Subgroups — C₄×#6780 #11754285

Order 960.

620 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#6780	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
5	#67⋊Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
6	#91559	C₂	1	1	yes	maximal, characteristic, complemented
7	#91532	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#1204	C₂	1	1	yes	maximal, characteristic, complemented
9	#91442	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#1201	C₂	1	1	yes	maximal, characteristic, complemented
11	#91400	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×D₃×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
13	#91394	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×D₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#91325	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#711	—	3	1	no	maximal, Hall
17	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
18	C₂²×Dic₁₅	C₂²	1	1	yes	characteristic
19	C₂²×Dic₁₅	C₂²	1	1	yes	characteristic
20	C₂×C₅×#67	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
24	C₂×#1204	C₂²	1	1	yes	characteristic
25	C₂×#1201	C₂²	1	1	yes	characteristic
26	C₂×D₃×Dic₅	C₂²	1	1	yes	characteristic
27	C₂×D₃×Dic₅	C₂²	1	1	yes	characteristic
28	#6780	C₄	1	8	yes	direct product factor
29	C₂×D₅×Dic₃	C₂²	1	1	yes	characteristic
30	C₂×D₅×Dic₃	C₂²	1	1	yes	characteristic
31	C₄×Dic₁₅	C₂²	1	1	yes	characteristic
32	C₄×Dic₁₅	C₂²	1	1	yes	characteristic
33	C₄×Dic₁₅	C₂²	1	1	yes	characteristic
34	C₄×Dic₁₅	C₂²	1	1	yes	characteristic
35	C₅×#217	C₂²	1	1	yes	characteristic
36	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
37	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
39	C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
40	C₃×#685	C₂²	1	1	yes	characteristic
41	C₃×#683	C₂²	1	1	yes	characteristic
42	C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
43	Dic₃⋊Dic₅	C₂²	1	1	yes	characteristic
44	#6669	C₂²	1	1	yes	characteristic
45	#6669	C₂²	1	1	yes	characteristic
46	#6668	C₂²	1	1	yes	characteristic
47	(C₂×D₃)⋊Dic₅	C₂²	1	1	yes	characteristic
48	#6665	C₂²	1	1	yes	characteristic
49	Dic₃×Dic₅	C₂²	1	1	yes	characteristic
50	Dic₃×Dic₅	C₂²	1	1	yes	characteristic
51	Dic₃×Dic₅	C₂²	1	1	yes	characteristic
52	Dic₃×Dic₅	C₂²	1	1	yes	characteristic
53	C₄×#237	—	5	1	no	maximal, Hall
54	C₂×#711	—	3	1	no	—
55	C₄×C₅×D₄	—	3	1	no	—
56	D₄×Dic₅	—	3	1	no	—
57	C₄×C₂²⋊D₅	—	3	1	no	—
