Subgroups — C₂×#11749234 #14416375

Order 1920.

1088 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	C₂×C₅×Q₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#688	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₃×D₂₀	C₂	1	1	yes	maximal, characteristic
4	C₂×#91119	C₂	1	1	yes	maximal, characteristic, complemented
5	#11749234	C₂	1	8	yes	maximal, direct product factor
6	C₂×#90988	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#90964	C₂	1	1	yes	maximal, characteristic
8	C₂×#90953	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65315	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
12	C₂²×D₅×Dic₃	—	2	1	no	—
13	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
14	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
15	C₅×Q₈×Dic₃	—	2	2	no	—
16	C₅×Q₈×Dic₃	C₂²	1	4	yes	complemented
17	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×Dic₃	—	2	1	no	—
20	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
21	C₂×C₃×#688	C₄	1	8	yes	complemented
22	C₂×C₃×#688	C₂²	1	4	yes	—
23	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
24	C₂×#6665	—	2	1	no	—
25	Dic₃×D₂₀	—	2	2	no	—
26	Dic₃×D₂₀	C₂²	1	4	yes	—
27	#91119	C₂²	1	4	yes	complemented
28	#90988	C₂²	1	4	yes	complemented
29	#90964	C₂²	1	4	yes	—
30	#90953	C₂²	1	4	yes	complemented
31	C₂×#5164	—	5	1	no	maximal, Hall
32	C₂×C₄×C₅×Q₈	—	3	1	no	—
33	C₂²×#688	D₃	1	1	yes	characteristic
34	C₂×C₄×D₂₀	—	3	1	no	—
35	C₂×#3967	—	3	1	no	—
36	#65315	—	3	8	no	—
37	C₂×#3941	—	3	1	no	—
38	C₂×#3939	—	3	1	no	—
39	C₂×#3935	—	3	1	no	—
40	C₂³×C₃×D₅	—	2	1	no	—
41	C₂×C₃×C₅×Q₈	—	2	1	no	—
42	C₂×C₃×C₅×Q₈	—	2	2	no	—
43	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
44	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	—	2	1	no	—
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×Dic₁₅	—	2	1	no	—
48	C₂²×C₅×Dic₃	—	2	1	no	—
49	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
50	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
51	C₂×C₃×D₂₀	—	2	1	no	—
52	C₂×C₃×D₂₀	—	2	2	no	—
53	C₂×C₃×D₂₀	C₂×C₄	1	4	yes	—
54	C₂×C₃×D₂₀	C₂³	1	2	yes	—
55	C₂×D₅×Dic₃	—	2	4	no	—
56	C₂×D₅×Dic₃	—	4	4	no	—
57	C₄⋊Dic₁₅	—	2	1	no	—
58	C₄⋊Dic₁₅	C₂³	1	2	yes	—
59	C₂×C₃⋊#168	—	2	2	no	—
60	C₂×C₃⋊#168	C₂³	1	2	yes	—
61	C₅×C₄⋊Dic₃	—	2	1	no	—
62	C₅×C₄⋊Dic₃	—	2	4	no	—
63	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
64	C₄×C₅×Dic₃	—	2	4	no	—
65	C₄×C₅×Dic₃	D₄	1	2	yes	—
66	C₄×C₅×Dic₃	C₂³	1	2	yes	—
67	C₃×#688	C₂×C₄	1	16	yes	complemented
68	C₂×C₃×#168	C₂×C₄	1	4	yes	complemented
