Subgroups — #12068587

Order 1280.

616 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10610746	C₂	1	2	yes	maximal
2	C₈×#709	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#334	C₂	1	1	yes	maximal, characteristic, complemented
4	#10601216	C₂	1	2	yes	maximal, complemented
5	#10600525	C₂	1	1	yes	maximal, characteristic, complemented
6	#10599328	C₂	1	2	yes	maximal, complemented
7	#10599327	C₂	1	2	yes	maximal, complemented
8	#10599323	C₂	1	1	yes	maximal, characteristic, complemented
9	#10599322	C₂	1	1	yes	maximal, characteristic, complemented
10	#10599320	C₂	1	1	yes	maximal, characteristic, complemented
11	D₅×#334	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#709	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
15	#65400	—	2	2	no	—
16	C₈×C₂²⋊D₅	—	2	2	no	—
17	C₈×C₂²⋊D₅	C₄	1	1	yes	characteristic
18	C₈×C₂²⋊D₅	C₄	1	1	yes	characteristic
19	C₈×C₂²⋊D₅	C₄	1	1	yes	characteristic
20	C₈×C₂²⋊D₅	C₄	1	1	yes	characteristic
21	#65215	C₂²	1	2	yes	—
22	#65214	C₂²	1	1	yes	characteristic
23	#65126	C₂²	1	2	yes	—
24	#65125	—	2	2	no	—
25	#65124	C₂²	1	2	yes	—
26	#65122	C₂²	1	2	yes	—
27	D₅×C₄⋊C₈	C₂²	1	2	yes	—
28	#65117	—	2	2	no	—
29	C₈×D₂₀	C₄	1	1	yes	characteristic
30	C₈×D₂₀	C₄	1	1	yes	characteristic
31	#64974	C₂²	1	1	yes	characteristic
32	#64974	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
35	C₈×Dic₁₀	C₄	1	1	yes	characteristic
36	C₈×Dic₁₀	C₄	1	1	yes	characteristic
37	C₅×#334	C₂²	1	1	yes	characteristic
38	C₅×#334	C₂²	1	1	yes	characteristic
39	C₅×#334	C₂²	1	2	yes	—
40	#64700	C₂²	1	2	yes	—
41	#64700	C₂²	1	2	yes	—
42	#64699	C₂²	1	2	yes	—
43	#64699	C₂²	1	2	yes	—
44	#64678	C₂²	1	2	yes	—
45	#64677	C₂²	1	1	yes	characteristic
46	#64677	C₂²	1	1	yes	characteristic
47	#17834	—	5	1	no	maximal, Sylow
48	C₂×#709	Q₈	1	1	yes	characteristic
49	C₂²×C₅×C₈	—	2	2	no	—
50	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
53	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
54	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
55	C₄×C₂²⋊D₅	D₄	1	1	yes	characteristic
56	C₄×C₂²⋊D₅	D₄	1	1	yes	characteristic
57	#4072	Q₈	1	1	yes	characteristic
58	C₂×#676	—	2	2	no	—
59	C₂×C₈×D₅	—	2	2	no	—
60	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
64	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
65	C₄×D₂₀	D₄	1	1	yes	characteristic
66	#4018	Q₈	1	1	yes	characteristic
67	#4018	Q₈	1	1	yes	characteristic
68	C₄²×D₅	C₂³	1	1	yes	characteristic
69	C₄²×D₅	C₂³	1	1	yes	characteristic
70	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
71	C₄×Dic₁₀	D₄	1	1	yes	characteristic
72	C₅×C₄⋊C₈	—	2	2	no	—
73	C₅×C₄⋊C₈	C₂³	1	2	yes	—
74	C₅×C₄⋊C₈	C₂³	1	2	yes	—
75	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
76	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
77	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₂²⋊#168	—	2	2	no	—