58	C₄×C₂²⋊D₅	D₃	1	1	yes	characteristic, complemented
59	C₂×C₄×Dic₅	—	3	1	no	—
60	C₂×C₄×Dic₅	—	3	1	no	—
61	#4038	—	3	1	no	—
62	#4033	—	3	1	no	—
63	#4027	—	3	1	no	—
64	#4027	—	3	1	no	—
65	#4023	—	3	1	no	—
66	#4023	—	3	1	no	—
67	C₄²×D₅	—	3	1	no	—
68	C₄×Dic₁₀	—	3	1	no	—
69	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
70	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
71	C₂²×C₃×D₅	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₄×C₅	—	2	2	no	—
73	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂×Dic₁₅	—	2	2	no	—
76	C₂×Dic₁₅	C₂×C₄	1	4	yes	complemented
77	C₂×Dic₁₅	C₂³	1	1	yes	characteristic
78	C₂×Dic₁₅	C₂³	1	1	yes	characteristic
79	C₂×Dic₁₅	C₂³	1	1	yes	characteristic
80	C₂×Dic₁₅	C₂³	1	1	yes	characteristic
81	C₅×#67	C₂×C₄	1	4	yes	complemented
82	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
83	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
84	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
85	C₄×C₅×D₃	—	2	2	no	—
86	C₃×C₂²⋊D₅	C₂×C₄	1	4	yes	complemented
87	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
88	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
89	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
90	C₃×C₄×D₅	—	2	2	no	—
91	#1204	C₂×C₄	1	4	yes	complemented
92	#1201	C₂×C₄	1	4	yes	complemented
93	D₃×Dic₅	—	2	2	no	—
94	D₃×Dic₅	C₂×C₄	1	4	yes	complemented
95	D₅×Dic₃	—	2	2	no	—
96	D₅×Dic₃	C₂×C₄	1	4	yes	complemented
97	C₂×#237	—	5	1	no	—
98	C₃×C₄×D₄	—	5	1	no	—
99	D₄×Dic₃	—	5	1	no	—
100	C₄×#67	—	5	1	no	—
101	C₄×#67	D₅	1	1	yes	characteristic, complemented
102	C₂×C₄×Dic₃	—	5	1	no	—
103	C₂×C₄×Dic₃	—	5	1	no	—
104	#892	—	5	1	no	—
105	#887	—	5	1	no	—
106	#67⋊C₄	—	5	1	no	—
107	#67⋊C₄	—	5	1	no	—
108	#877	—	5	1	no	—
109	#877	—	5	1	no	—
110	C₄²×D₃	—	5	1	no	—
111	C₄×Dic₆	—	5	1	no	—
112	C₂×C₅×D₄	—	3	1	no	—
113	C₂²×C₄×C₅	—	3	1	no	—
114	C₂²×C₄×C₅	C₂×D₃	1	1	yes	characteristic
115	C₂×C₂²⋊D₅	—	3	1	no	—
116	C₂×C₂²⋊D₅	C₂×D₃	1	1	yes	characteristic
117	C₂²×Dic₅	—	3	1	no	—
118	C₂²×Dic₅	—	3	1	no	—
119	C₂²×Dic₅	—	3	1	no	—
120	C₂²×Dic₅	—	3	1	no	—
121	#711	—	3	8	no	—
122	C₂×C₄×D₅	—	3	1	no	—
123	C₂×C₄×D₅	—	3	1	no	—
124	C₂×C₄×D₅	C₂×D₃	1	1	yes	characteristic
125	C₂×Dic₁₀	—	3	1	no	—
126	C₅×C₄⋊C₄	—	3	1	no	—
127	C₅×C₂²⋊C₄	—	3	1	no	—
128	C₅×C₂²⋊C₄	—	3	1	no	—
129	C₄²×C₅	—	3	1	no	—
130	C₂²⋊Dic₅	—	3	1	no	—
131	C₂²⋊Dic₅	C₂×D₃	1	1	yes	characteristic
132	#685	—	3	1	no	—
133	#685	C₂×D₃	1	1	yes	characteristic
134	C₄⋊Dic₅	—	3	1	no	—
