Subgroups — C₂×#10603886 #13034546

Order 1280.

786 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅⋊#108	C₂	1	1	yes	maximal, characteristic
2	C₂×#65721	C₂	1	1	yes	maximal, characteristic
3	C₂×#64997	C₂	1	1	yes	maximal, characteristic
4	C₂×#64894	C₂	1	2	yes	maximal
5	C₂×#64863	C₂	1	2	yes	maximal
6	#10603886	C₂	1	8	yes	maximal, direct product factor
7	C₂×#4130	C₂²	1	2	yes	—
8	C₂×D₅⋊M₁₆	C₂²	1	2	yes	—
9	C₂²×#676	C₂²	1	1	yes	characteristic
10	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
11	C₂×#4018	C₂²	1	1	yes	characteristic
12	D₅⋊#108	—	2	2	no	—
13	D₅⋊#108	C₂²	1	4	yes	—
14	C₂×#3996	—	2	1	no	—
15	C₂×#3995	—	2	1	no	—
16	#65721	—	2	2	no	—
17	#65721	C₂²	1	4	yes	—
18	C₂×#3994	—	2	1	no	—
19	C₂×#3993	—	2	1	no	—
20	C₂×C₅×#97	C₄	1	1	yes	characteristic, complemented
21	C₂×#3947	C₄	1	1	yes	characteristic, complemented
22	C₂×C₈×Dic₅	C₄	1	1	yes	characteristic, complemented
23	C₂×C₄×#168	C₄	1	1	yes	characteristic, complemented
24	#64997	C₄	1	4	yes	complemented
25	#64997	C₂²	1	4	yes	—
26	#64894	C₂²	1	8	yes	—
27	#64863	C₂²	1	8	yes	—
28	C₂×#1833	—	5	1	no	maximal, Sylow
29	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
30	C₂×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
31	C₂×#704	—	2	2	no	—
32	#4130	—	2	2	no	—
33	#4130	—	2	2	no	—
34	#4130	—	2	2	no	—
35	#4130	C₂³	1	4	yes	—
36	C₂×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
37	C₂×C₄×AGL(1,𝔽₅)	—	2	2	no	—
38	D₅⋊M₁₆	—	2	2	no	—
39	D₅⋊M₁₆	—	2	2	no	—
40	D₅⋊M₁₆	—	2	2	no	—
41	D₅⋊M₁₆	C₂³	1	4	yes	—
42	C₂×#700	—	2	2	no	—
43	C₂×D₅⋊C₈	—	2	2	no	—
44	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
47	C₂×#685	—	2	1	no	—
48	C₂×#683	—	2	1	no	—
49	C₂×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
50	C₂²×#168	C₂×C₄	1	1	yes	characteristic
51	C₂²×#168	C₂×C₄	1	1	yes	characteristic
52	C₂×#676	—	2	1	no	—
53	C₂×#676	—	2	1	no	—
54	C₂×#676	—	2	1	no	—
55	C₂×#676	—	2	1	no	—
56	C₂×#676	C₂×C₄	1	2	yes	—
57	C₂×#676	C₂³	1	2	yes	—
58	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
59	C₂×C₈×D₅	D₄	1	1	yes	characteristic
60	C₂×C₈×D₅	D₄	1	1	yes	characteristic
61	C₂×C₈×D₅	D₄	1	2	yes	—
62	C₂×C₈×D₅	Q₈	1	2	yes	—
63	C₂×C₈×D₅	Q₈	1	1	yes	characteristic
64	C₂×C₈×D₅	Q₈	1	1	yes	characteristic
65	C₂×C₈×D₅	C₂³	1	2	yes	—
66	#4018	—	2	1	no	—
67	#4018	—	2	1	no	—
68	#4018	C₂×C₄	1	2	yes	—
69	#4018	C₂³	1	2	yes	—
70	#3996	—	2	4	no	—
71	#3995	—	2	4	no	—
