Subgroups — C₂×#11750982 #14413345

Order 1920.

1072 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6705	C₂	1	1	yes	maximal, characteristic
2	C₂×#91781	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊C₄×D₁₅	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#91101	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#91092	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#91091	C₂	1	1	yes	maximal, characteristic, complemented
8	#11750982	C₂	1	8	yes	maximal, direct product factor
9	C₂×#65170	—	3	1	no	maximal, Hall
10	C₂²×C₄×D₁₅	—	2	1	no	—
11	C₂²×C₄×D₁₅	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×#6714	—	2	1	no	—
16	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Dic₁₅	C₂²	1	1	yes	characteristic
18	C₂×#6712	—	2	1	no	—
19	C₂×C₄×Dic₁₅	—	2	1	no	—
20	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
21	C₂×#6705	C₄	1	8	yes	complemented
22	C₂×#6705	C₂²	1	4	yes	—
23	#91781	—	2	2	no	—
24	#91781	C₂²	1	4	yes	—
25	C₄⋊C₄×D₁₅	—	2	2	no	—
26	C₄⋊C₄×D₁₅	C₂²	1	4	yes	—
27	C₃×C₅×#107	C₂²	1	4	yes	complemented
28	#91101	C₂²	1	4	yes	complemented
29	#91092	C₂²	1	4	yes	complemented
30	#91091	C₂²	1	4	yes	complemented
31	C₂×#4881	—	5	1	no	maximal, Hall
32	C₂²×#676	—	3	1	no	—
33	C₂×#4038	—	3	1	no	—
34	C₂×D₅×C₄⋊C₄	—	3	1	no	—
35	C₂×C₅×#107	D₃	1	1	yes	characteristic, complemented
36	C₂×#3949	—	3	1	no	—
37	C₂×#3940	—	3	1	no	—
38	C₂×#3939	—	3	1	no	—
39	#65170	—	3	8	no	—
40	C₂³×D₁₅	D₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂²×C₃×C₄×C₅	—	2	1	no	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×Dic₁₅	—	2	1	no	—
45	C₂²×Dic₁₅	—	2	1	no	—
46	C₂²×Dic₁₅	D₄	1	1	yes	characteristic
47	C₂×C₄×D₁₅	—	2	4	no	—
48	C₂×C₄×D₁₅	—	4	4	no	—
49	C₂×C₄×D₁₅	C₂×C₄	1	4	yes	—
50	C₂×C₄×D₁₅	D₄	1	2	yes	—
51	C₂×C₄×D₁₅	Q₈	1	4	yes	—
52	C₂×C₄×D₁₅	C₂³	1	2	yes	—
53	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
54	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
55	C₃×C₅×C₄⋊C₄	—	2	1	no	—
56	C₃×C₅×C₄⋊C₄	—	2	1	no	—
57	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
58	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
59	#6714	—	2	4	no	—
60	C₄⋊Dic₁₅	—	2	1	no	—
61	C₄⋊Dic₁₅	—	2	1	no	—
62	C₄⋊Dic₁₅	C₂³	1	2	yes	—
63	C₄⋊Dic₁₅	C₂³	1	2	yes	—
64	#6712	—	2	4	no	—
65	C₄×Dic₁₅	—	2	4	no	—
66	C₂×C₃⋊#168	C₂×C₄	1	4	yes	complemented
67	C₂×C₃⋊#168	C₂³	1	2	yes	—
68	#6705	C₂×C₄	1	16	yes	complemented
69	C₂²×ΓL(1,𝔽₂₅)	—	5	1	no	—
70	C₂×#892	—	5	1	no	—
71	C₂×D₃×C₄⋊C₄	—	5	1	no	—
72	C₂×C₃×#107	D₅	1	1	yes	characteristic, complemented
73	C₂×#817	—	5	1	no	—
74	C₂×#808	—	5	1	no	—
75	C₂×#807	—	5	1	no	—
76	#4881	—	5	8	no	—
77	C₂²×C₄×D₅	—	3	1	no	—
78	C₂²×C₄×D₅	—	6	1	no	—
79	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
80	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
81	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
82	C₂×#685	—	6	1	no	—
83	C₂×C₄⋊Dic₅	—	3	1	no	—
84	C₂×C₄⋊Dic₅	—	3	1	no	—
85	C₂×#683	—	6	1	no	—
86	C₂×C₄×Dic₅	—	6	1	no	—
