Subgroups — #67×#676 #14415714

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#676	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₅×#67	C₂	1	1	yes	maximal, characteristic
3	C₂×D₃×#676	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751212	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×C₈×#67	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748502	C₂	1	1	yes	maximal, characteristic, complemented
7	#11748499	C₂	1	1	yes	maximal, characteristic, complemented
8	#67×#168	C₂	1	1	yes	maximal, characteristic, complemented
9	#11748101	C₂	1	1	yes	maximal, characteristic, complemented
10	#11747717	C₂	1	1	yes	maximal, characteristic, complemented
11	#11747715	C₂	1	1	yes	maximal, characteristic, complemented
12	#11747713	C₂	1	1	yes	maximal, characteristic, complemented
13	#11747711	C₂	1	1	yes	maximal, characteristic, complemented
14	#11747596	C₂	1	1	yes	maximal, characteristic, complemented
15	Dic₃×#676	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×#676	—	3	1	no	maximal, Hall
17	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
18	C₂×D₅×#67	C₄	1	1	yes	characteristic
19	C₂×C₄×D₃×D₅	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
21	C₄×#1220	C₂²	1	1	yes	characteristic
22	C₂×#6705	C₂²	1	1	yes	characteristic, complemented
23	C₄×C₅×#67	C₂²	1	1	yes	characteristic
24	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₃×#168	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×#676	—	2	4	no	—
27	C₂×C₃×#676	C₂²	1	1	yes	characteristic
28	C₂×C₃×#676	C₂²	1	1	yes	characteristic
29	C₂×C₃×#676	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×#676	C₂²	1	1	yes	characteristic, complemented
31	#91552	C₄	1	1	yes	characteristic
32	Dic₅×#67	C₄	1	1	yes	characteristic
33	D₅×#217	C₄	1	1	yes	characteristic
34	D₅×(C₂×D₃)⋊C₄	C₄	1	1	yes	characteristic
35	#91444	C₄	1	1	yes	characteristic
36	C₄×#1202	C₂²	1	1	yes	characteristic
37	#91440	C₄	1	1	yes	characteristic
38	C₄×#1201	C₂²	1	1	yes	characteristic
39	D₅×Dic₃⋊C₄	C₄	1	1	yes	characteristic
40	C₄×D₅×Dic₃	C₂²	1	1	yes	characteristic
41	C₂×#6651	C₂²	1	1	yes	characteristic, complemented
42	C₂×#6649	C₂²	1	1	yes	characteristic
43	C₂×#6649	C₂²	1	1	yes	characteristic
44	C₂×D₃×#168	C₂²	1	1	yes	characteristic, complemented
45	D₃×#676	—	2	4	no	—
46	#91114	C₂²	1	1	yes	characteristic, complemented
47	#91104	C₂²	1	1	yes	characteristic, complemented
48	#91099	C₂²	1	1	yes	characteristic, complemented
49	#91098	C₂²	1	1	yes	characteristic, complemented
50	C₅×#830	C₂²	1	1	yes	characteristic, complemented
51	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
54	Dic₃⋊#168	C₂²	1	1	yes	characteristic, complemented
55	#90983	C₂²	1	1	yes	characteristic, complemented
56	#90957	C₂²	1	1	yes	characteristic, complemented
57	(C₂×D₃)⋊#168	C₂²	1	1	yes	characteristic, complemented
58	#90955	C₂²	1	1	yes	characteristic, complemented
59	#90955	C₂²	1	1	yes	characteristic, complemented
60	#90954	C₂²	1	1	yes	characteristic, complemented
61	Dic₃×#168	C₂²	1	1	yes	characteristic, complemented
62	M₁₆×#67	—	5	1	no	maximal, Hall
63	C₂²×#676	—	3	1	no	—
64	C₂²×#676	D₃	1	1	yes	characteristic, complemented
65	C₄×D₄×D₅	—	3	1	no	—
66	C₅×C₈×D₄	—	3	1	no	—
67	#65400	—	3	1	no	—
68	#65400	—	3	1	no	—
69	D₄×#168	—	3	1	no	—
70	#65127	—	3	1	no	—
71	#65126	—	3	1	no	—
72	#65019	—	3	1	no	—
73	#65019	—	3	1	no	—
74	#65015	—	3	1	no	—
75	#65015	—	3	1	no	—
76	#64977	—	3	1	no	—
77	C₄×#676	—	3	1	no	—
