Subgroups — #14418181

Order 1920.

916 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11754018	C₂	1	2	yes	maximal, complemented
2	#11753979	C₂	1	1	yes	maximal, characteristic
3	#11750994	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4894	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65184	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748236	C₂	1	2	yes	maximal, complemented
7	#11748204	C₂	1	2	yes	maximal, complemented
8	#11748202	C₂	1	2	yes	maximal, complemented
9	#11748067	C₂	1	1	yes	maximal, characteristic, complemented
10	#11748062	C₂	1	1	yes	maximal, characteristic, complemented
11	#11747592	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611629	—	3	1	no	maximal, Hall
13	#92016	C₂²	1	2	yes	—
14	M₁₆×D₁₅	C₂²	1	2	yes	—
15	C₂×#6705	C₂²	1	1	yes	characteristic
16	C₅×#907	C₂²	1	2	yes	complemented
17	C₅×#904	C₂²	1	1	yes	characteristic
18	C₃×#4053	C₂²	1	2	yes	complemented
19	C₃×#4050	C₂²	1	1	yes	characteristic
20	C₄×#1200	C₂²	1	1	yes	characteristic
21	#91297	C₂²	1	2	yes	—
22	C₂×#6651	C₂²	1	1	yes	characteristic
23	#91286	C₂²	1	2	yes	complemented
24	#91283	C₂²	1	2	yes	complemented
25	#91280	C₄	1	2	yes	complemented
26	#91278	C₄	1	2	yes	complemented
27	#91268	—	2	2	no	—
28	#91265	—	2	2	no	—
29	#91258	C₄	1	2	yes	complemented
30	#91257	C₄	1	2	yes	complemented
31	D₃×#676	—	2	2	no	—
32	D₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
33	C₃×C₅×#108	C₂²	1	1	yes	characteristic, complemented
34	#91106	C₂²	1	2	yes	complemented
35	#91103	C₂²	1	1	yes	characteristic, complemented
36	C₅×#825	C₂²	1	2	yes	complemented
37	C₅×#815	C₂²	1	1	yes	characteristic, complemented
38	C₃×#3957	C₂²	1	2	yes	complemented
39	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
40	#90979	C₂²	1	2	yes	complemented
41	#90977	C₂²	1	2	yes	complemented
42	#90953	C₂²	1	1	yes	characteristic, complemented
43	Dic₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	#79889	—	5	1	no	maximal, Hall
45	#66102	—	3	1	no	—
46	#66084	—	3	2	no	—
47	C₅×#444	—	3	1	no	—
48	#65485	—	3	1	no	—
49	#65433	—	3	2	no	—
50	#65184	D₃	1	1	yes	characteristic, complemented
51	#65182	—	3	1	no	—
52	#65112	—	3	2	no	—
53	D₅×#104	—	3	2	no	—
54	#65006	—	3	1	no	—
55	#64996	—	3	1	no	—
56	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
57	C₅×#235	C₂³	1	2	yes	—
58	C₃×#709	C₂³	1	2	yes	—
59	#6790	—	2	2	no	—
60	C₂×#1200	—	2	1	no	—
61	#6780	—	2	2	no	—
62	#6777	C₂×C₄	1	2	yes	—
63	C₄×D₃×D₅	—	2	2	no	—
64	#6771	—	2	2	no	—
65	D₁₅⋊Q₈	C₂×C₄	1	2	yes	—
66	#6768	C₂×C₄	1	2	yes	—
67	#6766	C₂×C₄	1	2	yes	—
