Subgroups — C₁₃₉×#23884 #48018480

Order 35584.

1684 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3586×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#3487×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#3025×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#3021×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#3005×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2010×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2008×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#1910×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#1905×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#1891×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#1796×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#585×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂×2₋¹⁺⁴×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
15	#578×C₁₃₉	—	2	4	no	—
16	#577×C₁₃₉	—	2	4	no	—
17	#575×C₁₃₉	—	2	2	no	—
18	#575×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#137×C₁₃₉	—	2	2	no	—
20	C₂×#137×C₁₃₉	C₂²	1	2	yes	—
21	C₂×AGL(1,ℤ/8)×C₁₃₉	C₂²	1	2	yes	—
22	#568×C₁₃₉	C₂²	1	1	yes	characteristic
23	#550×C₁₃₉	—	2	2	no	—
24	#550×C₁₃₉	—	2	2	no	—
25	#548×C₁₃₉	—	2	2	no	—
26	#548×C₁₃₉	—	2	2	no	—
27	#535×C₁₃₉	—	2	2	no	—
28	#535×C₁₃₉	C₂²	1	1	yes	characteristic
29	#535×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
30	#525×C₁₃₉	—	2	2	no	—
31	#525×C₁₃₉	C₂²	1	1	yes	characteristic
32	#525×C₁₃₉	C₂²	1	2	yes	—
33	#525×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
34	#519×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
35	#458×C₁₃₉	—	2	2	no	—
36	B(4,𝔽₂)×C₁₃₉	—	2	2	no	—
37	#454×C₁₃₉	—	2	2	no	—
38	#453×C₁₃₉	—	2	2	no	—
39	#452×C₁₃₉	—	2	4	no	—
40	#449×C₁₃₉	—	2	4	no	—
41	#421×C₁₃₉	C₂²	1	2	yes	—
42	#421×C₁₃₉	C₂²	1	2	yes	complemented
43	#419×C₁₃₉	C₂²	1	2	yes	complemented
44	#418×C₁₃₉	C₂²	1	2	yes	complemented
45	#413×C₁₃₉	C₂²	1	1	yes	characteristic
46	#410×C₁₃₉	C₂²	1	2	yes	—
47	#410×C₁₃₉	C₂²	1	1	yes	characteristic
48	#407×C₁₃₉	C₂²	1	2	yes	complemented
49	#344×C₁₃₉	C₂²	1	2	yes	complemented
50	H(3,ℤ/4)×C₁₃₉	C₂²	1	2	yes	complemented
51	2₋¹⁺⁴×C₁₃₉	—	2	4	no	—
52	2₋¹⁺⁴×C₁₃₉	—	2	2	no	—
53	2₋¹⁺⁴×C₁₃₉	—	2	1	no	—
54	2₋¹⁺⁴×C₁₃₉	—	4	2	no	—
55	H(5,𝔽₂)×C₁₃₉	—	2	2	no	—
56	H(5,𝔽₂)×C₁₃₉	—	2	2	no	—
57	H(5,𝔽₂)×C₁₃₉	—	2	1	no	—
58	C₂×#41×C₁₃₉	—	2	2	no	—
59	C₂×#41×C₁₃₉	—	2	2	no	—
60	C₂×#41×C₁₃₉	—	2	2	no	—
61	C₂×#41×C₁₃₉	—	2	1	no	—
62	C₂×#41×C₁₃₉	—	2	4	no	—
63	C₂×#41×C₁₃₉	—	2	2	no	—
64	C₂×#41×C₁₃₉	—	4	2	no	—
65	C₂×#41×C₁₃₉	—	4	2	no	—
66	C₂×#41×C₁₃₉	D₄	1	2	yes	complemented
67	C₂×#41×C₁₃₉	C₂³	1	2	yes	—
68	C₂×#41×C₁₃₉	C₂³	1	1	yes	characteristic
69	C₂×#41×C₁₃₉	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₁₃₉	—	2	1	no	—
71	C₂²×Q₈×C₁₃₉	D₄	1	2	yes	complemented
