Subgroups — #31820474

Order 17792.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22581676	C₂	1	1	yes	maximal, characteristic, complemented
2	#22581675	C₂	1	1	yes	maximal, characteristic, complemented
3	#22581660	C₂	1	1	yes	maximal, characteristic, complemented
4	#22581651	C₂	1	1	yes	maximal, characteristic, complemented
5	#22581649	C₂	1	2	yes	maximal, complemented
6	#22581638	C₂	1	1	yes	maximal, characteristic, complemented
7	#22581636	C₂	1	2	yes	maximal, complemented
8	#22581632	C₂	1	2	yes	maximal, complemented
9	#22581627	C₂	1	2	yes	maximal, complemented
10	#22581602	C₂	1	1	yes	maximal, characteristic, complemented
11	#22581598	C₂	1	1	yes	maximal, characteristic, complemented
12	#22581591	C₂	1	1	yes	maximal, characteristic, complemented
13	#22581574	C₂	1	1	yes	maximal, characteristic, complemented
14	#22581561	C₂	1	1	yes	maximal, characteristic, complemented
15	#22581550	C₂	1	2	yes	maximal, complemented
16	#22581536	C₂	1	2	yes	maximal, complemented
17	#22581490	C₂	1	1	yes	maximal, characteristic, complemented
18	#22581483	C₂	1	2	yes	maximal, complemented
19	#22581481	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#17984837	C₂	1	2	yes	maximal, complemented
21	#22581425	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#14555784	C₂	1	1	yes	maximal, characteristic, complemented
23	#520×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14555784	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₁₃₉	C₂²	1	1	yes	characteristic
26	#17984842	C₂²	1	1	yes	characteristic, complemented
27	#17984840	C₂²	1	1	yes	characteristic, complemented
28	#17984837	C₂²	1	2	yes	—
29	#17984837	C₂²	1	2	yes	—
30	#17984837	C₂²	1	2	yes	—
31	#17984837	C₂²	1	1	yes	characteristic
32	#17984837	C₂²	1	2	yes	complemented
33	#17984837	C₂²	1	2	yes	complemented
34	#17984837	C₂²	1	2	yes	complemented
35	#17984837	C₂²	1	2	yes	complemented
36	#17984837	C₂²	1	2	yes	complemented
37	#17984836	C₂²	1	2	yes	—
38	#17984836	C₂²	1	2	yes	complemented
39	#17984835	C₂²	1	1	yes	characteristic, complemented
40	#17984834	C₂²	1	2	yes	complemented
41	#17984833	C₂²	1	1	yes	characteristic, complemented
42	#17984833	C₂²	1	1	yes	characteristic, complemented
43	#17984832	C₂²	1	2	yes	complemented
44	#17984832	C₂²	1	2	yes	complemented
45	#17984832	C₂²	1	1	yes	characteristic, complemented
46	#17984831	C₂²	1	1	yes	characteristic
47	#17984830	C₂²	1	2	yes	—
48	#17984830	C₂²	1	1	yes	characteristic
49	#17984828	C₂²	1	1	yes	characteristic
50	#17984828	C₂²	1	2	yes	complemented
51	#17984827	C₂²	1	1	yes	characteristic
52	#17984827	C₂²	1	2	yes	complemented
53	#17984827	C₂²	1	2	yes	complemented
54	#17984826	C₂²	1	2	yes	—
55	#17984825	C₂²	1	2	yes	—
56	#17984825	C₂²	1	2	yes	—
57	#17984825	C₂²	1	2	yes	complemented
58	#17984824	C₂²	1	2	yes	complemented
59	#17984824	C₂²	1	1	yes	characteristic, complemented
60	#17984823	C₂²	1	2	yes	complemented
61	#17984822	C₂²	1	1	yes	characteristic
