107	—	5	1	no	—
128	C₂×#107	—	15	1	no	—
129	C₂×C₄×C₈	—	15	1	no	—
130	C₄×C₄⋊C₄	—	15	2	no	—
131	#340	—	15	2	no	—
132	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₃×D₅	C₄×D₄	1	1	yes	characteristic
134	C₂×C₃×D₅	C₄×D₄	1	1	yes	characteristic
135	C₂×C₃×D₅	C₂×D₈	1	1	yes	characteristic
136	C₂×C₃×D₅	C₂×Q₁₆	1	1	yes	characteristic
137	C₂×C₃×D₅	#135	1	1	yes	characteristic
138	C₂×C₃×D₅	#135	1	1	yes	characteristic
139	ΓL(1,𝔽₁₆)	—	4	4	no	—
140	C₃×AGL(1,𝔽₅)	—	4	4	no	—
141	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
142	C₃×C₄×C₅	#117	1	1	yes	characteristic
143	Dic₁₅	—	2	1	no	—
144	Dic₁₅	#107	1	2	yes	complemented
145	C₃×Dic₅	C₄×Q₈	1	1	yes	characteristic
146	C₃×Dic₅	C₄×Q₈	1	1	yes	characteristic
147	C₅×Dic₃	—	2	1	no	—
148	C₅×Dic₃	#107	1	2	yes	complemented
149	C₂²×C₃×C₄	—	5	1	no	—
150	C₂²×C₃×C₄	—	10	2	no	—
151	C₂²×Dic₃	—	5	1	no	—
152	C₂²×Dic₃	—	5	1	no	—
153	C₂²×Dic₃	—	10	2	no	—
154	C₂×C₃×C₈	—	5	1	no	—
155	C₂×C₃×C₈	—	5	2	no	—
156	C₂×C₃×C₈	—	5	2	no	—
157	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
158	C₃×C₄⋊C₄	—	5	4	no	—
159	C₃×C₄⋊C₄	—	10	2	no	—
160	C₄⋊Dic₃	—	5	4	no	—
161	C₄⋊Dic₃	—	10	2	no	—
162	C₄×Dic₃	—	5	1	no	—
163	C₄×Dic₃	—	5	1	no	—
164	C₄×Dic₃	—	5	1	no	—
165	C₄×Dic₃	—	20	4	no	—
166	C₄×Dic₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
167	C₂×C₃⋊C₈	—	5	1	no	—
168	C₂×C₃⋊C₈	—	10	1	no	—
169	C₂×C₃⋊C₈	—	10	1	no	—
170	C₂×C₃⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
171	C₂²×D₅	D₃×D₄	1	1	yes	characteristic
172	C₂×AGL(1,𝔽₅)	—	2	4	no	—
173	C₂×AGL(1,𝔽₅)	—	4	2	no	—
174	C₂×AGL(1,𝔽₅)	—	4	2	no	—
175	C₂×AGL(1,𝔽₅)	—	6	4	no	—
176	C₂×AGL(1,𝔽₅)	—	12	2	no	—
177	C₂×AGL(1,𝔽₅)	—	12	2	no	—
178	C₂×C₄×C₅	—	3	1	no	—
179	C₂×C₄×C₅	—	3	1	no	—
180	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
181	C₂×Dic₅	—	3	1	no	—
182	C₂×Dic₅	—	3	1	no	—
183	C₂×Dic₅	D₃×Q₈	1	1	yes	characteristic
184	C₄×D₅	—	3	2	no	—
185	C₄×D₅	—	3	2	no	—
186	C₄×D₅	—	6	1	no	—
187	C₄×D₅	—	6	1	no	—
188	C₄×D₅	C₂×C₄×D₃	1	1	yes	characteristic
189	C₄×D₅	#237	1	1	yes	characteristic
190	C₄×D₅	#239	1	1	yes	characteristic
191	C₄×D₅	C₂²×Dic₃	1	1	yes	characteristic
192	C₅×C₈	—	6	1	no	—
193	C₅×C₈	C₄×Dic₃	1	2	yes	complemented
194	#168	—	6	1	no	—
195	#168	C₄×Dic₃	1	2	yes	complemented
196	C₂²×C₈	—	5	1	no	—
197	C₂²×C₈	—	15	1	no	—
198	C₂×C₄⋊C₄	—	5	2	no	—
199	C₂×C₄⋊C₄	—	15	2	no	—
200	C₂×C₄²	—	15	1	no	—
201	C₂×C₄²	—	30	2	no	—
202	#107	—	5	4	no	—
203	#107	—	15	4	no	—
204	C₄×C₈	—	3	1	no	—
205	C₄×C₈	—	15	1	no	—
206	C₄×C₈	—	15	1	no	—
207	C₄×C₈	—	15	1	no	—
208	#95	—	30	2	no	—
209	C₂×C₃×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
210	C₂×C₃×C₅	C₂×#107	1	1	yes	characteristic
211	C₂×C₃×C₅	#427	1	1	yes	characteristic
212	C₃×D₅	C₄×D₈	1	1	yes	characteristic
213	C₃×D₅	C₄×D₈	1	1	yes	characteristic
214	C₃×D₅	C₄×Q₁₆	1	1	yes	characteristic
