Subgroups — C₁₃₉×#17764 #48012360

Order 35584.

964 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3511×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2989×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2906×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1560×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1559×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1551×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1550×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#1548×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#1547×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#333×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#1540×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#131×C₁₃₉	—	2	1	no	—
13	#556×C₁₃₉	C₄	1	2	yes	—
14	#555×C₁₃₉	—	2	1	no	—
15	#554×C₁₃₉	—	2	1	no	—
16	#553×C₁₃₉	—	2	2	no	—
17	#548×C₁₃₉	C₄	1	4	yes	—
18	#547×C₁₃₉	C₄	1	2	yes	—
19	#542×C₁₃₉	—	2	2	no	—
20	#537×C₁₃₉	—	2	1	no	—
21	#533×C₁₃₉	C₂²	1	2	yes	—
22	#532×C₁₃₉	C₂²	1	2	yes	—
23	#532×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	#520×C₁₃₉	—	2	1	no	—
26	C₄×#41×C₁₃₉	C₂²	1	1	yes	characteristic
27	#446×C₁₃₉	—	2	1	no	—
28	#436×C₁₃₉	—	2	1	no	—
29	#435×C₁₃₉	—	2	2	no	—
30	#432×C₁₃₉	C₂²	1	2	yes	—
31	#431×C₁₃₉	C₂²	1	1	yes	characteristic
32	#424×C₁₃₉	—	2	1	no	—
33	#424×C₁₃₉	—	2	2	no	—
34	#423×C₁₃₉	C₂²	1	1	yes	characteristic
35	#423×C₁₃₉	C₂²	1	2	yes	—
36	#423×C₁₃₉	C₂²	1	2	yes	—
37	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
40	#333×C₁₃₉	C₂²	1	2	yes	—
41	#333×C₁₃₉	C₂²	1	2	yes	—
42	#333×C₁₃₉	C₂²	1	2	yes	—
43	#333×C₁₃₉	C₂²	1	2	yes	—
44	#332×C₁₃₉	C₂²	1	1	yes	characteristic
45	#332×C₁₃₉	C₂²	1	1	yes	characteristic
46	#332×C₁₃₉	C₂²	1	2	yes	—
47	#331×C₁₃₉	C₂²	1	1	yes	characteristic
48	#331×C₁₃₉	C₂²	1	1	yes	characteristic
49	#331×C₁₃₉	C₂²	1	2	yes	—
50	C₂×#41×C₁₃₉	—	2	1	no	—
51	C₂×#41×C₁₃₉	C₂×C₄	1	4	yes	—
52	C₂×#41×C₁₃₉	D₄	1	1	yes	characteristic
53	C₂²×Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
54	#131×C₁₃₉	—	4	4	no	—
55	C₂×M₁₆×C₁₃₉	—	2	2	no	—
56	C₂×M₁₆×C₁₃₉	—	2	1	no	—
57	C₂×M₁₆×C₁₃₉	—	2	2	no	—
58	C₂²×C₈×C₁₃₉	—	2	2	no	—
59	C₂²×C₈×C₁₃₉	—	2	1	no	—
60	C₂²×C₈×C₁₃₉	—	2	1	no	—
61	C₄⋊Q₈×C₁₃₉	—	2	1	no	—
62	C₄⋊Q₈×C₁₃₉	—	2	1	no	—
63	C₄⋊Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
64	C₄⋊Q₈×C₁₃₉	C₂³	1	2	yes	—
65	C₄⋊Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
66	#127×C₁₃₉	C₂³	1	1	yes	characteristic
67	#126×C₁₃₉	—	2	4	no	—
68	#125×C₁₃₉	—	2	2	no	—
69	#124×C₁₃₉	—	2	4	no	—
70	#124×C₁₃₉	—	2	1	no	—
71	#124×C₁₃₉	C₂×C₄	1	4	yes	—
72	#123×C₁₃₉	—	2	4	no	—
73	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
74	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
75	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
76	C₂²⋊Q₈×C₁₃₉	C₂×C₄	1	4	yes	—
77	#121×C₁₃₉	—	2	2	no	—
78	#121×C₁₃₉	—	2	4	no	—
79	#121×C₁₃₉	—	2	2	no	—
80	#121×C₁₃₉	—	2	1	no	—
81	#121×C₁₃₉	—	2	2	no	—
82	#121×C₁₃₉	C₂×C₄	1	2	yes	—
83	C₄×Q₈×C₁₃₉	—	2	2	no	—