62	#17984821	C₂²	1	2	yes	complemented
63	#17984821	C₂²	1	1	yes	characteristic, complemented
64	#17984820	C₂²	1	1	yes	characteristic, complemented
65	#17984820	C₂²	1	2	yes	complemented
66	#17984820	C₂²	1	2	yes	complemented
67	#17984819	C₂²	1	2	yes	complemented
68	#17984819	C₂²	1	2	yes	complemented
69	#17984818	C₂²	1	1	yes	characteristic
70	#17984818	C₂²	1	1	yes	characteristic, complemented
71	#17984817	C₂²	1	1	yes	characteristic
72	#17984816	C₂²	1	2	yes	—
73	#17984816	C₂²	1	1	yes	characteristic
74	#17984816	C₂²	1	2	yes	complemented
75	#17984815	C₂²	1	1	yes	characteristic
76	#17984814	C₂²	1	2	yes	—
77	#17984814	C₂²	1	2	yes	complemented
78	#17984812	C₂²	1	2	yes	—
79	#17984810	C₂²	1	2	yes	—
80	C₄×Dic₂₇₈	C₂²	1	1	yes	characteristic, complemented
81	C₄×Dic₂₇₈	C₂²	1	2	yes	complemented
82	C₄×Dic₂₇₈	C₂²	1	1	yes	characteristic, complemented
83	#17984807	C₂²	1	1	yes	characteristic, complemented
84	C₄×D₅₅₆	C₂²	1	1	yes	characteristic
85	C₄×D₅₅₆	C₂²	1	1	yes	characteristic
86	C₄×D₅₅₆	C₂²	1	2	yes	complemented
87	D₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
88	D₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
89	#17984804	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊D₁₃₉	C₂²	1	2	yes	—
91	C₄×C₂²⋊D₁₃₉	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₁₃₉	C₂²	1	2	yes	complemented
93	C₄×C₂²⋊D₁₃₉	C₂²	1	1	yes	characteristic, complemented
94	C₄×C₂²⋊D₁₃₉	C₂²	1	2	yes	complemented
95	(C₂²⋊D₁₃₉)⋊C₄	C₂²	1	2	yes	—
96	(C₂²⋊D₁₃₉)⋊C₄	C₂²	1	2	yes	complemented
97	#17984801	C₂²	1	2	yes	complemented
98	#17984800	C₂²	1	1	yes	characteristic
99	#17984800	C₂²	1	1	yes	characteristic, complemented
100	#17984799	C₂²	1	1	yes	characteristic
101	#17984799	C₂²	1	2	yes	complemented
102	#17984799	C₂²	1	2	yes	complemented
103	#17984798	C₂²	1	2	yes	complemented
104	C₂×C₄⋊Dic₁₃₉	C₂²	1	2	yes	complemented
105	C₂×Dic₁₃₉⋊C₄	C₂²	1	2	yes	complemented
106	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	2	yes	—
107	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	2	yes	—
108	C₂×(C₂×D₁₃₉)⋊C₄	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₁₃₉	C₂²	1	2	yes	—
110	C₂×C₄×Dic₁₃₉	C₂²	1	2	yes	complemented
111	C₄²×D₁₃₉	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₁₃₉	C₂²	1	1	yes	characteristic
113	C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
114	C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
116	C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
117	C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
118	C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
119	#117×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
120	#117×C₁₃₉	C₂²	1	2	yes	complemented
121	C₂×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
122	C₂×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₃₉	C₂³	1	2	yes	—
124	#14555784	—	2	4	no	—
125	C₂×Dic₂₇₈	C₂³	1	1	yes	characteristic
126	C₂×Dic₂₇₈	C₂³	1	2	yes	—
127	C₂×Dic₂₇₈	C₂³	1	1	yes	characteristic