135	#683	—	3	1	no	—
136	#683	—	3	1	no	—
137	#683	—	3	1	no	—
138	#683	C₂×D₃	1	1	yes	characteristic
139	C₄×Dic₅	—	3	1	no	—
140	C₄×Dic₅	—	3	1	no	—
141	C₄×Dic₅	—	3	1	no	—
142	C₄×Dic₅	—	3	1	no	—
143	C₄×Dic₅	—	3	1	no	—
144	C₄×Dic₅	—	3	1	no	—
145	C₄×Dic₅	—	3	1	no	—
146	C₄×Dic₅	—	3	1	no	—
147	C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
148	C₄×#41	—	15	1	no	Sylow
149	C₂²×C₃×C₅	—	2	1	no	—
150	C₂²×C₃×C₅	—	2	1	no	—
151	C₂²×C₃×C₅	C₂²×C₄	1	2	yes	—
152	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
153	C₂×C₅×D₃	—	2	1	no	—
154	C₂×C₅×D₃	—	2	1	no	—
155	C₂×C₅×D₃	C₂²×C₄	1	2	yes	—
156	C₂×C₃×D₅	—	2	1	no	—
157	C₂×C₃×D₅	—	2	1	no	—
158	C₂×C₃×D₅	C₂²×C₄	1	2	yes	—
159	C₃×C₄×C₅	—	2	1	no	—
160	C₃×C₄×C₅	#41	1	2	yes	complemented
161	Dic₁₅	—	2	1	no	—
162	Dic₁₅	C₂²×C₄	1	2	yes	—
163	Dic₁₅	C₂²×C₄	1	2	yes	—
164	Dic₁₅	#41	1	2	yes	complemented
165	C₃×Dic₅	—	2	1	no	—
166	C₃×Dic₅	—	2	1	no	—
167	C₃×Dic₅	C₂²×C₄	1	2	yes	—
168	C₅×Dic₃	—	2	1	no	—
169	C₅×Dic₃	—	2	1	no	—
170	C₅×Dic₃	C₂²×C₄	1	2	yes	—
171	C₂×C₃×D₄	—	5	1	no	—
172	C₂²×C₃×C₄	—	5	1	no	—
173	C₂²×C₃×C₄	C₂×D₅	1	1	yes	characteristic
174	C₂×#67	—	5	1	no	—
175	C₂×#67	C₂×D₅	1	1	yes	characteristic
176	C₂²×Dic₃	—	5	1	no	—
177	C₂²×Dic₃	—	5	1	no	—
178	C₂²×Dic₃	—	5	1	no	—
179	C₂²×Dic₃	—	5	1	no	—
180	#237	—	5	8	no	—
181	C₂×C₄×D₃	—	5	1	no	—
182	C₂×C₄×D₃	—	5	1	no	—
183	C₂×C₄×D₃	C₂×D₅	1	1	yes	characteristic
184	C₂×Dic₆	—	5	1	no	—
185	C₃×C₄⋊C₄	—	5	1	no	—
186	C₃×C₂²⋊C₄	—	5	1	no	—
187	C₃×C₂²⋊C₄	—	5	1	no	—
188	C₃×C₄²	—	5	1	no	—
189	#217	—	5	1	no	—
190	#217	C₂×D₅	1	1	yes	characteristic
191	(C₂×D₃)⋊C₄	—	5	1	no	—
192	(C₂×D₃)⋊C₄	C₂×D₅	1	1	yes	characteristic
193	C₄⋊Dic₃	—	5	1	no	—
194	Dic₃⋊C₄	—	5	1	no	—
195	Dic₃⋊C₄	—	5	1	no	—
196	Dic₃⋊C₄	—	5	1	no	—
197	Dic₃⋊C₄	C₂×D₅	1	1	yes	characteristic
198	C₄×Dic₃	—	5	1	no	—
199	C₄×Dic₃	—	5	1	no	—
200	C₄×Dic₃	—	5	1	no	—
201	C₄×Dic₃	—	5	1	no	—
202	C₄×Dic₃	—	5	1	no	—
203	C₄×Dic₃	—	5	1	no	—
204	C₄×Dic₃	—	5	1	no	—
205	C₄×Dic₃	—	5	1	no	—
206	C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
207	C₂³×C₅	—	3	1	no	—
208	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
209	C₂²×D₅	C₂²×D₃	1	1	yes	characteristic
210	C₅×D₄	—	3	4	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	3	1	no	—
213	C₂×C₄×C₅	—	3	1	no	—
214	C₂×C₄×C₅	—	3	1	no	—
215	C₂×C₄×C₅	—	6	2	no	—
216	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
218	C₂²⋊D₅	—	3	4	no	—
219	C₂²⋊D₅	C₄×D₃	1	4	yes	complemented