84	C₄×Q₈×C₁₃₉	C₂×C₄	1	4	yes	—
85	C₄×Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₁₃₉	D₄	1	1	yes	characteristic
87	C₄×D₄×C₁₃₉	—	2	4	no	—
88	C₄×D₄×C₁₃₉	—	2	2	no	—
89	C₄×D₄×C₁₃₉	—	2	2	no	—
90	C₄×D₄×C₁₃₉	—	2	1	no	—
91	C₄×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
92	C₄×D₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
93	C₄×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
94	C₄×D₄×C₁₃₉	D₄	1	2	yes	—
95	C₄×D₄×C₁₃₉	D₄	1	1	yes	characteristic
96	#117×C₁₃₉	—	2	2	no	—
97	#117×C₁₃₉	—	2	2	no	—
98	#117×C₁₃₉	D₄	1	1	yes	characteristic
99	#117×C₁₃₉	D₄	1	2	yes	—
100	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
103	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
105	C₄⋊C₈×C₁₃₉	—	2	2	no	—
106	C₄⋊C₈×C₁₃₉	—	2	1	no	—
107	C₄⋊C₈×C₁₃₉	—	2	1	no	—
108	C₄⋊C₈×C₁₃₉	—	2	2	no	—
109	C₄⋊C₈×C₁₃₉	—	2	1	no	—
110	C₄⋊C₈×C₁₃₉	—	2	2	no	—
111	C₄⋊C₈×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₄⋊C₈×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₄⋊C₈×C₁₃₉	C₂³	1	2	yes	—
114	C₄⋊C₈×C₁₃₉	C₂³	1	2	yes	—
115	C₄⋊C₈×C₁₃₉	C₂³	1	1	yes	characteristic
116	C₄⋊C₈×C₁₃₉	C₂³	1	1	yes	characteristic
117	C₂²⋊C₈×C₁₃₉	—	2	1	no	—
118	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
119	#97×C₁₃₉	—	2	2	no	—
120	C₄×C₈×C₁₃₉	—	2	1	no	—
121	#41×C₁₃₉	—	2	2	no	—
122	#41×C₁₃₉	—	2	2	no	—
123	#41×C₁₃₉	—	4	2	no	—
124	#41×C₁₃₉	—	4	2	no	—
125	#41×C₁₃₉	—	8	4	no	—
126	C₂×Q₈×C₁₃₉	—	2	2	no	—
127	C₂×Q₈×C₁₃₉	—	2	1	no	—
128	C₂×Q₈×C₁₃₉	—	8	2	no	—
129	C₂×Q₈×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
130	C₂×Q₈×C₁₃₉	C₂²×C₄	1	4	yes	—
131	C₂×D₄×C₁₃₉	—	2	2	no	—
132	C₂×D₄×C₁₃₉	—	2	4	no	—
133	C₂×D₄×C₁₃₉	—	2	1	no	—
134	C₂×D₄×C₁₃₉	—	2	1	no	—
135	C₂×D₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
136	C₂×D₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
137	C₂×D₄×C₁₃₉	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₁₃₉	—	2	2	no	—
139	C₂²×C₄×C₁₃₉	—	2	2	no	—
140	C₂²×C₄×C₁₃₉	—	2	4	no	—
141	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
147	M₁₆×C₁₃₉	—	4	4	no	—
148	M₁₆×C₁₃₉	—	4	2	no	—
149	M₁₆×C₁₃₉	—	8	2	no	—
150	C₂×C₈×C₁₃₉	—	2	1	no	—
151	C₂×C₈×C₁₃₉	—	2	1	no	—
152	C₂×C₈×C₁₃₉	—	2	2	no	—
153	C₂×C₈×C₁₃₉	—	2	1	no	—
154	C₂×C₈×C₁₃₉	—	2	2	no	—
155	C₂×C₈×C₁₃₉	—	2	1	no	—
156	C₂×C₈×C₁₃₉	—	4	4	no	—
157	C₂×C₈×C₁₃₉	—	4	2	no	—
158	C₂×C₈×C₁₃₉	—	8	1	no	—
159	C₄⋊C₄×C₁₃₉	—	2	2	no	—
160	C₄⋊C₄×C₁₃₉	—	2	4	no	—
161	C₄⋊C₄×C₁₃₉	—	2	2	no	—
162	C₄⋊C₄×C₁₃₉	—	2	4	no	—
163	C₄⋊C₄×C₁₃₉	—	2	2	no	—
164	C₄⋊C₄×C₁₃₉	—	2	2	no	—
165	C₄⋊C₄×C₁₃₉	—	2	1	no	—
166	C₄⋊C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
167	C₄⋊C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
168	C₄⋊C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
169	C₄⋊C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
170	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
171	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
172	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
173	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