128	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
129	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
130	C₂×D₅₅₆	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₃₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₃₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₃₉	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₃₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₃₉	C₂³	1	1	yes	characteristic
136	D₄×D₁₃₉	—	2	4	no	—
137	C₂²×Dic₁₃₉	C₂³	1	2	yes	—
138	C₂²×Dic₁₃₉	C₂³	1	2	yes	—
139	C₂²×Dic₁₃₉	C₂³	1	2	yes	—
140	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₃₉	C₂³	1	2	yes	—
145	C₂×C₄×D₁₃₉	C₂³	1	2	yes	—
146	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
147	C₄⋊Dic₁₃₉	C₂³	1	2	yes	—
148	C₄⋊Dic₁₃₉	C₂³	1	2	yes	—
149	C₄⋊Dic₁₃₉	C₂³	1	2	yes	—
150	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₁₃₉	C₂³	1	2	yes	—
153	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
154	Dic₁₃₉⋊C₄	C₂³	1	1	yes	characteristic
155	Dic₁₃₉⋊C₄	C₂³	1	2	yes	—
156	Dic₁₃₉⋊C₄	C₂³	1	2	yes	—
157	Dic₁₃₉⋊C₄	C₂³	1	2	yes	—
158	Dic₁₃₉⋊C₄	C₂³	1	2	yes	—
159	Dic₁₃₉⋊C₄	C₂³	1	2	yes	—
160	Dic₁₃₉⋊C₄	C₂³	1	1	yes	characteristic
161	Dic₁₃₉⋊C₄	C₂³	1	1	yes	characteristic
162	Dic₁₃₉⋊C₄	C₂³	1	1	yes	characteristic
163	Dic₁₃₉⋊C₄	C₂³	1	2	yes	—
164	Dic₁₃₉⋊C₄	C₂³	1	2	yes	—
165	Dic₁₃₉⋊C₄	C₂³	1	1	yes	characteristic
166	Dic₁₃₉⋊C₄	C₂³	1	2	yes	—
167	Dic₁₃₉⋊C₄	C₂³	1	2	yes	—
168	Dic₁₃₉⋊C₄	C₂³	1	1	yes	characteristic
169	C₂²⋊Dic₁₃₉	C₂³	1	2	yes	—
170	C₂²⋊Dic₁₃₉	C₂³	1	2	yes	—
171	C₂²⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₁₃₉	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
174	(C₂×D₁₃₉)⋊C₄	C₂³	1	1	yes	characteristic
175	(C₂×D₁₃₉)⋊C₄	C₂³	1	2	yes	—
176	(C₂×D₁₃₉)⋊C₄	C₂³	1	1	yes	characteristic
177	(C₂×D₁₃₉)⋊C₄	C₂³	1	1	yes	characteristic
178	(C₂×D₁₃₉)⋊C₄	C₂³	1	1	yes	characteristic
179	(C₂×D₁₃₉)⋊C₄	C₂³	1	2	yes	—
180	(C₂×D₁₃₉)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₁₃₉)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₁₃₉)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₁₃₉)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₁₃₉)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₁₃₉)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₁₃₉)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₁₃₉)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₁₃₉)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₁₃₉)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₁₃₉)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₁₃₉)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₁₃₉)⋊C₄	C₂³	1	2	yes	—
193	C₄×Dic₁₃₉	C₂³	1	1	yes	characteristic
194	C₄×Dic₁₃₉	C₂³	1	1	yes	characteristic
195	C₄×Dic₁₃₉	C₂³	1	1	yes	characteristic
196	C₄×Dic₁₃₉	C₂³	1	2	yes	—
197	C₄×Dic₁₃₉	C₂³	1	2	yes	—
198	C₄×Dic₁₃₉	C₂³	1	2	yes	—
199	C₄×Dic₁₃₉	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₃₉	C₂³	1	2	yes	—
201	#41×C₁₃₉	—	2	4	no	—
