Subgroups — C₁₃₉×#17684 #48012280

Order 35584.

932 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3517×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2970×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2923×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1536×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1535×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1532×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1530×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#1530×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#1529×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#1525×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#1524×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#557×C₁₃₉	C₄	1	1	yes	characteristic
13	#553×C₁₃₉	—	2	1	no	—
14	#553×C₁₃₉	—	2	2	no	—
15	#550×C₁₃₉	—	2	1	no	—
16	#550×C₁₃₉	C₄	1	1	yes	characteristic
17	#550×C₁₃₉	C₄	1	2	yes	—
18	#550×C₁₃₉	C₄	1	1	yes	characteristic
19	#547×C₁₃₉	C₄	1	1	yes	characteristic
20	#547×C₁₃₉	C₄	1	2	yes	—
21	#540×C₁₃₉	—	2	1	no	—
22	#540×C₁₃₉	—	2	2	no	—
23	#532×C₁₃₉	C₂²	1	1	yes	characteristic
24	#532×C₁₃₉	C₂²	1	2	yes	—
25	#529×C₁₃₉	C₂²	1	1	yes	characteristic
26	#529×C₁₃₉	C₂²	1	2	yes	—
27	#520×C₁₃₉	—	2	1	no	—
28	C₄×#41×C₁₃₉	C₂²	1	1	yes	characteristic
29	#446×C₁₃₉	—	2	1	no	—
30	#435×C₁₃₉	—	2	2	no	—
31	C₈×D₄×C₁₃₉	—	2	1	no	—
32	#433×C₁₃₉	—	2	2	no	—
33	#432×C₁₃₉	C₂²	1	1	yes	characteristic
34	#432×C₁₃₉	C₂²	1	2	yes	—
35	#432×C₁₃₉	C₂²	1	2	yes	—
36	#432×C₁₃₉	C₂²	1	2	yes	—
37	#424×C₁₃₉	—	2	1	no	—
38	#408×C₁₃₉	—	2	1	no	—
39	C₄×M₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₄×M₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂×#97×C₁₃₉	C₂²	1	1	yes	characteristic
42	C₂×#97×C₁₃₉	C₂²	1	2	yes	—
43	#330×C₁₃₉	C₂²	1	1	yes	characteristic
44	#330×C₁₃₉	C₂²	1	1	yes	characteristic
45	#330×C₁₃₉	C₂²	1	2	yes	—
46	#329×C₁₃₉	C₂²	1	1	yes	characteristic
47	#329×C₁₃₉	C₂²	1	1	yes	characteristic
48	#329×C₁₃₉	C₂²	1	2	yes	—
49	#329×C₁₃₉	C₂²	1	2	yes	—
50	#329×C₁₃₉	C₂²	1	2	yes	—
51	#329×C₁₃₉	C₂²	1	2	yes	—
52	#329×C₁₃₉	C₂²	1	2	yes	—
53	C₂×#41×C₁₃₉	—	2	1	no	—
54	C₂×#41×C₁₃₉	C₂×C₄	1	2	yes	—
55	C₂×#41×C₁₃₉	C₂×C₄	1	2	yes	—
56	C₂×#41×C₁₃₉	C₂×C₄	1	2	yes	—
57	C₂×#41×C₁₃₉	D₄	1	1	yes	characteristic
58	C₂×M₁₆×C₁₃₉	—	2	1	no	—
59	C₂×M₁₆×C₁₃₉	—	2	1	no	—
60	C₂²×C₈×C₁₃₉	—	2	1	no	—
61	C₂²×C₈×C₁₃₉	—	2	2	no	—
62	C₄⋊Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
63	C₄⋊Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
64	#127×C₁₃₉	—	2	1	no	—
65	#127×C₁₃₉	—	2	2	no	—
66	#127×C₁₃₉	C₂×C₄	1	1	yes	characteristic
67	#127×C₁₃₉	C₂×C₄	1	2	yes	—
68	#126×C₁₃₉	—	2	1	no	—
69	#126×C₁₃₉	—	2	2	no	—
70	#125×C₁₃₉	—	2	2	no	—
71	#125×C₁₃₉	—	2	1	no	—
72	#125×C₁₃₉	C₂³	1	1	yes	characteristic
73	#124×C₁₃₉	C₂³	1	1	yes	characteristic
74	#124×C₁₃₉	C₂³	1	2	yes	—