72	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₁₃₉	—	2	1	no	—
74	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃₉	—	2	1	no	—
76	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
77	#137×C₁₃₉	—	2	8	no	—
78	#137×C₁₃₉	—	2	4	no	—
79	#137×C₁₃₉	—	2	2	no	—
80	#137×C₁₃₉	—	2	4	no	—
81	#137×C₁₃₉	—	2	4	no	—
82	#137×C₁₃₉	—	2	2	no	—
83	AGL(1,ℤ/8)×C₁₃₉	—	2	4	no	—
84	AGL(1,ℤ/8)×C₁₃₉	—	2	2	no	—
85	AGL(1,ℤ/8)×C₁₃₉	—	2	2	no	—
86	AGL(1,ℤ/8)×C₁₃₉	—	2	4	no	—
87	AGL(1,ℤ/8)×C₁₃₉	—	4	2	no	—
88	#135×C₁₃₉	—	2	8	no	—
89	#135×C₁₃₉	—	2	4	no	—
90	C₂×Q₁₆×C₁₃₉	—	2	4	no	—
91	C₂×Q₁₆×C₁₃₉	D₄	1	4	yes	complemented
92	C₂×SD₁₆×C₁₃₉	—	2	4	no	—
93	C₂×SD₁₆×C₁₃₉	—	2	2	no	—
94	C₂×SD₁₆×C₁₃₉	D₄	1	4	yes	complemented
95	C₂×D₈×C₁₃₉	—	2	2	no	—
96	#131×C₁₃₉	—	2	4	no	—
97	C₂×M₁₆×C₁₃₉	—	2	2	no	—
98	C₂×M₁₆×C₁₃₉	C₂³	1	2	yes	—
99	C₂×M₁₆×C₁₃₉	C₂³	1	2	yes	—
100	#127×C₁₃₉	—	2	4	no	—
101	#127×C₁₃₉	—	2	1	no	—
102	#127×C₁₃₉	D₄	1	2	yes	complemented
103	#124×C₁₃₉	—	2	4	no	—
104	#124×C₁₃₉	—	2	1	no	—
105	#124×C₁₃₉	D₄	1	2	yes	complemented
106	#123×C₁₃₉	—	2	1	no	—
107	#123×C₁₃₉	—	2	2	no	—
108	#123×C₁₃₉	D₄	1	2	yes	—
109	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
110	C₂²⋊Q₈×C₁₃₉	—	2	1	no	—
111	C₂²⋊Q₈×C₁₃₉	—	2	1	no	—
112	C₂²⋊Q₈×C₁₃₉	—	2	2	no	—
113	#121×C₁₃₉	—	2	4	no	—
114	#121×C₁₃₉	—	2	4	no	—
115	#121×C₁₃₉	—	2	4	no	—
116	#121×C₁₃₉	—	2	1	no	—
117	#121×C₁₃₉	—	2	1	no	—
118	#121×C₁₃₉	—	2	2	no	—
119	#121×C₁₃₉	—	2	2	no	—
120	#121×C₁₃₉	—	2	2	no	—
121	#120×C₁₃₉	—	2	1	no	—
122	#120×C₁₃₉	—	2	2	no	—
123	#120×C₁₃₉	—	2	2	no	—
124	#120×C₁₃₉	—	2	2	no	—
125	#120×C₁₃₉	D₄	1	2	yes	—
126	C₄×Q₈×C₁₃₉	—	2	2	no	—
127	C₄×Q₈×C₁₃₉	—	2	2	no	—
128	C₄×D₄×C₁₃₉	—	2	4	no	—
129	C₄×D₄×C₁₃₉	—	2	4	no	—
130	C₄×D₄×C₁₃₉	—	2	2	no	—
131	C₄×D₄×C₁₃₉	—	2	2	no	—
132	C₄×D₄×C₁₃₉	—	4	2	no	—
133	#117×C₁₃₉	—	2	2	no	—
134	#117×C₁₃₉	C₂³	1	2	yes	—
135	#117×C₁₃₉	C₂³	1	1	yes	characteristic
136	#117×C₁₃₉	C₂³	1	1	yes	characteristic
137	#104×C₁₃₉	—	2	4	no	—
138	#104×C₁₃₉	—	4	2	no	—
139	#103×C₁₃₉	—	2	4	no	—
140	#102×C₁₃₉	—	2	4	no	—
141	#101×C₁₃₉	—	2	1	no	—
142	#100×C₁₃₉	—	2	1	no	—
143	#99×C₁₃₉	—	2	2	no	—
144	#99×C₁₃₉	—	2	4	no	—
145	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
146	C₂⁴×C₁₃₉	—	2	1	no	—
147	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
148	#41×C₁₃₉	—	2	2	no	—
149	#41×C₁₃₉	—	2	2	no	—
150	#41×C₁₃₉	—	2	4	no	—
151	#41×C₁₃₉	—	2	4	no	—
152	#41×C₁₃₉	—	2	2	no	—
153	#41×C₁₃₉	—	2	2	no	—
154	#41×C₁₃₉	—	2	2	no	—
155	#41×C₁₃₉	—	2	2	no	—
156	#41×C₁₃₉	—	2	2	no	—
157	#41×C₁₃₉	—	2	2	no	—
158	#41×C₁₃₉	—	4	2	no	—
159	#41×C₁₃₉	—	4	8	no	—
160	#41×C₁₃₉	—	4	4	no	—
161	#41×C₁₃₉	—	4	2	no	—
162	#41×C₁₃₉	—	4	8	no	—
163	#41×C₁₃₉	—	4	4	no	—
164	#41×C₁₃₉	—	4	2	no	—
165	#41×C₁₃₉	—	4	2	no	—
166	#41×C₁₃₉	—	4	4	no	—
167	#41×C₁₃₉	—	4	4	no	—
168	#41×C₁₃₉	—	4	2	no	—
169	C₂×Q₈×C₁₃₉	—	2	2	no	—
170	C₂×Q₈×C₁₃₉	—	2	1	no	—