174	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
176	C₂²⋊C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
177	C₂²⋊C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
178	C₂²⋊C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
179	C₄²×C₁₃₉	—	2	4	no	—
180	C₄²×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
181	C₄²×C₁₃₉	C₂²×C₄	1	2	yes	—
182	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
184	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
185	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₁₃₉	C₂⁴	1	1	yes	characteristic
187	C₂³×C₁₃₉	—	2	2	no	—
188	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
189	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	Q₈×C₁₃₉	—	2	2	no	—
191	Q₈×C₁₃₉	—	4	4	no	—
192	Q₈×C₁₃₉	—	4	1	no	—
193	Q₈×C₁₃₉	—	4	1	no	—
194	Q₈×C₁₃₉	—	8	2	no	—
195	D₄×C₁₃₉	—	2	4	no	—
196	D₄×C₁₃₉	—	2	2	no	—
197	D₄×C₁₃₉	—	4	2	no	—
198	D₄×C₁₃₉	—	4	4	no	—
199	D₄×C₁₃₉	—	4	1	no	—
200	D₄×C₁₃₉	—	4	1	no	—
201	D₄×C₁₃₉	—	4	1	no	—
202	D₄×C₁₃₉	—	4	1	no	—
203	D₄×C₁₃₉	—	8	4	no	—
204	C₂×C₄×C₁₃₉	—	2	2	no	—
205	C₂×C₄×C₁₃₉	—	2	2	no	—
206	C₂×C₄×C₁₃₉	—	2	1	no	—
207	C₂×C₄×C₁₃₉	—	2	2	no	—
208	C₂×C₄×C₁₃₉	—	2	1	no	—
209	C₂×C₄×C₁₃₉	—	2	2	no	—
210	C₂×C₄×C₁₃₉	—	2	2	no	—
211	C₂×C₄×C₁₃₉	—	2	4	no	—
212	C₂×C₄×C₁₃₉	—	4	1	no	—
213	C₂×C₄×C₁₃₉	—	4	2	no	—
214	C₂×C₄×C₁₃₉	—	4	4	no	—
215	C₂×C₄×C₁₃₉	—	8	4	no	—
216	C₂×C₄×C₁₃₉	—	8	2	no	—
217	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
218	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
220	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
222	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃₉	AGL(1,ℤ/8)	1	2	yes	—
224	C₂×C₄×C₁₃₉	#137	1	2	yes	—
225	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
228	C₈×C₁₃₉	—	4	1	no	—
229	C₈×C₁₃₉	—	4	2	no	—
230	C₈×C₁₃₉	—	4	1	no	—
231	C₈×C₁₃₉	—	4	2	no	—
232	C₈×C₁₃₉	—	4	1	no	—
233	C₈×C₁₃₉	—	4	1	no	—
234	C₂²×C₁₃₉	—	2	1	no	—
235	C₂²×C₁₃₉	—	2	1	no	—
236	C₂²×C₁₃₉	—	2	2	no	—
237	C₂²×C₁₃₉	—	2	2	no	—
238	C₂²×C₁₃₉	—	2	2	no	—
239	C₂²×C₁₃₉	—	4	2	no	—
240	C₂²×C₁₃₉	—	4	2	no	—
241	C₂²×C₁₃₉	—	4	2	no	—
242	C₂²×C₁₃₉	#417	1	2	yes	—
243	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
244	C₄×C₁₃₉	—	2	1	no	—
245	C₄×C₁₃₉	—	2	2	no	—
246	C₄×C₁₃₉	—	2	1	no	—
247	C₄×C₁₃₉	—	2	2	no	—
248	C₄×C₁₃₉	—	2	1	no	—
249	C₄×C₁₃₉	—	2	2	no	—
250	C₄×C₁₃₉	—	4	4	no	—
251	C₄×C₁₃₉	—	4	2	no	—
252	C₄×C₁₃₉	#417	1	2	yes	—
253	C₄×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
254	C₄×C₁₃₉	C₂×#137	1	1	yes	characteristic
255	C₄×C₁₃₉	#577	1	1	yes	characteristic
256	C₄×C₁₃₉	#578	1	1	yes	characteristic
257	C₂×C₁₃₉	—	2	2	no	—
258	C₂×C₁₃₉	—	4	2	no	—
259	C₂×C₁₃₉	—	8	2	no	—
260	C₂×C₁₃₉	#2888	1	1	yes	characteristic
261	C₂×C₁₃₉	C₂×#417	1	1	yes	characteristic
262	C₂×C₁₃₉	#2898	1	1	yes	characteristic
263	#17764	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
264	C₁₃₉	#17764	1	1	yes	characteristic, direct product factor, Sylow
265	#3511	C₂×C₁₃₉	1	1	yes	characteristic
