Subgroups — #14282221

Order 1920.

532 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6821	C₂	1	1	yes	maximal, characteristic
2	#11750938	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#6705	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#11746356	C₂	1	1	yes	maximal, characteristic, complemented
6	#11746304	C₂	1	1	yes	maximal, characteristic, complemented
7	#11746280	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599031	—	3	1	no	maximal, Hall
9	C₂×#6821	C₄	1	1	yes	characteristic
10	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
11	Q₈×Dic₁₅	C₄	1	1	yes	characteristic
12	C₂×#6705	—	2	1	no	—
13	C₂×#6705	—	2	1	no	—
14	#91782	—	2	1	no	—
15	#91782	C₄	1	1	yes	characteristic
16	#91781	—	2	1	no	—
17	#91781	C₄	1	1	yes	characteristic
18	C₄×D₆₀	—	2	1	no	—
19	C₄×D₆₀	C₂²	1	1	yes	characteristic
20	C₄²×D₁₅	—	2	1	no	—
21	C₄²×D₁₅	C₂²	1	1	yes	characteristic
22	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
24	#91099	—	2	1	no	—
25	#91098	—	2	1	no	—
26	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
27	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
28	#68238	—	5	1	no	maximal, Hall
29	C₄×#713	—	3	1	no	—
30	#65126	—	3	1	no	—
31	C₄×#676	—	3	1	no	—
32	C₅×Q₈⋊C₈	D₃	1	1	yes	characteristic, complemented
33	Q₈⋊#168	—	3	1	no	—
34	#64703	—	3	1	no	—
35	#64679	—	3	1	no	—
36	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
37	#6821	—	2	2	no	—
38	#6821	—	2	2	no	—
39	C₂×D₆₀	—	2	1	no	—
40	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄×D₁₅	—	2	1	no	—
42	C₂×C₄×D₁₅	—	2	1	no	—
43	C₂×C₄×D₁₅	—	2	1	no	—
44	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×D₁₅	D₄	1	1	yes	characteristic
46	C₂×C₄×D₁₅	D₄	1	1	yes	characteristic
47	C₂×C₃×C₅×C₈	—	2	1	no	—
48	C₂×C₃×C₅×C₈	—	2	1	no	—
49	C₃×C₅×C₄⋊C₄	—	2	1	no	—
50	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₃×C₄²×C₅	—	2	1	no	—
52	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
53	#6714	—	2	1	no	—
54	#6714	—	2	1	no	—
55	#6714	—	2	1	no	—
56	C₄⋊Dic₁₅	—	2	1	no	—
57	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
58	C₄×Dic₁₅	—	2	1	no	—
59	C₄×Dic₁₅	—	2	1	no	—
60	C₄×Dic₁₅	C₂×C₄	1	1	yes	characteristic
61	C₄×Dic₁₅	D₄	1	1	yes	characteristic
62	C₄×Dic₁₅	D₄	1	1	yes	characteristic
63	C₂×C₃⋊#168	—	2	1	no	—
64	C₂×C₃⋊#168	—	2	1	no	—
65	#6705	—	2	4	no	—
66	#6705	—	4	2	no	—
67	C₄×#239	—	5	1	no	—
68	#4837	—	5	1	no	—
69	C₄×ΓL(1,𝔽₂₅)	—	5	1	no	—
70	C₃×Q₈⋊C₈	D₅	1	1	yes	characteristic, complemented
71	#4535	—	5	1	no	—
72	#4483	—	5	1	no	—
73	#4459	—	5	1	no	—
74	C₂×#713	—	3	1	no	—
75	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
76	Q₈×Dic₅	—	3	1	no	—
77	C₂×#676	—	6	1	no	—
78	C₂×#676	—	6	1	no	—
79	#4039	—	3	1	no	—
80	#4039	—	6	1	no	—