72	#3994	—	2	4	no	—
73	#3993	—	2	4	no	—
74	C₅×#97	C₂×C₄	1	4	yes	complemented
75	#3947	C₂×C₄	1	4	yes	complemented
76	C₈×Dic₅	C₂×C₄	1	4	yes	complemented
77	C₄×#168	C₂×C₄	1	4	yes	complemented
78	C₂²×#108	—	5	1	no	—
79	C₂×#427	—	5	1	no	—
80	C₂×#405	—	5	1	no	—
81	#1833	—	5	8	no	—
82	C₂×#344	—	5	2	no	—
83	C₂×H(3,ℤ/4)	—	5	2	no	—
84	C₂³×D₅	#41	1	1	yes	characteristic
85	C₂²×AGL(1,𝔽₅)	—	4	2	no	—
86	C₂²×C₄×C₅	—	2	1	no	—
87	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
88	C₂²×Dic₅	—	2	1	no	—
89	C₂²×Dic₅	#41	1	1	yes	characteristic
90	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
92	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
93	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
94	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
95	C₂×C₄×D₅	#41	1	1	yes	characteristic
96	C₂×C₄×D₅	#41	1	1	yes	characteristic
97	C₂×C₄×D₅	#41	1	1	yes	characteristic
98	C₂×C₄×D₅	#41	1	1	yes	characteristic
99	C₂×C₄×D₅	#41	1	1	yes	characteristic
100	C₂×C₄×D₅	#41	1	1	yes	characteristic
101	C₂×C₄×D₅	C₂⁴	1	1	yes	characteristic
102	C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
103	C₂²⋊AGL(1,𝔽₅)	—	4	2	no	—
104	#704	—	2	4	no	—
105	#704	—	4	2	no	—
106	C₂×#170	—	4	2	no	—
107	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
108	C₄⋊AGL(1,𝔽₅)	—	4	2	no	—
109	C₄×AGL(1,𝔽₅)	—	2	4	no	—
110	C₄×AGL(1,𝔽₅)	—	4	2	no	—
111	#700	—	2	4	no	—
112	#700	—	4	2	no	—
113	D₅⋊C₈	—	2	4	no	—
114	D₅⋊C₈	—	4	2	no	—
115	C₂×C₅×C₈	—	2	1	no	—
116	C₂×C₅×C₈	—	2	1	no	—
117	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
119	C₂×C₅×C₈	C₄⋊C₄	1	2	yes	—
120	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
121	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
122	C₄²×C₅	—	2	1	no	—
123	C₄²×C₅	C₂²×C₄	1	2	yes	—
124	#685	—	2	2	no	—
125	#685	—	2	2	no	—
126	#683	—	2	2	no	—
127	#683	—	2	2	no	—
128	C₄×Dic₅	—	2	1	no	—
129	C₄×Dic₅	C₂²×C₄	1	2	yes	—
130	C₂×#168	—	2	1	no	—
131	C₂×#168	—	2	1	no	—
132	C₂×#168	C₄⋊C₄	1	1	yes	characteristic
133	C₂×#168	C₄⋊C₄	1	1	yes	characteristic
134	C₂×#168	C₄⋊C₄	1	2	yes	—
135	C₂×#168	C₂²×C₄	1	2	yes	—
136	C₂×#168	C₂²×C₄	1	2	yes	—
137	#676	—	2	2	no	—
138	#676	—	2	2	no	—
139	#676	—	2	2	no	—
140	#676	—	2	2	no	—
141	C₈×D₅	C₄⋊C₄	1	2	yes	—
142	C₈×D₅	C₄⋊C₄	1	2	yes	—
143	C₈×D₅	C₄⋊C₄	1	2	yes	—
144	C₈×D₅	C₄⋊C₄	1	2	yes	—
145	C₈×D₅	C₂×D₄	1	2	yes	—
146	C₈×D₅	C₂×D₄	1	2	yes	—
147	C₈×D₅	C₂×Q₈	1	2	yes	—
