Subgroups — C₂²×#91394 #14478757

Order 1920.

3760 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₅×Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×#685	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₃⋊Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#6665	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₃×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#91394	C₂	1	24	yes	maximal, direct product factor
9	C₂²×#4038	—	3	1	no	maximal, Hall
10	C₂⁴×C₃×D₅	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂³×Dic₁₅	C₂²	1	1	yes	characteristic
13	C₂³×Dic₁₅	C₂²	1	1	yes	characteristic
14	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
15	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
16	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
17	C₂²×D₅×Dic₃	C₄	1	16	yes	complemented
18	C₂²×D₅×Dic₃	C₂²	1	12	yes	—
19	C₂×C₄×Dic₁₅	C₂²	1	12	yes	complemented
20	C₂×C₅×Dic₃⋊C₄	C₂²	1	12	yes	complemented
21	C₂×C₃×#685	C₂²	1	12	yes	—
22	C₂×Dic₃⋊Dic₅	C₂²	1	12	yes	complemented
23	C₂×#6665	C₂²	1	12	yes	—
24	C₂×Dic₃×Dic₅	C₂²	1	12	yes	complemented
25	#91394	C₂²	1	64	yes	direct product factor
26	C₂²×#877	—	5	1	no	maximal, Hall
27	C₂³×C₄×D₅	—	3	1	no	—
28	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
29	C₂²×#685	—	3	1	no	—
30	C₂²×#685	D₃	1	1	yes	characteristic
31	C₂²×C₄⋊Dic₅	—	3	1	no	—
32	C₂²×C₄×Dic₅	—	3	1	no	—
33	C₂²×C₄×Dic₅	—	3	1	no	—
34	C₂×#4038	—	3	24	no	—
35	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
36	C₂³×C₃×D₅	—	2	4	no	—
37	C₂³×C₃×D₅	—	2	4	no	—
38	C₂³×C₃×D₅	C₂×C₄	1	8	yes	—
39	C₂³×C₃×D₅	C₂³	1	6	yes	—
40	C₂²×C₃×C₄×C₅	—	2	4	no	—
41	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
42	C₂²×Dic₁₅	—	2	4	no	—
43	C₂²×Dic₁₅	C₂×C₄	1	8	yes	—
44	C₂²×Dic₁₅	C₂³	1	6	yes	—
45	C₂²×Dic₁₅	C₂³	1	6	yes	—
46	C₂²×C₅×Dic₃	—	2	4	no	—
47	C₂²×C₅×Dic₃	C₂×C₄	1	8	yes	—
48	C₂²×C₅×Dic₃	C₂³	1	6	yes	—
49	C₂²×C₅×Dic₃	C₂³	1	6	yes	—
50	C₂²×C₃×Dic₅	—	2	4	no	—
51	C₂²×C₃×Dic₅	C₂³	1	6	yes	—
52	C₂×D₅×Dic₃	C₂×C₄	1	96	yes	complemented
53	C₂×D₅×Dic₃	C₂³	1	16	yes	—
54	C₄×Dic₁₅	C₂³	1	16	yes	complemented
55	C₅×Dic₃⋊C₄	C₂³	1	16	yes	complemented
56	C₃×#685	C₂³	1	16	yes	—
