Subgroups — #11752850

Order 960.

644 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#1200	C₂	1	1	yes	maximal, characteristic
2	C₂×D₁₅⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊C₄×D₁₅	C₂	1	1	yes	maximal, characteristic
4	C₅×#878	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4024	C₂	1	1	yes	maximal, characteristic, complemented
6	#91575	C₂	1	1	yes	maximal, characteristic, complemented
7	#91574	C₂	1	1	yes	maximal, characteristic, complemented
8	#91561	C₂	1	1	yes	maximal, characteristic
9	#91437	C₂	1	1	yes	maximal, characteristic, complemented
10	#91429	C₂	1	1	yes	maximal, characteristic, complemented
11	#91424	C₂	1	1	yes	maximal, characteristic, complemented
12	#91419	C₂	1	1	yes	maximal, characteristic, complemented
13	#91411	C₂	1	1	yes	maximal, characteristic, complemented
14	#91404	C₂	1	1	yes	maximal, characteristic, complemented
15	#91404	C₂	1	1	yes	maximal, characteristic, complemented
16	D₅×C₂²⋊Q₈	—	3	1	no	maximal, Hall
17	C₂³×D₁₅	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₁₅	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₁₅	C₂²	1	1	yes	characteristic
20	C₂²×C₅×Dic₃	C₂²	1	1	yes	characteristic
21	C₂×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₃×Dic₅	C₂²	1	1	yes	characteristic
23	C₂×C₃×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
24	C₂×#1204	C₂²	1	1	yes	characteristic, complemented
25	C₂×#1204	C₂²	1	1	yes	characteristic, complemented
26	C₂×#1200	—	2	4	no	—
27	C₂×#1200	C₂²	1	1	yes	characteristic
28	C₂×#1200	C₂²	1	1	yes	characteristic
29	C₂×#1200	C₂²	1	1	yes	characteristic
30	C₂×#1200	C₂²	1	1	yes	characteristic
31	C₂×#1200	C₂²	1	1	yes	characteristic
32	C₂×#1200	C₂²	1	1	yes	characteristic
33	D₁₅⋊Q₈	—	2	4	no	—
34	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	#6719	C₂²	1	1	yes	characteristic
36	#6714	C₂²	1	1	yes	characteristic
37	#6714	C₂²	1	1	yes	characteristic
38	C₅×#217	C₂²	1	1	yes	characteristic
39	C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
40	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
43	C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
44	C₃×#683	C₂²	1	1	yes	characteristic, complemented