266	#2989	C₂×C₁₃₉	1	1	yes	characteristic, complemented
267	#2906	C₂×C₁₃₉	1	1	yes	characteristic, complemented
268	#1560	C₂×C₁₃₉	1	2	yes	complemented
269	#1559	C₂×C₁₃₉	1	2	yes	complemented
270	#1551	C₂×C₁₃₉	1	2	yes	complemented
271	#1550	C₂×C₁₃₉	1	2	yes	complemented
272	#1548	C₂×C₁₃₉	1	1	yes	characteristic, complemented
273	#1547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
274	C₂×#333	C₂×C₁₃₉	1	1	yes	characteristic, complemented
275	#1540	C₂×C₁₃₉	1	1	yes	characteristic, complemented
276	C₂×#131	—	2	1	no	—
277	#556	C₄×C₁₃₉	1	2	yes	—
278	#555	—	2	1	no	—
279	#554	—	2	1	no	—
280	#553	—	2	2	no	—
281	#548	C₄×C₁₃₉	1	4	yes	—
282	#547	C₄×C₁₃₉	1	2	yes	—
283	#542	—	2	2	no	—
284	#537	—	2	1	no	—
285	#533	C₂²×C₁₃₉	1	2	yes	—
286	#532	C₂²×C₁₃₉	1	2	yes	—
287	#532	C₂²×C₁₃₉	1	1	yes	characteristic
288	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
289	#520	—	2	1	no	—
290	C₄×#41	C₂²×C₁₃₉	1	1	yes	characteristic
291	#446	—	2	1	no	—
292	#436	—	2	1	no	—
293	#435	—	2	2	no	—
294	#432	C₂²×C₁₃₉	1	2	yes	—
295	#431	C₂²×C₁₃₉	1	1	yes	characteristic
296	#424	—	2	1	no	—
297	#424	—	2	2	no	—
298	#423	C₂²×C₁₃₉	1	1	yes	characteristic
299	#423	C₂²×C₁₃₉	1	2	yes	—
300	#423	C₂²×C₁₃₉	1	2	yes	—
301	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
302	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
303	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
304	#333	C₂²×C₁₃₉	1	2	yes	—
305	#333	C₂²×C₁₃₉	1	2	yes	—
306	#333	C₂²×C₁₃₉	1	2	yes	—
307	#333	C₂²×C₁₃₉	1	2	yes	—
308	#332	C₂²×C₁₃₉	1	1	yes	characteristic
309	#332	C₂²×C₁₃₉	1	1	yes	characteristic
310	#332	C₂²×C₁₃₉	1	2	yes	—
311	#331	C₂²×C₁₃₉	1	1	yes	characteristic
312	#331	C₂²×C₁₃₉	1	1	yes	characteristic
313	#331	C₂²×C₁₃₉	1	2	yes	—
314	C₂×#41	—	2	1	no	—
315	C₂×#41	C₂×C₄×C₁₃₉	1	4	yes	—
316	C₂×#41	D₄×C₁₃₉	1	1	yes	characteristic
317	C₂²×Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
318	#131	—	4	4	no	—
319	C₂×M₁₆	—	2	2	no	—
320	C₂×M₁₆	—	2	1	no	—
321	C₂×M₁₆	—	2	2	no	—
322	C₂²×C₈	—	2	2	no	—
323	C₂²×C₈	—	2	1	no	—
324	C₂²×C₈	—	2	1	no	—
325	C₄⋊Q₈	—	2	1	no	—
326	C₄⋊Q₈	—	2	1	no	—
327	C₄⋊Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
328	C₄⋊Q₈	C₂³×C₁₃₉	1	2	yes	—
329	C₄⋊Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
330	#127	C₂³×C₁₃₉	1	1	yes	characteristic
331	#126	—	2	4	no	—
332	#125	—	2	2	no	—
333	#124	—	2	4	no	—
334	#124	—	2	1	no	—
335	#124	C₂×C₄×C₁₃₉	1	4	yes	—
336	#123	—	2	4	no	—
337	C₂²⋊Q₈	—	2	2	no	—
338	C₂²⋊Q₈	—	2	2	no	—
339	C₂²⋊Q₈	—	2	4	no	—
340	C₂²⋊Q₈	C₂×C₄×C₁₃₉	1	4	yes	—
341	#121	—	2	2	no	—
342	#121	—	2	4	no	—
343	#121	—	2	2	no	—
344	#121	—	2	1	no	—
345	#121	—	2	2	no	—
346	#121	C₂×C₄×C₁₃₉	1	2	yes	—
347	C₄×Q₈	—	2	2	no	—
348	C₄×Q₈	C₂×C₄×C₁₃₉	1	4	yes	—
349	C₄×Q₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
350	C₄×Q₈	D₄×C₁₃₉	1	1	yes	characteristic
351	C₄×D₄	—	2	4	no	—
352	C₄×D₄	—	2	2	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	1	no	—
355	C₄×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
