Subgroups — #104×Dic₁₅ #14295579

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×Dic₁₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#104	C₂	1	1	yes	maximal, characteristic
3	C₂×#91121	C₂	1	1	yes	maximal, characteristic
4	M₁₆×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄²×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
6	#11746376	C₂	1	1	yes	maximal, characteristic, complemented
7	#11746344	C₂	1	1	yes	maximal, characteristic, complemented
8	Dic₅×#104	—	3	1	no	maximal, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	Q₈×Dic₁₅	C₄	1	2	yes	complemented
13	D₄×Dic₁₅	—	2	2	no	—
14	D₄×Dic₁₅	C₄	1	2	yes	complemented
15	#91815	—	2	1	no	—
16	#91815	C₂²	1	1	yes	characteristic
17	C₂×C₄×Dic₁₅	—	2	2	no	—
18	C₂×C₄×Dic₁₅	—	2	1	no	—
19	C₂×C₄×Dic₁₅	C₂²	1	1	yes	characteristic
20	C₂×C₄×Dic₁₅	C₂²	1	1	yes	characteristic
21	C₂×#6710	C₂²	1	1	yes	characteristic
22	C₃×C₅×#104	C₄	1	4	yes	complemented
23	#91121	C₄	1	4	yes	complemented
24	#91099	—	2	1	no	—
25	C₈×Dic₁₅	—	2	1	no	—
26	Dic₃×#104	—	5	1	no	maximal, Hall
27	#41×Dic₅	—	3	1	no	—
28	C₂×C₅×#104	D₃	1	1	yes	characteristic
29	C₂×#3969	—	3	1	no	—
30	M₁₆×Dic₅	—	3	1	no	—
31	C₄²×Dic₅	—	3	1	no	—
32	#64775	—	3	1	no	—
33	#64743	—	3	1	no	—
34	C₃×C₅×#41	—	2	1	no	—
35	C₃×C₅×#41	—	2	1	no	—
36	C₃×C₅×#41	C₂×C₄	1	2	yes	—
37	C₃×C₅×#41	C₂×C₄	1	2	yes	—
38	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
39	C₂×C₃×C₅×D₄	—	2	1	no	—
40	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂²×C₃×C₄×C₅	—	2	1	no	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×Dic₁₅	—	2	1	no	—
45	C₂²×Dic₁₅	—	2	2	no	—
46	C₂²×Dic₁₅	D₄	1	2	yes	—
47	C₃×C₅×M₁₆	—	2	1	no	—
48	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	complemented
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₃×C₄²×C₅	—	2	1	no	—
51	C₃×C₄²×C₅	C₂×C₄	1	2	yes	complemented
52	#6719	—	2	1	no	—
53	#6719	—	2	2	no	—
54	C₄⋊Dic₁₅	—	2	2	no	—
55	C₄⋊Dic₁₅	C₂×C₄	1	2	yes	—
56	C₄×Dic₁₅	—	2	8	no	—
57	C₄×Dic₁₅	—	2	1	no	—
58	C₄×Dic₁₅	—	2	1	no	—
59	C₄×Dic₁₅	—	2	2	no	—
60	C₄×Dic₁₅	C₂×C₄	1	2	yes	—
61	C₄×Dic₁₅	C₂×C₄	1	2	yes	complemented
62	C₄×Dic₁₅	D₄	1	1	yes	characteristic
63	C₄×Dic₁₅	D₄	1	1	yes	characteristic
64	#6710	—	2	1	no	—
65	#6710	C₂×C₄	1	2	yes	complemented
66	C₂×C₃⋊#168	—	2	1	no	—
67	Dic₃×#41	—	5	1	no	—
68	C₂×C₃×#104	D₅	1	1	yes	characteristic
69	C₂×#837	—	5	1	no	—
70	Dic₃×M₁₆	—	5	1	no	—
71	C₄²×Dic₃	—	5	1	no	—
72	#4555	—	5	1	no	—
73	#4523	—	5	1	no	—
74	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
75	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
76	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
77	Q₈×Dic₅	—	3	2	no	—
78	D₄×Dic₅	—	3	2	no	—
79	D₄×Dic₅	—	6	2	no	—
80	#4072	—	3	1	no	—
81	#4072	—	6	1	no	—
82	C₂×C₄×Dic₅	—	3	1	no	—
83	C₂×C₄×Dic₅	—	3	1	no	—
84	C₂×C₄×Dic₅	—	6	1	no	—
85	C₂×C₄×Dic₅	—	6	2	no	—
86	C₂×#681	—	3	1	no	—
87	C₅×#104	Dic₃	1	4	yes	complemented
88	#3969	—	3	4	no	—
89	#3947	—	6	1	no	—
90	C₈×Dic₅	—	6	1	no	—
91	C₄×#104	—	15	1	no	Sylow
92	C₂³×C₃×C₅	—	2	1	no	—
93	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
94	C₃×C₅×Q₈	—	2	1	no	—
95	C₃×C₅×Q₈	C₄²	1	2	yes	complemented
96	C₃×C₅×D₄	—	2	2	no	—
97	C₃×C₅×D₄	—	2	2	no	—
98	C₃×C₅×D₄	—	2	1	no	—
99	C₃×C₅×D₄	C₄²	1	2	yes	complemented