80	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
81	C₂²⋊#168	C₂×C₄	1	1	yes	characteristic
82	#3952	—	2	2	no	—
83	#3952	—	2	2	no	—
84	#3952	C₂×C₄	1	1	yes	characteristic
85	#3952	C₂×C₄	1	1	yes	characteristic
86	#3952	C₂×C₄	1	1	yes	characteristic
87	#3952	C₂×C₄	1	1	yes	characteristic
88	#3947	—	2	2	no	—
89	#3946	—	2	2	no	—
90	#3946	—	2	2	no	—
91	#3946	C₂×C₄	1	1	yes	characteristic
92	#3946	C₂×C₄	1	1	yes	characteristic
93	#3946	C₂×C₄	1	1	yes	characteristic
94	#3946	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₅	—	2	2	no	—
96	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
98	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
100	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
101	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
102	C₄⋊#168	C₂³	1	2	yes	—
103	C₄⋊#168	C₂³	1	2	yes	—
104	#3935	—	2	2	no	—
105	C₄×#168	C₂³	1	1	yes	characteristic
106	C₄×#168	C₂³	1	1	yes	characteristic
107	#2990	—	5	2	no	—
108	C₈×#41	—	5	1	no	—
109	#1574	—	5	2	no	—
110	#1573	—	5	2	no	—
111	#1573	—	5	2	no	—
112	#1568	—	5	1	no	—
113	#1568	—	5	1	no	—
114	#1566	—	5	1	no	—
115	#1564	—	5	1	no	—
116	C₂×#334	—	5	1	no	—
117	C₂×#334	D₅	1	1	yes	characteristic, complemented
118	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
121	C₂×C₂²⋊D₅	C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₂²⋊D₅	C₄⋊C₄	1	1	yes	characteristic
123	#709	—	2	4	no	—
124	C₂×D₂₀	C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
128	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
130	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
131	C₂×Dic₁₀	C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	—	4	1	no	—
136	C₂×C₅×C₈	—	8	2	no	—
137	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
141	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
142	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
144	C₄²×C₅	C₂⁴	1	1	yes	characteristic
145	C₂²⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
146	C₂²⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
147	#685	C₄⋊C₄	1	1	yes	characteristic
148	#685	C₄⋊C₄	1	1	yes	characteristic
149	#685	C₄⋊C₄	1	1	yes	characteristic
150	#685	C₄⋊C₄	1	1	yes	characteristic
151	C₄⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
152	C₄⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
153	#683	C₄⋊C₄	1	1	yes	characteristic
154	#683	C₄⋊C₄	1	1	yes	characteristic
155	#683	C₄⋊C₄	1	1	yes	characteristic
156	#683	C₄⋊C₄	1	1	yes	characteristic
157	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
158	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
159	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
160	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
161	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
162	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