78	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
79	C₂²×D₃×D₅	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂×#1220	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
83	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
85	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
86	C₂×C₃×C₄×D₅	—	2	2	no	—
87	C₂×C₃×C₄×D₅	—	2	2	no	—
88	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
92	D₅×#67	—	2	4	no	—
93	C₂×#1202	C₂×C₄	1	1	yes	characteristic
94	C₂×#1201	C₂×C₄	1	1	yes	characteristic
95	C₂×#1200	C₂×C₄	1	1	yes	characteristic
96	C₂×D₃×Dic₅	C₂×C₄	1	1	yes	characteristic
97	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
98	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
99	C₂×D₅×Dic₃	C₂×C₄	1	1	yes	characteristic
100	C₄×D₃×D₅	—	2	2	no	—
101	C₄×D₃×D₅	—	2	2	no	—
102	C₂×C₃×C₅×C₈	—	2	2	no	—
103	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
105	#6719	C₂×C₄	1	1	yes	characteristic
106	#6714	C₂×C₄	1	1	yes	characteristic
107	#6712	C₂×C₄	1	1	yes	characteristic
108	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
109	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
110	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
111	#6705	—	2	2	no	—
112	C₅×#217	C₂×C₄	1	1	yes	characteristic
113	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
114	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
115	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
116	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
117	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
118	C₅×D₃×C₈	—	2	2	no	—
119	C₂×C₃×#168	—	2	2	no	—
120	C₂×C₃×#168	C₂³	1	1	yes	characteristic
121	C₂×C₃×#168	C₂³	1	1	yes	characteristic
122	C₃×#676	—	2	2	no	—
123	C₃×#676	—	2	2	no	—
124	C₃×#676	—	2	2	no	—
125	C₃×#676	D₄	1	4	yes	complemented
126	Dic₃⋊Dic₅	C₂×C₄	1	1	yes	characteristic
127	#6669	C₂×C₄	1	1	yes	characteristic
128	#6667	C₂×C₄	1	1	yes	characteristic
129	(C₂×D₃)⋊Dic₅	C₂×C₄	1	1	yes	characteristic
130	#6665	C₂×C₄	1	1	yes	characteristic
131	#6665	C₂×C₄	1	1	yes	characteristic
132	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
133	Dic₃×Dic₅	C₂×C₄	1	1	yes	characteristic
134	#6651	—	2	2	no	—
135	#6649	—	2	2	no	—
136	#6649	—	2	2	no	—
137	D₃×#168	—	2	2	no	—
138	C₂²×C₃×M₁₆	—	5	1	no	—
139	C₂×C₄×#67	—	5	1	no	—
140	C₂×D₃×M₁₆	—	5	1	no	—
141	#5207	—	5	1	no	—
142	#5128	—	5	1	no	—
143	#5128	—	5	1	no	—
144	#5127	—	5	1	no	—
145	#5127	—	5	1	no	—
146	#5126	—	5	1	no	—
147	#5118	—	5	1	no	—
148	Dic₃×M₁₆	—	5	1	no	—
149	#5111	—	5	1	no	—
150	#5111	—	5	1	no	—
151	C₈×#67	—	5	1	no	—
152	C₈×#67	D₅	1	1	yes	characteristic, complemented
153	C₂×D₄×D₅	—	3	1	no	—
154	C₂²×C₄×D₅	—	3	1	no	—
155	C₂²×C₄×D₅	C₂×D₃	1	1	yes	characteristic
156	C₂²×C₅×C₈	—	3	1	no	—
157	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
158	C₄×C₅×D₄	—	3	1	no	—
159	D₄×Dic₅	—	3	1	no	—
160	C₄×C₂²⋊D₅	—	3	1	no	—
161	C₄×C₂²⋊D₅	—	3	1	no	—
162	C₂²×#168	—	3	1	no	—
163	C₂²×#168	C₂×D₃	1	1	yes	characteristic, complemented
164	C₂×#676	—	2	4	no	—
165	C₂×#676	—	3	1	no	—
166	C₂×#676	—	3	1	no	—
167	C₂×#676	—	3	1	no	—
168	C₂×#676	—	3	1	no	—
169	C₂×#676	—	6	4	no	—
170	C₂×#676	C₂×D₃	1	1	yes	characteristic
171	C₂×#676	C₂×D₃	1	1	yes	characteristic
172	C₂×#676	C₂×D₃	1	1	yes	characteristic, complemented
173	C₂×#676	C₂×D₃	1	1	yes	characteristic, complemented
174	#4039	—	3	1	no	—
175	D₅×C₄⋊C₄	—	3	1	no	—
176	#4027	—	3	1	no	—
177	#4027	—	3	1	no	—
178	D₅×C₂²⋊C₄	—	3	1	no	—
179	D₅×C₂²⋊C₄	—	3	1	no	—
180	C₄×D₂₀	—	3	1	no	—