75	#123×C₁₃₉	—	2	2	no	—
76	#123×C₁₃₉	—	2	1	no	—
77	#123×C₁₃₉	—	2	2	no	—
78	#123×C₁₃₉	—	2	2	no	—
79	#123×C₁₃₉	—	2	2	no	—
80	C₂²⋊Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
81	C₂²⋊Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
82	#121×C₁₃₉	—	2	1	no	—
83	#121×C₁₃₉	—	2	2	no	—
84	#121×C₁₃₉	—	2	2	no	—
85	#121×C₁₃₉	—	2	1	no	—
86	#121×C₁₃₉	—	2	1	no	—
87	#121×C₁₃₉	—	2	2	no	—
88	#121×C₁₃₉	—	2	2	no	—
89	#121×C₁₃₉	—	2	1	no	—
90	#121×C₁₃₉	—	2	2	no	—
91	#121×C₁₃₉	—	2	2	no	—
92	#121×C₁₃₉	—	2	2	no	—
93	#121×C₁₃₉	C₂×C₄	1	1	yes	characteristic
94	#121×C₁₃₉	C₂×C₄	1	2	yes	—
95	C₄×Q₈×C₁₃₉	—	2	1	no	—
96	C₄×Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
97	C₄×Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
98	C₄×Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
99	C₄×Q₈×C₁₃₉	D₄	1	1	yes	characteristic
100	C₄×D₄×C₁₃₉	—	2	1	no	—
101	C₄×D₄×C₁₃₉	—	2	2	no	—
102	C₄×D₄×C₁₃₉	—	2	2	no	—
103	C₄×D₄×C₁₃₉	—	2	1	no	—
104	C₄×D₄×C₁₃₉	—	2	1	no	—
105	C₄×D₄×C₁₃₉	—	2	2	no	—
106	C₄×D₄×C₁₃₉	—	2	1	no	—
107	C₄×D₄×C₁₃₉	—	2	2	no	—
108	C₄×D₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
109	C₄×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
110	C₄×D₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
111	C₄×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
112	C₄×D₄×C₁₃₉	D₄	1	1	yes	characteristic
113	C₄×D₄×C₁₃₉	D₄	1	2	yes	—
114	#117×C₁₃₉	—	2	1	no	—
115	#117×C₁₃₉	—	2	2	no	—
116	#117×C₁₃₉	D₄	1	1	yes	characteristic
117	#117×C₁₃₉	D₄	1	2	yes	—
118	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
119	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
120	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
122	C₄⋊C₈×C₁₃₉	—	2	2	no	—
123	C₄⋊C₈×C₁₃₉	—	2	2	no	—
124	C₄⋊C₈×C₁₃₉	—	2	1	no	—
125	C₄⋊C₈×C₁₃₉	—	2	2	no	—
126	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
127	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
128	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
129	C₂²⋊C₈×C₁₃₉	—	2	1	no	—
130	#97×C₁₃₉	—	2	1	no	—
131	#97×C₁₃₉	—	2	2	no	—
132	#97×C₁₃₉	C₂³	1	1	yes	characteristic
133	#97×C₁₃₉	C₂³	1	1	yes	characteristic
134	#97×C₁₃₉	C₂³	1	1	yes	characteristic
135	#97×C₁₃₉	C₂³	1	2	yes	—
136	#97×C₁₃₉	C₂³	1	1	yes	characteristic
137	#97×C₁₃₉	C₂³	1	2	yes	—
138	C₄×C₈×C₁₃₉	—	2	1	no	—
139	C₄×C₈×C₁₃₉	—	2	1	no	—
140	#41×C₁₃₉	—	4	2	no	—
141	#41×C₁₃₉	—	4	4	no	—
142	#41×C₁₃₉	—	8	2	no	—
143	#41×C₁₃₉	—	8	2	no	—
144	#41×C₁₃₉	—	8	2	no	—
145	C₂×Q₈×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
146	C₂×Q₈×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
147	C₂×Q₈×C₁₃₉	C₂²×C₄	1	2	yes	—
148	C₂×D₄×C₁₃₉	—	2	1	no	—
149	C₂×D₄×C₁₃₉	—	2	2	no	—
150	C₂×D₄×C₁₃₉	—	2	2	no	—
151	C₂×D₄×C₁₃₉	—	2	2	no	—
152	C₂×D₄×C₁₃₉	—	2	2	no	—
153	C₂×D₄×C₁₃₉	—	2	2	no	—
154	C₂×D₄×C₁₃₉	—	2	1	no	—
155	C₂×D₄×C₁₃₉	—	2	1	no	—