45	C₃×#683	C₂²	1	1	yes	characteristic, complemented
46	Dic₃⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
47	Dic₃⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
48	#6669	C₂²	1	1	yes	characteristic, complemented
49	#6669	C₂²	1	1	yes	characteristic, complemented
50	#6668	C₂²	1	1	yes	characteristic, complemented
51	#6668	C₂²	1	1	yes	characteristic, complemented
52	#6667	C₂²	1	1	yes	characteristic
53	#6667	C₂²	1	1	yes	characteristic
54	D₃×C₂²⋊Q₈	—	5	1	no	maximal, Hall
55	C₂×Q₈×D₅	—	3	1	no	—
56	C₂²×C₄×D₅	—	3	1	no	—
57	C₅×C₂²⋊Q₈	—	3	1	no	—
58	#4092	—	3	1	no	—
59	#4070	—	3	1	no	—
60	#4043	—	3	1	no	—
61	#4042	—	3	1	no	—
62	#4042	—	3	1	no	—
63	D₅×C₄⋊C₄	—	3	1	no	—
64	D₅×C₄⋊C₄	—	3	1	no	—
65	D₅×C₄⋊C₄	—	3	1	no	—
66	D₅×C₂²⋊C₄	—	3	1	no	—
67	D₅×C₂²⋊C₄	—	3	1	no	—
68	#4024	—	3	1	no	—
69	#4024	D₃	1	1	yes	characteristic, complemented
70	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
71	C₂²×D₁₅	—	2	2	no	—
72	C₂²×D₁₅	—	2	2	no	—
73	C₂²×D₁₅	Q₈	1	4	yes	complemented
74	C₂²×D₁₅	C₂³	1	1	yes	characteristic
75	C₂²×D₁₅	C₂³	1	1	yes	characteristic
76	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂×Dic₁₅	C₂³	1	1	yes	characteristic
79	C₂×Dic₁₅	C₂³	1	1	yes	characteristic
80	C₄×D₁₅	—	2	2	no	—
81	C₄×D₁₅	—	2	2	no	—
82	C₂×C₅×Dic₃	—	2	2	no	—
83	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
84	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
85	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
86	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
87	C₅×Dic₆	—	2	2	no	—
88	C₂×C₃×Dic₅	—	2	2	no	—
89	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
90	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
91	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
92	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
93	C₃×Dic₁₀	—	2	2	no	—
94	#1204	—	2	2	no	—
95	#1204	—	2	2	no	—
96	#1200	—	2	2	no	—
97	#1200	—	2	2	no	—
98	#1200	—	2	2	no	—
99	#1200	—	2	2	no	—
100	#1200	—	2	2	no	—
101	#1200	D₄	1	4	yes	—
102	C₂×D₃×Q₈	—	5	1	no	—
103	C₂²×C₄×D₃	—	5	1	no	—
104	C₃×C₂²⋊Q₈	—	5	1	no	—
105	#946	—	5	1	no	—
106	#924	—	5	1	no	—
107	#897	—	5	1	no	—
108	#896	—	5	1	no	—
109	#896	—	5	1	no	—
110	D₃×C₄⋊C₄	—	5	1	no	—
111	D₃×C₄⋊C₄	—	5	1	no	—