69	C₂×C₃×#168	C₂³	1	2	yes	—
70	#6665	—	2	4	no	—
71	C₂²×C₃×SD₁₆	—	5	1	no	—
72	C₂×Q₈×Dic₃	D₅	1	1	yes	characteristic, complemented
73	C₂×D₄×Dic₃	—	5	1	no	—
74	C₂×#835	—	5	1	no	—
75	C₂×#832	—	5	1	no	—
76	#5164	—	5	8	no	—
77	C₂×#818	—	5	1	no	—
78	C₂×#815	—	5	1	no	—
79	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
80	C₂²×D₂₀	C₂×D₃	1	1	yes	characteristic
81	C₂²×C₄×D₅	—	6	1	no	—
82	C₄×C₅×Q₈	—	3	4	no	—
83	C₄×C₅×Q₈	—	6	2	no	—
84	C₂×C₅×C₄⋊C₄	—	3	1	no	—
85	C₂×C₅×C₄⋊C₄	—	6	1	no	—
86	C₂×C₄²×C₅	—	3	1	no	—
87	C₂×C₄²×C₅	—	6	1	no	—
88	C₂×#688	Dic₃	1	8	yes	complemented
89	C₂×#688	C₂×D₃	1	4	yes	—
90	C₂×#685	—	6	1	no	—
91	C₂×C₄⋊Dic₅	—	3	1	no	—
92	C₂²×#168	—	3	1	no	—
93	C₂²×#168	C₂×D₃	1	1	yes	characteristic
94	C₄×D₂₀	—	3	4	no	—
95	C₄×D₂₀	—	6	2	no	—
96	#3967	—	3	4	no	—
97	#3941	—	3	4	no	—
98	#3939	—	3	4	no	—
99	#3935	—	3	4	no	—
100	C₂×#440	—	15	1	no	Sylow
101	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₃×D₅	—	2	4	no	—
103	C₂²×C₃×D₅	—	2	2	no	—
104	C₂²×C₃×D₅	—	4	2	no	—
105	C₂²×C₃×D₅	—	4	2	no	—
106	C₃×C₅×Q₈	—	2	4	no	—
107	C₃×C₅×Q₈	—	2	2	no	—
108	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	complemented
109	C₂×C₃×C₄×C₅	—	2	4	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	#41	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
115	C₂×Dic₁₅	—	2	2	no	—
116	C₂×Dic₁₅	—	4	2	no	—
117	C₂×C₅×Dic₃	—	2	2	no	—
118	C₂×C₅×Dic₃	—	2	2	no	—
119	C₂×C₅×Dic₃	—	2	2	no	—
120	C₂×C₅×Dic₃	—	4	2	no	—
121	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
122	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
123	C₃×D₂₀	—	2	4	no	—
124	C₃×D₂₀	—	2	2	no	—
125	C₃×D₂₀	C₂²×C₄	1	4	yes	—
126	D₅×Dic₃	—	4	8	no	—
127	C₃⋊#168	—	2	2	no	—
128	C₃×#168	C₂²×C₄	1	4	yes	complemented
129	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
130	C₂²×C₃×D₄	—	5	1	no	—
131	C₂³×Dic₃	—	10	1	no	—
132	C₂×C₃×SD₁₆	—	5	8	no	—
133	C₂×C₃×SD₁₆	—	5	4	no	—
134	C₂²×C₃×C₈	—	5	1	no	—
135	C₂×#217	—	10	1	no	—
136	Q₈×Dic₃	—	2	2	no	—
137	Q₈×Dic₃	C₂×D₅	1	4	yes	complemented
138	D₄×Dic₃	—	5	4	no	—
139	D₄×Dic₃	—	10	2	no	—
140	C₂×C₄⋊Dic₃	—	2	1	no	—
141	C₂×C₄⋊Dic₃	—	5	1	no	—
142	C₂×C₄⋊Dic₃	C₂×D₅	1	1	yes	characteristic
143	C₂×C₄×Dic₃	—	2	1	no	—
144	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
145	C₂²×C₃⋊C₈	—	5	1	no	—
146	#835	—	5	4	no	—
147	#832	—	5	4	no	—
148	#818	—	5	4	no	—
149	#815	—	5	4	no	—
150	C₂³×D₅	—	2	1	no	—
151	C₂×C₅×Q₈	—	2	1	no	—
152	C₂×C₅×Q₈	—	2	2	no	—
153	C₂×C₅×Q₈	C₂×Dic₃	1	4	yes	complemented
154	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
155	C₂²×C₄×C₅	—	2	1	no	—