68	C₃×C₅×M₁₆	C₂³	1	2	yes	—
69	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
70	#6710	C₂³	1	2	yes	—
71	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
72	#6705	—	2	2	no	—
73	#6705	C₂×C₄	1	2	yes	—
74	#6705	C₂×C₄	1	2	yes	—
75	C₈×D₁₅	—	2	2	no	—
76	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
77	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
78	C₅×Dic₁₂	C₂×C₄	1	1	yes	characteristic, complemented
79	C₅×D₂₄	C₂×C₄	1	1	yes	characteristic, complemented
80	C₅×#204	C₂×C₄	1	2	yes	complemented
81	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
82	C₅×D₃×C₈	—	2	2	no	—
83	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
84	C₂×C₃×#168	C₂³	1	1	yes	characteristic
85	C₃×Dic₂₀	C₂×C₄	1	1	yes	characteristic, complemented
86	C₃×D₄₀	C₂×C₄	1	1	yes	characteristic, complemented
87	C₃×#677	C₂×C₄	1	2	yes	complemented
88	C₃×#676	—	2	2	no	—
89	C₃×C₈×D₅	—	2	2	no	—
90	Dic₃×Dic₅	—	2	1	no	—
91	#6661	C₂×C₄	1	2	yes	complemented
92	#6656	C₂×C₄	1	2	yes	complemented
93	#6655	C₂×C₄	1	2	yes	complemented
94	#6652	C₂×C₄	1	2	yes	complemented
95	#6651	D₄	1	2	yes	—
96	#6651	D₄	1	2	yes	—
97	#6650	—	2	2	no	—
98	#6649	—	2	2	no	—
99	D₃×#168	—	2	2	no	—
100	D₅×C₃⋊C₈	—	2	2	no	—
101	#5768	—	5	1	no	—
102	#5750	—	5	2	no	—
103	C₃×#443	—	5	1	no	—
104	#5197	—	5	1	no	—
105	#5145	—	5	2	no	—
106	#4894	D₅	1	1	yes	characteristic, complemented
107	#4893	—	5	1	no	—
108	#4824	—	5	2	no	—
109	D₃×#104	—	5	2	no	—
110	#4700	—	5	1	no	—
111	C₄×ΓL(1,𝔽₂₅)	—	5	1	no	—
112	D₅×#41	—	3	2	no	—
113	C₅×#135	—	3	1	no	—
114	C₅×#131	—	3	2	no	—
115	#4096	—	3	2	no	—
116	#4094	—	3	2	no	—
117	#4064	—	3	2	no	—
118	#4061	—	3	2	no	—
119	#4060	—	3	2	no	—
120	#4057	—	3	2	no	—
121	#4053	—	6	2	no	—
122	#4053	C₂×D₃	1	2	yes	complemented
123	D₅×M₁₆	—	3	2	no	—
124	D₅×M₁₆	—	6	2	no	—
125	#4050	C₂×D₃	1	1	yes	characteristic
126	#4047	—	3	2	no	—
127	#4047	—	6	2	no	—
128	C₂×#676	—	3	1	no	—
129	C₂×#676	—	3	1	no	—
130	C₂×#676	—	6	2	no	—
131	C₄²×D₅	—	3	1	no	—
132	C₅×#108	C₂×D₃	1	1	yes	characteristic, complemented
133	C₅×#104	—	3	2	no	—
134	C₅×#97	—	3	1	no	—
135	#3969	—	3	2	no	—
136	#3957	C₂×D₃	1	2	yes	complemented
137	#3954	—	3	2	no	—
138	#3951	—	3	1	no	—
139	C₈×Dic₅	—	3	1	no	—
140	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic, complemented
141	#3937	—	3	2	no	—
142	#3935	—	3	1	no	—
143	#2956	—	15	1	no	Sylow
144	C₂²×D₁₅	#41	1	1	yes	characteristic
145	C₂×D₃×D₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
147	C₂×Dic₁₅	#41	1	1	yes	characteristic
148	C₄×D₁₅	C₂²×C₄	1	2	yes	—
149	C₄×D₁₅	C₂×D₄	1	2	yes	—
150	C₅×#67	—	2	2	no	—
