Subgroups — #21459549

Order 7808.

1142 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840474	C₂	1	2	yes	maximal, complemented
2	#16840461	C₂	1	2	yes	maximal, complemented
3	#16840455	C₂	1	2	yes	maximal, complemented
4	#16840442	C₂	1	2	yes	maximal, complemented
5	#16840441	C₂	1	2	yes	maximal, complemented
6	#16840411	C₂	1	2	yes	maximal, complemented
7	#16840401	C₂	1	2	yes	maximal, complemented
8	#16840400	C₂	1	2	yes	maximal, complemented
9	#16840389	C₂	1	1	yes	maximal, characteristic, complemented
10	#16840386	C₂	1	1	yes	maximal, characteristic, complemented
11	#16840377	C₂	1	1	yes	maximal, characteristic, complemented
12	#16840366	C₂	1	1	yes	maximal, characteristic, complemented
13	#16840363	C₂	1	1	yes	maximal, characteristic, complemented
14	#16840325	C₂	1	1	yes	maximal, characteristic, complemented
15	#16840307	C₂	1	1	yes	maximal, characteristic, complemented
16	#16840296	C₂	1	1	yes	maximal, characteristic, complemented
17	#16840293	C₂	1	1	yes	maximal, characteristic, complemented
18	#16840272	C₂	1	1	yes	maximal, characteristic, complemented
19	#121×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
20	#16840241	C₂	1	1	yes	maximal, characteristic, complemented
21	#16840234	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#14519734	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11758224	C₂²	1	1	yes	characteristic
25	C₂×#11758224	C₂²	1	2	yes	complemented
26	C₂×D₄×D₆₁	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₆₁	C₂²	1	2	yes	—
28	C₂²×C₄×D₆₁	C₂²	1	1	yes	characteristic
29	#14519776	C₂²	1	1	yes	characteristic, complemented
30	#14519775	C₂²	1	2	yes	complemented
31	#14519773	C₂²	1	1	yes	characteristic, complemented
32	#14519772	C₂²	1	2	yes	complemented
33	#14519771	C₂²	1	2	yes	complemented
34	#14519770	C₂²	1	2	yes	complemented
35	#14519770	C₂²	1	2	yes	complemented
36	#14519769	C₂²	1	1	yes	characteristic, complemented
37	#14519768	C₂²	1	1	yes	characteristic, complemented
38	#14519767	C₂²	1	2	yes	complemented
39	#14519766	C₂²	1	2	yes	complemented
40	#14519765	C₂²	1	1	yes	characteristic, complemented
41	#14519764	C₂²	1	1	yes	characteristic, complemented
42	#14519763	C₂²	1	2	yes	complemented
43	#14519763	C₂²	1	2	yes	complemented
44	#14519762	C₂²	1	2	yes	complemented
45	#14519760	C₂²	1	2	yes	complemented
46	#14519760	C₂²	1	2	yes	complemented
47	#14519760	C₂²	1	2	yes	complemented
48	#14519759	C₂²	1	2	yes	—
49	#14519759	C₂²	1	2	yes	complemented
50	#14519758	C₂²	1	2	yes	complemented
51	#14519758	C₂²	1	2	yes	complemented
52	#14519758	C₂²	1	2	yes	complemented
53	#14519757	C₂²	1	1	yes	characteristic, complemented
54	#14519756	C₂²	1	1	yes	characteristic, complemented
55	#14519756	C₂²	1	2	yes	complemented
56	#14519755	C₂²	1	2	yes	—
57	#14519753	C₂²	1	2	yes	—
58	#14519753	C₂²	1	2	yes	complemented
59	#14519752	C₂²	1	1	yes	characteristic
60	#14519751	C₂²	1	1	yes	characteristic