112	D₃×C₄⋊C₄	—	5	1	no	—
113	D₃×C₂²⋊C₄	—	5	1	no	—
114	D₃×C₂²⋊C₄	—	5	1	no	—
115	#878	—	5	1	no	—
116	#878	D₅	1	1	yes	characteristic, complemented
117	C₂³×D₅	—	3	1	no	—
118	C₂×C₅×Q₈	—	3	1	no	—
119	C₂²×C₄×C₅	—	3	1	no	—
120	C₂²×Dic₅	C₂×D₃	1	1	yes	characteristic
121	Q₈×D₅	—	6	4	no	—
122	C₂×C₄×D₅	—	3	1	no	—
123	C₂×C₄×D₅	—	3	1	no	—
124	C₂×C₄×D₅	—	3	1	no	—
125	C₂×C₄×D₅	—	3	1	no	—
126	C₂×C₄×D₅	—	3	1	no	—
127	C₂×C₄×D₅	—	3	1	no	—
128	C₂×C₄×D₅	—	3	1	no	—
129	C₂×C₄×D₅	—	3	1	no	—
130	C₂×C₄×D₅	—	6	4	no	—
131	C₂×Dic₁₀	—	3	1	no	—
132	C₂×Dic₁₀	—	3	1	no	—
133	C₂×Dic₁₀	C₂×D₃	1	1	yes	characteristic, complemented
134	C₅×C₄⋊C₄	—	3	1	no	—
135	C₅×C₄⋊C₄	—	3	1	no	—
136	C₅×C₄⋊C₄	—	3	1	no	—
137	C₅×C₂²⋊C₄	—	3	1	no	—
138	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
139	C₂²⋊Dic₅	—	3	1	no	—
140	C₂²⋊Dic₅	C₂×D₃	1	1	yes	characteristic
141	#685	—	3	1	no	—
142	#685	—	3	1	no	—
143	#685	—	3	1	no	—
144	#685	—	3	1	no	—
145	C₄⋊Dic₅	—	3	1	no	—
146	C₄⋊Dic₅	—	3	1	no	—
147	C₄⋊Dic₅	C₂×D₃	1	1	yes	characteristic, complemented
148	#683	—	3	1	no	—
149	#683	—	3	1	no	—
150	#683	—	3	1	no	—
151	#683	—	3	1	no	—
152	#683	C₂×D₃	1	1	yes	characteristic, complemented
153	#683	C₂×D₃	1	1	yes	characteristic, complemented
154	C₂×C₂²⋊Q₈	—	15	1	no	Sylow
155	C₂²×C₃×C₅	—	2	1	no	—
156	C₂²×C₃×C₅	—	2	1	no	—
157	C₂²×C₃×C₅	C₂×Q₈	1	2	yes	complemented
158	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
159	C₂×D₁₅	—	2	1	no	—
160	C₂×D₁₅	—	2	1	no	—
161	C₂×D₁₅	—	2	8	no	—
162	C₂×D₁₅	C₂×D₄	1	2	yes	—
163	C₂×D₁₅	C₂×Q₈	1	2	yes	—
164	C₂×D₁₅	C₂×Q₈	1	2	yes	complemented
165	C₂×D₁₅	#41	1	2	yes	—
166	C₃×C₄×C₅	—	2	1	no	—
167	C₃×C₄×C₅	—	2	1	no	—
168	Dic₁₅	—	2	1	no	—
169	Dic₁₅	—	2	1	no	—
170	C₃×Dic₅	—	2	1	no	—
171	C₃×Dic₅	—	2	1	no	—
172	C₃×Dic₅	—	2	1	no	—
173	C₃×Dic₅	C₂×D₄	1	2	yes	—
174	C₅×Dic₃	—	2	1	no	—
175	C₅×Dic₃	—	2	1	no	—
176	C₅×Dic₃	—	2	1	no	—
177	C₅×Dic₃	C₂×D₄	1	2	yes	—
178	C₂³×D₃	—	5	1	no	—
179	C₂×C₃×Q₈	—	5	1	no	—
180	C₂²×C₃×C₄	—	5	1	no	—
181	C₂²×Dic₃	C₂×D₅	1	1	yes	characteristic
182	D₃×Q₈	—	10	4	no	—
183	C₂×C₄×D₃	—	5	1	no	—
184	C₂×C₄×D₃	—	5	1	no	—
185	C₂×C₄×D₃	—	5	1	no	—
186	C₂×C₄×D₃	—	5	1	no	—
187	C₂×C₄×D₃	—	5	1	no	—
188	C₂×C₄×D₃	—	5	1	no	—
189	C₂×C₄×D₃	—	5	1	no	—
190	C₂×C₄×D₃	—	5	1	no	—