87	C₂²×#168	—	3	1	no	—
88	C₂×#676	—	3	8	no	—
89	C₂×#676	—	3	4	no	—
90	#4038	—	3	4	no	—
91	#4038	—	6	2	no	—
92	D₅×C₄⋊C₄	—	3	4	no	—
93	D₅×C₄⋊C₄	—	6	2	no	—
94	C₅×#107	C₂×D₃	1	4	yes	complemented
95	#3949	—	3	4	no	—
96	#3940	—	3	4	no	—
97	#3939	—	3	4	no	—
98	C₂×#428	—	15	1	no	Sylow
99	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂²×D₁₅	—	2	2	no	—
101	C₂²×D₁₅	—	2	2	no	—
102	C₂²×D₁₅	C₄⋊C₄	1	4	yes	—
103	C₂²×D₁₅	C₂×D₄	1	2	yes	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	4	2	no	—
107	C₂×C₃×C₄×C₅	—	4	2	no	—
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
109	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
112	C₂×Dic₁₅	—	2	2	no	—
113	C₂×Dic₁₅	—	2	2	no	—
114	C₂×Dic₁₅	—	4	2	no	—
115	C₂×Dic₁₅	—	4	2	no	—
116	C₂×Dic₁₅	C₄⋊C₄	1	4	yes	—
117	C₂×Dic₁₅	C₂×D₄	1	2	yes	—
118	C₄×D₁₅	—	4	8	no	—
119	C₄×D₁₅	C₄⋊C₄	1	8	yes	—
120	C₄×D₁₅	C₂²×C₄	1	4	yes	—
121	C₄×D₁₅	C₂×Q₈	1	4	yes	—
122	C₃×C₅×C₈	C₂²×C₄	1	4	yes	complemented
123	C₃⋊#168	C₂²×C₄	1	4	yes	complemented
124	C₂²×C₄×D₃	—	5	1	no	—
125	C₂²×C₄×D₃	—	10	1	no	—
126	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
127	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
128	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
129	C₂×(C₂×D₃)⋊C₄	—	10	1	no	—
130	C₂×C₄⋊Dic₃	—	5	1	no	—
131	C₂×C₄⋊Dic₃	—	5	1	no	—
132	C₂×Dic₃⋊C₄	—	10	1	no	—
133	C₂×C₄×Dic₃	—	10	1	no	—
134	C₂²×C₃⋊C₈	—	5	1	no	—
135	C₂×ΓL(1,𝔽₂₅)	—	5	8	no	—
136	C₂×ΓL(1,𝔽₂₅)	—	5	4	no	—
137	#892	—	5	4	no	—
138	#892	—	10	2	no	—
139	D₃×C₄⋊C₄	—	5	4	no	—
140	D₃×C₄⋊C₄	—	10	2	no	—
141	C₃×#107	C₂×D₅	1	4	yes	complemented
142	#817	—	5	4	no	—
143	#808	—	5	4	no	—
144	#807	—	5	4	no	—
145	C₂³×D₅	—	3	1	no	—
146	C₂²×C₄×C₅	—	2	1	no	—
147	C₂²×C₄×C₅	—	2	1	no	—
148	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
149	C₂²×Dic₅	—	3	1	no	—
150	C₂²×Dic₅	—	6	1	no	—
151	C₂²×Dic₅	—	6	1	no	—
152	C₂×C₄×D₅	—	3	4	no	—
153	C₂×C₄×D₅	—	3	2	no	—
154	C₂×C₄×D₅	—	3	4	no	—
155	C₂×C₄×D₅	—	3	2	no	—
156	C₂×C₄×D₅	—	6	4	no	—
157	C₂×C₄×D₅	—	12	4	no	—
158	C₂×C₅×C₈	C₄×D₃	1	4	yes	complemented
159	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
160	C₅×C₄⋊C₄	—	2	1	no	—
161	C₅×C₄⋊C₄	—	2	1	no	—
162	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
163	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
164	#685	—	6	4	no	—
165	C₄⋊Dic₅	—	3	2	no	—
166	C₄⋊Dic₅	—	3	2	no	—
167	C₄⋊Dic₅	—	6	1	no	—
168	C₄⋊Dic₅	—	6	1	no	—
169	#683	—	6	4	no	—
170	C₄×Dic₅	—	6	4	no	—
171	C₂×#168	—	3	4	no	—
172	C₂×#168	—	3	2	no	—
173	#676	—	3	16	no	—
174	C₂²×M₁₆	—	15	1	no	—
175	C₂×#117	—	15	1	no	—
176	C₂²×C₄⋊C₄	—	15	1	no	—
177	#428	—	15	8	no	—
178	C₂×#107	—	15	1	no	—
179	C₂×#107	D₁₅	1	1	yes	characteristic, complemented
180	C₂×#106	—	15	1	no	—
181	C₂×#106	—	15	1	no	—
182	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
183	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
184	C₂²×C₃×C₅	#137	1	2	yes	—
185	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
186	C₂×D₁₅	—	2	2	no	—
187	C₂×D₁₅	—	2	2	no	—