100	C₂×C₃×C₄×C₅	—	2	4	no	—
101	C₂×C₃×C₄×C₅	—	2	1	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
111	C₂×Dic₁₅	—	2	4	no	—
112	C₂×Dic₁₅	—	2	2	no	—
113	C₂×Dic₁₅	—	2	4	no	—
114	C₂×Dic₁₅	—	2	2	no	—
115	C₂×Dic₁₅	—	4	4	no	—
116	C₂×Dic₁₅	C₂²⋊C₄	1	2	yes	—
117	C₂×Dic₁₅	C₂²⋊C₄	1	2	yes	—
118	C₃×C₅×C₈	—	2	2	no	—
119	C₃⋊#168	—	2	2	no	—
120	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
121	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
122	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
123	Q₈×Dic₃	—	5	2	no	—
124	D₄×Dic₃	—	5	2	no	—
125	D₄×Dic₃	—	10	2	no	—
126	#926	—	5	1	no	—
127	#926	—	10	1	no	—
128	C₂×C₄×Dic₃	—	5	1	no	—
129	C₂×C₄×Dic₃	—	5	1	no	—
130	C₂×C₄×Dic₃	—	10	1	no	—
131	C₂×C₄×Dic₃	—	10	2	no	—
132	C₂×#208	—	5	1	no	—
133	C₃×#104	Dic₅	1	4	yes	complemented
134	#837	—	5	4	no	—
135	#815	—	10	1	no	—
136	C₈×Dic₃	—	10	1	no	—
137	C₅×#41	—	2	1	no	—
138	C₅×#41	—	2	1	no	—
139	C₅×#41	C₄×D₃	1	2	yes	—
140	C₅×#41	C₂×Dic₃	1	2	yes	—
141	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
142	C₂×C₅×D₄	—	2	1	no	—
143	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
144	C₂²×C₄×C₅	—	2	1	no	—
145	C₂²×C₄×C₅	—	2	1	no	—
146	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
147	C₂²×Dic₅	—	3	2	no	—
148	C₂²×Dic₅	—	6	2	no	—
149	C₂²×Dic₅	—	6	1	no	—
150	C₅×M₁₆	—	2	1	no	—
151	C₅×M₁₆	C₂×Dic₃	1	2	yes	complemented
152	C₂×C₅×C₈	—	2	1	no	—
153	C₄²×C₅	—	2	1	no	—
154	C₄²×C₅	C₂×Dic₃	1	2	yes	complemented
155	C₂²⋊Dic₅	—	6	2	no	—
156	C₂²⋊Dic₅	—	6	1	no	—
157	C₄⋊Dic₅	—	3	2	no	—
158	C₄⋊Dic₅	—	6	2	no	—
159	C₄×Dic₅	—	3	2	no	—
160	C₄×Dic₅	—	3	1	no	—
161	C₄×Dic₅	—	3	1	no	—
162	C₄×Dic₅	—	3	2	no	—
163	C₄×Dic₅	—	6	2	no	—
164	C₄×Dic₅	—	6	8	no	—
165	C₄×Dic₅	—	6	1	no	—
166	C₄×Dic₅	—	6	1	no	—
167	#681	—	3	2	no	—
168	#681	—	6	1	no	—
169	C₂×#168	—	6	1	no	—
170	C₄×#41	—	15	1	no	—
171	C₂×#104	—	15	1	no	—
172	C₂×#104	D₁₅	1	1	yes	characteristic
173	C₄×M₁₆	—	15	1	no	—
174	C₄³	—	15	1	no	—
175	#339	—	15	1	no	—
176	#339	—	15	1	no	—
177	C₂²×C₃×C₅	—	2	2	no	—
178	C₂²×C₃×C₅	—	2	2	no	—
179	C₂²×C₃×C₅	—	4	2	no	—
180	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
182	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
183	C₃×C₄×C₅	—	2	4	no	—
184	C₃×C₄×C₅	—	2	2	no	—
185	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
186	C₃×C₄×C₅	#117	1	1	yes	characteristic
187	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
188	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
189	Dic₁₅	—	2	4	no	—
190	Dic₁₅	—	2	2	no	—
191	Dic₁₅	—	4	2	no	—
192	Dic₁₅	#104	1	4	yes	direct product factor
193	C₃×#41	—	2	1	no	—
194	C₃×#41	—	2	1	no	—
195	C₃×#41	C₄×D₅	1	2	yes	—
196	C₃×#41	C₂×Dic₅	1	2	yes	—
197	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
198	C₂×C₃×D₄	—	2	1	no	—
199	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic
200	C₂²×C₃×C₄	—	2	1	no	—
201	C₂²×C₃×C₄	—	2	1	no	—
202	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
203	C₂²×Dic₃	—	5	2	no	—
204	C₂²×Dic₃	—	10	2	no	—
205	C₂²×Dic₃	—	10	1	no	—
206	C₃×M₁₆	—	2	1	no	—
207	C₃×M₁₆	C₂×Dic₅	1	2	yes	complemented
208	C₂×C₃×C₈	—	2	1	no	—
209	C₃×C₄²	—	2	1	no	—
210	C₃×C₄²	C₂×Dic₅	1	2	yes	complemented
211	#217	—	10	2	no	—
212	#217	—	10	1	no	—
213	C₄⋊Dic₃	—	5	2	no	—
214	C₄⋊Dic₃	—	10	2	no	—