202	C₂×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
203	C₂×D₄×C₁₃₉	C₂³	1	2	yes	—
204	C₂×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
205	C₂²×C₄×C₁₃₉	C₂³	1	2	yes	—
206	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₁₃₉	C₂³	1	2	yes	—
208	C₂²×C₄×C₁₃₉	C₂³	1	2	yes	—
209	C₂²×C₄×C₁₃₉	C₂³	1	2	yes	—
210	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
215	C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
221	C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
222	C₄²×C₁₃₉	C₂³	1	2	yes	—
223	C₄²×C₁₃₉	C₂³	1	2	yes	—
224	C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
225	C₂²×D₁₃₉	—	2	4	no	—
226	C₂²×D₁₃₉	—	4	2	no	—
227	C₂²×D₁₃₉	—	4	2	no	—
228	C₂²×D₁₃₉	C₂⁴	1	1	yes	characteristic
229	C₂²×D₁₃₉	C₂⁴	1	2	yes	—
230	C₂²×D₁₃₉	C₂⁴	1	1	yes	characteristic
231	Dic₂₇₈	—	2	2	no	—
232	Dic₂₇₈	—	4	1	no	—
233	Dic₂₇₈	—	4	2	no	—
234	D₅₅₆	—	2	2	no	—
235	D₅₅₆	—	4	2	no	—
236	D₅₅₆	—	4	1	no	—
237	C₂²⋊D₁₃₉	—	2	4	no	—
238	C₂²⋊D₁₃₉	—	2	4	no	—
239	C₂²⋊D₁₃₉	—	4	1	no	—
240	C₂²⋊D₁₃₉	—	4	1	no	—
241	C₂²⋊D₁₃₉	—	4	2	no	—
242	C₂×Dic₁₃₉	—	2	4	no	—
243	C₂×Dic₁₃₉	—	4	2	no	—
244	C₂×Dic₁₃₉	—	4	2	no	—
245	C₂×Dic₁₃₉	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₁₃₉	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₁₃₉	C₂⁴	1	2	yes	—
248	C₂×Dic₁₃₉	C₂⁴	1	2	yes	—
249	C₂×Dic₁₃₉	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₁₃₉	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₃₉	C₂⁴	1	2	yes	—
252	C₂×Dic₁₃₉	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₃₉	C₂⁴	1	1	yes	characteristic
254	C₄×D₁₃₉	—	2	2	no	—
255	C₄×D₁₃₉	—	2	2	no	—
256	C₄×D₁₃₉	—	4	2	no	—
257	C₄×D₁₃₉	—	4	1	no	—
258	C₄×D₁₃₉	—	4	2	no	—
259	C₄×D₁₃₉	—	4	1	no	—
260	C₂³×C₁₃₉	C₂⁴	1	1	yes	characteristic
261	C₂³×C₁₃₉	C₂⁴	1	2	yes	—
262	Q₈×C₁₃₉	—	2	2	no	—
263	D₄×C₁₃₉	—	2	4	no	—
264	D₄×C₁₃₉	#41	1	4	yes	—
265	C₂×C₄×C₁₃₉	—	2	4	no	—
266	C₂×C₄×C₁₃₉	—	2	2	no	—
267	C₂×C₄×C₁₃₉	—	4	2	no	—
268	C₂×C₄×C₁₃₉	—	4	2	no	—
269	C₂×C₄×C₁₃₉	—	4	2	no	—
270	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×C₁₃₉	C₂⁴	1	2	yes	—
273	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₁₃₉	C₂⁴	1	2	yes	—
275	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₁₃₉	C₂⁴	1	2	yes	—
277	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
279	C₂²×C₁₃₉	—	2	2	no	—
280	C₂²×C₁₃₉	—	2	2	no	—
281	C₂²×C₁₃₉	—	2	1	no	—
282	C₂²×C₁₃₉	—	2	1	no	—
283	C₂²×C₁₃₉	—	2	1	no	—
284	C₂²×C₁₃₉	C₂×#41	1	4	yes	—
285	C₂²×C₁₃₉	C₂⁵	1	1	yes	characteristic
286	C₂×D₁₃₉	—	2	1	no	—
287	C₂×D₁₃₉	—	2	1	no	—
288	C₂×D₁₃₉	—	2	2	no	—
289	C₂×D₁₃₉	—	2	1	no	—
290	C₂×D₁₃₉	—	2	2	no	—
291	C₂×D₁₃₉	—	2	1	no	—
292	C₂×D₁₃₉	—	2	2	no	—
293	C₂×D₁₃₉	—	2	1	no	—
294	C₂×D₁₃₉	—	2	1	no	—
295	C₂×D₁₃₉	—	8	4	no	—
296	C₄×C₁₃₉	—	2	1	no	—
297	C₄×C₁₃₉	—	2	2	no	—
298	C₄×C₁₃₉	—	2	1	no	—
299	C₄×C₁₃₉	—	2	2	no	—
300	C₄×C₁₃₉	—	2	2	no	—
301	C₄×C₁₃₉	—	2	1	no	—
302	C₄×C₁₃₉	—	2	1	no	—
303	C₄×C₁₃₉	—	2	1	no	—
304	C₄×C₁₃₉	C₂×#41	1	2	yes	—
305	Dic₁₃₉	—	2	1	no	—