148	C₈×D₅	C₂×Q₈	1	2	yes	—
149	C₂²×M₁₆	—	5	1	no	—
150	C₂²×M₁₆	—	5	2	no	—
151	C₂³×C₈	—	5	1	no	—
152	C₂×#117	—	5	1	no	—
153	C₂×#117	—	5	2	no	—
154	C₂×#108	—	5	4	no	—
155	C₂×#108	—	10	1	no	—
156	C₂×#108	—	10	1	no	—
157	C₂×#108	—	10	2	no	—
158	#427	—	5	4	no	—
159	#427	—	10	2	no	—
160	C₂×#107	—	10	1	no	—
161	C₂×#106	—	10	1	no	—
162	#405	—	5	4	no	—
163	#405	—	5	4	no	—
164	C₂×#97	—	5	1	no	—
165	C₂×#97	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
166	C₂×C₄×C₈	—	5	1	no	—
167	C₂×C₄×C₈	—	5	1	no	—
168	#344	—	5	8	no	—
169	H(3,ℤ/4)	—	5	8	no	—
170	C₂³×C₅	#117	1	1	yes	characteristic
171	C₂²×D₅	—	4	2	no	—
172	C₂²×D₅	#117	1	1	yes	characteristic
173	C₂²×D₅	#124	1	1	yes	characteristic
174	C₂²×D₅	#124	1	1	yes	characteristic
175	C₂²×D₅	#125	1	1	yes	characteristic
176	C₂²×D₅	#125	1	1	yes	characteristic
177	C₂²×D₅	C₂×#41	1	1	yes	characteristic
178	C₂×AGL(1,𝔽₅)	—	4	4	no	—
179	C₂×AGL(1,𝔽₅)	—	8	4	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	4	2	no	—
182	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₅	#117	1	1	yes	characteristic
185	C₂×C₄×C₅	#117	1	1	yes	characteristic
186	C₂×C₄×C₅	#117	1	1	yes	characteristic
187	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
188	C₂×Dic₅	—	2	2	no	—
189	C₂×Dic₅	—	4	2	no	—
190	C₂×Dic₅	#117	1	1	yes	characteristic
191	C₂×Dic₅	#124	1	1	yes	characteristic
192	C₂×Dic₅	#124	1	1	yes	characteristic
193	C₂×Dic₅	#125	1	1	yes	characteristic
194	C₂×Dic₅	#125	1	1	yes	characteristic
195	C₂×Dic₅	C₂×#41	1	1	yes	characteristic
196	C₄×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
197	C₄×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₄×D₅	#117	1	1	yes	characteristic
199	C₄×D₅	#117	1	1	yes	characteristic
200	C₄×D₅	#124	1	1	yes	characteristic
201	C₄×D₅	#124	1	1	yes	characteristic
202	C₄×D₅	#124	1	1	yes	characteristic
203	C₄×D₅	#124	1	1	yes	characteristic
204	C₄×D₅	#125	1	1	yes	characteristic
205	C₄×D₅	#125	1	1	yes	characteristic
206	C₄×D₅	#125	1	1	yes	characteristic
207	C₄×D₅	#125	1	1	yes	characteristic
208	C₄×D₅	C₂²×D₄	1	1	yes	characteristic
209	C₄×D₅	C₂²×Q₈	1	1	yes	characteristic
210	C₄×D₅	C₂×#41	1	1	yes	characteristic
211	C₄×D₅	C₂×#41	1	1	yes	characteristic
212	#170	—	4	4	no	—
213	C₅×C₈	—	2	2	no	—
214	C₅×C₈	C₂×C₄⋊C₄	1	2	yes	—
215	C₅×C₈	C₂×C₄⋊C₄	1	2	yes	—
216	#168	—	2	2	no	—
217	#168	C₂×C₄⋊C₄	1	2	yes	—
218	#168	C₂×C₄⋊C₄	1	2	yes	—