81	#4038	—	3	1	no	—
82	#4038	—	6	1	no	—
83	C₄×D₂₀	—	3	1	no	—
84	C₄×D₂₀	—	6	1	no	—
85	C₄²×D₅	—	3	1	no	—
86	C₄²×D₅	—	6	1	no	—
87	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
88	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
89	#3947	—	6	1	no	—
90	#3946	—	6	1	no	—
91	C₄⋊#168	—	3	1	no	—
92	C₄×#168	—	3	1	no	—
93	#1489	—	15	1	no	Sylow
94	C₂²×D₁₅	—	2	1	no	—
95	C₂²×D₁₅	C₂²⋊C₄	1	1	yes	characteristic
96	C₃×C₅×Q₈	—	2	1	no	—
97	C₃×C₅×Q₈	M₁₆	1	2	yes	complemented
98	C₂×C₃×C₄×C₅	—	2	1	no	—
99	C₂×C₃×C₄×C₅	—	2	1	no	—
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×Dic₁₅	—	2	1	no	—
104	C₂×Dic₁₅	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×Dic₁₅	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×Dic₁₅	C₂²⋊C₄	1	1	yes	characteristic
107	D₆₀	—	2	4	no	—
108	D₆₀	—	2	1	no	—
109	D₆₀	M₁₆	1	2	yes	complemented
110	C₄×D₁₅	—	2	4	no	—
111	C₄×D₁₅	—	2	1	no	—
112	C₄×D₁₅	—	2	1	no	—
113	C₄×D₁₅	—	2	1	no	—
114	C₄×D₁₅	—	2	1	no	—
115	C₄×D₁₅	—	2	2	no	—
116	C₄×D₁₅	—	4	1	no	—
117	C₄×D₁₅	—	4	1	no	—
118	C₄×D₁₅	—	4	2	no	—
119	C₃×C₅×C₈	—	2	2	no	—
120	C₃×C₅×C₈	—	4	1	no	—
121	C₃⋊#168	—	2	2	no	—
122	C₃⋊#168	—	4	1	no	—
123	C₂×#239	—	5	1	no	—
124	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
125	Q₈×Dic₃	—	5	1	no	—
126	C₂×ΓL(1,𝔽₂₅)	—	10	1	no	—
127	C₂×ΓL(1,𝔽₂₅)	—	10	1	no	—
128	#893	—	5	1	no	—
129	#893	—	10	1	no	—
130	#892	—	5	1	no	—
131	#892	—	10	1	no	—
132	C₄×D₁₂	—	5	1	no	—
133	C₄×D₁₂	—	10	1	no	—
134	C₄²×D₃	—	5	1	no	—
135	C₄²×D₃	—	10	1	no	—
136	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
137	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
138	#815	—	10	1	no	—
139	Dic₃⋊C₈	—	10	1	no	—
140	C₄⋊(C₃⋊C₈)	—	5	1	no	—
141	C₄×C₃⋊C₈	—	5	1	no	—
142	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
143	#713	—	6	2	no	—
144	#713	—	6	2	no	—
145	C₂×D₂₀	—	3	1	no	—
146	C₂×D₂₀	—	6	1	no	—
147	C₂×C₄×D₅	—	3	1	no	—
148	C₂×C₄×D₅	—	3	1	no	—
149	C₂×C₄×D₅	—	3	1	no	—
150	C₂×C₄×D₅	—	6	1	no	—
151	C₂×C₄×D₅	—	6	1	no	—
152	C₂×C₄×D₅	—	6	1	no	—
153	C₂×C₅×C₈	—	2	1	no	—
154	C₂×C₅×C₈	—	2	1	no	—
155	C₅×C₄⋊C₄	—	2	1	no	—
156	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
157	C₄²×C₅	—	2	1	no	—
158	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
159	#685	—	6	1	no	—
160	#685	—	6	1	no	—
161	#685	—	6	1	no	—
162	C₄⋊Dic₅	—	3	1	no	—
163	C₄⋊Dic₅	—	6	1	no	—
164	C₄×Dic₅	—	3	1	no	—
165	C₄×Dic₅	—	3	1	no	—
166	C₄×Dic₅	—	3	1	no	—
167	C₄×Dic₅	—	6	1	no	—
168	C₄×Dic₅	—	6	1	no	—
169	C₂×#168	—	6	1	no	—
170	C₂×#168	—	6	1	no	—
171	#676	—	6	4	no	—
172	#676	—	12	2	no	—
173	C₄×#41	—	15	1	no	—
174	#423	—	15	1	no	—
175	C₄×M₁₆	—	15	1	no	—
176	Q₈⋊C₈	—	15	1	no	—
177	Q₈⋊C₈	D₁₅	1	1	yes	characteristic, complemented
178	D₄⋊C₈	—	15	1	no	—