306	Dic₁₃₉	—	2	1	no	—
307	Dic₁₃₉	—	2	2	no	—
308	Dic₁₃₉	—	2	1	no	—
309	Dic₁₃₉	—	2	1	no	—
310	Dic₁₃₉	—	2	2	no	—
311	Dic₁₃₉	—	2	1	no	—
312	Dic₁₃₉	—	2	1	no	—
313	Dic₁₃₉	—	2	2	no	—
314	C₂×C₁₃₉	—	2	4	no	—
315	C₂×C₁₃₉	—	4	1	no	—
316	C₂×C₁₃₉	C₂²×#41	1	1	yes	characteristic
317	C₂×C₁₃₉	#585	1	1	yes	characteristic
318	C₂×C₁₃₉	#585	1	1	yes	characteristic
319	D₁₃₉	—	4	1	no	—
320	D₁₃₉	—	4	2	no	—
321	D₁₃₉	—	4	1	no	—
322	C₁₃₉	#3521	1	1	yes	characteristic, complemented, Sylow
323	#3521	—	139	1	no	maximal, Sylow
324	#556	—	139	1	no	—
325	#556	—	139	1	no	—
326	#554	—	139	1	no	—
327	#553	—	139	2	no	—
328	#553	—	139	1	no	—
329	#552	—	139	2	no	—
330	#552	—	139	1	no	—
331	#551	—	139	2	no	—
332	#551	—	139	2	no	—
333	#547	—	139	1	no	—
334	#546	—	139	1	no	—
335	#546	—	139	1	no	—
336	#542	—	139	1	no	—
337	#541	—	139	1	no	—
338	#539	—	139	2	no	—
339	#538	—	139	2	no	—
340	#529	—	139	1	no	—
341	#529	—	139	2	no	—
342	#529	—	139	1	no	—
343	C₂×#126	—	139	2	no	—
344	#520	D₁₃₉	1	1	yes	characteristic, complemented
345	#518	—	139	1	no	—
346	C₄×#41	—	139	1	no	—
347	C₂×#41	—	139	1	no	—
348	C₂×#41	C₂×D₁₃₉	1	1	yes	characteristic
349	C₂²×D₄	—	139	1	no	—
350	C₄⋊Q₈	—	139	1	no	—
351	C₄⋊Q₈	—	139	1	no	—
352	#126	—	139	1	no	—
353	#126	—	139	2	no	—
354	#126	—	139	2	no	—
355	#126	—	139	2	no	—
356	#126	—	139	2	no	—
357	#126	—	139	2	no	—
358	#126	—	139	2	no	—
359	#126	—	139	2	no	—
360	#126	—	139	2	no	—
361	#126	—	139	1	no	—
362	#126	—	139	2	no	—
363	#126	—	139	2	no	—
364	#125	—	139	2	no	—
365	#125	—	139	1	no	—
366	#125	—	139	1	no	—
367	#125	—	139	2	no	—
368	#125	—	139	1	no	—
369	#125	—	139	2	no	—
370	#124	—	139	1	no	—
371	#124	—	139	2	no	—
372	#124	—	139	1	no	—
373	#124	—	139	2	no	—
374	#124	—	139	1	no	—
375	#123	—	139	2	no	—
376	#123	—	139	2	no	—
377	#123	—	139	2	no	—
378	#123	—	139	2	no	—
379	#123	—	139	2	no	—
380	#123	—	139	1	no	—
381	#123	—	139	2	no	—
382	#123	—	139	2	no	—
383	#123	—	139	1	no	—
384	#123	—	139	2	no	—
385	C₂²⋊Q₈	—	139	1	no	—
386	C₂²⋊Q₈	—	139	1	no	—
387	C₂²⋊Q₈	—	139	2	no	—
388	C₂²⋊Q₈	—	139	1	no	—
389	C₂²⋊Q₈	—	139	1	no	—
390	C₂²⋊Q₈	—	139	2	no	—
391	C₂²⋊Q₈	—	139	1	no	—
392	C₂²⋊Q₈	—	139	2	no	—
393	C₂²⋊Q₈	—	139	2	no	—
394	C₂²⋊Q₈	—	139	2	no	—
395	#121	—	139	2	no	—
396	#121	—	139	2	no	—
397	#121	—	139	2	no	—
398	#121	—	139	2	no	—
399	#121	—	139	1	no	—
400	#121	—	139	1	no	—
401	#121	—	139	1	no	—
402	#120	—	139	2	no	—
403	#120	—	139	2	no	—
404	C₄×Q₈	—	139	1	no	—
405	C₄×Q₈	—	139	1	no	—
406	C₄×Q₈	—	139	2	no	—
407	C₄×Q₈	—	139	1	no	—
408	C₄×Q₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
409	C₄×Q₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
410	C₄×D₄	—	139	1	no	—
411	C₄×D₄	—	139	1	no	—
412	C₄×D₄	—	139	2	no	—
413	C₄×D₄	—	139	2	no	—
414	C₄×D₄	—	139	1	no	—
415	C₄×D₄	—	139	1	no	—
416	C₄×D₄	—	139	2	no	—
417	C₄×D₄	—	139	1	no	—
418	C₄×D₄	—	139	2	no	—
419	C₄×D₄	—	139	2	no	—
420	C₄×D₄	—	139	1	no	—
421	C₄×D₄	—	139	1	no	—
422	C₄×D₄	—	139	2	no	—