61	#14519751	C₂²	1	2	yes	complemented
62	#14519750	C₂²	1	2	yes	—
63	#14519750	C₂²	1	2	yes	complemented
64	#14519749	C₂²	1	2	yes	—
65	#14519749	C₂²	1	2	yes	complemented
66	#14519749	C₂²	1	2	yes	complemented
67	#14519749	C₂²	1	2	yes	complemented
68	#14519749	C₂²	1	2	yes	complemented
69	#14519749	C₂²	1	2	yes	complemented
70	#14519748	C₂²	1	1	yes	characteristic
71	#14519748	C₂²	1	1	yes	characteristic, complemented
72	#14519745	C₂²	1	2	yes	—
73	#14519745	C₂²	1	2	yes	—
74	#14519745	C₂²	1	2	yes	—
75	C₄×Dic₁₂₂	C₂²	1	1	yes	characteristic, complemented
76	#14519742	C₂²	1	1	yes	characteristic, complemented
77	C₄×D₂₄₄	C₂²	1	1	yes	characteristic, complemented
78	D₄×Dic₆₁	C₂²	1	2	yes	complemented
79	D₄×Dic₆₁	C₂²	1	2	yes	complemented
80	D₄×Dic₆₁	C₂²	1	1	yes	characteristic, complemented
81	D₄×Dic₆₁	C₂²	1	1	yes	characteristic, complemented
82	#14519739	C₂²	1	1	yes	characteristic, complemented
83	C₄×C₂²⋊D₆₁	C₂²	1	2	yes	—
84	C₄×C₂²⋊D₆₁	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊D₆₁	C₂²	1	2	yes	complemented
86	#14519737	C₂²	1	2	yes	—
87	#14519737	C₂²	1	2	yes	complemented
88	#14519737	C₂²	1	2	yes	complemented
89	#14519737	C₂²	1	2	yes	complemented
90	#14519735	C₂²	1	1	yes	characteristic
91	#14519734	C₂²	1	1	yes	characteristic
92	#14519734	C₂²	1	1	yes	characteristic
93	#14519734	C₂²	1	1	yes	characteristic
94	#14519734	C₂²	1	1	yes	characteristic
95	#14519734	C₂²	1	1	yes	characteristic, complemented
96	#14519734	C₂²	1	1	yes	characteristic, complemented
97	#14519734	C₂²	1	1	yes	characteristic, complemented
98	#14519734	C₂²	1	1	yes	characteristic, complemented
99	#14519734	C₂²	1	2	yes	complemented
100	#14519733	C₂²	1	2	yes	complemented
101	#14519733	C₂²	1	2	yes	complemented
102	C₂×#11758196	C₂²	1	1	yes	characteristic, complemented
103	C₂×#11758196	C₂²	1	2	yes	complemented
104	C₂×#11758196	C₂²	1	1	yes	characteristic, complemented
105	C₄⋊C₄×D₆₁	C₂²	1	1	yes	characteristic
106	C₂×#11758198	C₂²	1	1	yes	characteristic
107	C₂×#11758198	C₂²	1	1	yes	characteristic
108	C₂×#11758198	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₆₁	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₆₁	C₂²	1	2	yes	—
111	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₆₁	C₂²	1	2	yes	complemented
113	C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
114	#127×C₆₁	C₂²	1	1	yes	characteristic, complemented
115	#124×C₆₁	C₂²	1	2	yes	complemented
116	#121×C₆₁	C₂²	1	1	yes	characteristic
117	#121×C₆₁	C₂²	1	2	yes	complemented
118	#121×C₆₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₆₁	C₂²	1	2	yes	complemented
120	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₆₁	C₂³	1	1	yes	characteristic
124	C₂³×D₆₁	C₂³	1	2	yes	—
125	#41×C₆₁	—	4	4	no	—
126	C₂×Q₈×C₆₁	C₂³	1	2	yes	—
127	C₂×D₄×C₆₁	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₆₁	C₂³	1	2	yes	—
129	C₂×D₄×C₆₁	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₆₁	C₂³	1	2	yes	—