220	C₂×Dic₅	—	3	4	no	—
221	C₂×Dic₅	—	3	1	no	—
222	C₂×Dic₅	—	3	1	no	—
223	C₂×Dic₅	—	3	1	no	—
224	C₂×Dic₅	—	3	4	no	—
225	C₂×Dic₅	—	3	1	no	—
226	C₂×Dic₅	—	6	2	no	—
227	C₂×Dic₅	—	6	2	no	—
228	C₂×Dic₅	C₂²×D₃	1	1	yes	characteristic
229	C₂×Dic₅	C₂²×D₃	1	1	yes	characteristic
230	C₂×Dic₅	C₂²×D₃	1	1	yes	characteristic
231	C₄×D₅	—	2	2	no	—
232	C₄×D₅	—	3	4	no	—
233	C₄×D₅	—	6	2	no	—
234	Dic₁₀	—	3	4	no	—
235	C₂×#41	—	15	1	no	—
236	C₄×Q₈	—	15	1	no	—
237	C₄×Q₈	—	15	1	no	—
238	C₄×D₄	—	3	1	no	—
239	C₄×D₄	—	5	1	no	—
240	C₄×D₄	—	15	1	no	—
241	C₄×D₄	—	15	1	no	—
242	C₄×D₄	—	15	1	no	—
243	C₄×D₄	—	15	1	no	—
244	#117	—	15	1	no	—
245	#117	—	15	1	no	—
246	#117	—	15	1	no	—
247	C₂×C₄²	—	15	1	no	—
248	C₂×C₄²	—	15	1	no	—
249	C₂×C₄²	—	15	1	no	—
250	C₂×C₃×C₅	—	2	2	no	—
251	C₂×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
252	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
253	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
254	C₃×D₅	—	2	2	no	—
255	C₅×D₃	—	2	2	no	—
256	C₂³×C₃	—	5	1	no	—
257	C₂³×C₃	C₂²×D₅	1	1	yes	characteristic
258	C₂²×D₃	C₂²×D₅	1	1	yes	characteristic
259	C₃×D₄	—	5	4	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	5	1	no	—
262	C₂×C₃×C₄	—	5	1	no	—
263	C₂×C₃×C₄	—	5	1	no	—
264	C₂×C₃×C₄	—	10	2	no	—
265	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
267	#67	—	5	4	no	—
268	#67	C₄×D₅	1	4	yes	complemented
269	C₂×Dic₃	—	5	4	no	—
270	C₂×Dic₃	—	5	1	no	—
271	C₂×Dic₃	—	5	1	no	—
272	C₂×Dic₃	—	5	1	no	—
273	C₂×Dic₃	—	5	4	no	—
274	C₂×Dic₃	—	5	1	no	—
275	C₂×Dic₃	—	10	2	no	—
276	C₂×Dic₃	—	10	2	no	—
277	C₂×Dic₃	C₂²×D₅	1	1	yes	characteristic
278	C₂×Dic₃	C₂²×D₅	1	1	yes	characteristic
279	C₂×Dic₃	C₂²×D₅	1	1	yes	characteristic
280	C₄×D₃	—	2	2	no	—
281	C₄×D₃	—	5	4	no	—
282	C₄×D₃	—	10	2	no	—
283	Dic₆	—	5	4	no	—
284	C₂²×C₅	—	2	1	no	—
285	C₂²×C₅	—	2	1	no	—
286	C₂²×C₅	—	3	2	no	—
287	C₂²×C₅	—	6	1	no	—
288	C₂²×C₅	—	6	1	no	—
289	C₂²×C₅	C₂×C₄×D₃	1	2	yes	—
290	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
291	C₂×D₅	—	2	1	no	—
292	C₂×D₅	—	2	1	no	—
293	C₂×D₅	C₂×C₄×D₃	1	2	yes	—
294	C₄×C₅	—	2	1	no	—
295	C₄×C₅	—	3	2	no	—
296	C₄×C₅	—	6	1	no	—
297	C₄×C₅	—	6	1	no	—
298	C₄×C₅	#237	1	2	yes	complemented
299	Dic₅	—	2	1	no	—
300	Dic₅	—	2	1	no	—
301	Dic₅	—	3	2	no	—
302	Dic₅	—	3	2	no	—
303	Dic₅	—	3	2	no	—
304	Dic₅	—	6	1	no	—
305	Dic₅	C₂×C₄×D₃	1	2	yes	—
306	#41	—	15	8	no	—
307	C₂×Q₈	—	15	1	no	—
308	C₂×D₄	—	3	1	no	—
309	C₂×D₄	—	5	1	no	—
