Subgroups — #14418946

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₃⋊#170	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65748	C₂	1	1	yes	maximal, characteristic, complemented
4	#67⋊#170	C₂	1	4	yes	maximal, complemented
5	#11751867	C₂	1	2	yes	maximal, complemented
6	C₄×D₃×#170	C₂	1	2	yes	maximal, complemented
7	#11751793	C₂	1	2	yes	maximal, complemented
8	#11751755	C₂	1	2	yes	maximal, complemented
9	#41×#170	—	3	1	no	maximal, Hall
10	C₂×C₅×#235	C₄	1	1	yes	characteristic
11	C₂²×C₃⋊#170	C₂²	1	2	yes	—
12	C₂×D₃×#170	C₂²	1	4	yes	—
13	#91815	C₄	1	1	yes	characteristic
14	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
15	Dic₅×#67	C₄	1	2	yes	—
16	Dic₅×#67	C₂²	1	2	yes	—
17	Dic₅×D₁₂	C₄	1	1	yes	characteristic
18	Dic₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₄×D₃×Dic₅	C₂²	1	2	yes	—
20	#91371	C₄	1	2	yes	—
21	Dic₅×Dic₆	C₄	1	1	yes	characteristic
22	Dic₅×Dic₆	C₂²	1	1	yes	characteristic
23	C₄×C₃⋊#170	C₂²	1	2	yes	—
24	C₄×C₃⋊#170	C₂²	1	1	yes	characteristic
25	C₄×C₃⋊#170	C₂²	1	1	yes	characteristic
26	C₃×C₂²⋊#170	C₂²	1	2	yes	—
27	C₃×C₄⋊#170	C₂²	1	2	yes	—
28	C₃×C₄×#170	C₂²	1	2	yes	—
29	Dic₃⋊#170	C₂²	1	4	yes	—
30	(C₂×D₃)⋊#170	C₂²	1	4	yes	—
31	Dic₃×#170	C₂²	1	4	yes	—
32	#79276	—	5	1	no	maximal, Hall
33	#41×Dic₅	—	3	1	no	—
34	Q₈×#170	—	3	2	no	—
35	D₄×#170	—	3	4	no	—
36	D₄×#170	—	3	2	no	—
37	#65748	—	3	2	no	—
38	#65748	D₃	1	1	yes	characteristic, complemented
39	C₂×C₄×#170	—	3	1	no	—
40	C₂×C₄×#170	—	3	2	no	—
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂×C₅×#67	C₂×C₄	1	2	yes	—
43	C₅×#235	C₈	1	8	yes	complemented
44	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
46	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
49	C₂×D₃×Dic₅	C₂×C₄	1	2	yes	—
50	C₂×D₃×Dic₅	C₂³	1	2	yes	—
51	C₂×C₃⋊#170	—	2	4	no	—
52	C₂×C₃⋊#170	C₂³	1	2	yes	—
53	C₂×C₃⋊#170	C₂³	1	2	yes	—
54	C₂×C₃×#170	C₂³	1	4	yes	—
55	D₃×#170	—	2	8	no	—
56	#6719	C₂×C₄	1	2	yes	—
57	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
58	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
59	C₄×Dic₁₅	C₂×C₄	1	2	yes	—
60	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
61	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
62	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