181	C₄²×D₅	—	3	1	no	—
182	C₅×C₄⋊C₈	—	3	1	no	—
183	C₅×C₂²⋊C₈	—	3	1	no	—
184	C₅×C₂²⋊C₈	—	3	1	no	—
185	C₄×C₅×C₈	—	3	1	no	—
186	C₂²⋊#168	—	3	1	no	—
187	C₂²⋊#168	—	3	1	no	—
188	#3952	—	3	1	no	—
189	#3952	—	3	1	no	—
190	#3952	—	3	1	no	—
191	#3952	—	3	1	no	—
192	#3947	—	3	1	no	—
193	#3947	—	3	1	no	—
194	#3946	—	3	1	no	—
195	#3946	—	3	1	no	—
196	C₄⋊#168	—	3	1	no	—
197	C₄×#168	—	3	1	no	—
198	D₄×M₁₆	—	15	1	no	Sylow
199	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
200	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₃×D₅	—	2	2	no	—
203	C₂²×C₃×D₅	—	2	2	no	—
204	C₂²×C₃×D₅	—	4	1	no	—
205	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
206	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
207	C₂×D₃×D₅	—	2	2	no	—
208	C₂×D₃×D₅	—	2	2	no	—
209	C₂×D₃×D₅	—	4	1	no	—
210	C₂×C₃×C₄×C₅	—	2	1	no	—
211	C₂×C₃×C₄×C₅	—	2	1	no	—
212	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
213	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
214	#1220	—	2	2	no	—
215	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
216	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
217	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
218	C₄×D₁₅	—	2	1	no	—
219	C₄×D₁₅	—	2	1	no	—
220	C₅×#67	M₁₆	1	4	yes	complemented
221	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
222	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
223	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
224	C₄×C₅×D₃	—	2	1	no	—
225	C₄×C₅×D₃	—	2	1	no	—
226	C₂×C₃×Dic₅	—	2	2	no	—
227	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
228	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
229	C₃×C₄×D₅	—	2	2	no	—
230	C₃×C₄×D₅	—	2	1	no	—
231	C₃×C₄×D₅	—	2	1	no	—
232	C₃×C₄×D₅	—	2	2	no	—
233	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
234	C₃×C₄×D₅	#41	1	2	yes	—
235	#1202	—	2	2	no	—
236	#1201	—	2	2	no	—
237	#1200	—	2	2	no	—
238	D₃×Dic₅	—	2	2	no	—
239	D₅×Dic₃	—	2	2	no	—
240	D₅×Dic₃	—	2	2	no	—
241	D₅×Dic₃	—	4	1	no	—
242	C₃×C₅×C₈	—	2	1	no	—
243	C₃×C₅×C₈	C₂×D₄	1	2	yes	complemented
244	C₃⋊#168	—	2	1	no	—
245	C₃⋊#168	—	2	1	no	—
246	C₃×#168	—	2	1	no	—
247	C₃×#168	C₂×D₄	1	2	yes	complemented
248	C₅×C₃⋊C₈	—	2	1	no	—
249	C₅×C₃⋊C₈	—	2	1	no	—
250	C₂³×C₃×C₄	—	5	1	no	—
251	C₂²×#67	—	5	1	no	—
252	C₂²×C₄×D₃	—	5	1	no	—
253	C₂×C₃×M₁₆	—	5	1	no	—
254	C₂×C₃×M₁₆	—	5	1	no	—
255	C₂×C₃×M₁₆	—	5	1	no	—
256	C₂×C₃×M₁₆	—	5	1	no	—
257	C₂×C₃×M₁₆	—	10	4	no	—
258	C₂²×C₃×C₈	—	5	1	no	—
259	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic, complemented
260	C₂×#217	—	5	1	no	—
261	C₄×#67	—	5	1	no	—
262	C₄×#67	—	5	1	no	—
263	C₄×#67	—	5	1	no	—
264	C₄×#67	—	5	1	no	—
265	C₄×#67	—	5	1	no	—
266	C₄×#67	—	5	1	no	—
267	C₄×#67	—	5	1	no	—
268	C₄×#67	C₂×D₅	1	1	yes	characteristic
269	C₂×(C₂×D₃)⋊C₄	—	5	1	no	—
270	C₂×Dic₃⋊C₄	—	5	1	no	—
271	C₂×C₄×Dic₃	—	5	1	no	—
272	C₂×#208	—	5	1	no	—
273	C₂×#208	—	5	1	no	—
274	D₃×M₁₆	—	10	4	no	—
275	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
276	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
277	C₂×D₃×C₈	—	5	1	no	—
278	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic, complemented
279	#830	—	5	1	no	—
280	#830	—	5	1	no	—
281	#830	—	5	1	no	—
282	#830	C₂×D₅	1	1	yes	characteristic, complemented
283	(C₂×D₃)⋊C₈	—	5	1	no	—
284	(C₂×D₃)⋊C₈	—	5	1	no	—
285	(C₂×D₃)⋊C₈	—	5	1	no	—
286	(C₂×D₃)⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
287	#815	—	5	1	no	—
288	#815	—	5	1	no	—
289	Dic₃⋊C₈	—	5	1	no	—
290	Dic₃⋊C₈	—	5	1	no	—
291	Dic₃⋊C₈	—	5	1	no	—