156	C₂²×C₄×C₅	—	3	1	no	—
157	C₂²×C₄×C₅	—	3	1	no	—
158	C₂²×C₄×C₅	—	6	1	no	—
159	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
160	C₂²×Dic₅	—	6	1	no	—
161	C₂×D₂₀	—	2	1	no	—
162	C₂×D₂₀	—	2	2	no	—
163	C₂×D₂₀	C₂×Dic₃	1	4	yes	—
164	C₂×D₂₀	C₂²×D₃	1	2	yes	—
165	C₂×C₄×D₅	—	6	4	no	—
166	C₂×C₄×D₅	—	12	4	no	—
167	C₅×C₄⋊C₄	—	3	2	no	—
168	C₅×C₄⋊C₄	—	6	4	no	—
169	C₅×C₄⋊C₄	—	6	1	no	—
170	C₄²×C₅	—	3	2	no	—
171	C₄²×C₅	—	3	2	no	—
172	C₄²×C₅	—	6	4	no	—
173	#688	C₂×Dic₃	1	16	yes	complemented
174	#685	—	6	4	no	—
175	C₄⋊Dic₅	—	3	2	no	—
176	C₄⋊Dic₅	—	6	1	no	—
177	C₂×#168	—	3	2	no	—
178	C₂×#168	—	6	2	no	—
179	C₂×#168	C₂×Dic₃	1	4	yes	complemented
180	C₂×#168	C₂²×D₃	1	2	yes	—
181	C₂²×SD₁₆	—	5	1	no	—
182	C₂×C₄×Q₈	—	3	1	no	—
183	C₂×C₄×D₄	—	15	1	no	—
184	#440	—	15	8	no	—
185	C₂×#107	—	15	1	no	—
186	C₂×#103	—	15	1	no	—
187	C₂×#102	—	15	1	no	—
188	C₂×#97	—	15	1	no	—
189	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
190	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
191	C₂²×C₃×C₅	#137	1	2	yes	—
192	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₃×D₅	—	2	4	no	—
194	C₂×C₃×D₅	—	4	2	no	—
195	C₂×C₃×D₅	—	4	2	no	—
196	C₂×C₃×D₅	—	4	8	no	—
197	C₃×C₄×C₅	—	2	4	no	—
198	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
199	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
200	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
201	Dic₁₅	—	4	2	no	—
202	C₅×Dic₃	—	2	2	no	—
203	C₅×Dic₃	—	2	2	no	—
204	C₅×Dic₃	—	4	2	no	—
205	C₂⁴×C₃	—	10	1	no	—
206	C₂×C₃×Q₈	—	2	2	no	—
207	C₂×C₃×Q₈	—	2	1	no	—
208	C₂×C₃×Q₈	C₄×D₅	1	4	yes	complemented
209	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
210	C₂×C₃×D₄	—	5	4	no	—
211	C₂×C₃×D₄	—	5	2	no	—
212	C₂×C₃×D₄	—	10	2	no	—
213	C₂×C₃×D₄	—	10	1	no	—
214	C₂²×C₃×C₄	—	2	1	no	—
215	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
216	C₂²×Dic₃	—	2	1	no	—
217	C₂²×Dic₃	—	10	1	no	—
218	C₂²×Dic₃	—	10	4	no	—
219	C₂²×Dic₃	—	20	4	no	—
220	C₂²×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
221	C₂²×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
222	C₃×SD₁₆	—	5	16	no	—
223	C₂×C₃×C₈	—	5	4	no	—
224	C₂×C₃×C₈	—	5	2	no	—
225	#217	—	10	4	no	—
226	C₄⋊Dic₃	—	2	1	no	—
227	C₄⋊Dic₃	—	2	4	no	—
228	C₄⋊Dic₃	—	5	2	no	—
229	C₄⋊Dic₃	—	10	1	no	—
230	C₄⋊Dic₃	C₂²×D₅	1	2	yes	—
231	C₄×Dic₃	—	2	4	no	—
232	C₄×Dic₃	C₂²⋊D₅	1	2	yes	—
233	C₄×Dic₃	C₂²×D₅	1	2	yes	—
234	C₂×C₃⋊C₈	—	5	2	no	—
235	C₂×C₃⋊C₈	—	10	2	no	—
236	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
237	C₂²×D₅	—	2	4	no	—
238	C₂²×D₅	—	2	2	no	—