171	C₂×Q₈×C₁₃₉	—	2	2	no	—
172	C₂×Q₈×C₁₃₉	—	2	2	no	—
173	C₂×Q₈×C₁₃₉	—	2	4	no	—
174	C₂×Q₈×C₁₃₉	—	4	2	no	—
175	C₂×Q₈×C₁₃₉	—	4	4	no	—
176	C₂×Q₈×C₁₃₉	—	4	2	no	—
177	C₂×Q₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
178	C₂×Q₈×C₁₃₉	C₂×D₄	1	2	yes	—
179	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
180	C₂×Q₈×C₁₃₉	C₂×D₄	1	2	yes	—
181	C₂×Q₈×C₁₃₉	C₂×D₄	1	1	yes	characteristic
182	C₂×D₄×C₁₃₉	—	2	2	no	—
183	C₂×D₄×C₁₃₉	—	2	4	no	—
184	C₂×D₄×C₁₃₉	—	2	2	no	—
185	C₂×D₄×C₁₃₉	—	2	2	no	—
186	C₂×D₄×C₁₃₉	—	2	1	no	—
187	C₂×D₄×C₁₃₉	—	2	4	no	—
188	C₂×D₄×C₁₃₉	—	2	2	no	—
189	C₂×D₄×C₁₃₉	—	2	4	no	—
190	C₂×D₄×C₁₃₉	—	2	2	no	—
191	C₂×D₄×C₁₃₉	—	2	2	no	—
192	C₂×D₄×C₁₃₉	—	2	1	no	—
193	C₂×D₄×C₁₃₉	—	2	2	no	—
194	C₂×D₄×C₁₃₉	—	4	4	no	—
195	C₂×D₄×C₁₃₉	—	4	2	no	—
196	C₂×D₄×C₁₃₉	—	4	4	no	—
197	C₂×D₄×C₁₃₉	—	4	2	no	—
198	C₂×D₄×C₁₃₉	—	4	2	no	—
199	C₂×D₄×C₁₃₉	C₂×D₄	1	2	yes	—
200	C₂×D₄×C₁₃₉	C₂×D₄	1	2	yes	—
201	C₂×D₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
202	C₂×D₄×C₁₃₉	C₂×D₄	1	2	yes	—
203	C₂×D₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₁₃₉	—	2	1	no	—
205	C₂²×C₄×C₁₃₉	—	2	4	no	—
206	C₂²×C₄×C₁₃₉	—	2	2	no	—
207	C₂²×C₄×C₁₃₉	—	2	2	no	—
208	C₂²×C₄×C₁₃₉	—	2	2	no	—
209	C₂²×C₄×C₁₃₉	—	2	1	no	—
210	C₂²×C₄×C₁₃₉	—	2	1	no	—
211	C₂²×C₄×C₁₃₉	—	2	1	no	—
212	C₂²×C₄×C₁₃₉	—	2	2	no	—
213	C₂²×C₄×C₁₃₉	—	2	2	no	—
214	C₂²×C₄×C₁₃₉	—	4	4	no	—
215	C₂²×C₄×C₁₃₉	—	4	2	no	—
216	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
218	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
219	Q₁₆×C₁₃₉	—	2	4	no	—
220	Q₁₆×C₁₃₉	—	2	8	no	—
221	SD₁₆×C₁₃₉	—	2	4	no	—
222	SD₁₆×C₁₃₉	—	2	4	no	—
223	SD₁₆×C₁₃₉	—	2	8	no	—
224	SD₁₆×C₁₃₉	—	4	4	no	—
225	D₈×C₁₃₉	—	2	4	no	—
226	D₈×C₁₃₉	—	4	4	no	—
227	M₁₆×C₁₃₉	—	2	4	no	—
228	M₁₆×C₁₃₉	—	2	2	no	—
229	M₁₆×C₁₃₉	—	2	2	no	—
230	M₁₆×C₁₃₉	—	2	2	no	—
231	M₁₆×C₁₃₉	—	2	2	no	—
232	C₂×C₈×C₁₃₉	—	2	4	no	—
233	C₂×C₈×C₁₃₉	—	2	2	no	—
234	C₂×C₈×C₁₃₉	C₂×D₄	1	4	yes	—
235	C₄⋊C₄×C₁₃₉	—	2	4	no	—
236	C₄⋊C₄×C₁₃₉	—	2	2	no	—
237	C₄⋊C₄×C₁₃₉	—	2	2	no	—
238	C₄⋊C₄×C₁₃₉	—	2	1	no	—
239	C₄⋊C₄×C₁₃₉	—	2	1	no	—
240	C₄⋊C₄×C₁₃₉	—	2	2	no	—
241	C₄⋊C₄×C₁₃₉	—	4	2	no	—
242	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
243	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
244	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
245	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
246	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
247	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
248	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
249	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
250	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
251	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
252	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	2	yes	—
253	C₄²×C₁₃₉	—	2	4	no	—
254	C₄²×C₁₃₉	—	2	1	no	—