63	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
64	Dic₃⋊Dic₅	C₂×C₄	1	2	yes	—
65	Dic₃⋊Dic₅	C₂×C₄	1	2	yes	—
66	(C₂×D₃)⋊Dic₅	C₂×C₄	1	2	yes	—
67	(C₂×D₃)⋊Dic₅	C₂×C₄	1	2	yes	—
68	Dic₃×Dic₅	C₂×C₄	1	2	yes	—
69	Dic₃×Dic₅	C₂³	1	2	yes	—
70	C₄×#235	—	5	1	no	—
71	C₃×#431	—	5	1	no	—
72	C₂×C₄×C₃⋊C₈	—	5	1	no	—
73	#4834	—	5	2	no	—
74	#4830	—	5	2	no	—
75	#67⋊C₈	—	5	4	no	—
76	#4685	—	5	2	no	—
77	C₄×D₃×C₈	—	5	2	no	—
78	C₂×C₅×#41	—	3	1	no	—
79	C₂²×#170	—	3	2	no	—
80	C₂²×#170	—	3	4	no	—
81	Q₈×Dic₅	—	3	1	no	—
82	Q₈×Dic₅	—	3	1	no	—
83	D₄×Dic₅	—	3	2	no	—
84	D₄×Dic₅	—	3	2	no	—
85	D₄×Dic₅	—	3	1	no	—
86	D₄×Dic₅	—	3	1	no	—
87	#4072	—	3	1	no	—
88	#4072	—	3	2	no	—
89	C₂×C₄×Dic₅	—	3	2	no	—
90	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
91	C₂²⋊#170	—	3	4	no	—
92	C₂²⋊#170	C₂×D₃	1	2	yes	—
93	C₄⋊#170	—	3	4	no	—
94	C₄⋊#170	C₂×D₃	1	2	yes	—
95	C₄×#170	—	3	4	no	—
96	C₄×#170	—	3	1	no	—
97	C₄×#170	—	3	1	no	—
98	C₄×#170	—	3	2	no	—
99	C₄×#170	C₂×D₃	1	2	yes	—
100	C₈×#41	—	15	1	no	Sylow
101	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	C₂×C₈	1	4	yes	complemented
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
107	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
108	C₅×#67	C₂×C₈	1	8	yes	complemented
109	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
110	C₅×D₁₂	C₂×C₈	1	4	yes	complemented
111	C₄×C₅×D₃	C₂×C₈	1	8	yes	complemented
112	C₅×Dic₆	C₂×C₈	1	4	yes	complemented
113	C₂×C₃×Dic₅	—	2	2	no	—
114	C₂×C₃×Dic₅	—	2	2	no	—
115	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
119	D₃×Dic₅	—	2	4	no	—
120	D₃×Dic₅	—	2	4	no	—
121	C₃⋊#170	—	2	2	no	—
122	C₃⋊#170	#41	1	4	yes	complemented
123	C₃×#170	—	2	4	no	—
124	C₂×#235	AGL(1,𝔽₅)	1	1	yes	characteristic
125	C₂×C₃×C₄²	—	5	1	no	—
126	C₄×#67	—	5	2	no	—
127	C₄×#67	—	5	2	no	—
128	#926	—	5	1	no	—
129	C₂²×C₃⋊C₈	—	5	2	no	—
130	C₂×D₃×C₈	—	5	4	no	—
131	C₄×D₁₂	—	5	1	no	—
132	C₄×D₁₂	—	5	1	no	—
133	#872	—	5	2	no	—
134	C₄²×D₃	—	5	2	no	—
135	C₄×Dic₆	—	5	1	no	—
136	C₄×Dic₆	—	5	1	no	—
137	C₃×C₄⋊C₈	—	5	2	no	—
138	C₃×C₂²⋊C₈	—	5	2	no	—
139	C₃×C₄×C₈	—	5	2	no	—
140	(C₂×D₃)⋊C₈	—	5	4	no	—
141	Dic₃⋊C₈	—	5	4	no	—
142	C₈×Dic₃	—	5	4	no	—
143	C₄×C₃⋊C₈	—	5	1	no	—
144	C₄×C₃⋊C₈	—	5	1	no	—
145	C₄×C₃⋊C₈	—	5	2	no	—
146	C₅×#41	—	3	8	no	—
147	C₂×C₅×Q₈	—	3	1	no	—
148	C₂×C₅×D₄	—	3	2	no	—