423	C₄×D₄	C₂×D₁₃₉	1	1	yes	characteristic
424	C₄×D₄	C₂×D₁₃₉	1	1	yes	characteristic
425	C₄×D₄	C₂×D₁₃₉	1	2	yes	complemented
426	C₄×D₄	C₂×D₁₃₉	1	2	yes	complemented
427	#117	—	139	2	no	—
428	#117	—	139	1	no	—
429	#117	—	139	1	no	—
430	#117	—	139	2	no	—
431	#117	—	139	1	no	—
432	#117	—	139	2	no	—
433	#117	—	139	2	no	—
434	#117	C₂×D₁₃₉	1	1	yes	characteristic, complemented
435	#117	C₂×D₁₃₉	1	2	yes	complemented
436	C₂×C₄⋊C₄	—	139	2	no	—
437	C₂×C₄⋊C₄	—	139	2	no	—
438	C₂×C₄⋊C₄	C₂×D₁₃₉	1	2	yes	complemented
439	C₂×C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic, complemented
440	C₂×C₂²⋊C₄	—	139	2	no	—
441	C₂×C₂²⋊C₄	—	139	2	no	—
442	C₂×C₂²⋊C₄	—	139	2	no	—
443	C₂×C₂²⋊C₄	—	139	2	no	—
444	C₂×C₄²	—	139	2	no	—
445	C₂×C₄²	—	139	1	no	—
446	C₂⁴	—	139	2	no	—
447	#41	—	2	4	no	—
448	#41	—	278	4	no	—
449	C₂×Q₈	—	139	1	no	—
450	C₂×Q₈	—	139	1	no	—
451	C₂×Q₈	—	139	2	no	—
452	C₂×Q₈	C₂²×D₁₃₉	1	1	yes	characteristic
453	C₂×D₄	—	278	4	no	—
454	C₂×D₄	—	139	2	no	—
455	C₂×D₄	—	139	2	no	—
456	C₂×D₄	—	139	1	no	—
457	C₂×D₄	—	139	2	no	—
458	C₂×D₄	—	139	1	no	—
459	C₂×D₄	—	139	1	no	—
460	C₂×D₄	—	139	1	no	—
461	C₂×D₄	—	139	2	no	—
462	C₂×D₄	C₂²×D₁₃₉	1	2	yes	—
463	C₂×D₄	C₂²×D₁₃₉	1	1	yes	characteristic
464	C₂²×C₄	—	139	2	no	—
465	C₂²×C₄	—	139	1	no	—
466	C₂²×C₄	—	139	1	no	—
467	C₂²×C₄	—	139	2	no	—
468	C₂²×C₄	—	139	2	no	—
469	C₂²×C₄	—	139	1	no	—
470	C₂²×C₄	—	139	1	no	—
471	C₂²×C₄	—	139	2	no	—
472	C₂²×C₄	—	139	2	no	—
473	C₂²×C₄	C₂²×D₁₃₉	1	2	yes	—
474	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
475	C₂²×C₄	C₂²×D₁₃₉	1	2	yes	—
476	C₂²×C₄	C₂²×D₁₃₉	1	2	yes	—
477	C₂²×C₄	C₂²×D₁₃₉	1	2	yes	—
478	C₄⋊C₄	—	139	1	no	—
479	C₄⋊C₄	—	139	1	no	—
480	C₄⋊C₄	—	139	2	no	—
481	C₄⋊C₄	—	139	2	no	—
482	C₄⋊C₄	—	139	2	no	—
483	C₄⋊C₄	—	139	2	no	—
484	C₄⋊C₄	—	139	2	no	—
485	C₄⋊C₄	—	139	2	no	—
486	C₄⋊C₄	—	139	1	no	—
487	C₄⋊C₄	—	139	1	no	—
488	C₄⋊C₄	—	139	1	no	—
489	C₄⋊C₄	—	139	2	no	—
490	C₄⋊C₄	—	139	2	no	—
491	C₄⋊C₄	—	139	2	no	—
492	C₄⋊C₄	—	139	2	no	—
493	C₄⋊C₄	—	139	2	no	—
494	C₄⋊C₄	—	139	1	no	—
495	C₄⋊C₄	—	139	1	no	—
496	C₄⋊C₄	—	139	2	no	—
497	C₄⋊C₄	—	139	1	no	—
498	C₄⋊C₄	—	139	1	no	—
499	C₄⋊C₄	—	139	2	no	—
500	C₄⋊C₄	—	139	1	no	—
501	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₁₃₉	1	2	yes	—
503	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₁₃₉	1	2	yes	—
506	C₄⋊C₄	C₂²×D₁₃₉	1	2	yes	—
507	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
508	C₂²⋊C₄	—	139	2	no	—
509	C₂²⋊C₄	—	139	1	no	—
510	C₂²⋊C₄	—	139	2	no	—
511	C₂²⋊C₄	—	139	2	no	—
512	C₂²⋊C₄	—	139	1	no	—
513	C₂²⋊C₄	—	139	1	no	—
514	C₂²⋊C₄	—	139	2	no	—
515	C₂²⋊C₄	—	139	1	no	—
516	C₂²⋊C₄	—	139	1	no	—
517	C₂²⋊C₄	—	139	1	no	—
518	C₂²⋊C₄	—	139	2	no	—
519	C₂²⋊C₄	—	139	2	no	—
520	C₂²⋊C₄	—	139	2	no	—
521	C₂²⋊C₄	—	139	2	no	—
522	C₂²⋊C₄	—	139	2	no	—
523	C₂²⋊C₄	—	139	2	no	—
524	C₂²⋊C₄	—	139	2	no	—
525	C₂²⋊C₄	—	139	2	no	—
526	C₂²⋊C₄	—	139	2	no	—
527	C₂²⋊C₄	—	139	2	no	—
528	C₂²⋊C₄	—	139	2	no	—
529	C₂²⋊C₄	—	139	1	no	—
530	C₂²⋊C₄	—	139	2	no	—