255	C₄²×C₁₃₉	—	2	2	no	—
256	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
257	C₂³×C₁₃₉	—	2	1	no	—
258	C₂³×C₁₃₉	—	2	2	no	—
259	C₂³×C₁₃₉	—	2	1	no	—
260	C₂³×C₁₃₉	—	2	2	no	—
261	C₂³×C₁₃₉	—	2	2	no	—
262	C₂³×C₁₃₉	—	4	2	no	—
263	C₂³×C₁₃₉	—	4	2	no	—
264	C₂³×C₁₃₉	—	8	1	no	—
265	C₂³×C₁₃₉	—	8	2	no	—
266	C₂³×C₁₃₉	#120	1	2	yes	—
267	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
268	Q₈×C₁₃₉	—	2	2	no	—
269	Q₈×C₁₃₉	—	2	4	no	—
270	Q₈×C₁₃₉	—	2	2	no	—
271	Q₈×C₁₃₉	—	2	1	no	—
272	Q₈×C₁₃₉	—	2	2	no	—
273	Q₈×C₁₃₉	—	2	1	no	—
274	Q₈×C₁₃₉	—	2	2	no	—
275	Q₈×C₁₃₉	—	4	4	no	—
276	Q₈×C₁₃₉	—	4	2	no	—
277	Q₈×C₁₃₉	#120	1	4	yes	—
278	D₄×C₁₃₉	—	2	4	no	—
279	D₄×C₁₃₉	—	2	1	no	—
280	D₄×C₁₃₉	—	2	2	no	—
281	D₄×C₁₃₉	—	2	1	no	—
282	D₄×C₁₃₉	—	2	2	no	—
283	D₄×C₁₃₉	—	2	2	no	—
284	D₄×C₁₃₉	—	2	4	no	—
285	D₄×C₁₃₉	—	4	4	no	—
286	D₄×C₁₃₉	—	4	8	no	—
287	D₄×C₁₃₉	—	4	2	no	—
288	D₄×C₁₃₉	—	4	4	no	—
289	D₄×C₁₃₉	—	4	2	no	—
290	D₄×C₁₃₉	—	4	2	no	—
291	D₄×C₁₃₉	—	4	2	no	—
292	D₄×C₁₃₉	—	4	1	no	—
293	D₄×C₁₃₉	—	4	1	no	—
294	D₄×C₁₃₉	—	8	4	no	—
295	D₄×C₁₃₉	—	8	2	no	—
296	D₄×C₁₃₉	—	8	4	no	—
297	D₄×C₁₃₉	—	8	2	no	—
298	D₄×C₁₃₉	—	8	4	no	—
299	C₂×C₄×C₁₃₉	—	2	2	no	—
300	C₂×C₄×C₁₃₉	—	2	4	no	—
301	C₂×C₄×C₁₃₉	—	2	2	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	2	2	no	—
304	C₂×C₄×C₁₃₉	—	2	2	no	—
305	C₂×C₄×C₁₃₉	—	2	1	no	—
306	C₂×C₄×C₁₃₉	—	2	1	no	—
307	C₂×C₄×C₁₃₉	—	2	2	no	—
308	C₂×C₄×C₁₃₉	—	2	2	no	—
309	C₂×C₄×C₁₃₉	—	4	4	no	—
310	C₂×C₄×C₁₃₉	—	4	4	no	—
311	C₂×C₄×C₁₃₉	—	4	8	no	—
312	C₂×C₄×C₁₃₉	—	4	4	no	—
313	C₂×C₄×C₁₃₉	—	4	2	no	—
314	C₂×C₄×C₁₃₉	—	4	1	no	—
315	C₂×C₄×C₁₃₉	—	4	1	no	—
316	C₂×C₄×C₁₃₉	—	4	2	no	—
317	C₂×C₄×C₁₃₉	—	4	2	no	—
318	C₂×C₄×C₁₃₉	—	4	2	no	—
319	C₂×C₄×C₁₃₉	—	4	2	no	—
320	C₂×C₄×C₁₃₉	—	4	2	no	—
321	C₂×C₄×C₁₃₉	#120	1	2	yes	—
322	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
326	C₈×C₁₃₉	—	2	4	no	—
327	C₈×C₁₃₉	—	4	2	no	—
328	C₂²×C₁₃₉	—	2	2	no	—
329	C₂²×C₁₃₉	—	4	1	no	—
330	C₂²×C₁₃₉	—	4	2	no	—
331	C₂²×C₁₃₉	—	4	2	no	—
332	C₂²×C₁₃₉	—	4	1	no	—
333	C₂²×C₁₃₉	—	4	1	no	—
334	C₂²×C₁₃₉	—	4	4	no	—
335	C₂²×C₁₃₉	—	4	2	no	—
336	C₂²×C₁₃₉	—	4	2	no	—
337	C₂²×C₁₃₉	—	4	1	no	—
338	C₂²×C₁₃₉	—	4	2	no	—
339	C₂²×C₁₃₉	—	4	2	no	—
340	C₂²×C₁₃₉	—	4	1	no	—
341	C₂²×C₁₃₉	—	8	2	no	—
342	C₂²×C₁₃₉	—	8	4	no	—
343	C₂²×C₁₃₉	—	16	2	no	—
344	C₂²×C₁₃₉	C₂×#120	1	1	yes	characteristic
345	C₂²×C₁₃₉	D₄²	1	2	yes	—
346	C₄×C₁₃₉	—	2	4	no	—
347	C₄×C₁₃₉	—	2	2	no	—
348	C₄×C₁₃₉	—	4	2	no	—
349	C₄×C₁₃₉	—	4	2	no	—
350	C₄×C₁₃₉	—	4	1	no	—
351	C₄×C₁₃₉	—	4	2	no	—
352	C₄×C₁₃₉	—	4	1	no	—
353	C₄×C₁₃₉	—	8	2	no	—
354	C₄×C₁₃₉	C₂×#120	1	1	yes	characteristic
355	C₄×C₁₃₉	#534	1	1	yes	characteristic
356	C₄×C₁₃₉	D₄²	1	2	yes	—
357	C₂×C₁₃₉	—	2	1	no	—
358	C₂×C₁₃₉	—	2	2	no	—
359	C₂×C₁₃₉	—	4	2	no	—
360	C₂×C₁₃₉	—	8	1	no	—
361	C₂×C₁₃₉	—	8	1	no	—
362	C₂×C₁₃₉	—	8	2	no	—
363	C₂×C₁₃₉	—	8	2	no	—