131	C₂×D₄×C₆₁	C₂³	1	2	yes	—
132	C₂×D₄×C₆₁	C₂³	1	2	yes	—
133	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
137	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
145	C₂²×Dic₆₁	C₂³	1	1	yes	characteristic
146	C₂²×Dic₆₁	C₂³	1	2	yes	—
147	C₂²×Dic₆₁	C₂³	1	1	yes	characteristic
148	C₂²×Dic₆₁	C₂³	1	2	yes	—
149	C₂²×Dic₆₁	C₂³	1	1	yes	characteristic
150	C₂²×Dic₆₁	C₂³	1	2	yes	—
151	#11758224	—	2	4	no	—
152	#11758224	—	4	4	no	—
153	D₄×D₆₁	—	2	4	no	—
154	D₄×D₆₁	—	4	4	no	—
155	C₂×D₂₄₄	C₂³	1	1	yes	characteristic
156	C₂×D₂₄₄	C₂³	1	2	yes	—
157	C₂×C₄×D₆₁	—	2	4	no	—
158	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₆₁	C₂³	1	2	yes	—
162	C₂×C₄×D₆₁	C₂³	1	2	yes	—
163	C₂×C₄×D₆₁	C₂³	1	2	yes	—
164	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
165	C₂×Dic₁₂₂	C₂³	1	1	yes	characteristic
166	C₂×Dic₁₂₂	C₂³	1	2	yes	—
167	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
168	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
169	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
170	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
171	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
172	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
174	C₄²×C₆₁	C₂³	1	1	yes	characteristic
175	C₄²×C₆₁	C₂³	1	1	yes	characteristic
176	C₄²×C₆₁	C₂³	1	1	yes	characteristic
177	C₄²×C₆₁	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₆₁	C₂³	1	2	yes	—
179	C₂²⋊Dic₆₁	C₂³	1	2	yes	—
180	C₂²⋊Dic₆₁	C₂³	1	2	yes	—
181	C₂²⋊Dic₆₁	C₂³	1	2	yes	—
182	C₂²⋊Dic₆₁	C₂³	1	2	yes	—
183	C₂²⋊Dic₆₁	C₂³	1	2	yes	—
184	C₂²⋊Dic₆₁	C₂³	1	2	yes	—
185	#11758198	C₂³	1	1	yes	characteristic
186	#11758198	C₂³	1	2	yes	—
187	#11758198	C₂³	1	2	yes	—
188	#11758198	C₂³	1	2	yes	—
189	#11758198	C₂³	1	1	yes	characteristic
190	#11758198	C₂³	1	1	yes	characteristic
191	#11758198	C₂³	1	1	yes	characteristic
192	#11758198	C₂³	1	1	yes	characteristic
193	#11758198	C₂³	1	1	yes	characteristic
194	#11758198	C₂³	1	1	yes	characteristic
195	#11758198	C₂³	1	1	yes	characteristic
196	#11758198	C₂³	1	2	yes	—
197	#11758198	C₂³	1	2	yes	—
198	#11758198	C₂³	1	2	yes	—
199	#11758198	C₂³	1	2	yes	—
200	#11758198	C₂³	1	2	yes	—
201	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₆₁	C₂³	1	2	yes	—
204	C₄⋊Dic₆₁	C₂³	1	2	yes	—
205	#11758196	C₂³	1	2	yes	—
206	#11758196	C₂³	1	1	yes	characteristic
207	#11758196	C₂³	1	1	yes	characteristic
208	#11758196	C₂³	1	1	yes	characteristic
209	#11758196	C₂³	1	1	yes	characteristic
210	#11758196	C₂³	1	1	yes	characteristic
211	#11758196	C₂³	1	1	yes	characteristic
212	#11758196	C₂³	1	1	yes	characteristic
213	#11758196	C₂³	1	1	yes	characteristic
214	#11758196	C₂³	1	2	yes	—
215	#11758196	C₂³	1	2	yes	—
216	#11758196	C₂³	1	2	yes	—
217	#11758196	C₂³	1	2	yes	—
218	#11758196	C₂³	1	2	yes	—
219	#11758196	C₂³	1	2	yes	—
220	#11758196	C₂³	1	2	yes	—
221	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
222	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