156	C₂×D₄×C₁₃₉	—	2	2	no	—
157	C₂×D₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
158	C₂×D₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
159	C₂×D₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
160	C₂×D₄×C₁₃₉	C₂²×C₄	1	2	yes	—
161	C₂²×C₄×C₁₃₉	—	2	2	no	—
162	C₂²×C₄×C₁₃₉	—	2	1	no	—
163	C₂²×C₄×C₁₃₉	—	2	2	no	—
164	C₂²×C₄×C₁₃₉	—	2	2	no	—
165	C₂²×C₄×C₁₃₉	—	2	2	no	—
166	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
168	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
172	M₁₆×C₁₃₉	—	4	2	no	—
173	M₁₆×C₁₃₉	—	4	2	no	—
174	C₂×C₈×C₁₃₉	—	2	1	no	—
175	C₂×C₈×C₁₃₉	—	2	2	no	—
176	C₂×C₈×C₁₃₉	—	2	1	no	—
177	C₂×C₈×C₁₃₉	—	2	1	no	—
178	C₂×C₈×C₁₃₉	—	2	1	no	—
179	C₂×C₈×C₁₃₉	—	2	2	no	—
180	C₂×C₈×C₁₃₉	—	4	4	no	—
181	C₂×C₈×C₁₃₉	—	4	2	no	—
182	C₄⋊C₄×C₁₃₉	—	2	1	no	—
183	C₄⋊C₄×C₁₃₉	—	2	2	no	—
184	C₄⋊C₄×C₁₃₉	—	2	2	no	—
185	C₄⋊C₄×C₁₃₉	—	2	1	no	—
186	C₄⋊C₄×C₁₃₉	—	2	1	no	—
187	C₄⋊C₄×C₁₃₉	—	2	2	no	—
188	C₄⋊C₄×C₁₃₉	—	2	1	no	—
189	C₄⋊C₄×C₁₃₉	—	2	2	no	—
190	C₄⋊C₄×C₁₃₉	—	2	1	no	—
191	C₄⋊C₄×C₁₃₉	—	2	1	no	—
192	C₄⋊C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
193	C₄⋊C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
194	C₄⋊C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
195	C₄⋊C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
196	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
197	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
198	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
199	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
200	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
201	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
202	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
203	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
204	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
205	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
206	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
207	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
208	C₂²⋊C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
209	C₂²⋊C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
210	C₂²⋊C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
211	C₄²×C₁₃₉	—	2	2	no	—
212	C₄²×C₁₃₉	—	2	1	no	—
213	C₄²×C₁₃₉	C₂²×C₄	1	2	yes	—
214	C₄²×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
215	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
217	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
218	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
219	C₄²×C₁₃₉	C₂⁴	1	1	yes	characteristic
220	C₂³×C₁₃₉	—	2	2	no	—
221	C₂³×C₁₃₉	—	2	1	no	—
222	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
224	Q₈×C₁₃₉	—	2	2	no	—
225	Q₈×C₁₃₉	—	4	1	no	—
226	Q₈×C₁₃₉	—	4	2	no	—
227	D₄×C₁₃₉	—	2	2	no	—
228	D₄×C₁₃₉	—	4	2	no	—
229	D₄×C₁₃₉	—	4	1	no	—
230	D₄×C₁₃₉	—	4	2	no	—