215	C₄×Dic₃	—	5	2	no	—
216	C₄×Dic₃	—	5	1	no	—
217	C₄×Dic₃	—	5	1	no	—
218	C₄×Dic₃	—	5	2	no	—
219	C₄×Dic₃	—	10	2	no	—
220	C₄×Dic₃	—	10	8	no	—
221	C₄×Dic₃	—	10	1	no	—
222	C₄×Dic₃	—	10	1	no	—
223	#208	—	5	2	no	—
224	#208	—	10	1	no	—
225	C₂×C₃⋊C₈	—	10	1	no	—
226	C₂³×C₅	—	2	1	no	—
227	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
228	C₅×Q₈	—	2	1	no	—
229	C₅×Q₈	C₄×Dic₃	1	2	yes	complemented
230	C₅×D₄	—	2	2	no	—
231	C₅×D₄	—	2	2	no	—
232	C₅×D₄	—	2	1	no	—
233	C₅×D₄	C₄×Dic₃	1	2	yes	complemented
234	C₂×C₄×C₅	—	2	4	no	—
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
241	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
242	C₂×C₄×C₅	#237	1	1	yes	characteristic
243	C₂×C₄×C₅	#237	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
245	C₂×Dic₅	—	3	2	no	—
246	C₂×Dic₅	—	3	2	no	—
247	C₂×Dic₅	—	6	4	no	—
248	C₂×Dic₅	—	6	4	no	—
249	C₂×Dic₅	—	6	2	no	—
250	C₂×Dic₅	—	6	2	no	—
251	C₂×Dic₅	—	12	4	no	—
252	C₅×C₈	—	2	2	no	—
253	#168	—	6	2	no	—
254	C₂×#41	C₂×D₁₅	1	1	yes	characteristic
255	C₂×M₁₆	—	15	1	no	—
256	C₂×M₁₆	C₂×D₁₅	1	1	yes	characteristic
257	C₄×Q₈	—	15	2	no	—
258	C₄×D₄	—	15	2	no	—
259	C₄×D₄	—	30	2	no	—
260	#117	—	15	1	no	—
261	#117	—	30	1	no	—
262	C₂×C₄²	—	15	1	no	—
263	C₂×C₄²	—	15	1	no	—
264	C₂×C₄²	—	30	1	no	—
265	C₂×C₄²	—	30	2	no	—
266	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
267	#104	—	15	4	no	—
268	#104	Dic₁₅	1	4	yes	direct product factor
269	#97	—	30	1	no	—
270	C₄×C₈	—	30	1	no	—
271	C₂×C₃×C₅	—	2	1	no	—
272	C₂×C₃×C₅	—	2	1	no	—
273	C₂×C₃×C₅	—	4	2	no	—
274	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₃×C₅	C₂×#104	1	2	yes	—
276	C₂³×C₃	—	2	1	no	—
277	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
278	C₃×Q₈	—	2	1	no	—
279	C₃×Q₈	C₄×Dic₅	1	2	yes	complemented
280	C₃×D₄	—	2	2	no	—
281	C₃×D₄	—	2	2	no	—
282	C₃×D₄	—	2	1	no	—
283	C₃×D₄	C₄×Dic₅	1	2	yes	complemented
284	C₂×C₃×C₄	—	2	4	no	—
285	C₂×C₃×C₄	—	2	1	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
291	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
292	C₂×C₃×C₄	#711	1	1	yes	characteristic
293	C₂×C₃×C₄	#711	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
295	C₂×Dic₃	—	5	2	no	—
296	C₂×Dic₃	—	5	2	no	—
297	C₂×Dic₃	—	10	4	no	—
298	C₂×Dic₃	—	10	4	no	—
299	C₂×Dic₃	—	10	2	no	—
300	C₂×Dic₃	—	10	2	no	—
301	C₂×Dic₃	—	20	4	no	—
302	C₃×C₈	—	2	2	no	—
303	C₃⋊C₈	—	10	2	no	—
304	C₂²×C₅	—	2	2	no	—
305	C₂²×C₅	—	2	2	no	—
306	C₂²×C₅	—	4	2	no	—
307	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
308	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
309	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
310	C₄×C₅	—	2	4	no	—
311	C₄×C₅	—	2	2	no	—
312	C₄×C₅	#877	1	1	yes	characteristic
313	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
314	C₄×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
315	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
316	Dic₅	—	3	4	no	—
317	Dic₅	—	6	4	no	—
318	Dic₅	—	6	2	no	—
319	Dic₅	—	12	2	no	—
320	#41	—	2	1	no	—
321	#41	—	2	1	no	—
322	#41	C₄×D₁₅	1	2	yes	—
323	#41	C₂×Dic₁₅	1	2	yes	—
324	C₂×Q₈	C₄×D₁₅	1	1	yes	characteristic
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	C₄×D₁₅	1	1	yes	characteristic
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	15	2	no	—