239	C₂²×D₅	—	4	2	no	—
240	C₂²×D₅	—	4	2	no	—
241	C₅×Q₈	—	2	4	no	—
242	C₅×Q₈	—	2	2	no	—
243	C₅×Q₈	C₂²×Dic₃	1	4	yes	complemented
244	C₂×C₄×C₅	—	2	4	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	3	2	no	—
247	C₂×C₄×C₅	—	3	2	no	—
248	C₂×C₄×C₅	—	6	2	no	—
249	C₂×C₄×C₅	—	6	2	no	—
250	C₂×C₄×C₅	—	6	2	no	—
251	C₂×C₄×C₅	—	12	2	no	—
252	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
253	C₂×C₄×C₅	#237	1	2	yes	—
254	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
255	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
256	C₂×Dic₅	—	6	2	no	—
257	C₂×Dic₅	—	12	2	no	—
258	D₂₀	—	2	4	no	—
259	D₂₀	—	2	2	no	—
260	D₂₀	C₂²×Dic₃	1	4	yes	—
261	C₄×D₅	—	12	8	no	—
262	#168	—	6	2	no	—
263	#168	C₂²×Dic₃	1	4	yes	complemented
264	C₂²×Q₈	D₃×D₅	1	1	yes	characteristic
265	C₂²×D₄	—	5	1	no	—
266	C₂³×C₄	—	30	1	no	—
267	C₂×SD₁₆	—	5	8	no	—
268	C₂×SD₁₆	—	5	4	no	—
269	C₂²×C₈	—	5	1	no	—
270	C₂²×C₈	—	15	1	no	—
271	C₄×Q₈	—	3	4	no	—
272	C₄×Q₈	—	6	2	no	—
273	C₄×D₄	—	15	4	no	—
274	C₄×D₄	—	30	2	no	—
275	C₂×C₄⋊C₄	—	3	1	no	—
276	C₂×C₄⋊C₄	—	6	1	no	—
277	C₂×C₄⋊C₄	—	15	1	no	—
278	C₂×C₂²⋊C₄	—	30	1	no	—
279	C₂×C₄²	—	3	1	no	—
280	C₂×C₄²	—	6	1	no	—
281	#107	—	15	4	no	—
282	#103	—	15	4	no	—
283	#102	—	15	4	no	—
284	#97	—	15	4	no	—
285	C₂×C₃×C₅	#440	1	4	yes	complemented
286	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
287	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
288	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
289	C₃×D₅	—	4	4	no	—
290	C₂³×C₃	—	10	2	no	—
291	C₂³×C₃	—	10	4	no	—
292	C₂³×C₃	—	20	2	no	—
293	C₂³×C₃	—	20	2	no	—
294	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
295	C₃×Q₈	—	2	2	no	—
296	C₃×Q₈	—	2	4	no	—
297	C₃×Q₈	C₂×C₄×D₅	1	4	yes	complemented
298	C₃×D₄	—	5	4	no	—
299	C₃×D₄	—	10	2	no	—
300	C₃×D₄	—	10	4	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	2	4	no	—
303	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
304	C₂×C₃×C₄	#709	1	2	yes	—
305	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
306	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
307	C₂×Dic₃	—	2	2	no	—
308	C₂×Dic₃	—	2	2	no	—
309	C₂×Dic₃	—	2	2	no	—
310	C₂×Dic₃	—	4	2	no	—
311	C₂×Dic₃	—	10	2	no	—
312	C₂×Dic₃	—	20	8	no	—
313	C₂×Dic₃	—	20	2	no	—
314	C₂×Dic₃	C₂×C₂²⋊D₅	1	2	yes	—
315	C₂×Dic₃	C₂×C₂²⋊D₅	1	2	yes	—
316	C₃×C₈	—	5	4	no	—
317	C₃⋊C₈	—	10	2	no	—
318	C₂²×C₅	#914	1	2	yes	—
319	C₂²×C₅	#915	1	2	yes	—
320	C₂²×C₅	D₄×Dic₃	1	2	yes	—
321	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
322	C₂×D₅	—	2	4	no	—
323	C₂×D₅	—	4	8	no	—