364	C₂×C₁₃₉	#2403	1	1	yes	characteristic
365	#23884	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
366	C₁₃₉	#23884	1	1	yes	characteristic, direct product factor, Sylow
367	#3586	C₂×C₁₃₉	1	1	yes	characteristic, complemented
368	#3487	C₂×C₁₃₉	1	1	yes	characteristic, complemented
369	#3025	C₂×C₁₃₉	1	1	yes	characteristic, complemented
370	#3021	C₂×C₁₃₉	1	1	yes	characteristic, complemented
371	#3005	C₂×C₁₃₉	1	2	yes	complemented
372	#2010	C₂×C₁₃₉	1	2	yes	complemented
373	#2008	C₂×C₁₃₉	1	2	yes	complemented
374	#1910	C₂×C₁₃₉	1	1	yes	characteristic, complemented
375	#1905	C₂×C₁₃₉	1	2	yes	complemented
376	#1891	C₂×C₁₃₉	1	1	yes	characteristic, complemented
377	#1796	C₂×C₁₃₉	1	1	yes	characteristic, complemented
378	#585	C₂²×C₁₃₉	1	1	yes	characteristic
379	C₂×2₋¹⁺⁴	C₂²×C₁₃₉	1	1	yes	characteristic
380	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
381	#578	—	2	4	no	—
382	#577	—	2	4	no	—
383	#575	—	2	2	no	—
384	#575	C₂²×C₁₃₉	1	2	yes	—
385	C₂×#137	—	2	2	no	—
386	C₂×#137	C₂²×C₁₃₉	1	2	yes	—
387	C₂×AGL(1,ℤ/8)	C₂²×C₁₃₉	1	2	yes	—
388	#568	C₂²×C₁₃₉	1	1	yes	characteristic
389	#550	—	2	2	no	—
390	#550	—	2	2	no	—
391	#548	—	2	2	no	—
392	#548	—	2	2	no	—
393	#535	—	2	2	no	—
394	#535	C₂²×C₁₃₉	1	1	yes	characteristic
395	#535	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
396	#525	—	2	2	no	—
397	#525	C₂²×C₁₃₉	1	1	yes	characteristic
398	#525	C₂²×C₁₃₉	1	2	yes	—
399	#525	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
400	#519	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
401	#458	—	2	2	no	—
402	B(4,𝔽₂)	—	2	2	no	—
403	#454	—	2	2	no	—
404	#453	—	2	2	no	—
405	#452	—	2	4	no	—
406	#449	—	2	4	no	—
407	#421	C₂²×C₁₃₉	1	2	yes	—
408	#421	C₂²×C₁₃₉	1	2	yes	complemented
409	#419	C₂²×C₁₃₉	1	2	yes	complemented
410	#418	C₂²×C₁₃₉	1	2	yes	complemented
411	#413	C₂²×C₁₃₉	1	1	yes	characteristic
412	#410	C₂²×C₁₃₉	1	1	yes	characteristic
413	#410	C₂²×C₁₃₉	1	2	yes	—
414	#407	C₂²×C₁₃₉	1	2	yes	complemented
415	#344	C₂²×C₁₃₉	1	2	yes	complemented
416	H(3,ℤ/4)	C₂²×C₁₃₉	1	2	yes	complemented
417	2₋¹⁺⁴	—	2	4	no	—
418	2₋¹⁺⁴	—	2	2	no	—
419	2₋¹⁺⁴	—	2	1	no	—
420	2₋¹⁺⁴	—	4	2	no	—
421	H(5,𝔽₂)	—	2	2	no	—
422	H(5,𝔽₂)	—	2	2	no	—
423	H(5,𝔽₂)	—	2	1	no	—
424	C₂×#41	—	2	2	no	—
425	C₂×#41	—	2	2	no	—
426	C₂×#41	—	2	2	no	—
427	C₂×#41	—	2	1	no	—
428	C₂×#41	—	2	4	no	—
429	C₂×#41	—	2	2	no	—
430	C₂×#41	—	4	2	no	—
431	C₂×#41	—	4	2	no	—
432	C₂×#41	D₄×C₁₃₉	1	2	yes	complemented
433	C₂×#41	C₂³×C₁₃₉	1	2	yes	—
434	C₂×#41	C₂³×C₁₃₉	1	1	yes	characteristic
435	C₂×#41	C₂³×C₁₃₉	1	1	yes	characteristic
436	C₂²×Q₈	—	2	1	no	—
437	C₂²×Q₈	D₄×C₁₃₉	1	2	yes	complemented
438	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
439	C₂²×D₄	—	2	1	no	—
440	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
441	C₂³×C₄	—	2	1	no	—
442	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