330	C₂²×C₄	—	30	2	no	—
331	C₂²×C₄	—	30	1	no	—
332	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
333	M₁₆	—	2	1	no	—
334	M₁₆	—	15	2	no	—
335	M₁₆	—	30	1	no	—
336	M₁₆	C₂×Dic₁₅	1	2	yes	complemented
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	30	1	no	—
339	C₄⋊C₄	—	15	2	no	—
340	C₄⋊C₄	—	30	2	no	—
341	C₂²⋊C₄	—	30	2	no	—
342	C₂²⋊C₄	—	30	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	15	2	no	—
345	C₄²	—	15	1	no	—
346	C₄²	—	15	1	no	—
347	C₄²	—	15	2	no	—
348	C₄²	—	30	2	no	—
349	C₄²	—	30	8	no	—
350	C₄²	—	30	1	no	—
351	C₄²	—	30	1	no	—
352	C₄²	C₂×Dic₁₅	1	2	yes	complemented
353	C₃×C₅	C₄×#104	1	1	yes	characteristic, complemented, Hall
354	C₂²×C₃	—	2	2	no	—
355	C₂²×C₃	—	2	2	no	—
356	C₂²×C₃	—	4	2	no	—
357	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
358	C₂²×C₃	#4027	1	1	yes	characteristic
359	C₂²×C₃	D₄×Dic₅	1	1	yes	characteristic
360	C₃×C₄	—	2	4	no	—
361	C₃×C₄	—	2	2	no	—
362	C₃×C₄	#4023	1	1	yes	characteristic
363	C₃×C₄	#4027	1	1	yes	characteristic
364	C₃×C₄	C₂×C₄×Dic₅	1	1	yes	characteristic
365	C₃×C₄	D₄×Dic₅	1	1	yes	characteristic
366	Dic₃	—	5	4	no	—
367	Dic₃	—	10	4	no	—
368	Dic₃	—	10	2	no	—
369	Dic₃	—	20	2	no	—
370	C₂×C₅	—	2	1	no	—
371	C₂×C₅	—	2	1	no	—
372	C₂×C₅	—	4	2	no	—
373	C₂×C₅	D₃×#104	1	2	yes	—
374	C₂×C₅	Dic₃×C₂²⋊C₄	1	1	yes	characteristic
375	C₂³	—	2	1	no	—
376	C₂³	D₄×D₁₅	1	1	yes	characteristic
377	Q₈	—	2	1	no	—
378	Q₈	C₄×Dic₁₅	1	2	yes	complemented
379	D₄	—	2	2	no	—
380	D₄	—	2	2	no	—
381	D₄	—	2	1	no	—
382	D₄	C₄×Dic₁₅	1	2	yes	complemented
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	15	2	no	—
389	C₂×C₄	—	15	2	no	—
390	C₂×C₄	—	30	4	no	—
391	C₂×C₄	—	30	4	no	—
392	C₂×C₄	—	30	2	no	—
393	C₂×C₄	—	30	2	no	—
394	C₂×C₄	—	60	4	no	—
395	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
396	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
397	C₂×C₄	D₄×D₁₅	1	1	yes	characteristic
398	C₂×C₄	#6819	1	1	yes	characteristic
399	C₂×C₄	#6819	1	1	yes	characteristic
400	C₂×C₄	C₂²×Dic₁₅	1	1	yes	characteristic
401	C₈	—	2	2	no	—
402	C₈	—	30	2	no	—
403	C₂×C₃	—	2	1	no	—
404	C₂×C₃	—	2	1	no	—
405	C₂×C₃	—	4	2	no	—
406	C₂×C₃	D₅×#104	1	2	yes	—
407	C₂×C₃	C₂²⋊C₄×Dic₅	1	1	yes	characteristic
408	C₅	Dic₃×#104	1	1	yes	characteristic, complemented, Sylow
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	C₂²⋊C₄×D₁₅	1	1	yes	characteristic
413	C₂²	#91770	1	1	yes	characteristic
414	C₂²	D₄×Dic₁₅	1	1	yes	characteristic
415	C₄	—	2	4	no	—
416	C₄	—	2	2	no	—
417	C₄	—	15	4	no	—
418	C₄	—	30	4	no	—
419	C₄	—	30	2	no	—
420	C₄	—	60	2	no	—
421	C₄	#91766	1	1	yes	characteristic
422	C₄	#91770	1	1	yes	characteristic
423	C₄	C₂×C₄×Dic₁₅	1	1	yes	characteristic
424	C₄	D₄×Dic₁₅	1	1	yes	characteristic
425	C₃	Dic₅×#104	1	1	yes	characteristic, complemented, Sylow
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	4	2	no	—
429	C₂	D₁₅×#104	1	2	yes	—
430	C₂	C₂²⋊C₄×Dic₁₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₁₅
commutator	C₃×C₄×C₅	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₁₅
Fitting	C₂×C₃×C₅×#104	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₃×C₅×#41	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×#104	D₁₅
hypocenter	C₃×C₅	C₄×#104
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#104