57	Dic₃⋊Dic₅	C₂³	1	16	yes	complemented
58	#6665	C₂³	1	16	yes	—
59	Dic₃×Dic₅	C₂³	1	16	yes	complemented
60	C₂⁴×Dic₃	—	5	1	no	—
61	C₂²×C₃×C₂²⋊C₄	—	5	1	no	—
62	C₂²×#217	—	5	1	no	—
63	C₂²×Dic₃⋊C₄	—	5	1	no	—
64	C₂²×Dic₃⋊C₄	D₅	1	1	yes	characteristic, complemented
65	C₂²×C₄×Dic₃	—	5	1	no	—
66	C₂²×C₄×Dic₃	—	5	1	no	—
67	C₂×#877	—	5	24	no	—
68	C₂⁴×D₅	C₂×D₃	1	1	yes	characteristic
69	C₂³×C₄×C₅	—	3	1	no	—
70	C₂³×C₄×C₅	—	3	1	no	—
71	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
72	C₂³×Dic₅	—	3	1	no	—
73	C₂³×Dic₅	—	3	1	no	—
74	C₂³×Dic₅	C₂×D₃	1	1	yes	characteristic
75	C₂²×C₄×D₅	—	3	16	no	—
76	C₂²×C₄×D₅	—	3	12	no	—
77	C₂×C₅×C₄⋊C₄	—	3	12	no	—
78	C₂×#685	—	3	12	no	—
79	C₂×#685	C₂×D₃	1	12	yes	—
80	C₂×C₄⋊Dic₅	—	3	12	no	—
81	C₂×C₄×Dic₅	—	3	12	no	—
82	C₂×C₄×Dic₅	—	3	12	no	—
83	#4038	—	3	64	no	—
84	C₂²×#117	—	15	1	no	Sylow
85	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
86	C₂³×C₃×C₅	#41	1	4	yes	—
87	C₂³×C₃×C₅	#41	1	4	yes	—
88	C₂³×C₃×C₅	C₂⁴	1	3	yes	—
89	C₂²×C₃×D₅	—	2	32	no	—
90	C₂²×C₃×D₅	—	2	12	no	—
91	C₂²×C₃×D₅	—	2	12	no	—
92	C₂²×C₃×D₅	C₂²×C₄	1	24	yes	—
93	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
94	C₂×C₃×C₄×C₅	—	2	12	no	—
95	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
96	C₂×Dic₁₅	—	2	12	no	—
97	C₂×Dic₁₅	C₂²×C₄	1	24	yes	—
98	C₂×Dic₁₅	C₂⁴	1	4	yes	—
99	C₂×Dic₁₅	C₂⁴	1	4	yes	—
100	C₂×C₅×Dic₃	—	2	12	no	—
101	C₂×C₅×Dic₃	C₂²×C₄	1	24	yes	—
102	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
103	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
104	C₂×C₃×Dic₅	—	2	12	no	—
105	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
106	D₅×Dic₃	C₂²×C₄	1	64	yes	complemented
107	C₂⁵×C₃	—	5	1	no	—
108	C₂³×C₃×C₄	—	5	1	no	—
109	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
110	C₂³×Dic₃	—	5	1	no	—
111	C₂³×Dic₃	—	5	16	no	—
112	C₂³×Dic₃	—	5	12	no	—
113	C₂³×Dic₃	—	5	1	no	—
114	C₂³×Dic₃	C₂×D₅	1	1	yes	characteristic
115	C₂³×Dic₃	C₂×D₅	1	1	yes	characteristic
116	C₂×C₃×C₂²⋊C₄	—	5	12	no	—
117	C₂×#217	—	5	12	no	—
118	C₂×Dic₃⋊C₄	—	5	12	no	—
119	C₂×Dic₃⋊C₄	C₂×D₅	1	12	yes	complemented
120	C₂×C₄×Dic₃	—	5	12	no	—
121	C₂×C₄×Dic₃	—	5	12	no	—