163	C₂×#168	—	2	2	no	—
164	C₂×#168	—	2	2	no	—
165	C₂×#168	C₂²×C₄	1	1	yes	characteristic
166	C₂×#168	C₂²×C₄	1	1	yes	characteristic
167	C₂×#168	C₂²×C₄	1	1	yes	characteristic
168	C₂×#168	C₂²×C₄	1	1	yes	characteristic
169	#676	—	8	2	no	—
170	C₈×D₅	—	2	2	no	—
171	C₈×D₅	—	2	2	no	—
172	C₈×D₅	—	4	1	no	—
173	C₈×D₅	—	4	1	no	—
174	C₈×D₅	—	8	2	no	—
175	C₄×#41	—	5	1	no	—
176	#446	—	10	2	no	—
177	C₈×Q₈	—	5	1	no	—
178	C₈×Q₈	—	5	1	no	—
179	#435	—	10	2	no	—
180	#435	—	10	2	no	—
181	C₈×D₄	—	5	1	no	—
182	C₈×D₄	—	5	1	no	—
183	C₈×D₄	—	5	1	no	—
184	C₈×D₄	—	5	1	no	—
185	C₈×D₄	—	5	1	no	—
186	C₈×D₄	—	5	1	no	—
187	C₈×D₄	—	10	2	no	—
188	#432	—	5	2	no	—
189	#432	—	5	2	no	—
190	#431	—	5	1	no	—
191	#431	—	5	1	no	—
192	#431	—	5	1	no	—
193	#431	—	5	2	no	—
194	#423	—	5	2	no	—
195	C₂×C₄⋊C₈	—	5	2	no	—
196	C₂×C₄⋊C₈	C₂×D₅	1	2	yes	—
197	C₂×C₄×C₈	—	5	1	no	—
198	C₂×C₄×C₈	—	5	1	no	—
199	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
200	#335	—	5	2	no	—
201	#335	—	5	2	no	—
202	#335	—	5	2	no	—
203	#334	—	5	2	no	—
204	#334	—	5	2	no	—
205	#334	—	5	1	no	—
206	#334	—	5	1	no	—
207	#334	C₂×D₅	1	1	yes	characteristic
208	#334	C₂×D₅	1	1	yes	characteristic
209	#334	C₂×D₅	1	2	yes	—
210	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
211	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
212	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
223	C₂²⋊D₅	—	2	2	no	—
224	C₂²⋊D₅	#108	1	4	yes	—
225	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
226	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
227	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
230	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
231	D₂₀	—	2	2	no	—
232	C₄×D₅	—	2	2	no	—
233	C₄×D₅	—	2	1	no	—
234	C₄×D₅	—	2	1	no	—
235	C₄×D₅	—	2	1	no	—
236	C₄×D₅	—	2	1	no	—
237	C₄×D₅	—	2	2	no	—
238	C₄×D₅	—	2	2	no	—
239	C₄×D₅	—	2	2	no	—
240	Dic₁₀	—	2	2	no	—
241	C₅×C₈	—	2	1	no	—
242	C₅×C₈	—	2	1	no	—
243	C₅×C₈	—	2	1	no	—
244	C₅×C₈	—	4	2	no	—
245	C₅×C₈	—	4	2	no	—
246	C₅×C₈	#131	1	2	yes	—
247	#168	—	2	1	no	—
248	#168	—	2	1	no	—
249	#168	—	2	1	no	—
250	#168	—	2	1	no	—
251	#168	—	4	2	no	—
252	#168	—	4	2	no	—
253	C₂×#41	—	5	1	no	—
254	C₂×M₁₆	—	10	2	no	—
255	C₂²×C₈	—	2	2	no	—
256	C₂²×C₈	—	5	1	no	—
257	C₂²×C₈	—	5	1	no	—
258	C₂²×C₈	—	5	1	no	—
259	C₂²×C₈	—	5	1	no	—
260	C₂²×C₈	—	10	2	no	—
261	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
262	C₂²×C₈	C₄×D₅	1	1	yes	characteristic
263	C₄×Q₈	—	5	1	no	—
264	C₄×Q₈	—	5	1	no	—
265	C₄×D₄	—	5	1	no	—
266	C₄×D₄	—	5	1	no	—
267	C₄×D₄	—	5	1	no	—
268	C₄×D₄	—	5	1	no	—
269	C₄×D₄	—	5	1	no	—
270	C₄×D₄	—	5	1	no	—
271	#117	—	5	1	no	—
272	#117	—	5	1	no	—
273	#117	—	5	1	no	—
274	C₂×C₄²	—	5	1	no	—
275	C₂×C₄²	—	5	1	no	—
276	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	—	5	1	no	—
279	C₄⋊C₈	—	5	1	no	—
280	C₄⋊C₈	—	5	1	no	—
281	C₄⋊C₈	—	5	1	no	—
282	C₄⋊C₈	—	5	1	no	—