151	C₂×C₅×Dic₃	—	2	1	no	—
152	C₅×D₁₂	C₂²×C₄	1	2	yes	—
153	C₄×C₅×D₃	—	2	2	no	—
154	C₅×Dic₆	C₂²×C₄	1	2	yes	—
155	C₃×C₂²⋊D₅	—	2	2	no	—
156	C₂×C₃×Dic₅	—	2	1	no	—
157	C₃×D₂₀	C₂²×C₄	1	2	yes	—
158	C₃×C₄×D₅	—	2	2	no	—
159	C₃×Dic₁₀	C₂²×C₄	1	2	yes	—
160	#1204	—	2	2	no	—
161	#1203	—	2	2	no	—
162	#1202	—	2	2	no	—
163	#1201	—	2	2	no	—
164	#1200	—	2	2	no	—
165	#1200	—	4	2	no	—
166	D₃×Dic₅	—	2	2	no	—
167	D₅×Dic₃	—	2	2	no	—
168	C₃×C₅×C₈	—	2	2	no	—
169	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
170	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
171	C₃⋊#168	—	2	2	no	—
172	C₃⋊#168	C₂²×C₄	1	2	yes	—
173	C₃×#168	C₂×D₄	1	1	yes	characteristic
174	C₃×#168	C₂×D₄	1	1	yes	characteristic
175	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
176	D₃×#41	—	5	2	no	—
177	C₃×#135	—	5	1	no	—
178	C₃×#131	—	5	2	no	—
179	#950	—	5	2	no	—
180	#948	—	5	2	no	—
181	#918	—	5	2	no	—
182	#915	—	5	2	no	—
183	#914	—	5	2	no	—
184	#911	—	5	2	no	—
185	#907	—	10	2	no	—
186	#907	C₂×D₅	1	2	yes	complemented
187	D₃×M₁₆	—	5	2	no	—
188	D₃×M₁₆	—	10	2	no	—
189	#904	C₂×D₅	1	1	yes	characteristic
190	#901	—	5	2	no	—
191	#901	—	10	2	no	—
192	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
193	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
194	C₂×ΓL(1,𝔽₂₅)	—	10	2	no	—
195	C₄²×D₃	—	5	1	no	—
196	C₃×#108	C₂×D₅	1	1	yes	characteristic, complemented
197	C₃×#104	—	5	2	no	—
198	C₃×C₄×C₈	—	5	1	no	—
199	#837	—	5	2	no	—
200	#825	C₂×D₅	1	2	yes	complemented
201	#822	—	5	2	no	—
202	#819	—	5	1	no	—
203	#815	—	5	1	no	—
204	#815	C₂×D₅	1	1	yes	characteristic, complemented
205	#805	—	5	2	no	—
206	C₄×C₃⋊C₈	—	5	1	no	—
207	C₅×#41	—	3	2	no	—
208	#713	—	3	2	no	—
209	Q₈×D₅	—	3	2	no	—
210	#711	—	3	2	no	—
211	#711	—	6	2	no	—
212	D₄×D₅	—	3	2	no	—
213	D₄×D₅	—	6	2	no	—
214	#709	—	6	2	no	—
215	#709	C₂²×D₃	1	2	yes	—
216	C₂×C₄×D₅	—	3	1	no	—
217	C₂×C₄×D₅	—	6	2	no	—
218	C₂×C₄×D₅	—	6	1	no	—
219	C₅×Q₁₆	—	3	1	no	—
220	C₅×SD₁₆	—	3	2	no	—
221	C₅×D₈	—	3	1	no	—
222	C₅×M₁₆	—	6	2	no	—
223	C₅×M₁₆	C₂²×D₃	1	2	yes	—
224	C₂×C₅×C₈	—	3	1	no	—
225	C₂×C₅×C₈	—	6	2	no	—
226	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
227	C₄²×C₅	—	3	1	no	—
228	#689	—	3	2	no	—
229	#688	—	3	2	no	—
230	#687	—	3	2	no	—
231	#686	—	3	2	no	—
232	C₄×Dic₅	—	6	1	no	—
233	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
234	#681	—	3	2	no	—
235	#681	—	6	2	no	—
236	C₂×#168	—	3	1	no	—
237	C₂×#168	—	6	2	no	—
238	C₂×#168	C₂²×D₃	1	1	yes	characteristic
239	Dic₂₀	C₄×D₃	1	1	yes	characteristic, complemented
240	D₄₀	C₄×D₃	1	1	yes	characteristic, complemented