188	C₂×D₁₅	—	2	8	no	—
189	C₂×D₁₅	C₂×C₄⋊C₄	1	4	yes	—
190	C₃×C₄×C₅	—	4	2	no	—
191	C₃×C₄×C₅	—	4	2	no	—
192	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
193	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
194	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
195	Dic₁₅	—	4	2	no	—
196	Dic₁₅	—	4	2	no	—
197	Dic₁₅	C₂×C₄⋊C₄	1	4	yes	—
198	C₂³×D₃	—	5	1	no	—
199	C₂²×C₃×C₄	—	2	1	no	—
200	C₂²×C₃×C₄	—	2	1	no	—
201	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
202	C₂²×Dic₃	—	5	1	no	—
203	C₂²×Dic₃	—	10	1	no	—
204	C₂²×Dic₃	—	10	1	no	—
205	C₂×C₄×D₃	—	5	4	no	—
206	C₂×C₄×D₃	—	5	2	no	—
207	C₂×C₄×D₃	—	5	4	no	—
208	C₂×C₄×D₃	—	5	2	no	—
209	C₂×C₄×D₃	—	10	4	no	—
210	C₂×C₄×D₃	—	20	4	no	—
211	C₂×C₃×C₈	C₄×D₅	1	4	yes	complemented
212	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
213	C₃×C₄⋊C₄	—	2	1	no	—
214	C₃×C₄⋊C₄	—	2	1	no	—
215	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
216	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
217	(C₂×D₃)⋊C₄	—	10	4	no	—
218	C₄⋊Dic₃	—	5	2	no	—
219	C₄⋊Dic₃	—	5	2	no	—
220	C₄⋊Dic₃	—	10	1	no	—
221	C₄⋊Dic₃	—	10	1	no	—
222	Dic₃⋊C₄	—	10	4	no	—
223	C₄×Dic₃	—	10	4	no	—
224	C₂×C₃⋊C₈	—	5	4	no	—
225	C₂×C₃⋊C₈	—	5	2	no	—
226	ΓL(1,𝔽₂₅)	—	5	16	no	—
227	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
228	C₂²×D₅	—	3	4	no	—
229	C₂²×D₅	—	3	2	no	—
230	C₂²×D₅	—	6	2	no	—
231	C₂²×D₅	—	6	2	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	4	2	no	—
235	C₂×C₄×C₅	—	4	2	no	—
236	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
237	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
238	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
239	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
240	C₂×Dic₅	—	3	4	no	—
241	C₂×Dic₅	—	3	2	no	—
242	C₂×Dic₅	—	6	2	no	—
243	C₂×Dic₅	—	6	2	no	—
244	C₂×Dic₅	—	12	2	no	—
245	C₂×Dic₅	—	12	2	no	—
246	C₄×D₅	—	3	8	no	—
247	C₄×D₅	—	3	4	no	—
248	C₄×D₅	—	3	4	no	—
249	C₄×D₅	—	12	8	no	—
250	C₅×C₈	C₂×C₄×D₃	1	4	yes	complemented
251	#168	—	3	4	no	—
252	C₂³×C₄	—	15	1	no	—
253	C₂³×C₄	—	30	1	no	—
254	C₂×M₁₆	—	15	8	no	—
255	C₂×M₁₆	—	15	4	no	—
256	C₂²×C₈	—	15	1	no	—
257	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
258	#117	—	15	4	no	—
259	#117	—	30	2	no	—
260	C₂×C₄⋊C₄	—	15	1	no	—
261	C₂×C₄⋊C₄	—	15	1	no	—
262	C₂×C₄⋊C₄	—	15	4	no	—
263	C₂×C₄⋊C₄	—	30	2	no	—
264	C₂×C₄⋊C₄	—	30	1	no	—
265	C₂×C₄⋊C₄	C₂×D₁₅	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂×D₁₅	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	—	30	1	no	—
268	C₂×C₄²	—	30	1	no	—
269	#107	—	15	4	no	—
270	#107	C₂×D₁₅	1	4	yes	complemented
271	#106	—	15	4	no	—
272	#106	—	15	4	no	—
273	C₂×C₃×C₅	#428	1	4	yes	complemented
274	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
275	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
276	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
277	D₁₅	—	2	4	no	—
278	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
279	C₂²×D₃	—	5	2	no	—
280	C₂²×D₃	—	5	4	no	—