149	C₂×C₅×D₄	—	3	1	no	—
150	C₂²×C₄×C₅	—	3	2	no	—
151	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
152	C₂²×Dic₅	—	3	2	no	—
153	C₂²×Dic₅	—	3	2	no	—
154	C₂²×Dic₅	C₄×D₃	1	1	yes	characteristic
155	C₂²×Dic₅	C₂²×D₃	1	1	yes	characteristic
156	C₂×#170	—	3	2	no	—
157	C₂×#170	—	3	2	no	—
158	C₂×#170	—	6	8	no	—
159	C₂×#170	—	6	4	no	—
160	C₂×#170	C₂²×D₃	1	4	yes	—
161	C₂²⋊Dic₅	—	3	2	no	—
162	C₂²⋊Dic₅	—	3	2	no	—
163	C₂²⋊Dic₅	—	3	2	no	—
164	C₄⋊Dic₅	—	3	1	no	—
165	C₄⋊Dic₅	—	3	1	no	—
166	C₄⋊Dic₅	—	3	2	no	—
167	C₄⋊Dic₅	—	3	2	no	—
168	C₄×Dic₅	—	3	2	no	—
169	C₄×Dic₅	—	3	2	no	—
170	C₄×Dic₅	—	3	2	no	—
171	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
172	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
173	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
174	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
175	C₄×#41	—	15	1	no	—
176	C₈×Q₈	—	15	2	no	—
177	C₈×D₄	—	15	4	no	—
178	C₈×D₄	—	15	2	no	—
179	#431	—	5	1	no	—
180	#431	—	15	2	no	—
181	C₂×C₄×C₈	—	15	2	no	—
182	C₂×C₄×C₈	—	15	1	no	—
183	C₂²×C₃×C₅	—	2	1	no	—
184	C₂²×C₃×C₅	—	2	1	no	—
185	C₂²×C₃×C₅	C₂²×C₈	1	2	yes	—
186	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₅×D₃	—	2	2	no	—
188	C₂×C₅×D₃	—	2	2	no	—
189	C₂×C₅×D₃	C₂²×C₈	1	4	yes	—
190	C₃×C₄×C₅	C₂²×C₈	1	2	yes	—
191	C₃×C₄×C₅	C₂²×C₈	1	2	yes	—
192	Dic₁₅	—	2	2	no	—
193	Dic₁₅	—	2	2	no	—
194	C₃×Dic₅	—	2	1	no	—
195	C₃×Dic₅	—	2	1	no	—
196	C₃×Dic₅	#131	1	2	yes	—
197	C₃×Dic₅	C₂×#41	1	2	yes	—
198	C₅×Dic₃	C₂²×C₈	1	4	yes	—
199	C₂²×C₃×C₄	—	5	1	no	—
200	C₂²×C₃×C₄	—	5	1	no	—
201	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
202	C₂×#67	C₂×AGL(1,𝔽₅)	1	2	yes	—
203	#235	#170	1	8	yes	complemented
204	C₂×D₁₂	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
205	C₂×C₄×D₃	—	5	2	no	—
206	C₂×C₄×D₃	—	5	2	no	—
207	C₂×C₄×D₃	C₂×AGL(1,𝔽₅)	1	2	yes	—
208	C₂×Dic₆	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
209	C₂×C₃×C₈	—	5	4	no	—
210	C₃×C₄²	—	5	1	no	—
211	C₃×C₄²	—	5	1	no	—
212	C₃×C₄²	—	5	1	no	—
213	C₃×C₄²	—	5	1	no	—
214	#217	—	5	2	no	—
215	(C₂×D₃)⋊C₄	—	5	2	no	—
216	(C₂×D₃)⋊C₄	—	5	2	no	—
217	C₄⋊Dic₃	—	5	1	no	—
218	C₄⋊Dic₃	—	5	1	no	—
219	Dic₃⋊C₄	—	5	2	no	—
220	Dic₃⋊C₄	—	5	2	no	—
221	C₄×Dic₃	—	5	2	no	—
222	C₄×Dic₃	—	5	2	no	—
223	C₄×Dic₃	—	5	2	no	—
224	C₂×C₃⋊C₈	—	5	2	no	—