122	#877	—	5	64	no	—
123	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
124	C₂³×D₅	—	2	4	no	—
125	C₂³×D₅	—	2	4	no	—
126	C₂³×D₅	C₄×D₃	1	8	yes	—
127	C₂³×D₅	C₂²×D₃	1	6	yes	—
128	C₂²×C₄×C₅	—	2	4	no	—
129	C₂²×C₄×C₅	—	3	8	no	—
130	C₂²×C₄×C₅	—	3	6	no	—
131	C₂²×C₄×C₅	—	3	6	no	—
132	C₂²×C₄×C₅	—	6	4	no	—
133	C₂²×C₄×C₅	C₂²×D₃	1	6	yes	—
134	C₂²×Dic₅	—	2	4	no	—
135	C₂²×Dic₅	—	3	8	no	—
136	C₂²×Dic₅	—	3	6	no	—
137	C₂²×Dic₅	—	3	6	no	—
138	C₂²×Dic₅	—	6	4	no	—
139	C₂²×Dic₅	C₂²×D₃	1	6	yes	—
140	C₂×C₄×D₅	—	3	96	no	—
141	C₂×C₄×D₅	—	3	16	no	—
142	C₅×C₄⋊C₄	—	3	16	no	—
143	#685	—	3	16	no	—
144	#685	C₂²×D₃	1	16	yes	—
145	C₄⋊Dic₅	—	3	16	no	—
146	C₄×Dic₅	—	3	16	no	—
147	C₄×Dic₅	—	3	16	no	—
148	C₂⁴×C₄	—	15	1	no	—
149	C₂×#117	—	15	24	no	—
150	C₂²×C₄⋊C₄	—	3	1	no	—
151	C₂²×C₄⋊C₄	—	15	1	no	—
152	C₂²×C₂²⋊C₄	—	5	1	no	—
153	C₂²×C₂²⋊C₄	—	15	1	no	—
154	C₂²×C₄²	—	15	1	no	—
155	C₂²×C₄²	—	15	1	no	—
156	C₂²×C₃×C₅	#117	1	16	yes	complemented
157	C₂²×C₃×C₅	C₂³×C₄	1	6	yes	—
158	C₂²×C₃×C₅	C₂×#41	1	6	yes	—
159	C₂²×C₃×C₅	C₂×#41	1	6	yes	—
160	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
161	C₂×C₃×D₅	—	2	48	no	—
162	C₂×C₃×D₅	—	2	4	no	—
163	C₂×C₃×D₅	—	2	4	no	—
164	C₂×C₃×D₅	C₂³×C₄	1	8	yes	—
165	C₃×C₄×C₅	—	2	4	no	—
166	Dic₁₅	—	2	4	no	—
167	Dic₁₅	C₂³×C₄	1	8	yes	—
168	C₃×Dic₅	—	2	4	no	—
169	C₅×Dic₃	—	2	4	no	—
170	C₅×Dic₃	C₂³×C₄	1	8	yes	—
171	C₂⁴×C₃	—	5	8	no	—
172	C₂⁴×C₃	—	5	6	no	—
173	C₂⁴×C₃	—	10	4	no	—
174	C₂⁴×C₃	—	10	4	no	—
175	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
176	C₂²×C₃×C₄	—	2	4	no	—
177	C₂²×C₃×C₄	—	5	6	no	—
178	C₂²×C₃×C₄	—	10	4	no	—
179	C₂²×C₃×C₄	C₂²×D₅	1	6	yes	—
180	C₂²×Dic₃	—	2	4	no	—
181	C₂²×Dic₃	—	5	8	no	—
182	C₂²×Dic₃	—	5	6	no	—
183	C₂²×Dic₃	—	5	96	no	—
184	C₂²×Dic₃	—	5	16	no	—
185	C₂²×Dic₃	—	5	6	no	—
186	C₂²×Dic₃	—	10	4	no	—
187	C₂²×Dic₃	C₄×D₅	1	8	yes	—
188	C₂²×Dic₃	C₂²×D₅	1	6	yes	—
189	C₂²×Dic₃	C₂²×D₅	1	6	yes	—
190	C₃×C₂²⋊C₄	—	5	16	no	—
191	#217	—	5	16	no	—
192	Dic₃⋊C₄	—	5	16	no	—
193	Dic₃⋊C₄	C₂²×D₅	1	16	yes	complemented
194	C₄×Dic₃	—	5	16	no	—
195	C₄×Dic₃	—	5	16	no	—
196	C₂³×C₅	C₂×C₄×D₃	1	4	yes	—
197	C₂³×C₅	#237	1	4	yes	—
198	C₂³×C₅	#237	1	4	yes	—
199	C₂³×C₅	C₂³×D₃	1	3	yes	—