281	C₂²×D₃	—	10	2	no	—
282	C₂²×D₃	—	10	2	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	4	2	no	—
286	C₂×C₃×C₄	—	4	2	no	—
287	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
288	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
289	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
290	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
291	C₂×Dic₃	—	5	2	no	—
292	C₂×Dic₃	—	5	4	no	—
293	C₂×Dic₃	—	10	2	no	—
294	C₂×Dic₃	—	10	2	no	—
295	C₂×Dic₃	—	20	2	no	—
296	C₂×Dic₃	—	20	2	no	—
297	C₄×D₃	—	5	4	no	—
298	C₄×D₃	—	5	4	no	—
299	C₄×D₃	—	5	8	no	—
300	C₄×D₃	—	20	8	no	—
301	C₃×C₈	C₂×C₄×D₅	1	4	yes	complemented
302	C₃⋊C₈	—	5	4	no	—
303	C₂²×C₅	D₃×C₄⋊C₄	1	2	yes	—
304	C₂²×C₅	#911	1	2	yes	—
305	C₂²×C₅	#918	1	2	yes	—
306	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
307	C₂×D₅	—	3	4	no	—
308	C₂×D₅	—	6	8	no	—
309	C₂×D₅	—	6	2	no	—
310	C₂×D₅	—	6	2	no	—
311	C₄×C₅	—	4	2	no	—
312	C₄×C₅	—	4	2	no	—
313	C₄×C₅	D₃×C₄⋊C₄	1	2	yes	—
314	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
315	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
316	Dic₅	—	3	4	no	—
317	Dic₅	—	12	2	no	—
318	Dic₅	—	12	2	no	—
319	C₂⁴	—	15	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	15	1	no	—
323	C₂²×C₄	—	15	4	no	—
324	C₂²×C₄	—	15	2	no	—
325	C₂²×C₄	—	15	4	no	—
326	C₂²×C₄	—	15	2	no	—
327	C₂²×C₄	—	30	4	no	—
328	C₂²×C₄	—	30	1	no	—
329	C₂²×C₄	—	30	1	no	—
330	C₂²×C₄	—	60	4	no	—
331	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
332	M₁₆	—	15	16	no	—
333	C₂×C₈	—	15	4	no	—
334	C₂×C₈	—	15	2	no	—
335	C₂×C₈	C₄×D₁₅	1	4	yes	complemented
336	C₂×C₈	C₂²×D₁₅	1	2	yes	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	15	2	no	—
340	C₄⋊C₄	—	15	2	no	—
341	C₄⋊C₄	—	30	4	no	—
342	C₄⋊C₄	—	30	1	no	—
343	C₄⋊C₄	—	30	1	no	—
344	C₄⋊C₄	C₂²×D₁₅	1	2	yes	—
345	C₄⋊C₄	C₂²×D₁₅	1	2	yes	—
346	C₂²⋊C₄	—	30	4	no	—
347	C₄²	—	30	4	no	—
348	C₃×C₅	C₂×#428	1	1	yes	characteristic, complemented, Hall
349	C₂²×C₃	D₅×C₄⋊C₄	1	2	yes	—
350	C₂²×C₃	#4057	1	2	yes	—
351	C₂²×C₃	#4064	1	2	yes	—
352	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
353	C₂×D₃	—	5	4	no	—
354	C₂×D₃	—	10	2	no	—
355	C₂×D₃	—	10	2	no	—
356	C₂×D₃	—	10	8	no	—
357	C₃×C₄	—	4	2	no	—
358	C₃×C₄	—	4	2	no	—
359	C₃×C₄	D₅×C₄⋊C₄	1	2	yes	—
360	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
361	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
362	Dic₃	—	5	4	no	—
363	Dic₃	—	20	2	no	—
364	Dic₃	—	20	2	no	—
365	C₂×C₅	#4881	1	4	yes	complemented
366	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
367	C₂×C₅	C₂×#911	1	1	yes	characteristic
368	C₂×C₅	C₂×#918	1	1	yes	characteristic
369	D₅	—	6	4	no	—
370	C₂³	—	15	4	no	—
371	C₂³	—	15	2	no	—
372	C₂³	—	30	2	no	—
373	C₂³	—	30	2	no	—
374	C₂³	D₄×D₁₅	1	1	yes	characteristic
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	15	4	no	—
380	C₂×C₄	—	15	2	no	—
381	C₂×C₄	—	15	8	no	—
382	C₂×C₄	—	15	4	no	—
383	C₂×C₄	—	15	4	no	—
384	C₂×C₄	—	30	2	no	—
385	C₂×C₄	—	30	2	no	—