215	C₃×D₅	C₄×Q₁₆	1	1	yes	characteristic
216	C₂³×C₃	—	5	1	no	—
217	C₂×C₃×C₄	—	5	1	no	—
218	C₂×C₃×C₄	—	5	1	no	—
219	C₂×C₃×C₄	—	5	1	no	—
220	C₂×C₃×C₄	—	5	1	no	—
221	C₂×C₃×C₄	—	5	1	no	—
222	C₂×C₃×C₄	—	10	4	no	—
223	C₂×C₃×C₄	—	20	2	no	—
224	C₂×C₃×C₄	—	20	2	no	—
225	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
226	C₂×Dic₃	—	5	1	no	—
227	C₂×Dic₃	—	5	2	no	—
228	C₂×Dic₃	—	5	2	no	—
229	C₂×Dic₃	—	5	1	no	—
230	C₂×Dic₃	—	10	1	no	—
231	C₂×Dic₃	—	10	1	no	—
232	C₂×Dic₃	—	10	4	no	—
233	C₂×Dic₃	—	20	2	no	—
234	C₂×Dic₃	—	20	2	no	—
235	C₂×Dic₃	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
236	C₂×Dic₃	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
237	C₃×C₈	—	5	2	no	—
238	C₃×C₈	C₄×AGL(1,𝔽₅)	1	2	yes	complemented
239	C₃⋊C₈	—	2	1	no	—
240	C₃⋊C₈	—	10	1	no	—
241	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
242	C₂×D₅	#893	1	1	yes	characteristic
243	C₂×D₅	D₃×D₈	1	1	yes	characteristic
244	C₂×D₅	#912	1	1	yes	characteristic
245	C₂×D₅	D₃×Q₁₆	1	1	yes	characteristic
246	C₂×D₅	#919	1	1	yes	characteristic
247	C₂×D₅	D₄×Dic₃	1	1	yes	characteristic
248	AGL(1,𝔽₅)	—	4	4	no	—
249	AGL(1,𝔽₅)	—	12	4	no	—
250	C₄×C₅	—	3	2	no	—
251	C₄×C₅	—	6	1	no	—
252	C₄×C₅	#892	1	1	yes	characteristic
253	C₄×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
254	Dic₅	—	3	2	no	—
255	Dic₅	—	6	1	no	—
256	Dic₅	#887	1	1	yes	characteristic
257	Dic₅	Q₈×Dic₃	1	1	yes	characteristic
258	C₂²×C₄	—	5	1	no	—
259	C₂²×C₄	—	10	2	no	—
260	C₂²×C₄	—	15	1	no	—
261	C₂²×C₄	—	15	1	no	—
262	C₂²×C₄	—	30	2	no	—
263	C₂×C₈	—	3	1	no	—
264	C₂×C₈	—	5	1	no	—
265	C₂×C₈	—	5	2	no	—
266	C₂×C₈	—	5	2	no	—
267	C₂×C₈	—	15	1	no	—
268	C₂×C₈	—	30	1	no	—
269	C₂×C₈	—	30	1	no	—
270	C₂×C₈	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
271	C₄⋊C₄	—	5	4	no	—
272	C₄⋊C₄	—	10	2	no	—
273	C₄⋊C₄	—	15	4	no	—
274	C₄⋊C₄	—	30	2	no	—
275	C₄²	—	3	1	no	—
276	C₄²	—	15	1	no	—
277	C₄²	—	15	1	no	—
278	C₄²	—	15	1	no	—
279	C₄²	—	60	4	no	—
280	C₃×C₅	C₄×#107	1	1	yes	characteristic, complemented, Hall
281	C₂²×C₃	—	5	1	no	—
282	C₂²×C₃	—	5	1	no	—
283	C₂²×C₃	—	5	1	no	—
284	C₂²×C₃	—	5	1	no	—
285	C₂²×C₃	—	5	1	no	—
286	C₂²×C₃	—	5	1	no	—
287	C₂²×C₃	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
288	C₃×C₄	—	5	1	no	—
289	C₃×C₄	—	5	1	no	—
290	C₃×C₄	—	20	4	no	—
291	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
292	C₃×C₄	#4130	1	1	yes	characteristic
293	Dic₃	—	2	1	no	—
294	Dic₃	—	5	2	no	—
295	Dic₃	—	10	1	no	—
296	Dic₃	—	20	4	no	—
297	Dic₃	#3994	1	2	yes	direct product factor
298	C₂×C₅	D₃×#107	1	1	yes	characteristic
299	C₂×C₅	#4880	1	1	yes	characteristic
300	C₂×C₅	Dic₃×C₄⋊C₄	1	1	yes	characteristic
301	D₅	#4872	1	1	yes	characteristic
302	D₅	#4873	1	1	yes	characteristic
303	D₅	Dic₃×D₈	1	1	yes	characteristic
304	D₅	Dic₃×Q₁₆	1	1	yes	characteristic