531	C₂²⋊C₄	—	139	1	no	—
532	C₂²⋊C₄	C₂²×D₁₃₉	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₁₃₉	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
535	C₂²⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
536	C₄²	—	139	1	no	—
537	C₄²	—	139	1	no	—
538	C₄²	—	139	2	no	—
539	C₄²	—	139	2	no	—
540	C₄²	—	139	1	no	—
541	C₄²	—	139	2	no	—
542	C₄²	—	139	2	no	—
543	C₄²	—	139	1	no	—
544	C₄²	C₂²×D₁₃₉	1	1	yes	characteristic
545	C₄²	C₂²×D₁₃₉	1	2	yes	—
546	C₄²	C₂²×D₁₃₉	1	2	yes	—
547	C₄²	C₂²×D₁₃₉	1	1	yes	characteristic
548	C₂³	—	278	4	no	—
549	C₂³	—	556	2	no	—
550	C₂³	—	556	2	no	—
551	C₂³	—	139	1	no	—
552	C₂³	—	139	2	no	—
553	C₂³	—	139	1	no	—
554	C₂³	C₂³×D₁₃₉	1	1	yes	characteristic
555	C₂³	C₂³×D₁₃₉	1	2	yes	—
556	Q₈	—	2	2	no	—
557	Q₈	—	278	2	no	—
558	Q₈	—	556	1	no	—
559	Q₈	—	556	2	no	—
560	D₄	—	2	4	no	—
561	D₄	—	278	4	no	—
562	D₄	—	278	4	no	—
563	D₄	—	278	2	no	—
564	D₄	—	556	2	no	—
565	D₄	—	556	1	no	—
566	D₄	—	556	1	no	—
567	D₄	—	556	1	no	—
568	D₄	—	556	2	no	—
569	D₄	#14555785	1	4	yes	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	278	4	no	—
576	C₂×C₄	—	278	2	no	—
577	C₂×C₄	—	278	2	no	—
578	C₂×C₄	—	556	2	no	—
579	C₂×C₄	—	556	1	no	—
580	C₂×C₄	—	556	1	no	—
581	C₂×C₄	—	556	2	no	—
582	C₂×C₄	—	556	2	no	—
583	C₂×C₄	—	556	2	no	—
584	C₂×C₄	—	139	1	no	—
585	C₂×C₄	—	139	1	no	—
586	C₂×C₄	—	139	2	no	—
587	C₂×C₄	—	139	1	no	—
588	C₂×C₄	—	139	2	no	—
589	C₂×C₄	—	139	1	no	—
590	C₂×C₄	—	139	1	no	—
591	C₂×C₄	—	139	2	no	—
592	C₂×C₄	—	139	1	no	—
593	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₁₃₉	1	2	yes	—
595	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₁₃₉	1	2	yes	—
598	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₁₃₉	1	2	yes	—
600	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	278	1	no	—
608	C₂²	—	278	1	no	—
609	C₂²	—	278	2	no	—
610	C₂²	—	278	1	no	—
611	C₂²	—	278	2	no	—
612	C₂²	—	278	1	no	—
613	C₂²	—	278	1	no	—
614	C₂²	—	278	2	no	—
615	C₂²	—	278	1	no	—
616	C₂²	—	1112	4	no	—
617	C₂²	C₂×#14555785	1	4	yes	—
618	C₂²	C₂⁴×D₁₃₉	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	278	1	no	—
628	C₄	—	278	1	no	—
629	C₄	—	278	2	no	—
630	C₄	—	278	1	no	—
631	C₄	—	278	1	no	—
632	C₄	—	278	1	no	—
633	C₄	—	278	1	no	—
634	C₄	—	278	2	no	—
635	C₄	—	278	2	no	—
636	C₄	C₂×#14555785	1	2	yes	—
637	C₂	—	2	4	no	—
638	C₂	—	4	1	no	—
639	C₂	—	556	1	no	—
640	C₂	—	556	2	no	—
641	C₂	—	556	1	no	—
642	C₂	C₂²×#14555785	1	1	yes	characteristic
643	C₂	#22581788	1	1	yes	characteristic
644	C₂	#22581790	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃₉
commutator, socle, cosocle	C₂²×C₁₃₉	C₂⁵
Fitting	#520×C₁₃₉	C₂
hypercenter	#520	D₁₃₉
hypocenter	C₁₃₉	#3521
LCS	G ▷ C₂²×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ #520

Complements

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

N	H ≅ G/N	type
1. #22581676	C₂	semidirect
2. #22581675	C₂	semidirect
3. #22581660	C₂	semidirect
4. #22581651	C₂	semidirect
5. #22581649	C₂	semidirect