223	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
224	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
225	C₄×Dic₆₁	C₂³	1	2	yes	—
226	C₄×Dic₆₁	C₂³	1	2	yes	—
227	C₄×Dic₆₁	C₂³	1	2	yes	—
228	C₂³×C₆₁	C₂⁴	1	2	yes	—
229	C₂³×C₆₁	C₂⁴	1	2	yes	—
230	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
231	C₂²×D₆₁	—	2	2	no	—
232	C₂²×D₆₁	—	2	2	no	—
233	C₂²×D₆₁	—	2	4	no	—
234	C₂²×D₆₁	—	4	1	no	—
235	C₂²×D₆₁	—	4	2	no	—
236	C₂²×D₆₁	—	4	2	no	—
237	C₂²×D₆₁	C₂⁴	1	1	yes	characteristic
238	C₂²×D₆₁	C₂⁴	1	2	yes	—
239	C₂²×D₆₁	C₂⁴	1	1	yes	characteristic
240	Q₈×C₆₁	—	4	2	no	—
241	D₄×C₆₁	—	2	4	no	—
242	D₄×C₆₁	—	2	4	no	—
243	D₄×C₆₁	—	2	2	no	—
244	D₄×C₆₁	—	2	2	no	—
245	D₄×C₆₁	—	4	2	no	—
246	D₄×C₆₁	—	4	2	no	—
247	C₂×C₄×C₆₁	—	2	2	no	—
248	C₂×C₄×C₆₁	—	2	2	no	—
249	C₂×C₄×C₆₁	—	4	1	no	—
250	C₂×C₄×C₆₁	—	4	2	no	—
251	C₂×C₄×C₆₁	—	4	2	no	—
252	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
255	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
256	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
260	C₂²⋊D₆₁	—	2	4	no	—
261	C₂²⋊D₆₁	—	2	4	no	—
262	C₂²⋊D₆₁	—	2	4	no	—
263	C₂²⋊D₆₁	—	4	2	no	—
264	C₂²⋊D₆₁	—	4	2	no	—
265	C₂²⋊D₆₁	—	4	2	no	—
266	C₂²⋊D₆₁	—	4	2	no	—
267	C₂×Dic₆₁	—	2	2	no	—
268	C₂×Dic₆₁	—	2	2	no	—
269	C₂×Dic₆₁	—	2	4	no	—
270	C₂×Dic₆₁	—	4	2	no	—
271	C₂×Dic₆₁	—	4	2	no	—
272	C₂×Dic₆₁	—	4	1	no	—
273	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₆₁	C₂⁴	1	2	yes	—
278	C₂×Dic₆₁	C₂⁴	1	2	yes	—
279	C₂×Dic₆₁	C₂⁴	1	2	yes	—
280	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
282	D₂₄₄	—	2	2	no	—
283	D₂₄₄	—	4	2	no	—
284	C₄×D₆₁	—	2	2	no	—
285	C₄×D₆₁	—	2	2	no	—
286	C₄×D₆₁	—	2	2	no	—
287	C₄×D₆₁	—	4	2	no	—
288	C₄×D₆₁	—	4	2	no	—
289	C₄×D₆₁	—	4	2	no	—
290	C₄×D₆₁	#41	1	4	yes	complemented
291	Dic₁₂₂	—	2	2	no	—
292	Dic₁₂₂	—	4	2	no	—
293	C₂²×C₆₁	—	2	1	no	—
294	C₂²×C₆₁	—	2	1	no	—
295	C₂²×C₆₁	—	2	2	no	—
296	C₂²×C₆₁	—	2	2	no	—
297	C₂²×C₆₁	—	2	2	no	—
298	C₂²×C₆₁	—	2	2	no	—
299	C₂²×C₆₁	—	2	2	no	—
300	C₂²×C₆₁	—	2	2	no	—
301	C₂²×C₆₁	H(5,𝔽₂)	1	2	yes	—
302	C₂²×C₆₁	C₂⁵	1	1	yes	characteristic
303	C₂×D₆₁	—	2	1	no	—
304	C₂×D₆₁	—	2	1	no	—
305	C₂×D₆₁	—	2	1	no	—
306	C₂×D₆₁	—	2	2	no	—
307	C₂×D₆₁	—	2	2	no	—
308	C₂×D₆₁	—	2	1	no	—
309	C₂×D₆₁	—	2	2	no	—
310	C₂×D₆₁	—	2	1	no	—
311	C₂×D₆₁	—	4	4	no	—
312	C₂×D₆₁	—	8	4	no	—
313	C₂×D₆₁	C₂×#41	1	2	yes	—
314	C₄×C₆₁	—	2	1	no	—
315	C₄×C₆₁	—	2	2	no	—
316	C₄×C₆₁	—	2	2	no	—
317	C₄×C₆₁	—	2	1	no	—
318	C₄×C₆₁	—	2	1	no	—
319	C₄×C₆₁	—	2	1	no	—
320	C₄×C₆₁	—	2	1	no	—
321	C₄×C₆₁	C₂×#41	1	2	yes	—
322	Dic₆₁	—	2	2	no	—
323	Dic₆₁	—	2	1	no	—
324	Dic₆₁	—	2	1	no	—
325	Dic₆₁	—	2	2	no	—
326	Dic₆₁	—	2	1	no	—
327	Dic₆₁	—	2	2	no	—
328	Dic₆₁	—	2	1	no	—
329	Dic₆₁	—	2	1	no	—
330	Dic₆₁	C₂×#41	1	2	yes	—
331	#3494	—	61	1	no	maximal, Sylow
332	C₂×C₆₁	—	2	2	no	—
333	C₂×C₆₁	—	4	2	no	—
334	C₂×C₆₁	—	4	2	no	—
335	C₂×C₆₁	C₂²×#41	1	1	yes	characteristic
336	C₂×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