191	C₂×C₄×D₃	—	10	4	no	—
192	C₂×Dic₆	—	5	1	no	—
193	C₂×Dic₆	—	5	1	no	—
194	C₂×Dic₆	C₂×D₅	1	1	yes	characteristic, complemented
195	C₃×C₄⋊C₄	—	5	1	no	—
196	C₃×C₄⋊C₄	—	5	1	no	—
197	C₃×C₄⋊C₄	—	5	1	no	—
198	C₃×C₂²⋊C₄	—	5	1	no	—
199	C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
200	#217	—	5	1	no	—
201	#217	C₂×D₅	1	1	yes	characteristic
202	(C₂×D₃)⋊C₄	—	5	1	no	—
203	(C₂×D₃)⋊C₄	—	5	1	no	—
204	(C₂×D₃)⋊C₄	—	5	1	no	—
205	(C₂×D₃)⋊C₄	—	5	1	no	—
206	C₄⋊Dic₃	—	5	1	no	—
207	C₄⋊Dic₃	—	5	1	no	—
208	C₄⋊Dic₃	C₂×D₅	1	1	yes	characteristic, complemented
209	Dic₃⋊C₄	—	5	1	no	—
210	Dic₃⋊C₄	—	5	1	no	—
211	Dic₃⋊C₄	—	5	1	no	—
212	Dic₃⋊C₄	—	5	1	no	—
213	Dic₃⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
214	Dic₃⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
215	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
216	C₂²×D₅	—	3	1	no	—
217	C₂²×D₅	—	3	4	no	—
218	C₂²×D₅	—	3	1	no	—
219	C₂²×D₅	—	6	2	no	—
220	C₂²×D₅	—	6	2	no	—
221	C₅×Q₈	—	6	2	no	—
222	C₂×C₄×C₅	—	3	1	no	—
223	C₂×C₄×C₅	—	3	1	no	—
224	C₂×C₄×C₅	—	3	1	no	—
225	C₂×C₄×C₅	—	3	1	no	—
226	C₂×C₄×C₅	—	6	2	no	—
227	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
229	C₂×Dic₅	—	2	2	no	—
230	C₂×Dic₅	—	3	1	no	—
231	C₂×Dic₅	—	3	1	no	—
232	C₂×Dic₅	C₂²×D₃	1	1	yes	characteristic
233	C₂×Dic₅	C₂²×D₃	1	1	yes	characteristic
234	C₂×Dic₅	C₂²×D₃	1	1	yes	characteristic
235	C₂×Dic₅	C₂²×D₃	1	1	yes	characteristic
236	C₄×D₅	—	3	4	no	—
237	C₄×D₅	—	6	2	no	—
238	C₄×D₅	—	6	2	no	—
239	C₄×D₅	—	6	2	no	—
240	C₄×D₅	—	6	2	no	—
241	C₄×D₅	—	6	2	no	—
242	C₄×D₅	—	6	2	no	—
243	C₄×D₅	—	6	2	no	—
244	Dic₁₀	—	2	2	no	—
245	Dic₁₀	—	6	2	no	—
246	Dic₁₀	—	6	2	no	—
247	C₂²×Q₈	—	15	1	no	—
248	C₂³×C₄	—	15	1	no	—
249	C₂²⋊Q₈	—	3	1	no	—
250	C₂²⋊Q₈	—	5	1	no	—
251	C₂²⋊Q₈	—	15	1	no	—
252	C₂²⋊Q₈	—	15	1	no	—
253	C₂²⋊Q₈	—	15	1	no	—
254	C₂²⋊Q₈	—	15	1	no	—
255	C₂²⋊Q₈	—	15	1	no	—
256	C₂²⋊Q₈	—	15	1	no	—
257	C₂×C₄⋊C₄	—	15	1	no	—
258	C₂×C₄⋊C₄	—	15	1	no	—
259	C₂×C₄⋊C₄	—	15	1	no	—
260	C₂×C₂²⋊C₄	—	15	1	no	—
261	C₂×C₂²⋊C₄	—	15	1	no	—
262	C₂×C₃×C₅	—	2	2	no	—
263	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
265	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
266	D₁₅	—	2	2	no	—
267	D₁₅	C₂²⋊Q₈	1	4	yes	complemented