200	C₂²×D₅	—	2	32	no	—
201	C₂²×D₅	—	2	12	no	—
202	C₂²×D₅	—	2	12	no	—
203	C₂²×D₅	C₂×C₄×D₃	1	24	yes	—
204	C₂²×D₅	C₂³×D₃	1	4	yes	—
205	C₂×C₄×C₅	—	2	12	no	—
206	C₂×C₄×C₅	—	3	24	no	—
207	C₂×C₄×C₅	—	3	4	no	—
208	C₂×C₄×C₅	—	3	4	no	—
209	C₂×C₄×C₅	—	6	12	no	—
210	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
211	C₂×Dic₅	—	2	12	no	—
212	C₂×Dic₅	—	3	24	no	—
213	C₂×Dic₅	—	3	4	no	—
214	C₂×Dic₅	—	3	4	no	—
215	C₂×Dic₅	—	6	12	no	—
216	C₂×Dic₅	C₂³×D₃	1	4	yes	—
217	C₄×D₅	—	3	64	no	—
218	C₂⁵	—	5	1	no	—
219	C₂³×C₄	—	3	1	no	—
220	C₂³×C₄	—	3	1	no	—
221	C₂³×C₄	—	5	1	no	—
222	C₂³×C₄	—	15	12	no	—
223	C₂³×C₄	—	15	16	no	—
224	C₂³×C₄	—	15	1	no	—
225	C₂³×C₄	—	15	1	no	—
226	C₂³×C₄	D₃×D₅	1	1	yes	characteristic
227	#117	—	15	64	no	—
228	C₂×C₄⋊C₄	—	3	12	no	—
229	C₂×C₄⋊C₄	—	15	12	no	—
230	C₂×C₂²⋊C₄	—	5	12	no	—
231	C₂×C₂²⋊C₄	—	15	12	no	—
232	C₂×C₄²	—	15	12	no	—
233	C₂×C₄²	—	15	12	no	—
234	C₂×C₃×C₅	C₂×#117	1	12	yes	complemented
235	C₂×C₃×C₅	C₂⁴×C₄	1	1	yes	characteristic
236	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
237	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
238	C₃×D₅	—	2	8	no	—
239	C₂³×C₃	—	5	24	no	—
240	C₂³×C₃	—	5	4	no	—
241	C₂³×C₃	—	10	12	no	—
242	C₂³×C₃	—	10	12	no	—
243	C₂³×C₃	—	10	32	no	—
244	C₂³×C₃	C₂×C₄×D₅	1	4	yes	—
245	C₂³×C₃	#711	1	4	yes	—
246	C₂³×C₃	#713	1	4	yes	—
247	C₂³×C₃	C₂³×D₅	1	3	yes	—
248	C₂×C₃×C₄	—	2	12	no	—
249	C₂×C₃×C₄	—	5	4	no	—
250	C₂×C₃×C₄	—	10	12	no	—
251	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
252	C₂×Dic₃	—	2	12	no	—
253	C₂×Dic₃	—	5	24	no	—
254	C₂×Dic₃	—	5	4	no	—
255	C₂×Dic₃	—	5	64	no	—
256	C₂×Dic₃	—	5	4	no	—
257	C₂×Dic₃	—	10	12	no	—
258	C₂×Dic₃	C₂×C₄×D₅	1	24	yes	—
259	C₂×Dic₃	C₂³×D₅	1	4	yes	—
260	C₂×Dic₃	C₂³×D₅	1	4	yes	—
261	C₂²×C₅	#877	1	16	yes	complemented
262	C₂²×C₅	C₂²×C₄×D₃	1	6	yes	—
263	C₂²×C₅	C₂×#237	1	6	yes	—
264	C₂²×C₅	C₂×#237	1	6	yes	—
265	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
266	C₂×D₅	—	2	4	no	—
267	C₂×D₅	—	2	4	no	—
268	C₂×D₅	—	2	48	no	—
269	C₂×D₅	C₂²×C₄×D₃	1	8	yes	—
270	C₄×C₅	—	2	4	no	—
271	C₄×C₅	—	3	8	no	—
272	C₄×C₅	—	6	4	no	—
273	Dic₅	—	2	4	no	—
274	Dic₅	—	3	8	no	—