337	C₂×C₆₁	#585	1	1	yes	characteristic
338	D₆₁	—	2	2	no	—
339	D₆₁	—	4	1	no	—
340	D₆₁	—	4	2	no	—
341	#555	—	61	2	no	—
342	#553	—	61	2	no	—
343	#553	—	61	2	no	—
344	#551	—	61	2	no	—
345	#551	—	61	2	no	—
346	#547	—	61	2	no	—
347	#546	—	61	2	no	—
348	#546	—	61	2	no	—
349	#544	—	61	1	no	—
350	#542	—	61	1	no	—
351	#542	—	61	1	no	—
352	#540	—	61	1	no	—
353	#540	—	61	1	no	—
354	#535	—	61	1	no	—
355	#532	—	61	1	no	—
356	#532	D₆₁	1	1	yes	characteristic, complemented
357	#529	—	61	1	no	—
358	#529	—	61	1	no	—
359	#525	—	61	1	no	—
360	C₂×#121	—	61	1	no	—
361	#520	—	61	1	no	—
362	#518	—	61	1	no	—
363	C₂×#117	—	61	1	no	—
364	C₆₁	#3494	1	1	yes	characteristic, complemented, Sylow
365	C₂×#41	—	61	1	no	—
366	C₂×#41	—	61	2	no	—
367	C₂×#41	C₂×D₆₁	1	2	yes	complemented
368	C₂²×D₄	—	61	1	no	—
369	C₂²×D₄	—	61	2	no	—
370	C₂³×C₄	—	61	1	no	—
371	C₄⋊Q₈	—	61	2	no	—
372	C₄⋊Q₈	—	61	1	no	—
373	C₄⋊Q₈	C₂×D₆₁	1	1	yes	characteristic, complemented
374	#127	—	61	1	no	—
375	#127	C₂×D₆₁	1	1	yes	characteristic, complemented
376	#126	—	61	2	no	—
377	#126	—	61	2	no	—
378	#126	—	61	2	no	—
379	#126	—	61	2	no	—
380	#125	—	61	1	no	—
381	#125	—	61	2	no	—
382	#125	—	61	1	no	—
383	#124	—	61	2	no	—
384	#124	—	61	1	no	—
385	#124	—	61	2	no	—
386	#124	—	61	2	no	—
387	#124	—	61	1	no	—
388	#124	C₂×D₆₁	1	2	yes	complemented
389	#123	—	61	2	no	—
390	#123	—	61	2	no	—
391	#123	—	61	2	no	—
392	#123	—	61	2	no	—
393	#123	—	61	2	no	—
394	#123	—	61	2	no	—
395	#123	—	61	2	no	—
396	#123	—	61	2	no	—
397	#123	—	61	2	no	—
398	C₂²⋊Q₈	—	61	2	no	—
399	C₂²⋊Q₈	—	61	2	no	—
400	C₂²⋊Q₈	—	61	1	no	—
401	C₂²⋊Q₈	—	61	2	no	—
402	C₂²⋊Q₈	—	61	1	no	—
403	C₂²⋊Q₈	—	61	2	no	—
404	#121	—	61	1	no	—
405	#121	—	61	2	no	—
406	#121	—	61	1	no	—
407	#121	—	61	2	no	—
408	#121	—	61	2	no	—
409	#121	—	61	2	no	—
410	#121	—	61	2	no	—
411	#121	—	61	2	no	—
412	#121	—	61	1	no	—
413	#121	—	61	2	no	—
414	#121	—	61	1	no	—
415	#121	—	61	2	no	—
416	#121	—	61	2	no	—
417	#121	C₂×D₆₁	1	1	yes	characteristic
418	#121	C₂×D₆₁	1	1	yes	characteristic, complemented
419	#121	C₂×D₆₁	1	2	yes	complemented
420	#120	—	61	2	no	—
421	#120	—	61	2	no	—
422	#120	—	61	2	no	—
423	C₄×Q₈	—	61	1	no	—
424	C₄×Q₈	—	61	1	no	—
425	C₄×D₄	—	61	1	no	—
426	C₄×D₄	—	61	1	no	—
427	C₄×D₄	—	61	2	no	—
428	C₄×D₄	—	61	2	no	—
429	C₄×D₄	—	61	2	no	—
430	C₄×D₄	—	61	2	no	—
431	C₄×D₄	—	61	2	no	—
432	C₄×D₄	—	61	1	no	—
433	C₄×D₄	—	61	2	no	—
434	C₄×D₄	—	61	2	no	—
435	C₄×D₄	—	61	2	no	—
436	C₄×D₄	—	61	2	no	—
437	C₄×D₄	—	61	1	no	—
438	C₄×D₄	C₂×D₆₁	1	1	yes	characteristic, complemented
439	C₄×D₄	C₂×D₆₁	1	1	yes	characteristic, complemented
440	C₄×D₄	C₂×D₆₁	1	2	yes	complemented
441	#117	—	61	1	no	—
442	#117	—	61	2	no	—
443	#117	—	61	2	no	—
444	#117	—	61	1	no	—
445	#117	—	61	1	no	—
446	#117	—	61	1	no	—
447	#117	—	61	1	no	—
448	#117	—	61	1	no	—
449	#117	—	61	1	no	—
450	#117	—	61	1	no	—
451	#117	—	61	1	no	—
452	#117	—	61	2	no	—
453	C₂×C₄⋊C₄	—	61	1	no	—
454	C₂×C₄⋊C₄	—	61	1	no	—