443	#137	—	2	8	no	—
444	#137	—	2	4	no	—
445	#137	—	2	2	no	—
446	#137	—	2	4	no	—
447	#137	—	2	4	no	—
448	#137	—	2	2	no	—
449	AGL(1,ℤ/8)	—	2	4	no	—
450	AGL(1,ℤ/8)	—	2	2	no	—
451	AGL(1,ℤ/8)	—	2	2	no	—
452	AGL(1,ℤ/8)	—	2	4	no	—
453	AGL(1,ℤ/8)	—	4	2	no	—
454	#135	—	2	8	no	—
455	#135	—	2	4	no	—
456	C₂×Q₁₆	—	2	4	no	—
457	C₂×Q₁₆	D₄×C₁₃₉	1	4	yes	complemented
458	C₂×SD₁₆	—	2	4	no	—
459	C₂×SD₁₆	—	2	2	no	—
460	C₂×SD₁₆	D₄×C₁₃₉	1	4	yes	complemented
461	C₂×D₈	—	2	2	no	—
462	#131	—	2	4	no	—
463	C₂×M₁₆	—	2	2	no	—
464	C₂×M₁₆	C₂³×C₁₃₉	1	2	yes	—
465	C₂×M₁₆	C₂³×C₁₃₉	1	2	yes	—
466	#127	—	2	4	no	—
467	#127	—	2	1	no	—
468	#127	D₄×C₁₃₉	1	2	yes	complemented
469	#124	—	2	4	no	—
470	#124	—	2	1	no	—
471	#124	D₄×C₁₃₉	1	2	yes	complemented
472	#123	—	2	1	no	—
473	#123	—	2	2	no	—
474	#123	D₄×C₁₃₉	1	2	yes	—
475	C₂²⋊Q₈	—	2	4	no	—
476	C₂²⋊Q₈	—	2	1	no	—
477	C₂²⋊Q₈	—	2	1	no	—
478	C₂²⋊Q₈	—	2	2	no	—
479	#121	—	2	4	no	—
480	#121	—	2	4	no	—
481	#121	—	2	4	no	—
482	#121	—	2	1	no	—
483	#121	—	2	1	no	—
484	#121	—	2	2	no	—
485	#121	—	2	2	no	—
486	#121	—	2	2	no	—
487	#120	—	2	1	no	—
488	#120	—	2	2	no	—
489	#120	—	2	2	no	—
490	#120	—	2	2	no	—
491	#120	D₄×C₁₃₉	1	2	yes	—
492	C₄×Q₈	—	2	2	no	—
493	C₄×Q₈	—	2	2	no	—
494	C₄×D₄	—	2	4	no	—
495	C₄×D₄	—	2	4	no	—
496	C₄×D₄	—	2	2	no	—
497	C₄×D₄	—	2	2	no	—
498	C₄×D₄	—	4	2	no	—
499	#117	—	2	2	no	—
500	#117	C₂³×C₁₃₉	1	2	yes	—
501	#117	C₂³×C₁₃₉	1	1	yes	characteristic
502	#117	C₂³×C₁₃₉	1	1	yes	characteristic
503	#104	—	2	4	no	—
504	#104	—	4	2	no	—
505	#103	—	2	4	no	—
506	#102	—	2	4	no	—
507	#101	—	2	1	no	—
508	#100	—	2	1	no	—
509	#99	—	2	2	no	—
510	#99	—	2	4	no	—
511	C₂²⋊C₈	—	2	4	no	—
512	C₂⁴	—	2	1	no	—
513	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
514	#41	—	2	2	no	—
515	#41	—	2	2	no	—
516	#41	—	2	4	no	—
517	#41	—	2	4	no	—
518	#41	—	2	2	no	—
519	#41	—	2	2	no	—
520	#41	—	2	2	no	—
521	#41	—	2	2	no	—
522	#41	—	2	2	no	—
523	#41	—	2	2	no	—
524	#41	—	4	2	no	—
525	#41	—	4	8	no	—
526	#41	—	4	4	no	—
527	#41	—	4	2	no	—
528	#41	—	4	8	no	—
529	#41	—	4	4	no	—
530	#41	—	4	2	no	—
531	#41	—	4	2	no	—
532	#41	—	4	4	no	—
533	#41	—	4	4	no	—
534	#41	—	4	2	no	—
535	C₂×Q₈	—	2	2	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	2	no	—
538	C₂×Q₈	—	2	2	no	—
539	C₂×Q₈	—	2	4	no	—
540	C₂×Q₈	—	4	2	no	—
541	C₂×Q₈	—	4	4	no	—
542	C₂×Q₈	—	4	2	no	—
543	C₂×Q₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
544	C₂×Q₈	C₂×D₄×C₁₃₉	1	2	yes	—
545	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
546	C₂×Q₈	C₂×D₄×C₁₃₉	1	2	yes	—
547	C₂×Q₈	C₂×D₄×C₁₃₉	1	1	yes	characteristic
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	4	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	4	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	4	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	4	4	no	—