219	C₂³×C₄	—	5	1	no	—
220	C₂×M₁₆	—	5	2	no	—
221	C₂×M₁₆	—	5	2	no	—
222	C₂×M₁₆	—	5	4	no	—
223	C₂×M₁₆	—	10	1	no	—
224	C₂×M₁₆	—	10	1	no	—
225	C₂×M₁₆	—	10	1	no	—
226	C₂×M₁₆	—	10	1	no	—
227	C₂×M₁₆	—	10	2	no	—
228	C₂×M₁₆	—	10	2	no	—
229	C₂×M₁₆	—	10	2	no	—
230	C₂×M₁₆	—	10	2	no	—
231	C₂×M₁₆	—	10	2	no	—
232	C₂²×C₈	—	5	1	no	—
233	C₂²×C₈	—	5	1	no	—
234	C₂²×C₈	—	5	1	no	—
235	C₂²×C₈	—	5	2	no	—
236	C₂²×C₈	—	5	1	no	—
237	C₂²×C₈	—	5	1	no	—
238	C₂²×C₈	—	5	2	no	—
239	C₂²×C₈	—	5	2	no	—
240	C₂²×C₈	—	5	2	no	—
241	C₂²×C₈	—	5	1	no	—
242	C₂²×C₈	—	10	2	no	—
243	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
244	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
245	#117	—	5	2	no	—
246	#117	—	5	2	no	—
247	#117	—	5	4	no	—
248	#117	—	10	1	no	—
249	#117	—	10	1	no	—
250	#117	—	10	2	no	—
251	#117	—	10	2	no	—
252	#117	—	10	2	no	—
253	C₂×C₄⋊C₄	—	10	1	no	—
254	C₂×C₄⋊C₄	—	10	2	no	—
255	C₂×C₂²⋊C₄	—	10	1	no	—
256	C₂×C₂²⋊C₄	—	10	2	no	—
257	C₂×C₄²	—	5	1	no	—
258	C₂×C₄²	—	10	2	no	—
259	C₂×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
260	#108	—	10	4	no	—
261	#108	—	10	4	no	—
262	#107	—	10	4	no	—
263	#106	—	10	4	no	—
264	#97	—	5	4	no	—
265	#97	C₂×AGL(1,𝔽₅)	1	4	yes	complemented
266	C₄×C₈	—	5	4	no	—
267	C₄×C₈	—	5	4	no	—
268	C₂²×C₅	—	2	2	no	—
269	C₂²×C₅	#382	1	1	yes	characteristic
270	C₂²×C₅	#382	1	1	yes	characteristic
271	C₂²×C₅	C₂×#117	1	1	yes	characteristic
272	C₂×D₅	—	2	2	no	—
273	C₂×D₅	—	2	2	no	—
274	C₂×D₅	—	4	1	no	—
275	C₂×D₅	—	4	1	no	—
276	C₂×D₅	—	4	1	no	—
277	C₂×D₅	—	4	1	no	—
278	C₂×D₅	#382	1	1	yes	characteristic
279	C₂×D₅	#382	1	1	yes	characteristic
280	C₂×D₅	C₂×#124	1	1	yes	characteristic
281	C₂×D₅	C₂×#125	1	1	yes	characteristic
282	AGL(1,𝔽₅)	—	8	4	no	—
283	C₄×C₅	—	4	2	no	—
284	C₄×C₅	#382	1	1	yes	characteristic
285	C₄×C₅	#382	1	1	yes	characteristic
286	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
287	C₄×C₅	C₂×#117	1	1	yes	characteristic
288	Dic₅	—	4	2	no	—
289	Dic₅	#382	1	1	yes	characteristic
290	Dic₅	#382	1	1	yes	characteristic
291	Dic₅	C₂×#124	1	1	yes	characteristic
292	Dic₅	C₂×#125	1	1	yes	characteristic
293	C₂⁴	—	5	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	5	1	no	—
296	C₂²×C₄	—	5	1	no	—
297	C₂²×C₄	—	5	1	no	—
298	C₂²×C₄	—	5	1	no	—
299	C₂²×C₄	—	5	1	no	—
300	C₂²×C₄	—	5	1	no	—
301	C₂²×C₄	—	5	1	no	—
302	C₂²×C₄	—	5	1	no	—
303	C₂²×C₄	—	5	1	no	—
304	C₂²×C₄	—	5	1	no	—
305	C₂²×C₄	—	5	1	no	—