455	C₂×C₄⋊C₄	—	61	2	no	—
456	C₂×C₄⋊C₄	—	61	1	no	—
457	C₂×C₂²⋊C₄	—	61	1	no	—
458	C₂×C₂²⋊C₄	—	61	1	no	—
459	C₂×C₂²⋊C₄	—	61	2	no	—
460	C₂×C₂²⋊C₄	—	61	2	no	—
461	C₂×C₂²⋊C₄	—	61	2	no	—
462	C₂×C₄²	—	61	1	no	—
463	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic, complemented
464	C₂⁴	—	61	1	no	—
465	C₂⁴	—	61	2	no	—
466	#41	—	4	4	no	—
467	#41	—	122	4	no	—
468	#41	—	244	4	no	—
469	C₂×Q₈	—	61	1	no	—
470	C₂×Q₈	—	61	2	no	—
471	C₂×Q₈	C₂²×D₆₁	1	2	yes	—
472	C₂×D₄	—	61	2	no	—
473	C₂×D₄	—	61	2	no	—
474	C₂×D₄	—	61	2	no	—
475	C₂×D₄	—	61	2	no	—
476	C₂×D₄	—	61	2	no	—
477	C₂×D₄	—	61	2	no	—
478	C₂×D₄	—	61	2	no	—
479	C₂×D₄	—	61	1	no	—
480	C₂×D₄	—	61	2	no	—
481	C₂×D₄	—	122	4	no	—
482	C₂×D₄	—	244	4	no	—
483	C₂×D₄	C₂²×D₆₁	1	1	yes	characteristic
484	C₂×D₄	C₂²×D₆₁	1	1	yes	characteristic
485	C₂×D₄	C₂²×D₆₁	1	2	yes	—
486	C₂×D₄	C₂²×D₆₁	1	2	yes	—
487	C₂×D₄	C₂²×D₆₁	1	2	yes	—
488	C₂×D₄	C₂²×D₆₁	1	2	yes	—
489	C₂²×C₄	—	61	1	no	—
490	C₂²×C₄	—	61	1	no	—
491	C₂²×C₄	—	61	1	no	—
492	C₂²×C₄	—	61	2	no	—
493	C₂²×C₄	—	61	1	no	—
494	C₂²×C₄	—	61	2	no	—
495	C₂²×C₄	—	61	2	no	—
496	C₂²×C₄	—	61	1	no	—
497	C₂²×C₄	—	61	1	no	—
498	C₂²×C₄	—	61	1	no	—
499	C₂²×C₄	—	61	2	no	—
500	C₂²×C₄	—	61	2	no	—
501	C₂²×C₄	—	61	2	no	—
502	C₂²×C₄	—	122	4	no	—
503	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
504	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
505	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
506	C₂²×C₄	C₂²×D₆₁	1	2	yes	—
507	C₂²×C₄	C₂²×D₆₁	1	2	yes	—
508	C₄⋊C₄	—	61	1	no	—
509	C₄⋊C₄	—	61	2	no	—
510	C₄⋊C₄	—	61	1	no	—
511	C₄⋊C₄	—	61	1	no	—
512	C₄⋊C₄	—	61	1	no	—
513	C₄⋊C₄	—	61	1	no	—
514	C₄⋊C₄	—	61	1	no	—
515	C₄⋊C₄	—	61	1	no	—
516	C₄⋊C₄	—	61	1	no	—
517	C₄⋊C₄	—	61	2	no	—
518	C₄⋊C₄	—	61	2	no	—
519	C₄⋊C₄	—	61	1	no	—
520	C₄⋊C₄	—	61	2	no	—
521	C₄⋊C₄	—	61	2	no	—
522	C₄⋊C₄	—	61	2	no	—
523	C₄⋊C₄	—	61	2	no	—
524	C₄⋊C₄	—	61	2	no	—
525	C₄⋊C₄	—	61	1	no	—
526	C₄⋊C₄	—	61	2	no	—
527	C₄⋊C₄	—	61	2	no	—
528	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
529	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
530	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
531	C₂²⋊C₄	—	61	2	no	—
532	C₂²⋊C₄	—	61	2	no	—
533	C₂²⋊C₄	—	61	2	no	—
534	C₂²⋊C₄	—	61	2	no	—
535	C₂²⋊C₄	—	61	2	no	—
536	C₂²⋊C₄	—	61	2	no	—
537	C₂²⋊C₄	—	61	2	no	—
538	C₂²⋊C₄	—	61	1	no	—
539	C₂²⋊C₄	—	61	1	no	—
540	C₂²⋊C₄	—	61	2	no	—
541	C₂²⋊C₄	—	61	1	no	—
542	C₂²⋊C₄	—	61	1	no	—
543	C₂²⋊C₄	—	61	1	no	—
544	C₂²⋊C₄	—	61	1	no	—
545	C₂²⋊C₄	—	61	1	no	—
546	C₂²⋊C₄	—	61	1	no	—
547	C₂²⋊C₄	—	61	2	no	—
548	C₂²⋊C₄	—	61	2	no	—
549	C₂²⋊C₄	—	61	2	no	—
550	C₂²⋊C₄	—	61	2	no	—
551	C₂²⋊C₄	—	61	2	no	—
552	C₂²⋊C₄	—	61	2	no	—
553	C₂²⋊C₄	—	61	2	no	—
554	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
557	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
558	C₄²	—	61	1	no	—
559	C₄²	—	61	1	no	—
560	C₄²	—	61	1	no	—
561	C₄²	—	61	1	no	—
562	C₄²	—	61	2	no	—
563	C₄²	—	61	2	no	—
564	C₄²	—	61	2	no	—