310	C₂×D₄	—	15	1	no	—
311	C₂²×C₄	—	3	1	no	—
312	C₂²×C₄	—	5	1	no	—
313	C₂²×C₄	—	15	1	no	—
314	C₂²×C₄	—	15	1	no	—
315	C₂²×C₄	—	15	1	no	—
316	C₂²×C₄	—	15	1	no	—
317	C₂²×C₄	—	15	1	no	—
318	C₂²×C₄	—	15	1	no	—
319	C₂²×C₄	D₃×D₅	1	1	yes	characteristic
320	C₄⋊C₄	—	3	1	no	—
321	C₄⋊C₄	—	5	1	no	—
322	C₄⋊C₄	—	15	1	no	—
323	C₄⋊C₄	—	15	1	no	—
324	C₄⋊C₄	—	15	1	no	—
325	C₄⋊C₄	—	15	1	no	—
326	C₂²⋊C₄	—	3	1	no	—
327	C₂²⋊C₄	—	3	1	no	—
328	C₂²⋊C₄	—	5	1	no	—
329	C₂²⋊C₄	—	5	1	no	—
330	C₂²⋊C₄	—	15	1	no	—
331	C₂²⋊C₄	—	15	1	no	—
332	C₄²	—	3	1	no	—
333	C₄²	—	5	1	no	—
334	C₄²	—	15	1	no	—
335	C₄²	—	15	1	no	—
336	C₄²	—	15	1	no	—
337	C₄²	—	15	1	no	—
338	C₄²	—	15	1	no	—
339	C₄²	—	15	1	no	—
340	C₄²	—	15	1	no	—
341	C₄²	—	15	1	no	—
342	C₃×C₅	C₄×#41	1	1	yes	characteristic, complemented, Hall
343	C₂²×C₃	—	2	1	no	—
344	C₂²×C₃	—	2	1	no	—
345	C₂²×C₃	—	5	2	no	—
346	C₂²×C₃	—	10	1	no	—
347	C₂²×C₃	—	10	1	no	—
348	C₂²×C₃	C₂×C₄×D₅	1	2	yes	—
349	C₂²×C₃	C₂³×D₅	1	1	yes	characteristic
350	C₂×D₃	—	2	1	no	—
351	C₂×D₃	—	2	1	no	—
352	C₂×D₃	C₂×C₄×D₅	1	2	yes	—
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	—	5	2	no	—
355	C₃×C₄	—	10	1	no	—
356	C₃×C₄	—	10	1	no	—
357	C₃×C₄	#711	1	2	yes	complemented
358	Dic₃	—	2	1	no	—
359	Dic₃	—	2	1	no	—
360	Dic₃	—	5	2	no	—
361	Dic₃	—	5	2	no	—
362	Dic₃	—	5	2	no	—
363	Dic₃	—	10	1	no	—
364	Dic₃	C₂×C₄×D₅	1	2	yes	—
365	C₂×C₅	—	2	2	no	—
366	C₂×C₅	—	6	2	no	—
367	C₂×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
368	C₂×C₅	C₂×#237	1	1	yes	characteristic
369	C₂×C₅	D₃×#41	1	1	yes	characteristic
370	D₅	—	2	2	no	—
371	C₂³	—	3	1	no	—
372	C₂³	—	5	1	no	—
373	C₂³	C₂×D₃×D₅	1	1	yes	characteristic
374	Q₈	—	15	4	no	—
375	D₄	—	3	4	no	—
376	D₄	—	5	4	no	—
377	D₄	—	15	4	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	3	1	no	—
380	C₂×C₄	—	3	1	no	—
381	C₂×C₄	—	3	1	no	—
382	C₂×C₄	—	5	1	no	—
383	C₂×C₄	—	5	1	no	—
384	C₂×C₄	—	5	1	no	—
385	C₂×C₄	—	6	2	no	—
386	C₂×C₄	—	10	2	no	—
387	C₂×C₄	—	15	4	no	—
388	C₂×C₄	—	15	4	no	—
389	C₂×C₄	—	15	4	no	—
390	C₂×C₄	—	15	1	no	—
391	C₂×C₄	—	15	1	no	—
392	C₂×C₄	—	15	1	no	—
393	C₂×C₄	—	15	1	no	—
394	C₂×C₄	—	30	2	no	—
395	C₂×C₄	—	30	2	no	—
396	C₂×C₄	—	30	2	no	—
397	C₂×C₄	C₂×D₃×D₅	1	1	yes	characteristic
398	C₂×C₄	C₂×D₃×D₅	1	1	yes	characteristic
399	C₂×C₃	—	2	2	no	—
400	C₂×C₃	—	10	2	no	—
401	C₂×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
402	C₂×C₃	C₂×#711	1	1	yes	characteristic
403	C₂×C₃	D₅×#41	1	1	yes	characteristic