231	D₄×C₁₃₉	—	4	4	no	—
232	D₄×C₁₃₉	—	4	2	no	—
233	D₄×C₁₃₉	—	8	2	no	—
234	D₄×C₁₃₉	—	8	1	no	—
235	D₄×C₁₃₉	—	8	2	no	—
236	D₄×C₁₃₉	—	8	1	no	—
237	D₄×C₁₃₉	—	8	2	no	—
238	D₄×C₁₃₉	—	8	2	no	—
239	D₄×C₁₃₉	—	8	2	no	—
240	C₂×C₄×C₁₃₉	—	2	2	no	—
241	C₂×C₄×C₁₃₉	—	2	1	no	—
242	C₂×C₄×C₁₃₉	—	2	2	no	—
243	C₂×C₄×C₁₃₉	—	2	1	no	—
244	C₂×C₄×C₁₃₉	—	2	1	no	—
245	C₂×C₄×C₁₃₉	—	4	2	no	—
246	C₂×C₄×C₁₃₉	—	4	1	no	—
247	C₂×C₄×C₁₃₉	—	4	1	no	—
248	C₂×C₄×C₁₃₉	—	4	2	no	—
249	C₂×C₄×C₁₃₉	—	4	2	no	—
250	C₂×C₄×C₁₃₉	—	4	4	no	—
251	C₂×C₄×C₁₃₉	—	4	2	no	—
252	C₂×C₄×C₁₃₉	—	8	2	no	—
253	C₂×C₄×C₁₃₉	—	8	2	no	—
254	C₂×C₄×C₁₃₉	—	8	2	no	—
255	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
256	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
258	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
260	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
262	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
264	C₈×C₁₃₉	—	2	2	no	—
265	C₈×C₁₃₉	—	4	1	no	—
266	C₈×C₁₃₉	—	4	1	no	—
267	C₈×C₁₃₉	—	4	2	no	—
268	C₈×C₁₃₉	—	4	2	no	—
269	C₈×C₁₃₉	—	4	1	no	—
270	C₂²×C₁₃₉	—	2	1	no	—
271	C₂²×C₁₃₉	—	2	2	no	—
272	C₂²×C₁₃₉	—	2	1	no	—
273	C₂²×C₁₃₉	—	2	2	no	—
274	C₂²×C₁₃₉	—	2	2	no	—
275	C₂²×C₁₃₉	—	2	1	no	—
276	C₂²×C₁₃₉	—	4	2	no	—
277	C₂²×C₁₃₉	—	4	1	no	—
278	C₂²×C₁₃₉	—	4	2	no	—
279	C₂²×C₁₃₉	—	4	1	no	—
280	C₂²×C₁₃₉	—	4	2	no	—
281	C₂²×C₁₃₉	—	4	1	no	—
282	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
283	C₄×C₁₃₉	—	2	1	no	—
284	C₄×C₁₃₉	—	2	1	no	—
285	C₄×C₁₃₉	—	2	2	no	—
286	C₄×C₁₃₉	—	2	1	no	—
287	C₄×C₁₃₉	—	2	2	no	—
288	C₄×C₁₃₉	—	2	1	no	—
289	C₄×C₁₃₉	—	2	2	no	—
290	C₄×C₁₃₉	—	2	1	no	—
291	C₄×C₁₃₉	—	4	2	no	—
292	C₄×C₁₃₉	—	4	1	no	—
293	C₄×C₁₃₉	—	4	1	no	—
294	C₄×C₁₃₉	—	4	1	no	—
295	C₄×C₁₃₉	#421	1	2	yes	—
296	C₂×C₁₃₉	—	4	1	no	—
297	C₂×C₁₃₉	—	4	2	no	—
298	C₂×C₁₃₉	—	8	2	no	—
299	C₂×C₁₃₉	—	8	1	no	—
300	C₂×C₁₃₉	#2888	1	1	yes	characteristic
301	C₂×C₁₃₉	C₂×#421	1	1	yes	characteristic
302	C₂×C₁₃₉	#2901	1	1	yes	characteristic
303	#17684	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
304	C₁₃₉	#17684	1	1	yes	characteristic, direct product factor, Sylow
305	#3517	C₂×C₁₃₉	1	1	yes	characteristic
306	#2970	C₂×C₁₃₉	1	1	yes	characteristic, complemented
307	#2923	C₂×C₁₃₉	1	1	yes	characteristic, complemented
308	#1536	C₂×C₁₃₉	1	2	yes	complemented
309	#1535	C₂×C₁₃₉	1	2	yes	complemented
310	#1532	C₂×C₁₃₉	1	2	yes	complemented
311	#1530	C₂×C₁₃₉	1	2	yes	complemented
312	#1530	C₂×C₁₃₉	1	1	yes	characteristic, complemented
313	#1529	C₂×C₁₃₉	1	1	yes	characteristic, complemented
314	#1525	C₂×C₁₃₉	1	1	yes	characteristic, complemented
315	#1524	C₂×C₁₃₉	1	1	yes	characteristic, complemented
316	#557	C₄×C₁₃₉	1	1	yes	characteristic
317	#553	—	2	1	no	—
318	#553	—	2	2	no	—
319	#550	—	2	1	no	—
320	#550	C₄×C₁₃₉	1	1	yes	characteristic
321	#550	C₄×C₁₃₉	1	2	yes	—
322	#550	C₄×C₁₃₉	1	1	yes	characteristic