561	C₂×D₄	—	4	2	no	—
562	C₂×D₄	—	4	4	no	—
563	C₂×D₄	—	4	2	no	—
564	C₂×D₄	—	4	2	no	—
565	C₂×D₄	C₂×D₄×C₁₃₉	1	2	yes	—
566	C₂×D₄	C₂×D₄×C₁₃₉	1	2	yes	—
567	C₂×D₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
568	C₂×D₄	C₂×D₄×C₁₃₉	1	2	yes	—
569	C₂×D₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	4	4	no	—
581	C₂²×C₄	—	4	2	no	—
582	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
583	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
585	Q₁₆	—	2	4	no	—
586	Q₁₆	—	2	8	no	—
587	SD₁₆	—	2	4	no	—
588	SD₁₆	—	2	4	no	—
589	SD₁₆	—	2	8	no	—
590	SD₁₆	—	4	4	no	—
591	D₈	—	2	4	no	—
592	D₈	—	4	4	no	—
593	M₁₆	—	2	4	no	—
594	M₁₆	—	2	2	no	—
595	M₁₆	—	2	2	no	—
596	M₁₆	—	2	2	no	—
597	M₁₆	—	2	2	no	—
598	C₂×C₈	—	2	4	no	—
599	C₂×C₈	—	2	2	no	—
600	C₂×C₈	C₂×D₄×C₁₃₉	1	4	yes	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	—	4	2	no	—
608	C₂²⋊C₄	—	2	2	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	2	no	—
612	C₂²⋊C₄	—	2	1	no	—
613	C₂²⋊C₄	—	2	4	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	2	2	no	—
616	C₂²⋊C₄	—	4	2	no	—
617	C₂²⋊C₄	—	4	2	no	—
618	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	2	yes	—
619	C₄²	—	2	4	no	—
620	C₄²	—	2	1	no	—
621	C₄²	—	2	2	no	—
622	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	1	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	4	2	no	—
629	C₂³	—	4	2	no	—
630	C₂³	—	8	1	no	—
631	C₂³	—	8	2	no	—
632	C₂³	#120×C₁₃₉	1	2	yes	—
633	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
634	Q₈	—	2	2	no	—
635	Q₈	—	2	4	no	—
636	Q₈	—	2	2	no	—
637	Q₈	—	2	1	no	—
638	Q₈	—	2	2	no	—
639	Q₈	—	2	1	no	—
640	Q₈	—	2	2	no	—
641	Q₈	—	4	4	no	—
642	Q₈	—	4	2	no	—
643	Q₈	#120×C₁₃₉	1	4	yes	—
644	D₄	—	2	4	no	—
645	D₄	—	2	1	no	—
646	D₄	—	2	2	no	—
647	D₄	—	2	1	no	—
648	D₄	—	2	2	no	—
649	D₄	—	2	2	no	—
650	D₄	—	2	4	no	—
651	D₄	—	4	4	no	—
652	D₄	—	4	8	no	—
653	D₄	—	4	2	no	—
654	D₄	—	4	4	no	—
655	D₄	—	4	2	no	—
656	D₄	—	4	2	no	—
657	D₄	—	4	2	no	—
658	D₄	—	4	1	no	—
659	D₄	—	4	1	no	—
660	D₄	—	8	4	no	—
661	D₄	—	8	2	no	—
662	D₄	—	8	4	no	—
663	D₄	—	8	2	no	—
664	D₄	—	8	4	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	4	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	4	4	no	—
676	C₂×C₄	—	4	4	no	—
677	C₂×C₄	—	4	8	no	—
678	C₂×C₄	—	4	4	no	—
679	C₂×C₄	—	4	2	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	2	no	—
683	C₂×C₄	—	4	2	no	—
684	C₂×C₄	—	4	2	no	—
685	C₂×C₄	—	4	2	no	—
686	C₂×C₄	—	4	2	no	—
687	C₂×C₄	#120×C₁₃₉	1	2	yes	—
688	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
689	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
690	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
691	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
692	C₈	—	2	4	no	—
693	C₈	—	4	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	4	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	1	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	8	2	no	—