241	#677	C₄×D₃	1	2	yes	complemented
242	#676	—	2	2	no	—
243	#676	—	3	2	no	—
244	#676	—	3	2	no	—
245	#676	—	3	2	no	—
246	#676	—	3	2	no	—
247	#676	—	6	2	no	—
248	#676	—	6	2	no	—
249	C₈×D₅	—	2	2	no	—
250	C₈×D₅	—	6	2	no	—
251	C₈×D₅	—	6	2	no	—
252	#575	—	15	1	no	—
253	#568	—	15	2	no	—
254	#444	—	3	1	no	—
255	#444	—	15	1	no	—
256	#444	—	15	2	no	—
257	#443	—	5	1	no	—
258	#443	—	15	1	no	—
259	#443	—	15	2	no	—
260	#430	—	15	1	no	—
261	C₂×#104	—	15	2	no	—
262	C₄×M₁₆	—	15	1	no	—
263	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
264	C₂×D₁₅	—	4	1	no	—
265	C₂×D₁₅	C₄×D₄	1	2	yes	—
266	C₂×C₅×D₃	—	2	2	no	—
267	C₂×C₃×D₅	—	2	2	no	—
268	D₃×D₅	—	8	2	no	—
269	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
270	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
271	Dic₁₅	C₄×D₄	1	2	yes	—
272	C₃×Dic₅	—	2	2	no	—
273	C₃×Dic₅	—	2	2	no	—
274	C₅×Dic₃	—	2	2	no	—
275	C₅×Dic₃	—	4	1	no	—
276	C₃×#41	—	5	2	no	—
277	#239	—	5	2	no	—
278	D₃×Q₈	—	5	2	no	—
279	#237	—	5	2	no	—
280	#237	—	10	2	no	—
281	D₃×D₄	—	5	2	no	—
282	D₃×D₄	—	10	2	no	—
283	#235	—	10	2	no	—
284	#235	C₂²×D₅	1	2	yes	—
285	C₂×C₄×D₃	—	5	1	no	—
286	C₂×C₄×D₃	—	10	2	no	—
287	C₂×C₄×D₃	—	10	1	no	—
288	C₃×Q₁₆	—	5	1	no	—
289	C₃×SD₁₆	—	5	2	no	—
290	C₃×D₈	—	5	1	no	—
291	C₃×M₁₆	—	10	2	no	—
292	C₃×M₁₆	C₂²×D₅	1	2	yes	—
293	C₂×C₃×C₈	—	5	1	no	—
294	C₂×C₃×C₈	—	10	2	no	—
295	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
296	C₃×C₄²	—	5	1	no	—
297	#216	—	5	2	no	—
298	#215	—	5	2	no	—
299	#214	—	5	2	no	—
300	#213	—	5	2	no	—
301	C₄×Dic₃	—	10	1	no	—
302	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
303	#208	—	5	2	no	—
304	#208	—	10	2	no	—
305	C₂×C₃⋊C₈	—	5	1	no	—
306	C₂×C₃⋊C₈	—	10	2	no	—
307	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
308	Dic₁₂	C₄×D₅	1	1	yes	characteristic, complemented
309	D₂₄	C₄×D₅	1	1	yes	characteristic, complemented
310	#204	C₄×D₅	1	2	yes	complemented
311	ΓL(1,𝔽₂₅)	—	2	2	no	—
312	ΓL(1,𝔽₂₅)	—	5	2	no	—
313	ΓL(1,𝔽₂₅)	—	5	2	no	—
314	ΓL(1,𝔽₂₅)	—	5	2	no	—
315	ΓL(1,𝔽₂₅)	—	5	2	no	—
316	ΓL(1,𝔽₂₅)	—	10	2	no	—
317	ΓL(1,𝔽₂₅)	—	10	2	no	—
318	D₃×C₈	—	2	2	no	—
319	D₃×C₈	—	10	2	no	—
320	D₃×C₈	—	10	2	no	—
321	C₂²×D₅	—	3	1	no	—
322	C₂²×D₅	—	6	2	no	—
323	C₅×Q₈	—	3	2	no	—
324	C₅×D₄	—	3	2	no	—
325	C₅×D₄	—	6	2	no	—
326	C₂×C₄×C₅	—	6	2	no	—
327	C₂×C₄×C₅	—	6	1	no	—
328	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
329	C₂²⋊D₅	—	2	2	no	—
330	C₂²⋊D₅	—	6	2	no	—
331	C₂²⋊D₅	—	6	2	no	—
332	C₂×Dic₅	—	2	1	no	—
333	C₂×Dic₅	—	3	1	no	—
334	C₂×Dic₅	—	6	2	no	—
335	D₂₀	—	6	2	no	—
336	D₂₀	C₂×C₄×D₃	1	2	yes	—
337	C₄×D₅	—	2	2	no	—
338	C₄×D₅	—	3	2	no	—