179	D₄⋊C₈	—	15	1	no	—
180	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×D₁₅	—	2	1	no	—
182	C₂×D₁₅	—	2	2	no	—
183	C₂×D₁₅	—	2	1	no	—
184	C₂×D₁₅	—	2	1	no	—
185	C₂×D₁₅	—	4	1	no	—
186	C₂×D₁₅	—	4	1	no	—
187	C₃×C₄×C₅	—	2	2	no	—
188	C₃×C₄×C₅	—	2	1	no	—
189	C₃×C₄×C₅	—	4	1	no	—
190	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
191	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
192	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
193	C₃×C₄×C₅	#137	1	1	yes	characteristic
194	Dic₁₅	—	2	1	no	—
195	Dic₁₅	—	2	1	no	—
196	Dic₁₅	—	4	1	no	—
197	Dic₁₅	#104	1	2	yes	—
198	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
199	#239	—	10	2	no	—
200	#239	—	10	2	no	—
201	C₂×D₁₂	—	5	1	no	—
202	C₂×D₁₂	—	10	1	no	—
203	C₂×C₄×D₃	—	5	1	no	—
204	C₂×C₄×D₃	—	5	1	no	—
205	C₂×C₄×D₃	—	5	1	no	—
206	C₂×C₄×D₃	—	10	1	no	—
207	C₂×C₄×D₃	—	10	1	no	—
208	C₂×C₄×D₃	—	10	1	no	—
209	C₂×C₃×C₈	—	2	1	no	—
210	C₂×C₃×C₈	—	2	1	no	—
211	C₃×C₄⋊C₄	—	2	1	no	—
212	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
213	C₃×C₄²	—	2	1	no	—
214	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
215	(C₂×D₃)⋊C₄	—	10	1	no	—
216	(C₂×D₃)⋊C₄	—	10	1	no	—
217	(C₂×D₃)⋊C₄	—	10	1	no	—
218	C₄⋊Dic₃	—	5	1	no	—
219	C₄⋊Dic₃	—	10	1	no	—
220	C₄×Dic₃	—	5	1	no	—
221	C₄×Dic₃	—	5	1	no	—
222	C₄×Dic₃	—	5	1	no	—
223	C₄×Dic₃	—	10	1	no	—
224	C₄×Dic₃	—	10	1	no	—
225	C₂×C₃⋊C₈	—	10	1	no	—
226	C₂×C₃⋊C₈	—	10	1	no	—
227	ΓL(1,𝔽₂₅)	—	10	4	no	—
228	ΓL(1,𝔽₂₅)	—	20	2	no	—
229	C₂²×D₅	—	3	1	no	—
230	C₂²×D₅	—	6	1	no	—
231	C₅×Q₈	—	2	1	no	—
232	C₅×Q₈	ΓL(1,𝔽₂₅)	1	2	yes	complemented
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
236	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
237	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
238	C₂×Dic₅	—	3	1	no	—
239	C₂×Dic₅	—	3	1	no	—
240	C₂×Dic₅	—	3	1	no	—
241	C₂×Dic₅	—	6	1	no	—
242	D₂₀	—	3	2	no	—
243	D₂₀	—	6	4	no	—
244	D₂₀	—	6	1	no	—
245	C₄×D₅	—	6	2	no	—
246	C₄×D₅	—	6	4	no	—
247	C₄×D₅	—	6	1	no	—
248	C₄×D₅	—	6	1	no	—
249	C₄×D₅	—	6	1	no	—
250	C₄×D₅	—	6	1	no	—
251	C₄×D₅	—	12	2	no	—
252	C₄×D₅	—	12	1	no	—
253	C₄×D₅	—	12	1	no	—
254	C₅×C₈	—	2	2	no	—
255	C₅×C₈	—	4	1	no	—
256	#168	—	6	2	no	—
257	#168	—	12	1	no	—
258	C₂×#41	—	15	1	no	—
259	C₂×M₁₆	—	30	1	no	—
260	C₂×M₁₆	—	30	1	no	—
261	C₄×Q₈	—	15	1	no	—
262	C₄×Q₈	C₂×D₁₅	1	1	yes	characteristic
263	C₄×D₄	—	15	1	no	—
264	C₄×D₄	—	15	1	no	—
265	C₄×D₄	—	30	1	no	—
266	C₄×D₄	—	30	1	no	—
267	#117	—	15	1	no	—
268	#117	—	30	1	no	—
269	C₂×C₄²	—	15	1	no	—
270	C₂×C₄²	—	30	1	no	—
271	C₄⋊C₈	—	15	1	no	—
272	C₄⋊C₈	—	30	1	no	—
273	C₄⋊C₈	C₂×D₁₅	1	1	yes	characteristic
274	#97	—	30	1	no	—
275	C₄×C₈	—	15	1	no	—
276	C₄×C₈	C₂×D₁₅	1	1	yes	characteristic
277	C₂×C₃×C₅	#407	1	1	yes	characteristic