292	Dic₃⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
293	C₈×Dic₃	—	5	1	no	—
294	C₈×Dic₃	C₂×D₅	1	1	yes	characteristic, complemented
295	C₂³×D₅	—	3	1	no	—
296	C₂³×D₅	C₄×D₃	1	1	yes	characteristic
297	C₂×C₅×D₄	—	3	1	no	—
298	C₂²×C₄×C₅	—	3	1	no	—
299	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
300	C₂×C₂²⋊D₅	—	3	1	no	—
301	C₂×C₂²⋊D₅	—	3	1	no	—
302	C₂²×Dic₅	—	3	1	no	—
303	C₂²×Dic₅	C₄×D₃	1	1	yes	characteristic
304	D₄×D₅	—	6	4	no	—
305	C₂×D₂₀	—	3	1	no	—
306	C₂×C₄×D₅	—	2	2	no	—
307	C₂×C₄×D₅	—	2	2	no	—
308	C₂×C₄×D₅	—	3	1	no	—
309	C₂×C₄×D₅	—	3	1	no	—
310	C₂×C₄×D₅	—	3	1	no	—
311	C₂×C₄×D₅	—	3	1	no	—
312	C₂×C₄×D₅	—	3	1	no	—
313	C₂×C₄×D₅	—	6	2	no	—
314	C₂×C₄×D₅	—	6	2	no	—
315	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
316	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
317	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
318	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
319	C₂×C₅×C₈	—	2	2	no	—
320	C₂×C₅×C₈	—	3	1	no	—
321	C₂×C₅×C₈	—	3	1	no	—
322	C₂×C₅×C₈	—	6	2	no	—
323	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
324	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
325	C₅×C₄⋊C₄	—	3	1	no	—
326	C₅×C₂²⋊C₄	—	3	1	no	—
327	C₅×C₂²⋊C₄	—	3	1	no	—
328	C₄²×C₅	—	3	1	no	—
329	C₂²⋊Dic₅	—	3	1	no	—
330	C₂²⋊Dic₅	—	3	1	no	—
331	#685	—	3	1	no	—
332	#685	—	3	1	no	—
333	#685	—	3	1	no	—
334	#685	—	3	1	no	—
335	C₄⋊Dic₅	—	3	1	no	—
336	#683	—	3	1	no	—
337	#683	—	3	1	no	—
338	C₄×Dic₅	—	3	1	no	—
339	C₄×Dic₅	—	3	1	no	—
340	C₄×Dic₅	—	3	1	no	—
341	C₂×#168	—	2	2	no	—
342	C₂×#168	—	3	1	no	—
343	C₂×#168	—	3	1	no	—
344	C₂×#168	—	6	2	no	—
345	C₂×#168	C₂²×D₃	1	1	yes	characteristic
346	C₂×#168	C₂²×D₃	1	1	yes	characteristic
347	#676	—	2	2	no	—
348	#676	—	2	2	no	—
349	#676	—	2	2	no	—
350	#676	—	6	2	no	—
351	#676	—	6	2	no	—
352	#676	—	6	2	no	—
353	#676	—	6	2	no	—
354	#676	#67	1	4	yes	direct product factor
355	C₂²×M₁₆	—	5	1	no	—
356	C₂²×M₁₆	—	15	1	no	—
357	C₂×C₄×D₄	—	15	1	no	—
358	#436	—	15	1	no	—
359	#436	—	15	1	no	—
360	#435	—	15	1	no	—
361	#435	—	15	1	no	—
362	#435	—	15	1	no	—
363	#435	—	15	1	no	—
364	C₈×D₄	—	3	1	no	—
365	C₈×D₄	—	15	1	no	—
366	#423	—	15	1	no	—
367	#407	—	15	1	no	—
368	#407	—	15	1	no	—
369	C₄×M₁₆	—	15	1	no	—
370	C₂²×C₃×C₅	—	2	1	no	—
371	C₂²×C₃×C₅	—	2	1	no	—
372	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	complemented
373	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
374	C₂×D₁₅	—	2	1	no	—
375	C₂×D₁₅	—	2	1	no	—
376	C₂×D₁₅	—	2	1	no	—
377	C₂×C₅×D₃	—	2	1	no	—
378	C₂×C₅×D₃	—	2	1	no	—
379	C₂×C₅×D₃	C₂×M₁₆	1	2	yes	complemented
380	C₂×C₃×D₅	—	2	1	no	—
381	C₂×C₃×D₅	—	2	1	no	—
382	C₂×C₃×D₅	—	2	1	no	—
383	C₂×C₃×D₅	—	2	1	no	—
384	C₂×C₃×D₅	—	2	1	no	—
385	C₂×C₃×D₅	—	4	4	no	—
386	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
387	D₃×D₅	—	4	4	no	—
388	C₃×C₄×C₅	—	2	1	no	—
389	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
390	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
391	Dic₁₅	—	2	1	no	—
392	Dic₁₅	—	2	1	no	—
393	Dic₁₅	—	2	1	no	—
394	C₃×Dic₅	—	2	1	no	—
395	C₃×Dic₅	C₄×D₄	1	2	yes	—
396	C₅×Dic₃	—	2	1	no	—
397	C₅×Dic₃	—	2	1	no	—
398	C₅×Dic₃	C₂×M₁₆	1	2	yes	complemented
399	C₂⁴×C₃	—	5	1	no	—
400	C₂³×D₃	—	5	1	no	—
401	C₂²×C₃×C₄	—	5	1	no	—
402	C₂²×C₃×C₄	—	5	1	no	—
403	C₂²×C₃×C₄	—	5	1	no	—
404	C₂²×C₃×C₄	—	5	1	no	—
405	C₂²×C₃×C₄	—	5	1	no	—
406	C₂²×C₃×C₄	—	10	2	no	—
407	C₂²×C₃×C₄	—	10	2	no	—
408	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
409	C₂×#67	—	5	1	no	—
410	C₂×#67	—	5	1	no	—