324	C₂×D₅	—	4	2	no	—
325	C₂×D₅	—	4	2	no	—
326	C₄×C₅	—	2	4	no	—
327	C₄×C₅	—	6	2	no	—
328	C₄×C₅	—	6	2	no	—
329	C₄×C₅	—	12	2	no	—
330	C₄×C₅	D₄×Dic₃	1	2	yes	—
331	C₄×C₅	C₂×#237	1	1	yes	characteristic
332	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
333	Dic₅	—	12	2	no	—
334	C₂⁴	—	10	1	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	D₅×Dic₃	1	4	yes	complemented
338	C₂×Q₈	C₂×D₃×D₅	1	2	yes	—
339	C₂×D₄	—	5	4	no	—
340	C₂×D₄	—	5	2	no	—
341	C₂×D₄	—	10	2	no	—
342	C₂×D₄	—	10	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	3	1	no	—
345	C₂²×C₄	—	3	1	no	—
346	C₂²×C₄	—	6	1	no	—
347	C₂²×C₄	—	30	4	no	—
348	C₂²×C₄	—	30	1	no	—
349	C₂²×C₄	—	60	4	no	—
350	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
351	SD₁₆	—	5	16	no	—
352	C₂×C₈	—	5	4	no	—
353	C₂×C₈	—	5	2	no	—
354	C₂×C₈	—	15	2	no	—
355	C₂×C₈	—	30	2	no	—
356	C₄⋊C₄	—	3	2	no	—
357	C₄⋊C₄	—	6	4	no	—
358	C₄⋊C₄	—	6	1	no	—
359	C₄⋊C₄	—	15	2	no	—
360	C₄⋊C₄	—	30	1	no	—
361	C₂²⋊C₄	—	30	4	no	—
362	C₄²	—	3	2	no	—
363	C₄²	—	3	2	no	—
364	C₄²	—	6	4	no	—
365	C₃×C₅	C₂×#440	1	1	yes	characteristic, complemented, Hall
366	C₂²×C₃	—	10	4	no	—
367	C₂²×C₃	—	20	8	no	—
368	C₂²×C₃	—	20	2	no	—
369	C₂²×C₃	—	20	2	no	—
370	C₂²×C₃	C₄×C₂²⋊D₅	1	2	yes	—
371	C₂²×C₃	#4088	1	2	yes	—
372	C₂²×C₃	#4095	1	2	yes	—
373	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
374	C₃×C₄	—	2	4	no	—
375	C₃×C₄	C₄×C₂²⋊D₅	1	2	yes	—
376	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
377	C₃×C₄	C₂×#709	1	1	yes	characteristic
378	Dic₃	—	2	2	no	—
379	Dic₃	—	2	2	no	—
380	Dic₃	—	4	2	no	—
381	Dic₃	—	20	2	no	—
382	C₂×C₅	#5164	1	4	yes	complemented
383	C₂×C₅	C₂×#914	1	1	yes	characteristic
384	C₂×C₅	C₂×#915	1	1	yes	characteristic
385	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
386	D₅	—	4	4	no	—
387	C₂³	—	10	2	no	—
388	C₂³	—	10	4	no	—
389	C₂³	—	20	2	no	—
390	C₂³	—	20	2	no	—
391	C₂³	D₃×C₂²⋊D₅	1	1	yes	characteristic
392	Q₈	—	2	2	no	—
393	Q₈	—	2	4	no	—
394	Q₈	C₂×D₅×Dic₃	1	4	yes	complemented
395	D₄	—	5	4	no	—
396	D₄	—	10	2	no	—
397	D₄	—	10	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	3	2	no	—
401	C₂×C₄	—	3	2	no	—
402	C₂×C₄	—	6	2	no	—
403	C₂×C₄	—	6	2	no	—
404	C₂×C₄	—	6	2	no	—
405	C₂×C₄	—	12	2	no	—
406	C₂×C₄	—	30	2	no	—
407	C₂×C₄	—	60	8	no	—
408	C₂×C₄	—	60	2	no	—
409	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
410	C₂×C₄	#6779	1	2	yes	—
411	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
413	C₈	—	5	4	no	—
414	C₈	—	30	2	no	—
415	C₂×C₃	—	20	4	no	—
416	C₂×C₃	#65315	1	4	yes	complemented