225	C₂×C₃⋊C₈	—	5	2	no	—
226	C₂×C₃⋊C₈	—	10	4	no	—
227	D₃×C₈	—	10	8	no	—
228	C₂³×C₅	—	3	2	no	—
229	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
230	C₅×Q₈	—	3	4	no	—
231	C₅×D₄	—	3	8	no	—
232	C₅×D₄	—	3	4	no	—
233	C₂×C₄×C₅	—	3	2	no	—
234	C₂×C₄×C₅	—	3	8	no	—
235	C₂×C₄×C₅	D₃×C₈	1	4	yes	complemented
236	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
238	C₂×Dic₅	—	2	2	no	—
239	C₂×Dic₅	—	2	2	no	—
240	C₂×Dic₅	—	3	2	no	—
241	C₂×Dic₅	—	3	2	no	—
242	C₂×Dic₅	—	6	4	no	—
243	C₂×Dic₅	—	6	4	no	—
244	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
245	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
246	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
247	C₂×Dic₅	C₂³×D₃	1	1	yes	characteristic
248	#170	—	2	4	no	—
249	#170	—	3	4	no	—
250	#170	—	6	2	no	—
251	C₂×#41	—	3	1	no	—
252	C₂²×C₈	—	15	4	no	—
253	C₂²×C₈	—	15	2	no	—
254	C₄×Q₈	—	15	1	no	—
255	C₄×Q₈	—	15	1	no	—
256	C₄×D₄	—	15	1	no	—
257	C₄×D₄	—	15	1	no	—
258	C₄×D₄	—	15	2	no	—
259	C₄×D₄	—	15	2	no	—
260	#117	—	15	2	no	—
261	#117	—	15	1	no	—
262	C₂×C₄²	—	5	1	no	—
263	C₂×C₄²	—	15	2	no	—
264	C₄⋊C₈	—	5	2	no	—
265	C₄⋊C₈	—	15	4	no	—
266	C₂²⋊C₈	—	5	2	no	—
267	C₂²⋊C₈	—	15	4	no	—
268	C₄×C₈	—	5	2	no	—
269	C₄×C₈	—	15	1	no	—
270	C₄×C₈	—	15	1	no	—
271	C₄×C₈	—	15	2	no	—
272	C₄×C₈	—	15	4	no	—
273	C₂×C₃×C₅	—	2	2	no	—
274	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
275	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
276	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
277	C₅×D₃	—	2	4	no	—
278	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
279	C₂²×D₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
280	C₂×C₃×C₄	—	5	1	no	—
281	C₂×C₃×C₄	—	5	1	no	—
282	C₂×C₃×C₄	—	5	1	no	—
283	C₂×C₃×C₄	—	5	1	no	—
284	C₂×C₃×C₄	—	10	2	no	—
285	C₂×C₃×C₄	—	10	2	no	—
286	C₂×C₃×C₄	C₂×#170	1	4	yes	complemented
287	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
289	#67	C₂×#170	1	8	yes	complemented
290	C₂×Dic₃	—	5	2	no	—
291	C₂×Dic₃	—	5	2	no	—
292	C₂×Dic₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
293	D₁₂	C₂×#170	1	4	yes	complemented
294	C₄×D₃	—	10	4	no	—
295	C₄×D₃	—	10	4	no	—
296	C₄×D₃	C₂×#170	1	8	yes	complemented
297	Dic₆	C₂×#170	1	4	yes	complemented
298	C₃×C₈	—	10	4	no	—
299	C₃⋊C₈	—	5	4	no	—
300	C₃⋊C₈	—	10	2	no	—