411	C₂×#67	—	5	1	no	—
412	C₂×#67	—	10	4	no	—
413	C₂×#67	C₄×D₅	1	1	yes	characteristic
414	C₂²×Dic₃	—	5	1	no	—
415	C₂²×Dic₃	—	5	1	no	—
416	C₂²×Dic₃	—	5	1	no	—
417	C₂×C₄×D₃	—	5	1	no	—
418	C₂×C₄×D₃	—	5	1	no	—
419	C₂×C₄×D₃	—	5	1	no	—
420	C₂×C₄×D₃	—	10	2	no	—
421	C₂×C₄×D₃	—	10	2	no	—
422	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
423	C₃×M₁₆	—	5	4	no	—
424	C₃×M₁₆	—	10	2	no	—
425	C₃×M₁₆	—	10	2	no	—
426	C₃×M₁₆	—	10	2	no	—
427	C₂×C₃×C₈	—	2	2	no	—
428	C₂×C₃×C₈	—	5	1	no	—
429	C₂×C₃×C₈	—	5	1	no	—
430	C₂×C₃×C₈	—	10	2	no	—
431	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
432	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
433	#217	—	5	1	no	—
434	#217	—	5	1	no	—
435	#217	—	5	1	no	—
436	#217	C₄×D₅	1	1	yes	characteristic
437	(C₂×D₃)⋊C₄	—	5	1	no	—
438	(C₂×D₃)⋊C₄	—	5	1	no	—
439	(C₂×D₃)⋊C₄	—	5	1	no	—
440	(C₂×D₃)⋊C₄	C₄×D₅	1	1	yes	characteristic
441	Dic₃⋊C₄	—	5	1	no	—
442	Dic₃⋊C₄	—	5	1	no	—
443	Dic₃⋊C₄	—	5	1	no	—
444	Dic₃⋊C₄	C₄×D₅	1	1	yes	characteristic
445	C₄×Dic₃	—	5	1	no	—
446	C₄×Dic₃	—	5	1	no	—
447	C₄×Dic₃	—	5	1	no	—
448	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
449	#208	—	10	2	no	—
450	#208	—	10	2	no	—
451	C₂×C₃⋊C₈	—	5	1	no	—
452	C₂×C₃⋊C₈	—	5	1	no	—
453	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
454	C₂×C₃⋊C₈	C₂²×D₅	1	1	yes	characteristic
455	ΓL(1,𝔽₂₅)	—	10	2	no	—
456	ΓL(1,𝔽₂₅)	—	10	2	no	—
457	D₃×C₈	—	2	2	no	—
458	D₃×C₈	—	10	2	no	—
459	C₂³×C₅	—	3	1	no	—
460	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
461	C₂²×D₅	—	2	2	no	—
462	C₂²×D₅	—	2	2	no	—
463	C₂²×D₅	—	3	1	no	—
464	C₂²×D₅	—	4	1	no	—
465	C₂²×D₅	—	6	2	no	—
466	C₂²×D₅	—	6	2	no	—
467	C₂²×D₅	—	12	1	no	—
468	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
469	C₂²×D₅	C₂×C₄×D₃	1	1	yes	characteristic
470	C₅×D₄	—	3	4	no	—
471	C₂×C₄×C₅	—	2	1	no	—
472	C₂×C₄×C₅	—	2	1	no	—
473	C₂×C₄×C₅	—	3	1	no	—
474	C₂×C₄×C₅	—	3	1	no	—
475	C₂×C₄×C₅	—	3	1	no	—
476	C₂×C₄×C₅	—	6	1	no	—
477	C₂×C₄×C₅	—	6	1	no	—
478	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
479	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
480	C₂²⋊D₅	—	6	2	no	—
481	C₂²⋊D₅	—	6	2	no	—
482	C₂×Dic₅	—	2	2	no	—
483	C₂×Dic₅	—	3	1	no	—
484	C₂×Dic₅	—	3	1	no	—
485	C₂×Dic₅	—	3	1	no	—
486	C₂×Dic₅	—	6	2	no	—
487	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
488	C₂×Dic₅	C₂×C₄×D₃	1	1	yes	characteristic
489	D₂₀	—	6	2	no	—
490	C₄×D₅	—	2	2	no	—
491	C₄×D₅	—	2	1	no	—
492	C₄×D₅	—	2	1	no	—
493	C₄×D₅	—	2	2	no	—
494	C₄×D₅	—	6	2	no	—
495	C₄×D₅	—	6	2	no	—
496	C₄×D₅	—	6	1	no	—
497	C₄×D₅	—	6	1	no	—
498	C₄×D₅	—	6	2	no	—
499	C₄×D₅	—	12	1	no	—
500	C₄×D₅	#235	1	2	yes	—
501	C₄×D₅	C₂×#67	1	2	yes	—
502	C₅×C₈	—	2	1	no	—
503	C₅×C₈	—	6	1	no	—
504	C₅×C₈	—	6	1	no	—
505	C₅×C₈	C₂×#67	1	2	yes	complemented
506	#168	—	2	1	no	—
507	#168	—	6	1	no	—
508	#168	—	6	1	no	—
509	#168	C₂×#67	1	2	yes	complemented
510	C₂²×D₄	—	15	1	no	—
511	C₂³×C₄	—	5	1	no	—
512	C₂³×C₄	—	15	1	no	—
513	C₂×M₁₆	—	5	1	no	—
514	C₂×M₁₆	—	5	1	no	—
515	C₂×M₁₆	—	5	1	no	—
516	C₂×M₁₆	—	5	1	no	—
517	C₂×M₁₆	—	10	4	no	—
518	C₂×M₁₆	—	15	1	no	—
519	C₂×M₁₆	—	15	1	no	—
520	C₂×M₁₆	—	15	1	no	—
521	C₂×M₁₆	—	15	1	no	—
522	C₂×M₁₆	—	30	4	no	—
523	C₂²×C₈	—	3	1	no	—
524	C₂²×C₈	—	5	1	no	—
525	C₂²×C₈	—	15	1	no	—
526	C₂²×C₈	D₃×D₅	1	1	yes	characteristic, complemented
527	C₄×D₄	—	3	1	no	—
528	C₄×D₄	—	15	1	no	—
529	C₄×D₄	—	15	1	no	—
530	C₄×D₄	—	15	1	no	—
531	C₄×D₄	—	15	1	no	—
532	C₄×D₄	—	15	1	no	—
533	C₄×D₄	—	15	1	no	—
534	C₄×D₄	—	15	1	no	—
535	C₂×C₄⋊C₄	—	15	1	no	—