339	C₄×D₅	—	3	2	no	—
340	C₄×D₅	—	6	2	no	—
341	C₄×D₅	—	6	2	no	—
342	C₄×D₅	—	12	2	no	—
343	Dic₁₀	—	6	2	no	—
344	Dic₁₀	C₂×C₄×D₃	1	2	yes	—
345	C₅×C₈	—	2	2	no	—
346	C₅×C₈	—	3	2	no	—
347	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
348	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
349	#168	—	3	2	no	—
350	#168	—	6	2	no	—
351	#168	D₃×D₄	1	1	yes	characteristic
352	#168	D₃×D₄	1	1	yes	characteristic
353	C₂×#41	—	15	2	no	—
354	#137	—	15	2	no	—
355	#137	—	15	2	no	—
356	AGL(1,ℤ/8)	—	15	2	no	—
357	AGL(1,ℤ/8)	—	15	2	no	—
358	#135	—	3	1	no	—
359	#135	—	5	1	no	—
360	#135	—	15	2	no	—
361	#131	—	3	2	no	—
362	#131	—	5	2	no	—
363	#131	—	15	2	no	—
364	#131	—	15	2	no	—
365	#131	—	30	2	no	—
366	#131	—	30	2	no	—
367	C₂×M₁₆	—	15	1	no	—
368	C₂×M₁₆	—	15	1	no	—
369	C₂×M₁₆	—	15	2	no	—
370	C₂×M₁₆	—	30	2	no	—
371	C₂×M₁₆	—	30	2	no	—
372	C₂×C₄²	—	15	1	no	—
373	#108	—	15	2	no	—
374	#108	—	15	1	no	—
375	#108	D₃×D₅	1	1	yes	characteristic, complemented
376	#104	—	3	2	no	—
377	#104	—	5	2	no	—
378	#104	—	15	2	no	—
379	#104	—	15	2	no	—
380	#97	—	3	1	no	—
381	#97	—	15	1	no	—
382	C₄×C₈	—	5	1	no	—
383	C₄×C₈	—	15	1	no	—
384	C₂×C₃×C₅	—	2	1	no	—
385	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
386	D₁₅	—	2	2	no	—
387	C₃×D₅	—	4	2	no	—
388	C₅×D₃	—	4	2	no	—
389	C₂²×D₃	—	5	1	no	—
390	C₂²×D₃	—	10	2	no	—
391	C₃×Q₈	—	5	2	no	—
392	C₃×D₄	—	5	2	no	—
393	C₃×D₄	—	10	2	no	—
394	C₂×C₃×C₄	—	10	1	no	—
395	C₂×C₃×C₄	—	10	2	no	—
396	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
397	#67	—	2	2	no	—
398	#67	—	10	2	no	—
399	#67	—	10	2	no	—
400	C₂×Dic₃	—	2	1	no	—
401	C₂×Dic₃	—	5	1	no	—
402	C₂×Dic₃	—	10	2	no	—
403	D₁₂	—	10	2	no	—
404	D₁₂	C₂×C₄×D₅	1	2	yes	—
405	C₄×D₃	—	2	2	no	—
406	C₄×D₃	—	5	2	no	—
407	C₄×D₃	—	5	2	no	—
408	C₄×D₃	—	10	2	no	—
409	C₄×D₃	—	10	2	no	—
410	C₄×D₃	—	20	2	no	—
411	Dic₆	—	10	2	no	—
412	Dic₆	C₂×C₄×D₅	1	2	yes	—
413	C₃×C₈	—	2	2	no	—
414	C₃×C₈	—	5	1	no	—
415	C₃×C₈	—	5	1	no	—
416	C₃×C₈	C₂×C₄×D₅	1	1	yes	characteristic
417	C₃×C₈	C₂×C₄×D₅	1	1	yes	characteristic
418	C₃⋊C₈	—	5	2	no	—
419	C₃⋊C₈	—	10	2	no	—
420	C₃⋊C₈	D₄×D₅	1	2	yes	—
421	C₂²×C₅	—	6	2	no	—
422	C₂²×C₅	D₃×#41	1	1	yes	characteristic
423	C₂×D₅	—	2	2	no	—
424	C₂×D₅	—	3	2	no	—
425	C₂×D₅	—	12	1	no	—
426	C₂×D₅	—	24	2	no	—
427	C₄×C₅	—	6	2	no	—
428	C₄×C₅	—	12	1	no	—
429	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
430	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
431	Dic₅	—	2	2	no	—
432	Dic₅	—	2	2	no	—
433	Dic₅	—	3	2	no	—
434	#41	—	3	2	no	—
435	#41	—	5	2	no	—
436	#41	—	15	2	no	—
437	#41	—	15	2	no	—
438	#41	—	30	2	no	—