283	C₄⋊C₈	—	5	1	no	—
284	C₄⋊C₈	—	5	2	no	—
285	C₄⋊C₈	—	5	2	no	—
286	C₄⋊C₈	—	10	2	no	—
287	C₄⋊C₈	—	10	2	no	—
288	C₄⋊C₈	C₂²×D₅	1	2	yes	—
289	C₄⋊C₈	C₂²×D₅	1	2	yes	—
290	C₂²⋊C₈	—	5	1	no	—
291	C₂²⋊C₈	—	5	1	no	—
292	C₂²⋊C₈	—	5	1	no	—
293	C₂²⋊C₈	—	5	1	no	—
294	C₂²⋊C₈	—	5	1	no	—
295	C₂²⋊C₈	—	5	1	no	—
296	C₂²⋊C₈	—	10	2	no	—
297	C₂²⋊C₈	—	10	2	no	—
298	C₂²⋊C₈	—	10	2	no	—
299	#97	—	10	2	no	—
300	#97	—	10	2	no	—
301	C₄×C₈	—	5	1	no	—
302	C₄×C₈	—	5	1	no	—
303	C₄×C₈	—	5	1	no	—
304	C₄×C₈	—	5	1	no	—
305	C₄×C₈	—	5	1	no	—
306	C₄×C₈	—	5	1	no	—
307	C₄×C₈	—	10	2	no	—
308	C₄×C₈	C₄×D₅	1	1	yes	characteristic
309	C₄×C₈	C₄×D₅	1	1	yes	characteristic
310	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
311	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
312	C₂²×C₅	—	2	1	no	—
313	C₂²×C₅	—	2	1	no	—
314	C₂²×C₅	C₂×#108	1	2	yes	—
315	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
316	C₂×D₅	—	2	1	no	—
317	C₂×D₅	—	2	1	no	—
318	C₂×D₅	—	2	1	no	—
319	C₂×D₅	—	2	1	no	—
320	C₂×D₅	—	2	1	no	—
321	C₂×D₅	C₂×#108	1	2	yes	—
322	C₄×C₅	—	2	1	no	—
323	C₄×C₅	—	2	1	no	—
324	C₄×C₅	—	2	1	no	—
325	C₄×C₅	—	2	1	no	—
326	C₄×C₅	C₂×#131	1	1	yes	characteristic
327	C₄×C₅	#568	1	1	yes	characteristic
328	C₄×C₅	#577	1	2	yes	—
329	Dic₅	—	2	1	no	—
330	Dic₅	—	2	1	no	—
331	Dic₅	—	2	1	no	—
332	Dic₅	—	2	1	no	—
333	Dic₅	—	2	1	no	—
334	Dic₅	C₂×#108	1	2	yes	—
335	#41	—	10	4	no	—
336	C₂×Q₈	—	5	1	no	—
337	C₂×D₄	—	5	1	no	—
338	C₂×D₄	—	5	1	no	—
339	C₂×D₄	—	5	1	no	—
340	C₂²×C₄	—	5	1	no	—
341	C₂²×C₄	—	5	1	no	—
342	C₂²×C₄	—	5	1	no	—
343	C₂²×C₄	—	5	1	no	—
344	C₂²×C₄	—	5	1	no	—
345	C₂²×C₄	—	5	1	no	—
346	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
347	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
348	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
349	M₁₆	—	40	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	4	1	no	—
354	C₂×C₈	—	5	1	no	—
355	C₂×C₈	—	5	1	no	—
356	C₂×C₈	—	5	1	no	—
357	C₂×C₈	—	5	1	no	—
358	C₂×C₈	—	8	2	no	—
359	C₂×C₈	—	10	2	no	—
360	C₂×C₈	—	10	2	no	—
361	C₂×C₈	—	10	2	no	—
362	C₂×C₈	—	10	2	no	—
363	C₂×C₈	—	20	1	no	—
364	C₂×C₈	—	20	1	no	—
365	C₂×C₈	—	40	2	no	—
366	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
367	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
368	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
369	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
370	C₄⋊C₄	—	5	1	no	—
371	C₄⋊C₄	—	5	1	no	—
372	C₄⋊C₄	—	5	1	no	—
373	C₄⋊C₄	—	5	1	no	—
374	C₄⋊C₄	—	5	1	no	—
375	C₄⋊C₄	—	5	1	no	—
376	C₂²⋊C₄	—	5	1	no	—
377	C₂²⋊C₄	—	5	1	no	—
378	C₂²⋊C₄	—	5	1	no	—
379	C₂²⋊C₄	—	5	1	no	—
380	C₂²⋊C₄	—	5	1	no	—
381	C₂²⋊C₄	—	5	1	no	—
382	C₄²	—	5	1	no	—
383	C₄²	—	5	1	no	—
384	C₄²	—	5	1	no	—
385	C₄²	—	5	1	no	—
386	C₄²	—	5	1	no	—
387	C₄²	—	5	1	no	—
388	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
389	C₄²	D₄×D₅	1	1	yes	characteristic