268	C₂³×C₃	C₂²×D₅	1	1	yes	characteristic
269	C₂²×D₃	—	5	1	no	—
270	C₂²×D₃	—	5	4	no	—
271	C₂²×D₃	—	5	1	no	—
272	C₂²×D₃	—	10	2	no	—
273	C₂²×D₃	—	10	2	no	—
274	C₃×Q₈	—	10	2	no	—
275	C₂×C₃×C₄	—	5	1	no	—
276	C₂×C₃×C₄	—	5	1	no	—
277	C₂×C₃×C₄	—	5	1	no	—
278	C₂×C₃×C₄	—	5	1	no	—
279	C₂×C₃×C₄	—	10	2	no	—
280	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
282	C₂×Dic₃	—	2	2	no	—
283	C₂×Dic₃	—	5	1	no	—
284	C₂×Dic₃	—	5	1	no	—
285	C₂×Dic₃	C₂²×D₅	1	1	yes	characteristic
286	C₂×Dic₃	C₂²×D₅	1	1	yes	characteristic
287	C₂×Dic₃	C₂²×D₅	1	1	yes	characteristic
288	C₂×Dic₃	C₂²×D₅	1	1	yes	characteristic
289	C₄×D₃	—	5	4	no	—
290	C₄×D₃	—	10	2	no	—
291	C₄×D₃	—	10	2	no	—
292	C₄×D₃	—	10	2	no	—
293	C₄×D₃	—	10	2	no	—
294	C₄×D₃	—	10	2	no	—
295	C₄×D₃	—	10	2	no	—
296	C₄×D₃	—	10	2	no	—
297	Dic₆	—	2	2	no	—
298	Dic₆	—	10	2	no	—
299	Dic₆	—	10	2	no	—
300	C₂²×C₅	—	2	1	no	—
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	D₃×Q₈	1	2	yes	complemented
303	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
304	C₂×D₅	—	3	2	no	—
305	C₂×D₅	—	3	2	no	—
306	C₂×D₅	—	3	2	no	—
307	C₂×D₅	—	3	2	no	—
308	C₂×D₅	—	6	8	no	—
309	C₂×D₅	—	6	1	no	—
310	C₂×D₅	—	6	1	no	—
311	C₄×C₅	—	2	1	no	—
312	C₄×C₅	—	2	1	no	—
313	C₄×C₅	—	3	2	no	—
314	C₄×C₅	—	6	1	no	—
315	C₄×C₅	—	6	1	no	—
316	C₄×C₅	—	6	1	no	—
317	Dic₅	—	2	1	no	—
318	Dic₅	—	2	1	no	—
319	Dic₅	—	2	1	no	—
320	Dic₅	—	6	1	no	—
321	Dic₅	—	6	1	no	—
322	Dic₅	D₃×D₄	1	2	yes	—
323	C₂⁴	—	15	1	no	—
324	C₂×Q₈	—	3	1	no	—
325	C₂×Q₈	—	5	1	no	—
326	C₂×Q₈	—	15	1	no	—
327	C₂×Q₈	—	15	1	no	—
328	C₂×Q₈	—	30	4	no	—
329	C₂²×C₄	—	3	1	no	—
330	C₂²×C₄	—	5	1	no	—
331	C₂²×C₄	—	15	1	no	—
332	C₂²×C₄	—	15	1	no	—
333	C₂²×C₄	—	15	1	no	—
334	C₂²×C₄	—	15	1	no	—
335	C₂²×C₄	—	15	1	no	—
336	C₂²×C₄	—	15	1	no	—
337	C₂²×C₄	—	15	1	no	—
338	C₂²×C₄	—	15	1	no	—
339	C₂²×C₄	—	30	4	no	—
340	C₄⋊C₄	—	3	1	no	—
341	C₄⋊C₄	—	3	1	no	—
342	C₄⋊C₄	—	3	1	no	—
343	C₄⋊C₄	—	5	1	no	—
344	C₄⋊C₄	—	5	1	no	—
345	C₄⋊C₄	—	5	1	no	—
346	C₄⋊C₄	—	15	1	no	—
347	C₄⋊C₄	—	15	1	no	—
348	C₄⋊C₄	—	15	1	no	—
349	C₄⋊C₄	—	15	1	no	—
350	C₄⋊C₄	—	15	1	no	—
351	C₄⋊C₄	—	15	1	no	—
352	C₂²⋊C₄	—	3	1	no	—
353	C₂²⋊C₄	—	5	1	no	—
354	C₂²⋊C₄	—	15	1	no	—
355	C₂²⋊C₄	—	15	1	no	—