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	2	1	no	—
303	C₂²×C₅	—	3	4	no	—
304	C₂²×C₅	—	6	2	no	—
305	C₂²×C₅	—	6	2	no	—
306	C₂²×C₅	C₂×D₃×C₈	1	2	yes	—
307	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
308	C₄×C₅	—	3	4	no	—
309	C₄×C₅	C₂×D₃×C₈	1	2	yes	—
310	C₄×C₅	C₂×D₃×C₈	1	2	yes	—
311	Dic₅	—	2	1	no	—
312	Dic₅	—	2	1	no	—
313	Dic₅	—	6	2	no	—
314	Dic₅	—	6	2	no	—
315	Dic₅	#907	1	2	yes	—
316	Dic₅	D₃×#41	1	2	yes	—
317	#41	—	3	8	no	—
318	C₂×Q₈	—	3	1	no	—
319	C₂×D₄	—	3	2	no	—
320	C₂×D₄	—	3	1	no	—
321	C₂²×C₄	—	3	2	no	—
322	C₂²×C₄	—	5	1	no	—
323	C₂²×C₄	—	5	1	no	—
324	C₂²×C₄	—	15	2	no	—
325	C₂²×C₄	—	15	2	no	—
326	C₂²×C₄	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
327	C₂×C₈	—	5	4	no	—
328	C₂×C₈	—	15	2	no	—
329	C₂×C₈	—	15	2	no	—
330	C₂×C₈	—	30	8	no	—
331	C₂×C₈	—	30	4	no	—
332	C₄⋊C₄	—	15	2	no	—
333	C₄⋊C₄	—	15	2	no	—
334	C₄⋊C₄	—	15	1	no	—
335	C₄⋊C₄	—	15	1	no	—
336	C₂²⋊C₄	—	15	2	no	—
337	C₂²⋊C₄	—	15	2	no	—
338	C₂²⋊C₄	—	15	2	no	—
339	C₄²	—	5	1	no	—
340	C₄²	—	5	1	no	—
341	C₄²	—	5	1	no	—
342	C₄²	—	5	1	no	—
343	C₄²	—	15	2	no	—
344	C₄²	—	15	2	no	—
345	C₄²	—	15	2	no	—
346	C₃×C₅	C₈×#41	1	1	yes	characteristic, complemented, Hall
347	C₂²×C₃	—	2	1	no	—
348	C₂²×C₃	—	2	1	no	—
349	C₂²×C₃	C₂²×#170	1	2	yes	—
350	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
351	C₂×D₃	—	2	2	no	—
352	C₂×D₃	—	2	2	no	—
353	C₂×D₃	C₂²×#170	1	4	yes	—
354	C₃×C₄	—	5	2	no	—
355	C₃×C₄	—	5	2	no	—
356	C₃×C₄	—	10	1	no	—
357	C₃×C₄	—	10	1	no	—
358	C₃×C₄	C₂²×#170	1	2	yes	—
359	C₃×C₄	C₂²×#170	1	2	yes	—
360	Dic₃	—	10	2	no	—
361	Dic₃	—	10	2	no	—
362	Dic₃	C₂²×#170	1	4	yes	—
363	C₂×C₅	—	2	2	no	—
364	C₂×C₅	—	6	4	no	—
365	C₂×C₅	#5522	1	1	yes	characteristic
366	C₂×C₅	C₂²×D₃×C₈	1	1	yes	characteristic
367	C₂×C₅	C₂×#907	1	1	yes	characteristic
368	C₂³	—	3	2	no	—
369	C₂³	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
370	Q₈	—	3	4	no	—
371	D₄	—	3	8	no	—
372	D₄	—	3	4	no	—
373	C₂×C₄	—	3	2	no	—
374	C₂×C₄	—	3	8	no	—
375	C₂×C₄	—	5	1	no	—
376	C₂×C₄	—	5	1	no	—
377	C₂×C₄	—	5	1	no	—
378	C₂×C₄	—	5	1	no	—
379	C₂×C₄	—	10	2	no	—
380	C₂×C₄	—	10	2	no	—
381	C₂×C₄	—	15	2	no	—
382	C₂×C₄	—	15	2	no	—
383	C₂×C₄	—	30	4	no	—
384	C₂×C₄	—	30	4	no	—
385	C₂×C₄	D₃×#170	1	4	yes	complemented
386	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