390	C₄²	Q₈×D₅	1	1	yes	characteristic
391	C₄²	C₂³×D₅	1	1	yes	characteristic
392	C₂×C₅	—	2	2	no	—
393	C₂×C₅	#2906	1	1	yes	characteristic
394	C₂×C₅	#2912	1	1	yes	characteristic
395	C₂×C₅	C₂²×#108	1	1	yes	characteristic
396	D₅	—	2	2	no	—
397	D₅	—	4	1	no	—
398	C₂³	—	5	1	no	—
399	C₂³	—	5	1	no	—
400	C₂³	D₅×C₄⋊C₄	1	1	yes	characteristic
401	Q₈	—	10	2	no	—
402	D₄	—	5	4	no	—
403	D₄	—	10	2	no	—
404	D₄	—	10	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	5	1	no	—
410	C₂×C₄	—	5	1	no	—
411	C₂×C₄	—	5	1	no	—
412	C₂×C₄	—	5	1	no	—
413	C₂×C₄	—	5	1	no	—
414	C₂×C₄	—	5	1	no	—
415	C₂×C₄	—	10	2	no	—
416	C₂×C₄	—	10	2	no	—
417	C₂×C₄	—	10	1	no	—
418	C₂×C₄	—	10	1	no	—
419	C₂×C₄	—	10	1	no	—
420	C₂×C₄	—	10	1	no	—
421	C₂×C₄	—	10	2	no	—
422	C₂×C₄	—	10	2	no	—
423	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
424	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
425	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
426	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
427	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
428	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
429	C₈	—	2	1	no	—
430	C₈	—	2	1	no	—
431	C₈	—	2	1	no	—
432	C₈	—	4	2	no	—
433	C₈	—	4	2	no	—
434	C₈	—	10	1	no	—
435	C₈	—	10	1	no	—
436	C₈	—	10	1	no	—
437	C₈	—	10	1	no	—
438	C₈	—	20	2	no	—
439	C₈	—	20	2	no	—
440	C₈	#4047	1	2	yes	—
441	C₅	#17834	1	1	yes	characteristic, complemented, Sylow
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	5	2	no	—
445	C₂²	—	10	1	no	—
446	C₂²	—	10	1	no	—
447	C₂²	—	10	1	no	—
448	C₂²	—	10	1	no	—
449	C₂²	—	10	1	no	—
450	C₂²	D₅×#108	1	2	yes	—
451	C₂²	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	5	2	no	—
457	C₄	—	10	1	no	—
458	C₄	—	10	1	no	—
459	C₄	—	10	1	no	—
460	C₄	—	10	1	no	—
461	C₄	—	10	1	no	—
462	C₄	C₂×#4047	1	1	yes	characteristic
463	C₄	#66079	1	1	yes	characteristic
464	C₄	#66096	1	2	yes	—
465	C₂	—	2	2	no	—
466	C₂	—	10	2	no	—
467	C₂	—	20	1	no	—
468	C₂	#10610743	1	1	yes	characteristic
469	C₂	#10610847	1	1	yes	characteristic
470	C₂	C₂×D₅×#108	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₂×C₅×#334	C₂
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂×#709	Q₈
cosocle	C₄²×C₅	C₂⁴
hypercenter	C₂×#334	D₅
hypocenter	C₅	#17834
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
3. C₂×C₅×#334	C₂	semidirect
4. #10601216	C₂	semidirect
5. #10600525	C₂	semidirect
6. #10599328	C₂	semidirect
7. #10599327	C₂	semidirect
8. #10599323	C₂	semidirect
9. #10599322	C₂	semidirect
10. #10599320	C₂	semidirect
11. D₅×#334	C₂	semidirect
117. C₂×#334	D₅	semidirect
441. C₅	#17834	semidirect

Maximal subgroups

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

subgroup	index
#10610746	2
C₈×#709	2
C₂×C₅×#334	2
#10601216	2
#10600525	2
#10599328	2
#10599327	2
#10599323	2
#10599322	2
#10599320	2
D₅×#334	2
#17834	5