278	C₂×C₃×C₅	#417	1	1	yes	characteristic
279	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
280	D₁₅	—	4	1	no	—
281	D₁₅	—	4	2	no	—
282	C₂²×D₃	—	5	1	no	—
283	C₂²×D₃	—	10	1	no	—
284	C₃×Q₈	—	2	1	no	—
285	C₃×Q₈	#676	1	2	yes	complemented
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
289	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
290	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
291	C₂×Dic₃	—	5	1	no	—
292	C₂×Dic₃	—	5	1	no	—
293	C₂×Dic₃	—	5	1	no	—
294	C₂×Dic₃	—	10	1	no	—
295	D₁₂	—	5	2	no	—
296	D₁₂	—	10	4	no	—
297	D₁₂	—	10	1	no	—
298	C₄×D₃	—	10	2	no	—
299	C₄×D₃	—	10	4	no	—
300	C₄×D₃	—	10	1	no	—
301	C₄×D₃	—	10	1	no	—
302	C₄×D₃	—	10	1	no	—
303	C₄×D₃	—	10	1	no	—
304	C₄×D₃	—	20	2	no	—
305	C₄×D₃	—	20	1	no	—
306	C₄×D₃	—	20	1	no	—
307	C₃×C₈	—	2	2	no	—
308	C₃×C₈	—	4	1	no	—
309	C₃⋊C₈	—	10	2	no	—
310	C₃⋊C₈	—	20	1	no	—
311	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
312	C₂×D₅	—	6	2	no	—
313	C₂×D₅	—	6	1	no	—
314	C₂×D₅	—	6	1	no	—
315	C₂×D₅	—	6	1	no	—
316	C₂×D₅	—	12	1	no	—
317	C₂×D₅	—	12	1	no	—
318	C₄×C₅	—	2	2	no	—
319	C₄×C₅	—	2	1	no	—
320	C₄×C₅	—	4	1	no	—
321	C₄×C₅	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
322	C₄×C₅	D₃×M₁₆	1	1	yes	characteristic
323	C₄×C₅	#914	1	1	yes	characteristic
324	C₄×C₅	#918	1	1	yes	characteristic
325	Dic₅	—	3	2	no	—
326	Dic₅	—	6	1	no	—
327	Dic₅	—	6	1	no	—
328	Dic₅	—	12	1	no	—
329	#41	—	30	2	no	—
330	#41	—	30	2	no	—
331	C₂×Q₈	C₄×D₁₅	1	1	yes	characteristic
332	C₂×D₄	—	15	1	no	—
333	C₂×D₄	—	30	1	no	—
334	C₂²×C₄	—	15	1	no	—
335	C₂²×C₄	—	15	1	no	—
336	C₂²×C₄	—	15	1	no	—
337	C₂²×C₄	—	30	1	no	—
338	C₂²×C₄	—	30	1	no	—
339	C₂²×C₄	—	30	1	no	—
340	M₁₆	—	30	4	no	—
341	M₁₆	—	60	2	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	30	1	no	—
345	C₂×C₈	—	30	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	15	1	no	—
348	C₄⋊C₄	—	30	1	no	—
349	C₄⋊C₄	C₄×D₁₅	1	1	yes	characteristic
350	C₂²⋊C₄	—	30	1	no	—
351	C₂²⋊C₄	—	30	1	no	—
352	C₂²⋊C₄	—	30	1	no	—
353	C₄²	—	2	1	no	—
354	C₄²	—	15	1	no	—
355	C₄²	—	15	1	no	—
356	C₄²	—	15	1	no	—
357	C₄²	—	30	1	no	—
358	C₄²	—	30	1	no	—
359	C₄²	C₂²×D₁₅	1	1	yes	characteristic
360	C₃×C₅	#1489	1	1	yes	characteristic, complemented, Hall
361	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
362	C₂×D₃	—	10	1	no	—
363	C₂×D₃	—	10	1	no	—
364	C₂×D₃	—	10	2	no	—
365	C₂×D₃	—	10	1	no	—
366	C₂×D₃	—	20	1	no	—
367	C₂×D₃	—	20	1	no	—
368	C₃×C₄	—	2	1	no	—
369	C₃×C₄	—	2	2	no	—
370	C₃×C₄	—	4	1	no	—
371	C₃×C₄	C₂×#676	1	1	yes	characteristic
372	C₃×C₄	D₅×M₁₆	1	1	yes	characteristic
373	C₃×C₄	#4060	1	1	yes	characteristic
374	C₃×C₄	#4064	1	1	yes	characteristic
375	Dic₃	—	5	2	no	—
376	Dic₃	—	10	1	no	—
377	Dic₃	—	10	1	no	—
378	Dic₃	—	20	1	no	—