404	D₃	—	2	2	no	—
405	C₅	C₄×#237	1	1	yes	characteristic, complemented, Sylow
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	3	2	no	—
409	C₂²	—	5	2	no	—
410	C₂²	—	6	1	no	—
411	C₂²	—	6	1	no	—
412	C₂²	—	10	1	no	—
413	C₂²	—	10	1	no	—
414	C₂²	C₄×D₃×D₅	1	2	yes	—
415	C₂²	C₂²×D₃×D₅	1	1	yes	characteristic
416	C₄	—	2	1	no	—
417	C₄	—	3	2	no	—
418	C₄	—	5	2	no	—
419	C₄	—	6	1	no	—
420	C₄	—	6	1	no	—
421	C₄	—	10	1	no	—
422	C₄	—	10	1	no	—
423	C₄	—	15	2	no	—
424	C₄	—	15	2	no	—
425	C₄	—	15	2	no	—
426	C₄	—	30	1	no	—
427	C₄	#6780	1	2	yes	direct product factor
428	C₃	C₄×#711	1	1	yes	characteristic, complemented, Sylow
429	C₂	—	2	2	no	—
430	C₂	—	6	2	no	—
431	C₂	—	10	2	no	—
432	C₂	C₂×C₄×D₃×D₅	1	1	yes	characteristic
433	C₂	#92016	1	1	yes	characteristic
434	C₂	C₂×#6780	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃×D₅
commutator	C₂×C₃×C₅	C₂³×C₄
Frattini	C₂²	C₂²×D₃×D₅
Fitting	C₂²×C₃×C₄×C₅	C₂²
socle, cosocle	C₂²×C₃×C₅	C₂⁴
prime radical	C₂×#6780	C₂
hypercenter	C₂²×C₄	D₃×D₅
hypocenter	C₃×C₅	C₄×#41
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Dic₁₅	C₂	semidirect
3. C₄×C₅×#67	C₂	semidirect
4. C₃×C₄×C₂²⋊D₅	C₂	semidirect
5. #67⋊Dic₅	C₂	semidirect
6. #91559	C₂	semidirect
7. #91532	C₂	semidirect
8. C₄×#1204	C₂	semidirect
9. #91442	C₂	semidirect
10. C₄×#1201	C₂	semidirect
11. #91400	C₂	semidirect
12. C₄×D₃×Dic₅	C₂	semidirect
13. #91394	C₂	semidirect
14. C₄×D₅×Dic₃	C₂	semidirect
15. #91325	C₂	semidirect
28. #6780	C₄	direct (N × H)
58. C₄×C₂²⋊D₅	D₃	semidirect
76. C₂×Dic₁₅	C₂×C₄	semidirect
81. C₅×#67	C₂×C₄	semidirect
86. C₃×C₂²⋊D₅	C₂×C₄	semidirect
91. #1204	C₂×C₄	semidirect
92. #1201	C₂×C₄	semidirect
94. D₃×Dic₅	C₂×C₄	semidirect
96. D₅×Dic₃	C₂×C₄	semidirect
101. C₄×#67	D₅	semidirect
160. C₃×C₄×C₅	#41	semidirect
164. Dic₁₅	#41	semidirect
219. C₂²⋊D₅	C₄×D₃	semidirect
268. #67	C₄×D₅	semidirect
298. C₄×C₅	#237	semidirect
342. C₃×C₅	C₄×#41	semidirect
357. C₃×C₄	#711	semidirect
405. C₅	C₄×#237	semidirect
427. C₄	#6780	direct (N × H)
428. C₃	C₄×#711	semidirect

Maximal subgroups

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

subgroup	index
C₂×#6780	2
C₂×C₄×Dic₁₅	2
C₄×C₅×#67	2
C₃×C₄×C₂²⋊D₅	2
#67⋊Dic₅	2
#91559	2
#91532	2
C₄×#1204	2
#91442	2
C₄×#1201	2
#91400	2
C₄×D₃×Dic₅	2
#91394	2
C₄×D₅×Dic₃	2
#91325	2
C₄×#711	3
C₄×#237	5

Subgroups — C4×#6780 #11754285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#6780 #11754285