387	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
388	C₈	—	10	4	no	—
389	C₈	—	15	4	no	—
390	C₈	—	30	2	no	—
391	C₂×C₃	—	2	2	no	—
392	C₂×C₃	D₅⋊#131	1	1	yes	characteristic
393	C₂×C₃	#41×AGL(1,𝔽₅)	1	1	yes	characteristic
394	C₂×C₃	C₂³×#170	1	1	yes	characteristic
395	D₃	—	2	4	no	—
396	C₅	#79276	1	1	yes	characteristic, complemented, Sylow
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	3	4	no	—
400	C₂²	—	6	2	no	—
401	C₂²	—	6	2	no	—
402	C₂²	C₂×D₃×#170	1	2	yes	—
403	C₂²	C₂²×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
404	C₄	—	3	4	no	—
405	C₄	—	5	2	no	—
406	C₄	—	5	2	no	—
407	C₄	—	10	1	no	—
408	C₄	—	10	1	no	—
409	C₄	—	30	2	no	—
410	C₄	—	30	2	no	—
411	C₄	C₂×D₃×#170	1	2	yes	—
412	C₄	C₂×D₃×#170	1	2	yes	—
413	C₃	#41×#170	1	1	yes	characteristic, complemented, Sylow
414	C₂	—	2	2	no	—
415	C₂	—	6	4	no	—
416	C₂	D₅⋊#907	1	1	yes	characteristic
417	C₂	#11756835	1	1	yes	characteristic
418	C₂	C₂²×D₃×#170	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)
commutator	C₂×C₃×C₅	C₂³×C₈
Frattini	C₂²	C₂²×D₃×AGL(1,𝔽₅)
Fitting	C₂²×C₃×C₄×C₅	C₂×C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₅×#235	C₄
cosocle	C₂×C₃×Dic₅	C₂⁴
hypercenter	C₂²×C₄	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₈×#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×C₃⋊#170	C₂	semidirect
3. C₃×#65748	C₂	semidirect
4. #67⋊#170	C₂	semidirect
5. #11751867	C₂	semidirect
6. C₄×D₃×#170	C₂	semidirect
7. #11751793	C₂	semidirect
8. #11751755	C₂	semidirect
38. #65748	D₃	semidirect
43. C₅×#235	C₈	semidirect
103. C₂×C₃×C₄×C₅	C₂×C₈	semidirect
108. C₅×#67	C₂×C₈	semidirect
110. C₅×D₁₂	C₂×C₈	semidirect
111. C₄×C₅×D₃	C₂×C₈	semidirect
112. C₅×Dic₆	C₂×C₈	semidirect
122. C₃⋊#170	#41	semidirect
203. #235	#170	semidirect
235. C₂×C₄×C₅	D₃×C₈	semidirect
286. C₂×C₃×C₄	C₂×#170	semidirect
289. #67	C₂×#170	semidirect
293. D₁₂	C₂×#170	semidirect
296. C₄×D₃	C₂×#170	semidirect
297. Dic₆	C₂×#170	semidirect
346. C₃×C₅	C₈×#41	semidirect
385. C₂×C₄	D₃×#170	semidirect
396. C₅	#79276	semidirect
413. C₃	#41×#170	semidirect

Maximal subgroups

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

subgroup	index
Dic₅×#235	2
C₂×C₄×C₃⋊#170	2
C₃×#65748	2
#67⋊#170	2
#11751867	2
C₄×D₃×#170	2
#11751793	2
#11751755	2
#41×#170	3
#79276	5