417	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
418	C₂×C₃	C₂×#4088	1	1	yes	characteristic
419	C₂×C₃	C₂×#4095	1	1	yes	characteristic
420	C₅	C₂×#5164	1	1	yes	characteristic, complemented, Sylow
421	C₂²	—	10	4	no	—
422	C₂²	—	20	2	no	—
423	C₂²	—	20	2	no	—
424	C₂²	—	20	8	no	—
425	C₂²	#91504	1	2	yes	—
426	C₂²	#91518	1	2	yes	—
427	C₂²	Dic₃×C₂²⋊D₅	1	2	yes	—
428	C₂²	C₂×D₃×C₂²⋊D₅	1	1	yes	characteristic
429	C₄	—	2	4	no	—
430	C₄	—	6	2	no	—
431	C₄	—	6	2	no	—
432	C₄	—	12	2	no	—
433	C₄	—	60	2	no	—
434	C₄	Dic₃×C₂²⋊D₅	1	2	yes	—
435	C₄	C₂²×D₅×Dic₃	1	1	yes	characteristic
436	C₄	C₂×#6779	1	1	yes	characteristic
437	C₃	C₂×#65315	1	1	yes	characteristic, complemented, Sylow
438	C₂	—	20	4	no	—
439	C₂	#11749234	1	4	yes	direct product factor
440	C₂	C₂×#91504	1	1	yes	characteristic
441	C₂	C₂×#91518	1	1	yes	characteristic
442	C₂	C₂×Dic₃×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₃×C₂²⋊D₅
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂²×C₃×C₅×Q₈	C₂²
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×D₂₀	C₂²
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂²×Q₈	D₃×D₅
hypocenter	C₃×C₅	C₂×#440
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×Q₈×Dic₃	C₂	semidirect
4. C₂×#91119	C₂	semidirect
5. #11749234	C₂	direct (N × H)
6. C₂×#90988	C₂	semidirect
8. C₂×#90953	C₂	semidirect
16. C₅×Q₈×Dic₃	C₂²	semidirect
21. C₂×C₃×#688	C₄	semidirect
27. #91119	C₂²	semidirect
28. #90988	C₂²	semidirect
30. #90953	C₂²	semidirect
43. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
67. C₃×#688	C₂×C₄	semidirect
68. C₂×C₃×#168	C₂×C₄	semidirect
72. C₂×Q₈×Dic₃	D₅	semidirect
88. C₂×#688	Dic₃	semidirect
108. C₃×C₅×Q₈	C₂²×C₄	semidirect
128. C₃×#168	C₂²×C₄	semidirect
137. Q₈×Dic₃	C₂×D₅	semidirect
153. C₂×C₅×Q₈	C₂×Dic₃	semidirect
173. #688	C₂×Dic₃	semidirect
179. C₂×#168	C₂×Dic₃	semidirect
208. C₂×C₃×Q₈	C₄×D₅	semidirect
243. C₅×Q₈	C₂²×Dic₃	semidirect
263. #168	C₂²×Dic₃	semidirect
285. C₂×C₃×C₅	#440	semidirect
297. C₃×Q₈	C₂×C₄×D₅	semidirect
337. C₂×Q₈	D₅×Dic₃	semidirect
365. C₃×C₅	C₂×#440	semidirect
382. C₂×C₅	#5164	semidirect
394. Q₈	C₂×D₅×Dic₃	semidirect
416. C₂×C₃	#65315	semidirect
420. C₅	C₂×#5164	semidirect
437. C₃	C₂×#65315	semidirect
439. C₂	#11749234	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×C₅×Q₈×Dic₃	2
C₂²×C₃×#688	2
C₂×Dic₃×D₂₀	2
C₂×#91119	2
#11749234	2
C₂×#90988	2
C₂×#90964	2
C₂×#90953	2
C₂×#65315	3
C₂×#5164	5

Subgroups — C2×#11749234 #14416375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11749234 #14416375