275	Dic₅	—	6	4	no	—
276	C₂⁴	—	5	8	no	—
277	C₂⁴	—	5	6	no	—
278	C₂⁴	—	10	4	no	—
279	C₂⁴	—	10	4	no	—
280	C₂⁴	C₂×D₃×D₅	1	1	yes	characteristic
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	3	8	no	—
283	C₂²×C₄	—	3	6	no	—
284	C₂²×C₄	—	3	6	no	—
285	C₂²×C₄	—	5	6	no	—
286	C₂²×C₄	—	6	4	no	—
287	C₂²×C₄	—	10	4	no	—
288	C₂²×C₄	—	15	16	no	—
289	C₂²×C₄	—	15	96	no	—
290	C₂²×C₄	—	15	8	no	—
291	C₂²×C₄	—	15	6	no	—
292	C₂²×C₄	—	15	6	no	—
293	C₂²×C₄	—	30	4	no	—
294	C₂²×C₄	C₂×D₃×D₅	1	6	yes	—
295	C₄⋊C₄	—	3	16	no	—
296	C₄⋊C₄	—	15	16	no	—
297	C₂²⋊C₄	—	5	16	no	—
298	C₂²⋊C₄	—	15	16	no	—
299	C₄²	—	15	16	no	—
300	C₄²	—	15	16	no	—
301	C₃×C₅	C₂²×#117	1	1	yes	characteristic, complemented, Hall
302	C₂²×C₃	—	5	8	no	—
303	C₂²×C₃	—	10	48	no	—
304	C₂²×C₃	—	10	4	no	—
305	C₂²×C₃	—	10	4	no	—
306	C₂²×C₃	#4038	1	16	yes	complemented
307	C₂²×C₃	C₂²×C₄×D₅	1	6	yes	—
308	C₂²×C₃	C₂×#711	1	6	yes	—
309	C₂²×C₃	C₂×#713	1	6	yes	—
310	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
311	C₃×C₄	—	2	4	no	—
312	C₃×C₄	—	10	4	no	—
313	Dic₃	—	2	4	no	—
314	Dic₃	—	5	8	no	—
315	Dic₃	—	10	4	no	—
316	Dic₃	C₂²×C₄×D₅	1	8	yes	—
317	C₂×C₅	C₂×#877	1	12	yes	complemented
318	C₂×C₅	C₂³×C₄×D₃	1	1	yes	characteristic
319	C₂×C₅	C₂²×#237	1	1	yes	characteristic
320	C₂×C₅	C₂²×#237	1	1	yes	characteristic
321	D₅	—	2	8	no	—
322	C₂³	—	5	24	no	—
323	C₂³	—	5	4	no	—
324	C₂³	—	10	32	no	—
325	C₂³	—	10	12	no	—
326	C₂³	—	10	12	no	—
327	C₂³	#6766	1	4	yes	—
328	C₂³	C₄×D₃×D₅	1	4	yes	—
329	C₂³	#6780	1	4	yes	—
330	C₂³	C₂²×D₃×D₅	1	3	yes	—
331	C₂×C₄	—	2	12	no	—
332	C₂×C₄	—	3	24	no	—
333	C₂×C₄	—	3	4	no	—
334	C₂×C₄	—	3	4	no	—
335	C₂×C₄	—	5	4	no	—
336	C₂×C₄	—	6	12	no	—
337	C₂×C₄	—	10	12	no	—
338	C₂×C₄	—	15	64	no	—
339	C₂×C₄	—	15	24	no	—
340	C₂×C₄	—	15	4	no	—
341	C₂×C₄	—	15	4	no	—
342	C₂×C₄	—	30	12	no	—
343	C₂×C₄	C₂²×D₃×D₅	1	4	yes	—
344	C₂×C₃	—	10	8	no	—
345	C₂×C₃	C₂×#4038	1	12	yes	complemented
346	C₂×C₃	C₂³×C₄×D₅	1	1	yes	characteristic
347	C₂×C₃	C₂²×#711	1	1	yes	characteristic
348	C₂×C₃	C₂²×#713	1	1	yes	characteristic
349	C₅	C₂²×#877	1	1	yes	characteristic, complemented, Sylow
350	C₂²	—	5	8	no	—
351	C₂²	—	10	4	no	—
352	C₂²	—	10	48	no	—
353	C₂²	—	10	4	no	—