306	C₂²×C₄	—	5	1	no	—
307	C₂²×C₄	—	5	1	no	—
308	C₂²×C₄	—	10	1	no	—
309	C₂²×C₄	—	20	2	no	—
310	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
311	M₁₆	—	10	2	no	—
312	M₁₆	—	10	2	no	—
313	M₁₆	—	10	2	no	—
314	M₁₆	—	10	2	no	—
315	M₁₆	—	10	4	no	—
316	M₁₆	—	10	4	no	—
317	M₁₆	—	20	2	no	—
318	M₁₆	—	20	2	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	5	1	no	—
322	C₂×C₈	—	5	1	no	—
323	C₂×C₈	—	5	2	no	—
324	C₂×C₈	—	5	2	no	—
325	C₂×C₈	—	5	2	no	—
326	C₂×C₈	—	5	2	no	—
327	C₂×C₈	—	5	2	no	—
328	C₂×C₈	—	5	2	no	—
329	C₂×C₈	—	5	2	no	—
330	C₂×C₈	—	5	2	no	—
331	C₂×C₈	—	5	2	no	—
332	C₂×C₈	—	5	2	no	—
333	C₂×C₈	—	5	2	no	—
334	C₂×C₈	—	10	1	no	—
335	C₂×C₈	—	10	1	no	—
336	C₂×C₈	—	10	4	no	—
337	C₂×C₈	—	20	2	no	—
338	C₂×C₈	—	20	2	no	—
339	C₂×C₈	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
340	C₂×C₈	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
341	C₂×C₈	C₄⋊AGL(1,𝔽₅)	1	2	yes	—
342	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	—
343	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	—
344	C₄⋊C₄	—	10	2	no	—
345	C₄⋊C₄	—	10	2	no	—
346	C₄⋊C₄	—	10	4	no	—
347	C₄⋊C₄	—	20	2	no	—
348	C₂²⋊C₄	—	10	2	no	—
349	C₂²⋊C₄	—	10	2	no	—
350	C₂²⋊C₄	—	10	4	no	—
351	C₂²⋊C₄	—	20	2	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	5	2	no	—
354	C₄²	—	10	4	no	—
355	C₄²	—	10	1	no	—
356	C₄²	—	20	2	no	—
357	C₄²	C₂²×AGL(1,𝔽₅)	1	2	yes	—
358	C₂×C₅	—	2	1	no	—
359	C₂×C₅	—	2	1	no	—
360	C₂×C₅	#1833	1	2	yes	complemented
361	C₂×C₅	C₂×#382	1	1	yes	characteristic
362	D₅	—	2	1	no	—
363	D₅	—	2	1	no	—
364	D₅	—	2	1	no	—
365	D₅	—	2	1	no	—
366	C₂³	—	5	1	no	—
367	C₂³	—	5	1	no	—
368	C₂³	—	5	1	no	—
369	C₂³	—	5	1	no	—
370	C₂³	—	5	1	no	—
371	C₂³	—	5	1	no	—
372	C₂³	—	20	2	no	—
373	C₂³	#4130	1	1	yes	characteristic
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	5	1	no	—
377	C₂×C₄	—	5	1	no	—
378	C₂×C₄	—	5	1	no	—
379	C₂×C₄	—	5	1	no	—
380	C₂×C₄	—	5	1	no	—
381	C₂×C₄	—	5	1	no	—
382	C₂×C₄	—	5	1	no	—
383	C₂×C₄	—	5	1	no	—
384	C₂×C₄	—	5	1	no	—
385	C₂×C₄	—	5	1	no	—
386	C₂×C₄	—	5	1	no	—
387	C₂×C₄	—	5	1	no	—
388	C₂×C₄	—	5	1	no	—
389	C₂×C₄	—	5	1	no	—
390	C₂×C₄	—	5	1	no	—
391	C₂×C₄	—	5	1	no	—
392	C₂×C₄	—	5	1	no	—
393	C₂×C₄	—	5	1	no	—
394	C₂×C₄	—	5	1	no	—
395	C₂×C₄	—	5	1	no	—
396	C₂×C₄	—	5	1	no	—
397	C₂×C₄	—	5	1	no	—
398	C₂×C₄	—	10	2	no	—
399	C₂×C₄	—	20	2	no	—
400	C₂×C₄	—	20	4	no	—
401	C₂×C₄	—	40	4	no	—