356	C₂²⋊C₄	—	15	1	no	—
357	C₂²⋊C₄	—	15	1	no	—
358	C₂²⋊C₄	—	15	1	no	—
359	C₂²⋊C₄	D₃×D₅	1	1	yes	characteristic
360	C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Hall
361	C₂²×C₃	—	2	1	no	—
362	C₂²×C₃	—	2	1	no	—
363	C₂²×C₃	Q₈×D₅	1	2	yes	complemented
364	C₂²×C₃	C₂³×D₅	1	1	yes	characteristic
365	C₂×D₃	—	5	2	no	—
366	C₂×D₃	—	5	2	no	—
367	C₂×D₃	—	5	2	no	—
368	C₂×D₃	—	5	2	no	—
369	C₂×D₃	—	10	8	no	—
370	C₂×D₃	—	10	1	no	—
371	C₂×D₃	—	10	1	no	—
372	C₃×C₄	—	2	1	no	—
373	C₃×C₄	—	2	1	no	—
374	C₃×C₄	—	5	2	no	—
375	C₃×C₄	—	10	1	no	—
376	C₃×C₄	—	10	1	no	—
377	C₃×C₄	—	10	1	no	—
378	Dic₃	—	2	1	no	—
379	Dic₃	—	2	1	no	—
380	Dic₃	—	2	1	no	—
381	Dic₃	—	10	1	no	—
382	Dic₃	—	10	1	no	—
383	Dic₃	D₄×D₅	1	2	yes	—
384	C₂×C₅	—	2	2	no	—
385	C₂×C₅	C₂×D₃×D₄	1	1	yes	characteristic
386	C₂×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
387	C₂×C₅	D₃×#41	1	1	yes	characteristic
388	D₅	—	3	4	no	—
389	D₅	—	6	2	no	—
390	C₂³	—	15	1	no	—
391	C₂³	—	15	4	no	—
392	C₂³	—	15	1	no	—
393	C₂³	—	30	2	no	—
394	C₂³	—	30	2	no	—
395	C₂³	C₂×D₃×D₅	1	1	yes	characteristic
396	Q₈	—	6	2	no	—
397	Q₈	—	10	2	no	—
398	Q₈	—	30	2	no	—
399	Q₈	—	30	2	no	—
400	C₂×C₄	—	3	1	no	—
401	C₂×C₄	—	3	1	no	—
402	C₂×C₄	—	3	1	no	—
403	C₂×C₄	—	3	1	no	—
404	C₂×C₄	—	5	1	no	—
405	C₂×C₄	—	5	1	no	—
406	C₂×C₄	—	5	1	no	—
407	C₂×C₄	—	5	1	no	—
408	C₂×C₄	—	6	2	no	—
409	C₂×C₄	—	10	2	no	—
410	C₂×C₄	—	15	4	no	—
411	C₂×C₄	—	15	1	no	—
412	C₂×C₄	—	15	1	no	—
413	C₂×C₄	—	30	2	no	—
414	C₂×C₄	—	30	2	no	—
415	C₂×C₄	—	30	2	no	—
416	C₂×C₄	—	30	2	no	—
417	C₂×C₄	—	30	2	no	—
418	C₂×C₄	—	30	2	no	—
419	C₂×C₄	—	30	2	no	—
420	C₂×C₄	C₂×D₃×D₅	1	1	yes	characteristic
421	C₂×C₄	C₂×D₃×D₅	1	1	yes	characteristic
422	C₂×C₃	—	2	2	no	—
423	C₂×C₃	C₂×D₄×D₅	1	1	yes	characteristic
424	C₂×C₃	C₂×Q₈×D₅	1	1	yes	characteristic
425	C₂×C₃	D₅×#41	1	1	yes	characteristic
426	D₃	—	5	4	no	—
427	D₃	—	10	2	no	—
428	C₅	D₃×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	15	2	no	—
432	C₂²	—	15	2	no	—
433	C₂²	—	15	2	no	—
434	C₂²	—	15	2	no	—
435	C₂²	—	30	8	no	—
436	C₂²	—	30	1	no	—
437	C₂²	—	30	1	no	—
438	C₂²	D₁₅⋊Q₈	1	2	yes	complemented
439	C₂²	C₂²×D₃×D₅	1	1	yes	characteristic
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	3	2	no	—