356	C₄×D₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
357	C₄×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
358	C₄×D₄	D₄×C₁₃₉	1	2	yes	—
359	C₄×D₄	D₄×C₁₃₉	1	1	yes	characteristic
360	#117	—	2	2	no	—
361	#117	—	2	2	no	—
362	#117	D₄×C₁₃₉	1	1	yes	characteristic
363	#117	D₄×C₁₃₉	1	2	yes	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	2	no	—
367	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
368	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
369	C₄⋊C₈	—	2	2	no	—
370	C₄⋊C₈	—	2	1	no	—
371	C₄⋊C₈	—	2	1	no	—
372	C₄⋊C₈	—	2	2	no	—
373	C₄⋊C₈	—	2	1	no	—
374	C₄⋊C₈	—	2	2	no	—
375	C₄⋊C₈	C₂³×C₁₃₉	1	1	yes	characteristic
376	C₄⋊C₈	C₂³×C₁₃₉	1	1	yes	characteristic
377	C₄⋊C₈	C₂³×C₁₃₉	1	2	yes	—
378	C₄⋊C₈	C₂³×C₁₃₉	1	2	yes	—
379	C₄⋊C₈	C₂³×C₁₃₉	1	1	yes	characteristic
380	C₄⋊C₈	C₂³×C₁₃₉	1	1	yes	characteristic
381	C₂²⋊C₈	—	2	1	no	—
382	C₂²⋊C₈	—	2	2	no	—
383	#97	—	2	2	no	—
384	C₄×C₈	—	2	1	no	—
385	#41	—	2	2	no	—
386	#41	—	2	2	no	—
387	#41	—	4	2	no	—
388	#41	—	4	2	no	—
389	#41	—	8	4	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	8	2	no	—
393	C₂×Q₈	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
394	C₂×Q₈	C₂²×C₄×C₁₃₉	1	4	yes	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	4	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
400	C₂×D₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
401	C₂×D₄	C₂²×C₄×C₁₃₉	1	2	yes	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
406	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
407	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
409	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
410	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
411	M₁₆	—	4	4	no	—
412	M₁₆	—	4	2	no	—
413	M₁₆	—	8	2	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	4	4	no	—
421	C₂×C₈	—	4	2	no	—
422	C₂×C₈	—	8	1	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
431	C₄⋊C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
432	C₄⋊C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
433	C₄⋊C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
434	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
435	C₂²⋊C₄	—	2	4	no	—
436	C₂²⋊C₄	—	2	4	no	—
437	C₂²⋊C₄	—	2	4	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
441	C₂²⋊C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
442	C₂²⋊C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
443	C₄²	—	2	4	no	—
444	C₄²	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
445	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
446	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
447	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
448	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
449	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
450	C₄²	C₂⁴×C₁₃₉	1	1	yes	characteristic
451	C₂³	—	2	2	no	—
452	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
453	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
454	Q₈	—	2	2	no	—
455	Q₈	—	4	4	no	—
456	Q₈	—	4	1	no	—