305	C₂³	—	5	1	no	—
306	C₂×C₄	—	3	1	no	—
307	C₂×C₄	—	3	1	no	—
308	C₂×C₄	—	5	1	no	—
309	C₂×C₄	—	5	1	no	—
310	C₂×C₄	—	5	1	no	—
311	C₂×C₄	—	5	1	no	—
312	C₂×C₄	—	5	1	no	—
313	C₂×C₄	—	10	4	no	—
314	C₂×C₄	—	15	2	no	—
315	C₂×C₄	—	15	2	no	—
316	C₂×C₄	—	15	1	no	—
317	C₂×C₄	—	15	1	no	—
318	C₂×C₄	—	20	2	no	—
319	C₂×C₄	—	20	2	no	—
320	C₂×C₄	—	30	1	no	—
321	C₂×C₄	—	30	1	no	—
322	C₂×C₄	—	30	4	no	—
323	C₂×C₄	—	60	2	no	—
324	C₂×C₄	—	60	2	no	—
325	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
326	C₈	—	5	2	no	—
327	C₈	—	6	1	no	—
328	C₈	—	30	1	no	—
329	C₈	Dic₃×AGL(1,𝔽₅)	1	2	yes	complemented
330	C₂×C₃	—	5	1	no	—
331	C₂×C₃	—	5	1	no	—
332	C₂×C₃	—	5	1	no	—
333	C₂×C₃	—	5	1	no	—
334	C₂×C₃	C₄×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
335	C₂×C₃	C₂×#3994	1	1	yes	characteristic
336	C₂×C₃	#65721	1	1	yes	characteristic
337	C₅	Dic₃×#107	1	1	yes	characteristic, complemented, Sylow
338	C₂²	—	5	1	no	—
339	C₂²	—	5	1	no	—
340	C₂²	—	5	1	no	—
341	C₂²	—	5	1	no	—
342	C₂²	—	5	1	no	—
343	C₂²	—	5	1	no	—
344	C₂²	D₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
345	C₄	—	3	2	no	—
346	C₄	—	5	1	no	—
347	C₄	—	5	1	no	—
348	C₄	—	6	1	no	—
349	C₄	—	15	2	no	—
350	C₄	—	20	4	no	—
351	C₄	—	30	1	no	—
352	C₄	—	60	4	no	—
353	C₄	#91907	1	1	yes	characteristic
354	C₄	C₂×Dic₃×AGL(1,𝔽₅)	1	1	yes	characteristic
355	C₃	C₄×#3994	1	1	yes	characteristic, complemented, Sylow
356	C₂	—	5	1	no	—
357	C₂	—	5	1	no	—
358	C₂	—	5	1	no	—
359	C₂	—	5	1	no	—
360	C₂	D₃×#3994	1	1	yes	characteristic
361	C₂	#11751658	1	1	yes	characteristic
362	C₂	Dic₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃×C₄⋊AGL(1,𝔽₅)
commutator	C₃×C₄×C₅	C₂×C₄²
Frattini	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×C₈	C₂×C₄
socle	C₂²×C₃×C₅	C₂×C₄⋊C₄
prime radical	C₂²×C₃×D₅	C₂×D₄
cosocle	C₂×C₃×C₄×D₅	C₂³
hypercenter	C₂×C₈	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₄×#107
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
13. #91223	C₄	semidirect
14. C₃×#3994	C₄	semidirect
16. C₈×Dic₁₅	C₄	semidirect
17. C₅×C₈×Dic₃	C₄	semidirect
18. #90951	C₄	semidirect
19. Dic₃×#168	C₄	semidirect
61. #3994	Dic₃	direct (N × H)
88. C₃×C₅×C₈	C₄²	semidirect
90. C₃×#168	C₄²	semidirect
104. C₈×Dic₃	AGL(1,𝔽₅)	semidirect
144. Dic₁₅	#107	semidirect
148. C₅×Dic₃	#107	semidirect
193. C₅×C₈	C₄×Dic₃	semidirect
195. #168	C₄×Dic₃	semidirect
238. C₃×C₈	C₄×AGL(1,𝔽₅)	semidirect
280. C₃×C₅	C₄×#107	semidirect
297. Dic₃	#3994	direct (N × H)
329. C₈	Dic₃×AGL(1,𝔽₅)	semidirect
337. C₅	Dic₃×#107	semidirect
355. C₃	C₄×#3994	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91223	2
C₂×C₃×#3994	2
Dic₃×C₄⋊AGL(1,𝔽₅)	2
C₈×D₅×Dic₃	2
#11746529	2
C₄×#3994	3
Dic₃×#107	5

Subgroups — Dic3×#3994 #14296647

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃×#3994 #14296647