323	#547	C₄×C₁₃₉	1	1	yes	characteristic
324	#547	C₄×C₁₃₉	1	2	yes	—
325	#540	—	2	1	no	—
326	#540	—	2	2	no	—
327	#532	C₂²×C₁₃₉	1	2	yes	—
328	#532	C₂²×C₁₃₉	1	1	yes	characteristic
329	#529	C₂²×C₁₃₉	1	1	yes	characteristic
330	#529	C₂²×C₁₃₉	1	2	yes	—
331	#520	—	2	1	no	—
332	C₄×#41	C₂²×C₁₃₉	1	1	yes	characteristic
333	#446	—	2	1	no	—
334	#435	—	2	2	no	—
335	C₈×D₄	—	2	1	no	—
336	#433	—	2	2	no	—
337	#432	C₂²×C₁₃₉	1	2	yes	—
338	#432	C₂²×C₁₃₉	1	2	yes	—
339	#432	C₂²×C₁₃₉	1	2	yes	—
340	#432	C₂²×C₁₃₉	1	1	yes	characteristic
341	#424	—	2	1	no	—
342	#408	—	2	1	no	—
343	C₄×M₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
344	C₄×M₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
345	C₂×#97	C₂²×C₁₃₉	1	1	yes	characteristic
346	C₂×#97	C₂²×C₁₃₉	1	2	yes	—
347	#330	C₂²×C₁₃₉	1	1	yes	characteristic
348	#330	C₂²×C₁₃₉	1	1	yes	characteristic
349	#330	C₂²×C₁₃₉	1	2	yes	—
350	#329	C₂²×C₁₃₉	1	1	yes	characteristic
351	#329	C₂²×C₁₃₉	1	2	yes	—
352	#329	C₂²×C₁₃₉	1	2	yes	—
353	#329	C₂²×C₁₃₉	1	2	yes	—
354	#329	C₂²×C₁₃₉	1	1	yes	characteristic
355	#329	C₂²×C₁₃₉	1	2	yes	—
356	#329	C₂²×C₁₃₉	1	2	yes	—
357	C₂×#41	—	2	1	no	—
358	C₂×#41	C₂×C₄×C₁₃₉	1	2	yes	—
359	C₂×#41	C₂×C₄×C₁₃₉	1	2	yes	—
360	C₂×#41	C₂×C₄×C₁₃₉	1	2	yes	—
361	C₂×#41	D₄×C₁₃₉	1	1	yes	characteristic
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂²×C₈	—	2	1	no	—
365	C₂²×C₈	—	2	2	no	—
366	C₄⋊Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
367	C₄⋊Q₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
368	#127	—	2	1	no	—
369	#127	—	2	2	no	—
370	#127	C₂×C₄×C₁₃₉	1	2	yes	—
371	#127	C₂×C₄×C₁₃₉	1	1	yes	characteristic
372	#126	—	2	1	no	—
373	#126	—	2	2	no	—
374	#125	—	2	2	no	—
375	#125	—	2	1	no	—
376	#125	C₂³×C₁₃₉	1	1	yes	characteristic
377	#124	C₂³×C₁₃₉	1	1	yes	characteristic
378	#124	C₂³×C₁₃₉	1	2	yes	—
379	#123	—	2	2	no	—
380	#123	—	2	1	no	—
381	#123	—	2	2	no	—
382	#123	—	2	2	no	—
383	#123	—	2	2	no	—
384	C₂²⋊Q₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
385	C₂²⋊Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
386	#121	—	2	1	no	—
387	#121	—	2	2	no	—
388	#121	—	2	2	no	—
389	#121	—	2	1	no	—
390	#121	—	2	1	no	—
391	#121	—	2	2	no	—
392	#121	—	2	2	no	—
393	#121	—	2	1	no	—
394	#121	—	2	2	no	—
395	#121	—	2	2	no	—
396	#121	—	2	2	no	—
397	#121	C₂×C₄×C₁₃₉	1	1	yes	characteristic
398	#121	C₂×C₄×C₁₃₉	1	2	yes	—
399	C₄×Q₈	—	2	1	no	—
400	C₄×Q₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
401	C₄×Q₈	C₂×C₄×C₁₃₉	1	2	yes	—
402	C₄×Q₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
403	C₄×Q₈	D₄×C₁₃₉	1	1	yes	characteristic
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	—	2	1	no	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	—	2	2	no	—
412	C₄×D₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
413	C₄×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