439	#41	—	30	2	no	—
440	C₂×Q₈	—	15	2	no	—
441	C₂×D₄	—	15	2	no	—
442	C₂×D₄	—	30	2	no	—
443	C₂²×C₄	—	15	1	no	—
444	C₂²×C₄	—	30	2	no	—
445	C₂²×C₄	—	30	1	no	—
446	Q₁₆	—	3	1	no	—
447	Q₁₆	—	5	1	no	—
448	Q₁₆	—	15	2	no	—
449	SD₁₆	—	3	2	no	—
450	SD₁₆	—	5	2	no	—
451	SD₁₆	—	15	2	no	—
452	SD₁₆	—	15	2	no	—
453	D₈	—	3	1	no	—
454	D₈	—	5	1	no	—
455	D₈	—	15	2	no	—
456	M₁₆	—	6	2	no	—
457	M₁₆	—	10	2	no	—
458	M₁₆	—	15	2	no	—
459	M₁₆	—	15	2	no	—
460	M₁₆	—	15	2	no	—
461	M₁₆	—	15	2	no	—
462	M₁₆	—	15	2	no	—
463	M₁₆	—	30	2	no	—
464	M₁₆	—	30	2	no	—
465	M₁₆	—	30	2	no	—
466	M₁₆	C₂×D₃×D₅	1	2	yes	—
467	C₂×C₈	—	3	1	no	—
468	C₂×C₈	—	5	1	no	—
469	C₂×C₈	—	6	2	no	—
470	C₂×C₈	—	10	2	no	—
471	C₂×C₈	—	15	1	no	—
472	C₂×C₈	—	30	2	no	—
473	C₂×C₈	—	30	2	no	—
474	C₂×C₈	—	30	2	no	—
475	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
476	C₄²	—	3	1	no	—
477	C₄²	—	5	1	no	—
478	C₄²	—	30	1	no	—
479	C₃×C₅	#2956	1	1	yes	characteristic, complemented, Hall
480	C₂²×C₃	—	10	2	no	—
481	C₂²×C₃	D₅×#41	1	1	yes	characteristic
482	C₂×D₃	—	2	2	no	—
483	C₂×D₃	—	5	2	no	—
484	C₂×D₃	—	20	1	no	—
485	C₂×D₃	—	40	2	no	—
486	C₃×C₄	—	10	2	no	—
487	C₃×C₄	—	10	2	no	—
488	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
489	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
490	Dic₃	—	2	2	no	—
491	Dic₃	—	4	1	no	—
492	Dic₃	—	5	2	no	—
493	C₂×C₅	—	2	1	no	—
494	C₂×C₅	—	12	2	no	—
495	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
496	D₅	—	4	2	no	—
497	D₅	—	6	2	no	—
498	C₂³	—	15	1	no	—
499	C₂³	—	30	2	no	—
500	Q₈	—	3	2	no	—
501	Q₈	—	5	2	no	—
502	Q₈	—	30	2	no	—
503	D₄	—	3	2	no	—
504	D₄	—	5	2	no	—
505	D₄	—	6	2	no	—
506	D₄	—	10	2	no	—
507	D₄	—	30	2	no	—
508	D₄	—	30	2	no	—
509	D₄	—	30	2	no	—
510	C₂×C₄	—	6	2	no	—
511	C₂×C₄	—	6	1	no	—
512	C₂×C₄	—	10	1	no	—
513	C₂×C₄	—	10	2	no	—
514	C₂×C₄	—	15	1	no	—
515	C₂×C₄	—	15	2	no	—
516	C₂×C₄	—	15	2	no	—
517	C₂×C₄	—	30	2	no	—
518	C₂×C₄	—	30	2	no	—
519	C₂×C₄	—	30	2	no	—
520	C₂×C₄	—	60	2	no	—
521	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
522	C₈	—	2	2	no	—
523	C₈	—	3	2	no	—
524	C₈	—	5	1	no	—
525	C₈	—	5	1	no	—
526	C₈	—	15	2	no	—
527	C₈	—	30	2	no	—
528	C₈	C₄×D₃×D₅	1	1	yes	characteristic
529	C₈	C₄×D₃×D₅	1	1	yes	characteristic
530	C₂×C₃	—	2	1	no	—
531	C₂×C₃	—	20	2	no	—
532	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
533	D₃	—	4	2	no	—
534	D₃	—	10	2	no	—
535	C₅	#79889	1	1	yes	characteristic, complemented, Sylow
536	C₂²	—	6	2	no	—
537	C₂²	—	10	2	no	—
538	C₂²	—	15	2	no	—
539	C₂²	—	60	1	no	—
540	C₂²	—	120	2	no	—
541	C₂²	#92034	1	1	yes	characteristic
542	C₄	—	6	2	no	—