565	C₄²	C₂²×D₆₁	1	1	yes	characteristic
566	C₄²	C₂²×D₆₁	1	1	yes	characteristic
567	C₄²	C₂²×D₆₁	1	1	yes	characteristic
568	C₄²	C₂²×D₆₁	1	1	yes	characteristic
569	C₂³	—	61	1	no	—
570	C₂³	—	61	1	no	—
571	C₂³	—	61	2	no	—
572	C₂³	—	122	4	no	—
573	C₂³	—	122	2	no	—
574	C₂³	—	122	2	no	—
575	C₂³	—	244	2	no	—
576	C₂³	—	244	2	no	—
577	C₂³	—	244	1	no	—
578	C₂³	C₂³×D₆₁	1	2	yes	—
579	C₂³	C₂³×D₆₁	1	2	yes	—
580	C₂³	C₂³×D₆₁	1	1	yes	characteristic
581	Q₈	—	4	2	no	—
582	Q₈	—	122	2	no	—
583	Q₈	—	244	2	no	—
584	D₄	—	2	4	no	—
585	D₄	—	2	4	no	—
586	D₄	—	2	2	no	—
587	D₄	—	2	2	no	—
588	D₄	—	4	2	no	—
589	D₄	—	4	2	no	—
590	D₄	—	122	4	no	—
591	D₄	—	122	4	no	—
592	D₄	—	122	4	no	—
593	D₄	—	122	2	no	—
594	D₄	—	244	2	no	—
595	D₄	—	244	2	no	—
596	D₄	—	244	2	no	—
597	D₄	—	244	2	no	—
598	D₄	—	244	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	61	1	no	—
605	C₂×C₄	—	61	4	no	—
606	C₂×C₄	—	61	1	no	—
607	C₂×C₄	—	61	2	no	—
608	C₂×C₄	—	61	1	no	—
609	C₂×C₄	—	61	1	no	—
610	C₂×C₄	—	61	1	no	—
611	C₂×C₄	—	61	2	no	—
612	C₂×C₄	—	61	2	no	—
613	C₂×C₄	—	61	1	no	—
614	C₂×C₄	—	122	2	no	—
615	C₂×C₄	—	122	2	no	—
616	C₂×C₄	—	122	2	no	—
617	C₂×C₄	—	122	4	no	—
618	C₂×C₄	—	122	2	no	—
619	C₂×C₄	—	122	2	no	—
620	C₂×C₄	—	244	2	no	—
621	C₂×C₄	—	244	2	no	—
622	C₂×C₄	—	244	2	no	—
623	C₂×C₄	—	244	2	no	—
624	C₂×C₄	—	244	1	no	—
625	C₂×C₄	—	244	2	no	—
626	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₆₁	1	2	yes	—
629	C₂×C₄	C₂³×D₆₁	1	2	yes	—
630	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
631	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
632	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
634	C₂²	—	2	1	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	61	2	no	—
643	C₂²	—	122	1	no	—
644	C₂²	—	122	1	no	—
645	C₂²	—	122	1	no	—
646	C₂²	—	122	2	no	—
647	C₂²	—	122	2	no	—
648	C₂²	—	122	1	no	—
649	C₂²	—	122	2	no	—
650	C₂²	—	122	1	no	—
651	C₂²	—	488	4	no	—
652	C₂²	—	244	4	no	—
653	C₂²	#14519822	1	2	yes	—
654	C₂²	C₂⁴×D₆₁	1	1	yes	characteristic
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	2	no	—
660	C₄	—	2	1	no	—
661	C₄	—	2	1	no	—
662	C₄	—	61	2	no	—
663	C₄	—	122	1	no	—
664	C₄	—	122	2	no	—
665	C₄	—	122	1	no	—
666	C₄	—	122	1	no	—
667	C₄	—	122	2	no	—
668	C₄	—	122	1	no	—
669	C₄	—	122	2	no	—
670	C₄	—	122	1	no	—
671	C₄	#41×D₆₁	1	2	yes	—
672	C₂	—	2	2	no	—
673	C₂	—	4	2	no	—
674	C₂	—	4	2	no	—
675	C₂	—	122	2	no	—
676	C₂	—	244	2	no	—
677	C₂	—	244	1	no	—
678	C₂	C₂×#41×D₆₁	1	1	yes	characteristic
679	C₂	C₂×#14519822	1	1	yes	characteristic
680	C₂	#16840598	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₁
commutator, socle	C₂²×C₆₁	C₂⁵
Fitting	C₆₁×#532	C₂
hypercenter	#532	D₆₁
hypocenter	C₆₁	#3494
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. #16840474	C₂	semidirect
2. #16840461	C₂	semidirect
3. #16840455	C₂	semidirect
4. #16840442	C₂	semidirect
5. #16840441	C₂	semidirect
6. #16840411	C₂	semidirect
7. #16840401	C₂	semidirect
8. #16840400	C₂	semidirect