536	C₂×C₂²⋊C₄	—	15	1	no	—
537	C₂×C₂²⋊C₄	—	15	1	no	—
538	C₂×C₄²	—	15	1	no	—
539	C₄⋊C₈	—	3	1	no	—
540	C₄⋊C₈	—	15	1	no	—
541	C₄⋊C₈	—	15	1	no	—
542	C₄⋊C₈	—	15	1	no	—
543	C₂²⋊C₈	—	3	1	no	—
544	C₂²⋊C₈	—	3	1	no	—
545	C₂²⋊C₈	—	15	1	no	—
546	C₂²⋊C₈	—	15	1	no	—
547	C₂²⋊C₈	—	15	1	no	—
548	C₂²⋊C₈	—	15	1	no	—
549	C₂²⋊C₈	—	15	1	no	—
550	C₂²⋊C₈	—	15	1	no	—
551	#97	—	15	1	no	—
552	#97	—	15	1	no	—
553	C₄×C₈	—	3	1	no	—
554	C₄×C₈	—	15	1	no	—
555	C₂×C₃×C₅	—	2	2	no	—
556	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
557	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
558	C₂×C₃×C₅	#568	1	1	yes	characteristic
559	D₁₅	—	4	1	no	—
560	C₃×D₅	—	2	2	no	—
561	C₃×D₅	—	4	1	no	—
562	C₅×D₃	—	2	2	no	—
563	C₂³×C₃	—	5	1	no	—
564	C₂³×C₃	—	5	1	no	—
565	C₂³×C₃	—	10	2	no	—
566	C₂³×C₃	—	10	2	no	—
567	C₂³×C₃	—	20	1	no	—
568	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
569	C₂²×D₃	—	5	1	no	—
570	C₂²×D₃	—	10	2	no	—
571	C₂²×D₃	—	10	2	no	—
572	C₂²×D₃	—	20	1	no	—
573	C₂²×D₃	C₂×C₄×D₅	1	1	yes	characteristic
574	C₂×C₃×C₄	—	2	1	no	—
575	C₂×C₃×C₄	—	2	1	no	—
576	C₂×C₃×C₄	—	5	1	no	—
577	C₂×C₃×C₄	—	5	2	no	—
578	C₂×C₃×C₄	—	5	2	no	—
579	C₂×C₃×C₄	—	5	1	no	—
580	C₂×C₃×C₄	—	10	2	no	—
581	C₂×C₃×C₄	—	10	2	no	—
582	C₂×C₃×C₄	—	10	2	no	—
583	C₂×C₃×C₄	—	10	1	no	—
584	C₂×C₃×C₄	—	10	1	no	—
585	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
586	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
587	#67	—	10	2	no	—
588	#67	—	10	2	no	—
589	#67	—	10	2	no	—
590	#67	#676	1	4	yes	direct product factor
591	C₂×Dic₃	—	5	1	no	—
592	C₂×Dic₃	—	5	1	no	—
593	C₂×Dic₃	—	5	1	no	—
594	C₂×Dic₃	—	10	2	no	—
595	C₂×Dic₃	—	10	2	no	—
596	C₂×Dic₃	—	20	1	no	—
597	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
598	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
599	C₂×Dic₃	C₂×C₄×D₅	1	1	yes	characteristic
600	C₄×D₃	—	2	1	no	—
601	C₄×D₃	—	2	1	no	—
602	C₄×D₃	—	10	2	no	—
603	C₄×D₃	—	10	2	no	—
604	C₄×D₃	—	10	1	no	—
605	C₄×D₃	—	10	1	no	—
606	C₃×C₈	—	2	1	no	—
607	C₃×C₈	—	5	2	no	—
608	C₃×C₈	—	10	1	no	—
609	C₃×C₈	D₄×D₅	1	2	yes	complemented
610	C₃⋊C₈	—	2	1	no	—
611	C₃⋊C₈	—	2	1	no	—
612	C₃⋊C₈	—	10	1	no	—
613	C₃⋊C₈	—	10	1	no	—
614	C₂²×C₅	—	2	1	no	—
615	C₂²×C₅	—	2	1	no	—
616	C₂²×C₅	—	3	2	no	—
617	C₂²×C₅	—	6	1	no	—
618	C₂²×C₅	—	6	1	no	—
619	C₂²×C₅	D₃×M₁₆	1	2	yes	complemented
620	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
621	C₂×D₅	—	2	1	no	—
622	C₂×D₅	—	2	1	no	—
623	C₂×D₅	—	2	1	no	—
624	C₂×D₅	—	2	1	no	—
625	C₂×D₅	—	2	1	no	—
626	C₂×D₅	—	4	4	no	—
627	C₂×D₅	—	6	1	no	—
628	C₂×D₅	—	6	1	no	—
629	C₂×D₅	—	6	1	no	—
630	C₂×D₅	—	12	4	no	—
631	C₂×D₅	C₄×#67	1	2	yes	—
632	C₄×C₅	—	2	1	no	—
633	C₄×C₅	—	3	2	no	—
634	C₄×C₅	—	6	1	no	—
635	C₄×C₅	—	6	1	no	—
636	C₄×C₅	C₂×#235	1	1	yes	characteristic
637	C₄×C₅	C₂²×#67	1	1	yes	characteristic
638	Dic₅	—	2	1	no	—
639	Dic₅	—	6	1	no	—
640	Dic₅	—	6	1	no	—
641	Dic₅	—	6	1	no	—
642	Dic₅	C₄×#67	1	2	yes	—
643	C₂⁴	—	5	1	no	—
644	C₂⁴	—	15	1	no	—
645	C₂×D₄	—	3	1	no	—
646	C₂×D₄	—	15	1	no	—
647	C₂×D₄	—	15	1	no	—
648	C₂×D₄	—	15	1	no	—
649	C₂×D₄	—	30	4	no	—
650	C₂²×C₄	—	3	1	no	—
651	C₂²×C₄	—	5	1	no	—
652	C₂²×C₄	—	5	1	no	—
653	C₂²×C₄	—	5	1	no	—
654	C₂²×C₄	—	5	1	no	—
655	C₂²×C₄	—	5	1	no	—
656	C₂²×C₄	—	10	2	no	—
657	C₂²×C₄	—	10	2	no	—
658	C₂²×C₄	—	15	1	no	—
659	C₂²×C₄	—	15	1	no	—
660	C₂²×C₄	—	15	1	no	—
661	C₂²×C₄	—	15	1	no	—
662	C₂²×C₄	—	15	1	no	—
663	C₂²×C₄	—	15	1	no	—
664	C₂²×C₄	—	30	2	no	—
665	C₂²×C₄	—	30	2	no	—
666	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