402	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
403	C₂×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
404	C₂×C₄	#4130	1	1	yes	characteristic
405	C₂×C₄	#4130	1	1	yes	characteristic
406	C₂×C₄	#4130	1	1	yes	characteristic
407	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	—	5	2	no	—
410	C₈	—	5	2	no	—
411	C₈	—	10	2	no	—
412	C₈	—	20	4	no	—
413	C₈	C₂×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
414	C₈	C₂×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
415	C₅	C₂×#1833	1	1	yes	characteristic, complemented, Sylow
416	C₂²	—	2	2	no	—
417	C₂²	—	5	1	no	—
418	C₂²	—	5	1	no	—
419	C₂²	—	5	1	no	—
420	C₂²	—	5	1	no	—
421	C₂²	—	10	2	no	—
422	C₂²	—	10	2	no	—
423	C₂²	—	20	1	no	—
424	C₂²	—	20	1	no	—
425	C₂²	—	20	1	no	—
426	C₂²	—	20	1	no	—
427	C₂²	#65689	1	1	yes	characteristic
428	C₂²	#65689	1	1	yes	characteristic
429	C₂²	C₂×#4130	1	1	yes	characteristic
430	C₄	—	4	2	no	—
431	C₄	—	5	1	no	—
432	C₄	—	5	1	no	—
433	C₄	—	5	1	no	—
434	C₄	—	5	1	no	—
435	C₄	—	20	2	no	—
436	C₄	—	40	4	no	—
437	C₄	#65689	1	1	yes	characteristic
438	C₄	#65689	1	1	yes	characteristic
439	C₄	C₂²×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
440	C₄	C₂×#4130	1	1	yes	characteristic
441	C₂	—	2	1	no	—
442	C₂	—	2	1	no	—
443	C₂	—	10	1	no	—
444	C₂	—	10	1	no	—
445	C₂	—	10	1	no	—
446	C₂	—	10	1	no	—
447	C₂	#10603886	1	2	yes	direct product factor
448	C₂	C₂×#65689	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#4130
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
Fitting	C₂×C₅×#97	C₄
socle	C₂²×C₅	#382
prime radical	C₂³×D₅	#41
cosocle	C₂×C₄×D₅	C₂⁴
hypercenter	C₂×#97	AGL(1,𝔽₅)
hypocenter	C₅	C₂×#1833
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
6. #10603886	C₂	direct (N × H)
20. C₂×C₅×#97	C₄	semidirect
21. C₂×#3947	C₄	semidirect
22. C₂×C₈×Dic₅	C₄	semidirect
23. C₂×C₄×#168	C₄	semidirect
24. #64997	C₄	semidirect
74. C₅×#97	C₂×C₄	semidirect
75. #3947	C₂×C₄	semidirect
76. C₈×Dic₅	C₂×C₄	semidirect
77. C₄×#168	C₂×C₄	semidirect
165. C₂×#97	AGL(1,𝔽₅)	semidirect
265. #97	C₂×AGL(1,𝔽₅)	semidirect
360. C₂×C₅	#1833	semidirect
415. C₅	C₂×#1833	semidirect
447. C₂	#10603886	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×D₅⋊#108	2
C₂×#65721	2
C₂×#64997	2
C₂×#64894	2
C₂×#64863	2
#10603886	2
C₂×#1833	5

Subgroups — C2×#10603886 #13034546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10603886 #13034546