6. #22581638	C₂	semidirect
7. #22581636	C₂	semidirect
8. #22581632	C₂	semidirect
9. #22581627	C₂	semidirect
10. #22581602	C₂	semidirect
11. #22581598	C₂	semidirect
12. #22581591	C₂	semidirect
13. #22581574	C₂	semidirect
14. #22581561	C₂	semidirect
15. #22581550	C₂	semidirect
16. #22581536	C₂	semidirect
17. #22581490	C₂	semidirect
18. #22581483	C₂	semidirect
19. #22581481	C₂	semidirect
20. C₂×#17984837	C₂	semidirect
21. #22581425	C₂	semidirect
22. C₄×#14555784	C₂	semidirect
23. #520×C₁₃₉	C₂	semidirect
26. #17984842	C₂²	semidirect
27. #17984840	C₂²	semidirect
32. #17984837	C₂²	semidirect
33. #17984837	C₂²	semidirect
34. #17984837	C₂²	semidirect
35. #17984837	C₂²	semidirect
36. #17984837	C₂²	semidirect
38. #17984836	C₂²	semidirect
39. #17984835	C₂²	semidirect
40. #17984834	C₂²	semidirect
41. #17984833	C₂²	semidirect
42. #17984833	C₂²	semidirect
43. #17984832	C₂²	semidirect
44. #17984832	C₂²	semidirect
45. #17984832	C₂²	semidirect
50. #17984828	C₂²	semidirect
52. #17984827	C₂²	semidirect
53. #17984827	C₂²	semidirect
57. #17984825	C₂²	semidirect
58. #17984824	C₂²	semidirect
59. #17984824	C₂²	semidirect
60. #17984823	C₂²	semidirect
62. #17984821	C₂²	semidirect
63. #17984821	C₂²	semidirect
64. #17984820	C₂²	semidirect
65. #17984820	C₂²	semidirect
66. #17984820	C₂²	semidirect
67. #17984819	C₂²	semidirect
68. #17984819	C₂²	semidirect
70. #17984818	C₂²	semidirect
74. #17984816	C₂²	semidirect
77. #17984814	C₂²	semidirect
80. C₄×Dic₂₇₈	C₂²	semidirect
81. C₄×Dic₂₇₈	C₂²	semidirect
82. C₄×Dic₂₇₈	C₂²	semidirect
83. #17984807	C₂²	semidirect
86. C₄×D₅₅₆	C₂²	semidirect
92. C₄×C₂²⋊D₁₃₉	C₂²	semidirect
93. C₄×C₂²⋊D₁₃₉	C₂²	semidirect
94. C₄×C₂²⋊D₁₃₉	C₂²	semidirect
96. (C₂²⋊D₁₃₉)⋊C₄	C₂²	semidirect
97. #17984801	C₂²	semidirect
99. #17984800	C₂²	semidirect
101. #17984799	C₂²	semidirect
102. #17984799	C₂²	semidirect
103. #17984798	C₂²	semidirect
104. C₂×C₄⋊Dic₁₃₉	C₂²	semidirect
105. C₂×Dic₁₃₉⋊C₄	C₂²	semidirect
110. C₂×C₄×Dic₁₃₉	C₂²	semidirect
111. C₄²×D₁₃₉	C₂²	semidirect
113. C₄×Q₈×C₁₃₉	C₂²	semidirect
114. C₄×Q₈×C₁₃₉	C₂²	semidirect
117. C₄×D₄×C₁₃₉	C₂²	semidirect
118. C₄×D₄×C₁₃₉	C₂²	semidirect
119. #117×C₁₃₉	C₂²	semidirect
120. #117×C₁₃₉	C₂²	semidirect
121. C₂×C₄⋊C₄×C₁₃₉	C₂²	semidirect
122. C₂×C₄⋊C₄×C₁₃₉	C₂²	semidirect
322. C₁₃₉	#3521	semidirect
344. #520	D₁₃₉	semidirect
408. C₄×Q₈	C₂×D₁₃₉	semidirect
409. C₄×Q₈	C₂×D₁₃₉	semidirect
425. C₄×D₄	C₂×D₁₃₉	semidirect
426. C₄×D₄	C₂×D₁₃₉	semidirect
434. #117	C₂×D₁₃₉	semidirect
435. #117	C₂×D₁₃₉	semidirect
438. C₂×C₄⋊C₄	C₂×D₁₃₉	semidirect
439. C₂×C₄⋊C₄	C₂×D₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#22581676	2
#22581675	2
#22581660	2
#22581651	2
#22581649	2
#22581638	2
#22581636	2
#22581632	2
#22581627	2
#22581602	2
#22581598	2
#22581591	2
#22581574	2
#22581561	2
#22581550	2
#22581536	2
#22581490	2
#22581483	2
#22581481	2
C₂×#17984837	2
#22581425	2
C₄×#14555784	2
#520×C₁₃₉	2
#3521	139