667	M₁₆	—	5	4	no	—
668	M₁₆	—	10	2	no	—
669	M₁₆	—	10	2	no	—
670	M₁₆	—	10	2	no	—
671	M₁₆	—	30	2	no	—
672	M₁₆	—	30	2	no	—
673	M₁₆	—	30	2	no	—
674	M₁₆	—	30	2	no	—
675	C₂×C₈	—	2	2	no	—
676	C₂×C₈	—	3	1	no	—
677	C₂×C₈	—	3	1	no	—
678	C₂×C₈	—	5	1	no	—
679	C₂×C₈	—	5	1	no	—
680	C₂×C₈	—	6	2	no	—
681	C₂×C₈	—	10	2	no	—
682	C₂×C₈	—	15	1	no	—
683	C₂×C₈	—	15	1	no	—
684	C₂×C₈	—	30	2	no	—
685	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
686	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
687	C₄⋊C₄	—	3	1	no	—
688	C₄⋊C₄	—	15	1	no	—
689	C₄⋊C₄	—	15	1	no	—
690	C₄⋊C₄	—	15	1	no	—
691	C₂²⋊C₄	—	3	1	no	—
692	C₂²⋊C₄	—	3	1	no	—
693	C₂²⋊C₄	—	15	1	no	—
694	C₂²⋊C₄	—	15	1	no	—
695	C₂²⋊C₄	—	15	1	no	—
696	C₂²⋊C₄	—	15	1	no	—
697	C₂²⋊C₄	—	15	1	no	—
698	C₂²⋊C₄	—	15	1	no	—
699	C₄²	—	3	1	no	—
700	C₄²	—	15	1	no	—
701	C₄²	—	15	1	no	—
702	C₄²	—	15	1	no	—
703	C₃×C₅	D₄×M₁₆	1	1	yes	characteristic, complemented, Hall
704	C₂²×C₃	—	2	1	no	—
705	C₂²×C₃	—	2	1	no	—
706	C₂²×C₃	—	5	2	no	—
707	C₂²×C₃	—	10	1	no	—
708	C₂²×C₃	—	10	1	no	—
709	C₂²×C₃	—	10	1	no	—
710	C₂²×C₃	—	10	1	no	—
711	C₂²×C₃	—	10	1	no	—
712	C₂²×C₃	—	20	4	no	—
713	C₂²×C₃	C₂×#676	1	2	yes	complemented
714	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
715	C₂×D₃	—	2	1	no	—
716	C₂×D₃	—	2	1	no	—
717	C₂×D₃	—	10	1	no	—
718	C₂×D₃	—	10	1	no	—
719	C₂×D₃	—	10	1	no	—
720	C₂×D₃	—	20	4	no	—
721	C₂×D₃	C₂×#676	1	2	yes	complemented
722	C₃×C₄	—	2	1	no	—
723	C₃×C₄	—	5	2	no	—
724	C₃×C₄	—	10	1	no	—
725	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
726	C₃×C₄	D₅×#41	1	1	yes	characteristic
727	Dic₃	—	2	1	no	—
728	Dic₃	—	2	1	no	—
729	Dic₃	—	10	1	no	—
730	Dic₃	—	10	1	no	—
731	Dic₃	—	10	1	no	—
732	Dic₃	C₂×#676	1	2	yes	complemented
733	C₂×C₅	—	2	2	no	—
734	C₂×C₅	—	6	2	no	—
735	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
736	C₂×C₅	#5745	1	1	yes	characteristic
737	C₂×C₅	C₂×C₄×#67	1	1	yes	characteristic
738	D₅	—	2	2	no	—
739	D₅	—	4	1	no	—
740	D₅	—	12	1	no	—
741	C₂³	—	3	1	no	—
742	C₂³	—	5	1	no	—
743	C₂³	—	5	1	no	—
744	C₂³	—	10	2	no	—
745	C₂³	—	10	2	no	—
746	C₂³	—	15	1	no	—
747	C₂³	—	20	1	no	—
748	C₂³	—	30	2	no	—
749	C₂³	—	30	2	no	—
750	C₂³	—	60	1	no	—
751	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
752	D₄	—	3	4	no	—
753	D₄	—	30	2	no	—
754	D₄	—	30	2	no	—
755	D₄	—	30	2	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	3	1	no	—
759	C₂×C₄	—	3	1	no	—
760	C₂×C₄	—	3	1	no	—
761	C₂×C₄	—	5	1	no	—
762	C₂×C₄	—	5	2	no	—
763	C₂×C₄	—	5	2	no	—
764	C₂×C₄	—	5	1	no	—
765	C₂×C₄	—	6	1	no	—
766	C₂×C₄	—	6	1	no	—
767	C₂×C₄	—	10	2	no	—
768	C₂×C₄	—	10	2	no	—
769	C₂×C₄	—	10	2	no	—
770	C₂×C₄	—	10	1	no	—
771	C₂×C₄	—	10	1	no	—
772	C₂×C₄	—	15	1	no	—
773	C₂×C₄	—	15	1	no	—
774	C₂×C₄	—	15	1	no	—
775	C₂×C₄	—	30	2	no	—
776	C₂×C₄	—	30	2	no	—
777	C₂×C₄	—	30	2	no	—
778	C₂×C₄	—	30	2	no	—
779	C₂×C₄	—	30	1	no	—
780	C₂×C₄	—	30	1	no	—
781	C₂×C₄	—	60	1	no	—
782	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
784	C₈	—	2	1	no	—
785	C₈	—	5	2	no	—
786	C₈	—	6	1	no	—
787	C₈	—	6	1	no	—
788	C₈	—	10	1	no	—
789	C₈	—	30	1	no	—
790	C₈	—	30	1	no	—
791	C₈	D₅×#67	1	2	yes	complemented
792	C₂×C₃	—	2	2	no	—
793	C₂×C₃	—	10	2	no	—
794	C₂×C₃	—	20	1	no	—
795	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
796	C₂×C₃	C₂²×#676	1	1	yes	characteristic
797	C₂×C₃	#66084	1	1	yes	characteristic
798	D₃	—	2	2	no	—
799	D₃	—	20	1	no	—
800	C₅	M₁₆×#67	1	1	yes	characteristic, complemented, Sylow
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	3	2	no	—