414	C₄×D₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
415	C₄×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
416	C₄×D₄	D₄×C₁₃₉	1	1	yes	characteristic
417	C₄×D₄	D₄×C₁₃₉	1	2	yes	—
418	#117	—	2	1	no	—
419	#117	—	2	2	no	—
420	#117	D₄×C₁₃₉	1	1	yes	characteristic
421	#117	D₄×C₁₃₉	1	2	yes	—
422	C₂×C₄⋊C₄	—	2	2	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
425	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
426	C₄⋊C₈	—	2	2	no	—
427	C₄⋊C₈	—	2	2	no	—
428	C₄⋊C₈	—	2	1	no	—
429	C₄⋊C₈	—	2	2	no	—
430	C₂²⋊C₈	—	2	2	no	—
431	C₂²⋊C₈	—	2	2	no	—
432	C₂²⋊C₈	—	2	2	no	—
433	C₂²⋊C₈	—	2	1	no	—
434	#97	—	2	1	no	—
435	#97	—	2	2	no	—
436	#97	C₂³×C₁₃₉	1	1	yes	characteristic
437	#97	C₂³×C₁₃₉	1	1	yes	characteristic
438	#97	C₂³×C₁₃₉	1	2	yes	—
439	#97	C₂³×C₁₃₉	1	1	yes	characteristic
440	#97	C₂³×C₁₃₉	1	1	yes	characteristic
441	#97	C₂³×C₁₃₉	1	2	yes	—
442	C₄×C₈	—	2	1	no	—
443	C₄×C₈	—	2	1	no	—
444	#41	—	4	2	no	—
445	#41	—	4	4	no	—
446	#41	—	8	2	no	—
447	#41	—	8	2	no	—
448	#41	—	8	2	no	—
449	C₂×Q₈	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
450	C₂×Q₈	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
451	C₂×Q₈	C₂²×C₄×C₁₃₉	1	2	yes	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	2	no	—
461	C₂×D₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
462	C₂×D₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
463	C₂×D₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
464	C₂×D₄	C₂²×C₄×C₁₃₉	1	2	yes	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
471	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
472	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
473	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
474	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
475	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
476	M₁₆	—	4	2	no	—
477	M₁₆	—	4	2	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	2	no	—
484	C₂×C₈	—	4	4	no	—
485	C₂×C₈	—	4	2	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
497	C₄⋊C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
498	C₄⋊C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
499	C₄⋊C₄	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	1	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	1	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
513	C₂²⋊C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
514	C₂²⋊C₄	C₂²⋊C₄×C₁₃₉	1	2	yes	—
515	C₄²	—	2	2	no	—
516	C₄²	—	2	1	no	—
517	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
518	C₄²	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
519	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
520	C₄²	C₂×D₄×C₁₃₉	1	1	yes	characteristic
521	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
522	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