379	C₂×C₅	#4726	1	1	yes	characteristic
380	C₂×C₅	#4803	1	1	yes	characteristic
381	C₂×C₅	D₃×#104	1	1	yes	characteristic
382	D₅	—	12	1	no	—
383	D₅	—	12	2	no	—
384	C₂³	—	15	1	no	—
385	C₂³	—	30	1	no	—
386	Q₈	—	2	1	no	—
387	Q₈	#6705	1	2	yes	complemented
388	D₄	—	15	2	no	—
389	D₄	—	30	4	no	—
390	D₄	—	30	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	15	1	no	—
394	C₂×C₄	—	15	1	no	—
395	C₂×C₄	—	15	1	no	—
396	C₂×C₄	—	30	2	no	—
397	C₂×C₄	—	30	4	no	—
398	C₂×C₄	—	30	1	no	—
399	C₂×C₄	—	30	1	no	—
400	C₂×C₄	—	30	1	no	—
401	C₂×C₄	—	30	1	no	—
402	C₂×C₄	—	30	1	no	—
403	C₂×C₄	—	60	2	no	—
404	C₂×C₄	—	60	1	no	—
405	C₂×C₄	—	60	1	no	—
406	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
407	C₂×C₄	D₄×D₁₅	1	1	yes	characteristic
408	C₂×C₄	D₄×D₁₅	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	4	1	no	—
411	C₈	—	30	2	no	—
412	C₈	—	60	1	no	—
413	C₂×C₃	#65015	1	1	yes	characteristic
414	C₂×C₃	#65092	1	1	yes	characteristic
415	C₂×C₃	D₅×#104	1	1	yes	characteristic
416	D₃	—	20	1	no	—
417	D₃	—	20	2	no	—
418	C₅	#68238	1	1	yes	characteristic, complemented, Sylow
419	C₂²	—	30	1	no	—
420	C₂²	—	30	2	no	—
421	C₂²	—	30	1	no	—
422	C₂²	—	30	1	no	—
423	C₂²	—	60	1	no	—
424	C₂²	—	60	1	no	—
425	C₂²	C₂²⋊C₄×D₁₅	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	2	no	—
428	C₄	—	4	1	no	—
429	C₄	—	15	2	no	—
430	C₄	—	30	1	no	—
431	C₄	—	30	1	no	—
432	C₄	—	60	1	no	—
433	C₄	C₂×#6705	1	1	yes	characteristic
434	C₄	M₁₆×D₁₅	1	1	yes	characteristic
435	C₄	#91803	1	1	yes	characteristic
436	C₄	#91807	1	1	yes	characteristic
437	C₃	#10599031	1	1	yes	characteristic, complemented, Sylow
438	C₂	—	60	1	no	—
439	C₂	—	60	2	no	—
440	C₂	#11750827	1	1	yes	characteristic
441	C₂	#11750904	1	1	yes	characteristic
442	C₂	D₁₅×#104	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₁₅
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₄²	C₂²×D₁₅
Fitting	C₃×C₅×Q₈⋊C₈	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×#6821	C₄
cosocle	C₃×C₄²×C₅	C₂³
hypercenter	Q₈⋊C₈	D₁₅
hypocenter	C₃×C₅	#1489
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
2. #11750938	C₂	semidirect
3. C₄×#6705	C₂	semidirect
4. C₃×C₅×Q₈⋊C₈	C₂	semidirect
5. #11746356	C₂	semidirect
6. #11746304	C₂	semidirect
7. #11746280	C₂	semidirect
32. C₅×Q₈⋊C₈	D₃	semidirect
70. C₃×Q₈⋊C₈	D₅	semidirect
97. C₃×C₅×Q₈	M₁₆	semidirect
109. D₆₀	M₁₆	semidirect
177. Q₈⋊C₈	D₁₅	semidirect
232. C₅×Q₈	ΓL(1,𝔽₂₅)	semidirect
285. C₃×Q₈	#676	semidirect
360. C₃×C₅	#1489	semidirect
387. Q₈	#6705	semidirect
418. C₅	#68238	semidirect
437. C₃	#10599031	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6821	2
#11750938	2
C₄×#6705	2
C₃×C₅×Q₈⋊C₈	2
#11746356	2
#11746304	2
#11746280	2
#10599031	3
#68238	5