708	C₂²	—	8	4	no	—
709	C₂²	—	16	2	no	—
710	C₂²	C₂×#120×C₁₃₉	1	1	yes	characteristic
711	C₂²	D₄²×C₁₃₉	1	2	yes	—
712	C₄	—	2	4	no	—
713	C₄	—	2	2	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	1	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	1	no	—
719	C₄	—	8	2	no	—
720	C₄	C₂×#120×C₁₃₉	1	1	yes	characteristic
721	C₄	#534×C₁₃₉	1	1	yes	characteristic
722	C₄	D₄²×C₁₃₉	1	2	yes	—
723	C₂	—	2	1	no	—
724	C₂	—	2	2	no	—
725	C₂	—	4	2	no	—
726	C₂	—	8	1	no	—
727	C₂	—	8	2	no	—
728	C₂	—	8	1	no	—
729	C₂	—	8	2	no	—
730	C₂	#2403×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃₉	#2403
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃₉ ◁ C₂²×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3586×C₁₃₉	C₂	semidirect
2. #3487×C₁₃₉	C₂	semidirect
3. #3025×C₁₃₉	C₂	semidirect
4. #3021×C₁₃₉	C₂	semidirect
5. #3005×C₁₃₉	C₂	semidirect
6. #2010×C₁₃₉	C₂	semidirect
7. #2008×C₁₃₉	C₂	semidirect
8. #1910×C₁₃₉	C₂	semidirect
9. #1905×C₁₃₉	C₂	semidirect
10. #1891×C₁₃₉	C₂	semidirect
11. #1796×C₁₃₉	C₂	semidirect
14. C₂²×#41×C₁₃₉	C₂²	semidirect
29. #535×C₁₃₉	C₂²	semidirect
33. #525×C₁₃₉	C₂²	semidirect
34. #519×C₁₃₉	C₂²	semidirect
42. #421×C₁₃₉	C₂²	semidirect
43. #419×C₁₃₉	C₂²	semidirect
44. #418×C₁₃₉	C₂²	semidirect
48. #407×C₁₃₉	C₂²	semidirect
49. #344×C₁₃₉	C₂²	semidirect
50. H(3,ℤ/4)×C₁₃₉	C₂²	semidirect
66. C₂×#41×C₁₃₉	D₄	semidirect
71. C₂²×Q₈×C₁₃₉	D₄	semidirect
91. C₂×Q₁₆×C₁₃₉	D₄	semidirect
94. C₂×SD₁₆×C₁₃₉	D₄	semidirect
102. #127×C₁₃₉	D₄	semidirect
105. #124×C₁₃₉	D₄	semidirect
365. #23884	C₁₃₉	direct (N × H)
366. C₁₃₉	#23884	direct (N × H)
367. #3586	C₂×C₁₃₉	semidirect
368. #3487	C₂×C₁₃₉	semidirect
369. #3025	C₂×C₁₃₉	semidirect
370. #3021	C₂×C₁₃₉	semidirect
371. #3005	C₂×C₁₃₉	semidirect
372. #2010	C₂×C₁₃₉	semidirect
373. #2008	C₂×C₁₃₉	semidirect
374. #1910	C₂×C₁₃₉	semidirect
375. #1905	C₂×C₁₃₉	semidirect
376. #1891	C₂×C₁₃₉	semidirect
377. #1796	C₂×C₁₃₉	semidirect
380. C₂²×#41	C₂²×C₁₃₉	semidirect
395. #535	C₂²×C₁₃₉	semidirect
399. #525	C₂²×C₁₃₉	semidirect
400. #519	C₂²×C₁₃₉	semidirect
408. #421	C₂²×C₁₃₉	semidirect
409. #419	C₂²×C₁₃₉	semidirect
410. #418	C₂²×C₁₃₉	semidirect
414. #407	C₂²×C₁₃₉	semidirect
415. #344	C₂²×C₁₃₉	semidirect
416. H(3,ℤ/4)	C₂²×C₁₃₉	semidirect
432. C₂×#41	D₄×C₁₃₉	semidirect
437. C₂²×Q₈	D₄×C₁₃₉	semidirect
457. C₂×Q₁₆	D₄×C₁₃₉	semidirect
460. C₂×SD₁₆	D₄×C₁₃₉	semidirect
468. #127	D₄×C₁₃₉	semidirect
471. #124	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#3586×C₁₃₉	2
#3487×C₁₃₉	2
#3025×C₁₃₉	2
#3021×C₁₃₉	2
#3005×C₁₃₉	2
#2010×C₁₃₉	2
#2008×C₁₃₉	2
#1910×C₁₃₉	2
#1905×C₁₃₉	2
#1891×C₁₃₉	2
#1796×C₁₃₉	2
#23884	139

Subgroups — C139×#23884 #48018480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#23884 #48018480