523	C₄²	C₂⁴×C₁₃₉	1	1	yes	characteristic
524	C₂³	—	2	2	no	—
525	C₂³	—	2	1	no	—
526	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
527	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
528	Q₈	—	2	2	no	—
529	Q₈	—	4	1	no	—
530	Q₈	—	4	2	no	—
531	D₄	—	2	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	1	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	4	no	—
536	D₄	—	4	2	no	—
537	D₄	—	8	2	no	—
538	D₄	—	8	1	no	—
539	D₄	—	8	2	no	—
540	D₄	—	8	2	no	—
541	D₄	—	8	2	no	—
542	D₄	—	8	2	no	—
543	D₄	—	8	1	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	4	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	8	2	no	—
557	C₂×C₄	—	8	2	no	—
558	C₂×C₄	—	8	2	no	—
559	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
560	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
561	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
562	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
563	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
564	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
565	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
566	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
567	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
568	C₈	—	2	2	no	—
569	C₈	—	4	1	no	—
570	C₈	—	4	1	no	—
571	C₈	—	4	2	no	—
572	C₈	—	4	2	no	—
573	C₈	—	4	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	1	no	—
586	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	2	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	2	no	—
594	C₄	—	2	1	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	#421×C₁₃₉	1	2	yes	—
600	C₂	—	4	1	no	—
601	C₂	—	4	2	no	—
602	C₂	—	8	2	no	—
603	C₂	—	8	1	no	—
604	C₂	#2888×C₁₃₉	1	1	yes	characteristic
605	C₂	C₂×#421×C₁₃₉	1	1	yes	characteristic
606	C₂	#2901×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	#3517×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. #2970×C₁₃₉	C₂	semidirect
3. #2923×C₁₃₉	C₂	semidirect
4. #1536×C₁₃₉	C₂	semidirect
5. #1535×C₁₃₉	C₂	semidirect
6. #1532×C₁₃₉	C₂	semidirect
7. #1530×C₁₃₉	C₂	semidirect
8. #1530×C₁₃₉	C₂	semidirect
9. #1529×C₁₃₉	C₂	semidirect
10. #1525×C₁₃₉	C₂	semidirect
11. #1524×C₁₃₉	C₂	semidirect
303. #17684	C₁₃₉	direct (N × H)
304. C₁₃₉	#17684	direct (N × H)
306. #2970	C₂×C₁₃₉	semidirect
307. #2923	C₂×C₁₃₉	semidirect
308. #1536	C₂×C₁₃₉	semidirect
309. #1535	C₂×C₁₃₉	semidirect
310. #1532	C₂×C₁₃₉	semidirect
311. #1530	C₂×C₁₃₉	semidirect
312. #1530	C₂×C₁₃₉	semidirect
313. #1529	C₂×C₁₃₉	semidirect
314. #1525	C₂×C₁₃₉	semidirect
315. #1524	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#3517×C₁₃₉	2
#2970×C₁₃₉	2
#2923×C₁₃₉	2
#1536×C₁₃₉	2
#1535×C₁₃₉	2
#1532×C₁₃₉	2
#1530×C₁₃₉	2
#1529×C₁₃₉	2
#1525×C₁₃₉	2
#1524×C₁₃₉	2
#17684	139

Subgroups — C139×#17684 #48012280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#17684 #48012280