804	C₂²	—	5	2	no	—
805	C₂²	—	6	1	no	—
806	C₂²	—	6	1	no	—
807	C₂²	—	10	1	no	—
808	C₂²	—	10	1	no	—
809	C₂²	—	10	1	no	—
810	C₂²	—	10	1	no	—
811	C₂²	—	10	1	no	—
812	C₂²	—	20	4	no	—
813	C₂²	—	30	1	no	—
814	C₂²	—	30	1	no	—
815	C₂²	—	30	1	no	—
816	C₂²	—	60	4	no	—
817	C₂²	D₃×#676	1	2	yes	complemented
818	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
819	C₄	—	2	1	no	—
820	C₄	—	3	2	no	—
821	C₄	—	5	2	no	—
822	C₄	—	6	1	no	—
823	C₄	—	6	1	no	—
824	C₄	—	10	1	no	—
825	C₄	—	30	1	no	—
826	C₄	—	30	1	no	—
827	C₄	—	30	1	no	—
828	C₄	D₅×#235	1	1	yes	characteristic
829	C₄	C₂×D₅×#67	1	1	yes	characteristic
830	C₃	D₄×#676	1	1	yes	characteristic, complemented, Sylow
831	C₂	—	2	2	no	—
832	C₂	—	6	2	no	—
833	C₂	—	10	2	no	—
834	C₂	—	20	1	no	—
835	C₂	—	60	1	no	—
836	C₂	C₂×D₃×#676	1	1	yes	characteristic
837	C₂	#11753949	1	1	yes	characteristic
838	C₂	C₄×D₅×#67	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₂²×C₃×C₅×C₈	C₂²
prime radical	C₂×D₅×#67	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	D₄×M₁₆
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×#676	C₂	semidirect
3. C₂×D₃×#676	C₂	semidirect
4. #11751212	C₂	semidirect
5. C₅×C₈×#67	C₂	semidirect
6. #11748502	C₂	semidirect
7. #11748499	C₂	semidirect
8. #67×#168	C₂	semidirect
9. #11748101	C₂	semidirect
10. #11747717	C₂	semidirect
11. #11747715	C₂	semidirect
12. #11747713	C₂	semidirect
13. #11747711	C₂	semidirect
14. #11747596	C₂	semidirect
15. Dic₃×#676	C₂	semidirect
20. C₂²×C₃×C₅×C₈	C₂²	semidirect
22. C₂×#6705	C₂²	semidirect
24. C₂×C₅×D₃×C₈	C₂²	semidirect
25. C₂²×C₃×#168	C₂²	semidirect
29. C₂×C₃×#676	C₂²	semidirect
30. C₂×C₃×#676	C₂²	semidirect
41. C₂×#6651	C₂²	semidirect
44. C₂×D₃×#168	C₂²	semidirect
46. #91114	C₂²	semidirect
47. #91104	C₂²	semidirect
48. #91099	C₂²	semidirect
49. #91098	C₂²	semidirect
50. C₅×#830	C₂²	semidirect
51. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
52. C₅×Dic₃⋊C₈	C₂²	semidirect
53. C₅×C₈×Dic₃	C₂²	semidirect
54. Dic₃⋊#168	C₂²	semidirect
55. #90983	C₂²	semidirect
56. #90957	C₂²	semidirect
57. (C₂×D₃)⋊#168	C₂²	semidirect
58. #90955	C₂²	semidirect
59. #90955	C₂²	semidirect
60. #90954	C₂²	semidirect
61. Dic₃×#168	C₂²	semidirect
64. C₂²×#676	D₃	semidirect
125. C₃×#676	D₄	semidirect
152. C₈×#67	D₅	semidirect
157. C₂²×C₅×C₈	C₂×D₃	semidirect
163. C₂²×#168	C₂×D₃	semidirect
172. C₂×#676	C₂×D₃	semidirect
173. C₂×#676	C₂×D₃	semidirect
220. C₅×#67	M₁₆	semidirect
243. C₃×C₅×C₈	C₂×D₄	semidirect
247. C₃×#168	C₂×D₄	semidirect
259. C₂²×C₃×C₈	C₂×D₅	semidirect
278. C₂×D₃×C₈	C₂×D₅	semidirect
282. #830	C₂×D₅	semidirect
286. (C₂×D₃)⋊C₈	C₂×D₅	semidirect
292. Dic₃⋊C₈	C₂×D₅	semidirect
294. C₈×Dic₃	C₂×D₅	semidirect
354. #676	#67	direct (N × H)
372. C₂²×C₃×C₅	C₂×M₁₆	semidirect
379. C₂×C₅×D₃	C₂×M₁₆	semidirect
398. C₅×Dic₃	C₂×M₁₆	semidirect
505. C₅×C₈	C₂×#67	semidirect
509. #168	C₂×#67	semidirect
526. C₂²×C₈	D₃×D₅	semidirect
590. #67	#676	direct (N × H)
609. C₃×C₈	D₄×D₅	semidirect
619. C₂²×C₅	D₃×M₁₆	semidirect
703. C₃×C₅	D₄×M₁₆	semidirect
713. C₂²×C₃	C₂×#676	semidirect
721. C₂×D₃	C₂×#676	semidirect
732. Dic₃	C₂×#676	semidirect
791. C₈	D₅×#67	semidirect
800. C₅	M₁₆×#67	semidirect
817. C₂²	D₃×#676	semidirect
830. C₃	D₄×#676	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×#676	2
C₄×D₅×#67	2
C₂×D₃×#676	2
#11751212	2
C₅×C₈×#67	2
#11748502	2
#11748499	2
#67×#168	2
#11748101	2
#11747717	2
#11747715	2
#11747713	2
#11747711	2
#11747596	2
Dic₃×#676	2
D₄×#676	3
M₁₆×#67	5