457	Q₈	—	4	1	no	—
458	Q₈	—	8	2	no	—
459	D₄	—	2	4	no	—
460	D₄	—	2	2	no	—
461	D₄	—	4	2	no	—
462	D₄	—	4	4	no	—
463	D₄	—	4	1	no	—
464	D₄	—	4	1	no	—
465	D₄	—	4	1	no	—
466	D₄	—	4	1	no	—
467	D₄	—	8	4	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	8	4	no	—
480	C₂×C₄	—	8	2	no	—
481	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
482	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
483	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
484	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
485	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
486	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
487	C₂×C₄	AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
488	C₂×C₄	#137×C₁₃₉	1	2	yes	—
489	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
490	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
491	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
492	C₈	—	4	1	no	—
493	C₈	—	4	2	no	—
494	C₈	—	4	1	no	—
495	C₈	—	4	2	no	—
496	C₈	—	4	1	no	—
497	C₈	—	4	1	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	2	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	#417×C₁₃₉	1	2	yes	—
507	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
508	C₄	—	2	1	no	—
509	C₄	—	2	2	no	—
510	C₄	—	2	1	no	—
511	C₄	—	2	2	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	2	no	—
514	C₄	—	4	4	no	—
515	C₄	—	4	2	no	—
516	C₄	#417×C₁₃₉	1	2	yes	—
517	C₄	C₂×AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
518	C₄	C₂×#137×C₁₃₉	1	1	yes	characteristic
519	C₄	#577×C₁₃₉	1	1	yes	characteristic
520	C₄	#578×C₁₃₉	1	1	yes	characteristic
521	C₂	—	2	2	no	—
522	C₂	—	4	2	no	—
523	C₂	—	8	2	no	—
524	C₂	#2888×C₁₃₉	1	1	yes	characteristic
525	C₂	C₂×#417×C₁₃₉	1	1	yes	characteristic
526	C₂	#2898×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₉	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₄²	C₂⁴×C₁₃₉
prime radical	#3511×C₁₃₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ C₄×#41×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2989×C₁₃₉	C₂	semidirect
3. #2906×C₁₃₉	C₂	semidirect
4. #1560×C₁₃₉	C₂	semidirect
5. #1559×C₁₃₉	C₂	semidirect
6. #1551×C₁₃₉	C₂	semidirect
7. #1550×C₁₃₉	C₂	semidirect
8. #1548×C₁₃₉	C₂	semidirect
9. #1547×C₁₃₉	C₂	semidirect
10. C₂×#333×C₁₃₉	C₂	semidirect
11. #1540×C₁₃₉	C₂	semidirect
263. #17764	C₁₃₉	direct (N × H)
264. C₁₃₉	#17764	direct (N × H)
266. #2989	C₂×C₁₃₉	semidirect
267. #2906	C₂×C₁₃₉	semidirect
268. #1560	C₂×C₁₃₉	semidirect
269. #1559	C₂×C₁₃₉	semidirect
270. #1551	C₂×C₁₃₉	semidirect
271. #1550	C₂×C₁₃₉	semidirect
272. #1548	C₂×C₁₃₉	semidirect
273. #1547	C₂×C₁₃₉	semidirect
274. C₂×#333	C₂×C₁₃₉	semidirect
275. #1540	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#3511×C₁₃₉	2
#2989×C₁₃₉	2
#2906×C₁₃₉	2
#1560×C₁₃₉	2
#1559×C₁₃₉	2
#1551×C₁₃₉	2
#1550×C₁₃₉	2
#1548×C₁₃₉	2
#1547×C₁₃₉	2
C₂×#333×C₁₃₉	2
#1540×C₁₃₉	2
#17764	139

Subgroups — C139×#17764 #48012360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#17764 #48012360