443	C₄	—	5	2	no	—
444	C₄	—	6	1	no	—
445	C₄	—	6	1	no	—
446	C₄	—	6	1	no	—
447	C₄	—	10	1	no	—
448	C₄	—	10	1	no	—
449	C₄	—	10	1	no	—
450	C₄	—	30	1	no	—
451	C₄	—	30	1	no	—
452	C₃	D₅×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
453	C₂	—	2	2	no	—
454	C₂	—	15	4	no	—
455	C₂	—	30	2	no	—
456	C₂	C₂×D₁₅⋊Q₈	1	1	yes	characteristic
457	C₂	D₃×D₄×D₅	1	1	yes	characteristic
458	C₂	#92024	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃×D₅
commutator, socle, cosocle	C₂²×C₃×C₅	C₂⁴
Fitting	C₃×C₅×C₂²⋊C₄	C₂²
prime radical	C₂³×D₁₅	C₂²
hypercenter	C₂²⋊C₄	D₃×D₅
hypocenter	C₃×C₅	C₂×C₂²⋊Q₈
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×D₁₅⋊Q₈	C₂	semidirect
4. C₅×#878	C₂	semidirect
5. C₃×#4024	C₂	semidirect
6. #91575	C₂	semidirect
7. #91574	C₂	semidirect
9. #91437	C₂	semidirect
10. #91429	C₂	semidirect
11. #91424	C₂	semidirect
12. #91419	C₂	semidirect
13. #91411	C₂	semidirect
14. #91404	C₂	semidirect
15. #91404	C₂	semidirect
21. C₂×C₅×Dic₆	C₂²	semidirect
23. C₂×C₃×Dic₁₀	C₂²	semidirect
24. C₂×#1204	C₂²	semidirect
25. C₂×#1204	C₂²	semidirect
39. C₅×C₄⋊Dic₃	C₂²	semidirect
40. C₅×Dic₃⋊C₄	C₂²	semidirect
41. C₅×Dic₃⋊C₄	C₂²	semidirect
43. C₃×C₄⋊Dic₅	C₂²	semidirect
44. C₃×#683	C₂²	semidirect
45. C₃×#683	C₂²	semidirect
46. Dic₃⋊Dic₅	C₂²	semidirect
47. Dic₃⋊Dic₅	C₂²	semidirect
48. #6669	C₂²	semidirect
49. #6669	C₂²	semidirect
50. #6668	C₂²	semidirect
51. #6668	C₂²	semidirect
69. #4024	D₃	semidirect
73. C₂²×D₁₅	Q₈	semidirect
116. #878	D₅	semidirect
133. C₂×Dic₁₀	C₂×D₃	semidirect
147. C₄⋊Dic₅	C₂×D₃	semidirect
152. #683	C₂×D₃	semidirect
153. #683	C₂×D₃	semidirect
157. C₂²×C₃×C₅	C₂×Q₈	semidirect
164. C₂×D₁₅	C₂×Q₈	semidirect
194. C₂×Dic₆	C₂×D₅	semidirect
208. C₄⋊Dic₃	C₂×D₅	semidirect
213. Dic₃⋊C₄	C₂×D₅	semidirect
214. Dic₃⋊C₄	C₂×D₅	semidirect
267. D₁₅	C₂²⋊Q₈	semidirect
302. C₂²×C₅	D₃×Q₈	semidirect
360. C₃×C₅	C₂×C₂²⋊Q₈	semidirect
363. C₂²×C₃	Q₈×D₅	semidirect
428. C₅	D₃×C₂²⋊Q₈	semidirect
438. C₂²	D₁₅⋊Q₈	semidirect
452. C₃	D₅×C₂²⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#1200	2
C₂×D₁₅⋊Q₈	2
C₂²⋊C₄×D₁₅	2
C₅×#878	2
C₃×#4024	2
#91575	2
#91574	2
#91561	2
#91437	2
#91429	2
#91424	2
#91419	2
#91411	2
#91404	2
D₅×C₂²⋊Q₈	3
D₃×C₂²⋊Q₈	5