9. #16840389	C₂	semidirect
10. #16840386	C₂	semidirect
11. #16840377	C₂	semidirect
12. #16840366	C₂	semidirect
13. #16840363	C₂	semidirect
14. #16840325	C₂	semidirect
15. #16840307	C₂	semidirect
16. #16840296	C₂	semidirect
17. #16840293	C₂	semidirect
18. #16840272	C₂	semidirect
19. #121×D₆₁	C₂	semidirect
20. #16840241	C₂	semidirect
21. #16840234	C₂	semidirect
22. C₂×#14519734	C₂	semidirect
23. C₆₁×#532	C₂	semidirect
25. C₂×#11758224	C₂²	semidirect
29. #14519776	C₂²	semidirect
30. #14519775	C₂²	semidirect
31. #14519773	C₂²	semidirect
32. #14519772	C₂²	semidirect
33. #14519771	C₂²	semidirect
34. #14519770	C₂²	semidirect
35. #14519770	C₂²	semidirect
36. #14519769	C₂²	semidirect
37. #14519768	C₂²	semidirect
38. #14519767	C₂²	semidirect
39. #14519766	C₂²	semidirect
40. #14519765	C₂²	semidirect
41. #14519764	C₂²	semidirect
42. #14519763	C₂²	semidirect
43. #14519763	C₂²	semidirect
44. #14519762	C₂²	semidirect
45. #14519760	C₂²	semidirect
46. #14519760	C₂²	semidirect
47. #14519760	C₂²	semidirect
49. #14519759	C₂²	semidirect
50. #14519758	C₂²	semidirect
51. #14519758	C₂²	semidirect
52. #14519758	C₂²	semidirect
53. #14519757	C₂²	semidirect
54. #14519756	C₂²	semidirect
55. #14519756	C₂²	semidirect
58. #14519753	C₂²	semidirect
61. #14519751	C₂²	semidirect
63. #14519750	C₂²	semidirect
65. #14519749	C₂²	semidirect
66. #14519749	C₂²	semidirect
67. #14519749	C₂²	semidirect
68. #14519749	C₂²	semidirect
69. #14519749	C₂²	semidirect
71. #14519748	C₂²	semidirect
75. C₄×Dic₁₂₂	C₂²	semidirect
76. #14519742	C₂²	semidirect
77. C₄×D₂₄₄	C₂²	semidirect
78. D₄×Dic₆₁	C₂²	semidirect
79. D₄×Dic₆₁	C₂²	semidirect
80. D₄×Dic₆₁	C₂²	semidirect
81. D₄×Dic₆₁	C₂²	semidirect
82. #14519739	C₂²	semidirect
84. C₄×C₂²⋊D₆₁	C₂²	semidirect
85. C₄×C₂²⋊D₆₁	C₂²	semidirect
87. #14519737	C₂²	semidirect
88. #14519737	C₂²	semidirect
89. #14519737	C₂²	semidirect
95. #14519734	C₂²	semidirect
96. #14519734	C₂²	semidirect
97. #14519734	C₂²	semidirect
98. #14519734	C₂²	semidirect
99. #14519734	C₂²	semidirect
100. #14519733	C₂²	semidirect
101. #14519733	C₂²	semidirect
102. C₂×#11758196	C₂²	semidirect
103. C₂×#11758196	C₂²	semidirect
104. C₂×#11758196	C₂²	semidirect
111. C₂×C₄×Dic₆₁	C₂²	semidirect
112. C₂×#41×C₆₁	C₂²	semidirect
113. C₄⋊Q₈×C₆₁	C₂²	semidirect
114. #127×C₆₁	C₂²	semidirect
115. #124×C₆₁	C₂²	semidirect
117. #121×C₆₁	C₂²	semidirect
118. #121×C₆₁	C₂²	semidirect
119. C₄×D₄×C₆₁	C₂²	semidirect
120. C₄×D₄×C₆₁	C₂²	semidirect
121. C₄×D₄×C₆₁	C₂²	semidirect
122. C₂×C₄²×C₆₁	C₂²	semidirect
290. C₄×D₆₁	#41	semidirect
356. #532	D₆₁	semidirect
364. C₆₁	#3494	semidirect
367. C₂×#41	C₂×D₆₁	semidirect
373. C₄⋊Q₈	C₂×D₆₁	semidirect
375. #127	C₂×D₆₁	semidirect
388. #124	C₂×D₆₁	semidirect
418. #121	C₂×D₆₁	semidirect
419. #121	C₂×D₆₁	semidirect
438. C₄×D₄	C₂×D₆₁	semidirect
439. C₄×D₄	C₂×D₆₁	semidirect
440. C₄×D₄	C₂×D₆₁	semidirect
463. C₂×C₄²	C₂×D₆₁	semidirect