386	C₂×C₄	—	60	8	no	—
387	C₂×C₄	—	60	2	no	—
388	C₂×C₄	—	60	2	no	—
389	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
390	C₂×C₄	D₄×D₁₅	1	1	yes	characteristic
391	C₂×C₄	Q₈×D₁₅	1	2	yes	—
392	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
393	C₈	—	15	4	no	—
394	C₈	C₂×C₄×D₁₅	1	4	yes	complemented
395	C₂×C₃	#65170	1	4	yes	complemented
396	C₂×C₃	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
397	C₂×C₃	C₂×#4057	1	1	yes	characteristic
398	C₂×C₃	C₂×#4064	1	1	yes	characteristic
399	D₃	—	10	4	no	—
400	C₅	C₂×#4881	1	1	yes	characteristic, complemented, Sylow
401	C₂²	—	15	4	no	—
402	C₂²	—	30	8	no	—
403	C₂²	—	30	2	no	—
404	C₂²	—	30	2	no	—
405	C₂²	C₄⋊C₄×D₁₅	1	2	yes	—
406	C₂²	#91800	1	2	yes	—
407	C₂²	#91807	1	2	yes	—
408	C₂²	C₂×D₄×D₁₅	1	1	yes	characteristic
409	C₄	—	4	2	no	—
410	C₄	—	4	2	no	—
411	C₄	—	15	4	no	—
412	C₄	—	60	2	no	—
413	C₄	—	60	2	no	—
414	C₄	C₄⋊C₄×D₁₅	1	2	yes	—
415	C₄	C₂²×C₄×D₁₅	1	1	yes	characteristic
416	C₄	C₂×Q₈×D₁₅	1	1	yes	characteristic
417	C₃	C₂×#65170	1	1	yes	characteristic, complemented, Sylow
418	C₂	—	30	4	no	—
419	C₂	#11750982	1	4	yes	direct product factor
420	C₂	C₂×C₄⋊C₄×D₁₅	1	1	yes	characteristic
421	C₂	C₂×#91800	1	1	yes	characteristic
422	C₂	C₂×#91807	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₅
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₂×C₃×C₅×#107	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂³×D₁₅	D₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×#107	D₁₅
hypocenter	C₃×C₅	C₂×#428
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

Complements

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

N	H ≅ G/N	type
4. C₂×C₃×C₅×#107	C₂	semidirect
5. C₂×#91101	C₂	semidirect
6. C₂×#91092	C₂	semidirect
7. C₂×#91091	C₂	semidirect
8. #11750982	C₂	direct (N × H)
21. C₂×#6705	C₄	semidirect
27. C₃×C₅×#107	C₂²	semidirect
28. #91101	C₂²	semidirect
29. #91092	C₂²	semidirect
30. #91091	C₂²	semidirect
35. C₂×C₅×#107	D₃	semidirect
53. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
66. C₂×C₃⋊#168	C₂×C₄	semidirect
68. #6705	C₂×C₄	semidirect
72. C₂×C₃×#107	D₅	semidirect
94. C₅×#107	C₂×D₃	semidirect
122. C₃×C₅×C₈	C₂²×C₄	semidirect
123. C₃⋊#168	C₂²×C₄	semidirect
141. C₃×#107	C₂×D₅	semidirect
158. C₂×C₅×C₈	C₄×D₃	semidirect
179. C₂×#107	D₁₅	semidirect
211. C₂×C₃×C₈	C₄×D₅	semidirect
250. C₅×C₈	C₂×C₄×D₃	semidirect
270. #107	C₂×D₁₅	semidirect
273. C₂×C₃×C₅	#428	semidirect
301. C₃×C₈	C₂×C₄×D₅	semidirect
335. C₂×C₈	C₄×D₁₅	semidirect
348. C₃×C₅	C₂×#428	semidirect
365. C₂×C₅	#4881	semidirect
394. C₈	C₂×C₄×D₁₅	semidirect
395. C₂×C₃	#65170	semidirect
400. C₅	C₂×#4881	semidirect
417. C₃	C₂×#65170	semidirect
419. C₂	#11750982	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#6705	2
C₂×#91781	2
C₂×C₄⋊C₄×D₁₅	2
C₂×C₃×C₅×#107	2
C₂×#91101	2
C₂×#91092	2
C₂×#91091	2
#11750982	2
C₂×#65170	3
C₂×#4881	5

Subgroups — C2×#11750982 #14413345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11750982 #14413345