Complements

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

N	H ≅ G/N	type
4. M₁₆×Dic₁₅	C₂	semidirect
5. C₄²×Dic₁₅	C₂	semidirect
6. #11746376	C₂	semidirect
7. #11746344	C₂	semidirect
12. Q₈×Dic₁₅	C₄	semidirect
14. D₄×Dic₁₅	C₄	semidirect
22. C₃×C₅×#104	C₄	semidirect
23. #91121	C₄	semidirect
48. C₃×C₅×M₁₆	C₂×C₄	semidirect
51. C₃×C₄²×C₅	C₂×C₄	semidirect
61. C₄×Dic₁₅	C₂×C₄	semidirect
65. #6710	C₂×C₄	semidirect
87. C₅×#104	Dic₃	semidirect
95. C₃×C₅×Q₈	C₄²	semidirect
99. C₃×C₅×D₄	C₄²	semidirect
133. C₃×#104	Dic₅	semidirect
151. C₅×M₁₆	C₂×Dic₃	semidirect
154. C₄²×C₅	C₂×Dic₃	semidirect
192. Dic₁₅	#104	direct (N × H)
207. C₃×M₁₆	C₂×Dic₅	semidirect
210. C₃×C₄²	C₂×Dic₅	semidirect
229. C₅×Q₈	C₄×Dic₃	semidirect
233. C₅×D₄	C₄×Dic₃	semidirect
268. #104	Dic₁₅	direct (N × H)
279. C₃×Q₈	C₄×Dic₅	semidirect
283. C₃×D₄	C₄×Dic₅	semidirect
336. M₁₆	C₂×Dic₁₅	semidirect
352. C₄²	C₂×Dic₁₅	semidirect
353. C₃×C₅	C₄×#104	semidirect
378. Q₈	C₄×Dic₁₅	semidirect
382. D₄	C₄×Dic₁₅	semidirect
408. C₅	Dic₃×#104	semidirect
425. C₃	Dic₅×#104	semidirect

Maximal subgroups

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

subgroup	index
#41×Dic₁₅	2
C₂×C₃×C₅×#104	2
C₂×#91121	2
M₁₆×Dic₁₅	2
C₄²×Dic₁₅	2
#11746376	2
#11746344	2
Dic₅×#104	3
Dic₃×#104	5

Subgroups — #104×Dic15 #14295579

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #104×Dic₁₅ #14295579