543	C₄	—	10	2	no	—
544	C₄	—	10	2	no	—
545	C₄	—	12	1	no	—
546	C₄	—	15	2	no	—
547	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
548	C₄	D₃×D₄×D₅	1	1	yes	characteristic
549	C₃	#10611629	1	1	yes	characteristic, complemented, Sylow
550	C₂	—	2	1	no	—
551	C₂	—	12	2	no	—
552	C₂	—	20	2	no	—
553	C₂	—	30	2	no	—
554	C₂	#11753840	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₃×D₄×D₅
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₅×#108	C₂²
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	#11753979	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	#108	D₃×D₅
hypocenter	C₃×C₅	#2956
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
1. #11754018	C₂	semidirect
3. #11750994	C₂	semidirect
4. C₅×#4894	C₂	semidirect
5. C₃×#65184	C₂	semidirect
6. #11748236	C₂	semidirect
7. #11748204	C₂	semidirect
8. #11748202	C₂	semidirect
9. #11748067	C₂	semidirect
10. #11748062	C₂	semidirect
11. #11747592	C₂	semidirect
16. C₅×#907	C₂²	semidirect
18. C₃×#4053	C₂²	semidirect
23. #91286	C₂²	semidirect
24. #91283	C₂²	semidirect
25. #91280	C₄	semidirect
26. #91278	C₄	semidirect
29. #91258	C₄	semidirect
30. #91257	C₄	semidirect
33. C₃×C₅×#108	C₂²	semidirect
34. #91106	C₂²	semidirect
35. #91103	C₂²	semidirect
36. C₅×#825	C₂²	semidirect
37. C₅×#815	C₂²	semidirect
38. C₃×#3957	C₂²	semidirect
39. C₃×C₈×Dic₅	C₂²	semidirect
40. #90979	C₂²	semidirect
41. #90977	C₂²	semidirect
42. #90953	C₂²	semidirect
43. Dic₅×C₃⋊C₈	C₂²	semidirect
50. #65184	D₃	semidirect
78. C₅×Dic₁₂	C₂×C₄	semidirect
79. C₅×D₂₄	C₂×C₄	semidirect
80. C₅×#204	C₂×C₄	semidirect
85. C₃×Dic₂₀	C₂×C₄	semidirect
86. C₃×D₄₀	C₂×C₄	semidirect
87. C₃×#677	C₂×C₄	semidirect
91. #6661	C₂×C₄	semidirect
92. #6656	C₂×C₄	semidirect
93. #6655	C₂×C₄	semidirect
94. #6652	C₂×C₄	semidirect
106. #4894	D₅	semidirect
122. #4053	C₂×D₃	semidirect
132. C₅×#108	C₂×D₃	semidirect
136. #3957	C₂×D₃	semidirect
140. C₈×Dic₅	C₂×D₃	semidirect
186. #907	C₂×D₅	semidirect
196. C₃×#108	C₂×D₅	semidirect
200. #825	C₂×D₅	semidirect
204. #815	C₂×D₅	semidirect
239. Dic₂₀	C₄×D₃	semidirect
240. D₄₀	C₄×D₃	semidirect
241. #677	C₄×D₃	semidirect
308. Dic₁₂	C₄×D₅	semidirect
309. D₂₄	C₄×D₅	semidirect
310. #204	C₄×D₅	semidirect
375. #108	D₃×D₅	semidirect
479. C₃×C₅	#2956	semidirect
535. C₅	#79889	semidirect
549. C₃	#10611629	semidirect

Maximal subgroups

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

subgroup	index
#11754018	2
#11753979	2
#11750994	2
C₅×#4894	2
C₃×#65184	2
#11748236	2
#11748204	2
#11748202	2
#11748067	2
#11748062	2
#11747592	2
#10611629	3
#79889	5