354	C₂²	#91394	1	16	yes	direct product factor
355	C₂²	C₂×#6766	1	6	yes	—
356	C₂²	C₂×C₄×D₃×D₅	1	6	yes	—
357	C₂²	C₂×#6780	1	6	yes	—
358	C₂²	C₂³×D₃×D₅	1	1	yes	characteristic
359	C₄	—	2	4	no	—
360	C₄	—	3	8	no	—
361	C₄	—	6	4	no	—
362	C₄	—	10	4	no	—
363	C₄	—	15	8	no	—
364	C₄	—	30	4	no	—
365	C₃	C₂²×#4038	1	1	yes	characteristic, complemented, Sylow
366	C₂	—	10	8	no	—
367	C₂	C₂×#91394	1	12	yes	direct product factor
368	C₂	C₂²×#6766	1	1	yes	characteristic
369	C₂	C₂²×C₄×D₃×D₅	1	1	yes	characteristic
370	C₂	C₂²×#6780	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₃×D₅
commutator	C₂×C₃×C₅	C₂⁴×C₄
Frattini	C₂²	C₂³×D₃×D₅
Fitting	C₂³×C₃×C₄×C₅	C₂²
socle	C₂⁴×C₃×C₅	C₂³
prime radical	C₂⁴×C₃×D₅	C₂²
cosocle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₂³×C₄	D₃×D₅
hypocenter	C₃×C₅	C₂²×#117
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×Dic₁₅	C₂	semidirect
3. C₂²×C₅×Dic₃⋊C₄	C₂	semidirect
5. C₂²×Dic₃⋊Dic₅	C₂	semidirect
7. C₂²×Dic₃×Dic₅	C₂	semidirect
8. C₂×#91394	C₂	direct (N × H)
17. C₂²×D₅×Dic₃	C₄	semidirect
19. C₂×C₄×Dic₁₅	C₂²	semidirect
20. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
22. C₂×Dic₃⋊Dic₅	C₂²	semidirect
24. C₂×Dic₃×Dic₅	C₂²	semidirect
25. #91394	C₂²	direct (N × H)
52. C₂×D₅×Dic₃	C₂×C₄	semidirect
54. C₄×Dic₁₅	C₂³	semidirect
55. C₅×Dic₃⋊C₄	C₂³	semidirect
57. Dic₃⋊Dic₅	C₂³	semidirect
59. Dic₃×Dic₅	C₂³	semidirect
64. C₂²×Dic₃⋊C₄	D₅	semidirect
106. D₅×Dic₃	C₂²×C₄	semidirect
119. C₂×Dic₃⋊C₄	C₂×D₅	semidirect
156. C₂²×C₃×C₅	#117	semidirect
193. Dic₃⋊C₄	C₂²×D₅	semidirect
234. C₂×C₃×C₅	C₂×#117	semidirect
261. C₂²×C₅	#877	semidirect
301. C₃×C₅	C₂²×#117	semidirect
306. C₂²×C₃	#4038	semidirect
317. C₂×C₅	C₂×#877	semidirect
345. C₂×C₃	C₂×#4038	semidirect
349. C₅	C₂²×#877	semidirect
354. C₂²	#91394	direct (N × H)
365. C₃	C₂²×#4038	semidirect
367. C₂	C₂×#91394	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₅×Dic₃	2
C₂²×C₄×Dic₁₅	2
C₂²×C₅×Dic₃⋊C₄	2
C₂²×C₃×#685	2
C₂²×Dic₃⋊Dic₅	2
C₂²×#6665	2
C₂²×Dic₃×Dic₅	2
C₂×#91394	2
C₂²×#4038	3
C₂²×#877	5

Subgroups — C22×#91394 #14478757

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#91394 #14478757