Subgroups — C₁₃₉×#32894 #48027490

Order 35584.

3638 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	H(7,𝔽₂)×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#3027×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#3021×C₁₃₉	C₂	1	3	yes	maximal, complemented
4	#3008×C₁₃₉	C₂	1	3	yes	maximal, complemented
5	#1795×C₁₃₉	C₂	1	3	yes	maximal, complemented
6	#1794×C₁₃₉	C₂	1	3	yes	maximal, complemented
7	#1791×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#585×C₁₃₉	—	2	6	no	—
9	#585×C₁₃₉	—	2	6	no	—
10	#585×C₁₃₉	C₂²	1	3	yes	—
11	#585×C₁₃₉	C₂²	1	1	yes	characteristic
12	C₂×H(5,𝔽₂)×C₁₃₉	—	2	4	no	—
13	C₂×H(5,𝔽₂)×C₁₃₉	—	2	6	no	—
14	C₂×H(5,𝔽₂)×C₁₃₉	—	2	6	no	—
15	C₂×H(5,𝔽₂)×C₁₃₉	C₂²	1	3	yes	—
16	C₂×AGL(1,ℤ/8)×C₁₃₉	C₂²	1	3	yes	complemented
17	C₂²×D₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
18	#535×C₁₃₉	C₂²	1	3	yes	complemented
19	B(4,𝔽₂)×C₁₃₉	—	2	4	no	—
20	#454×C₁₃₉	—	2	6	no	—
21	#453×C₁₃₉	—	2	6	no	—
22	#449×C₁₃₉	—	2	6	no	—
23	#447×C₁₃₉	—	2	6	no	—
24	#421×C₁₃₉	C₂²	1	6	yes	complemented
25	#418×C₁₃₉	C₂²	1	3	yes	complemented
26	#416×C₁₃₉	C₂²	1	3	yes	complemented
27	#413×C₁₃₉	C₂²	1	3	yes	complemented
28	#410×C₁₃₉	C₂²	1	3	yes	complemented
29	#408×C₁₃₉	C₂²	1	3	yes	complemented
30	2₋¹⁺⁴×C₁₃₉	—	2	4	no	—
31	2₋¹⁺⁴×C₁₃₉	—	2	12	no	—
32	2₋¹⁺⁴×C₁₃₉	—	2	3	no	—
33	2₋¹⁺⁴×C₁₃₉	—	2	6	no	—
34	2₋¹⁺⁴×C₁₃₉	D₄	1	6	yes	complemented
35	H(5,𝔽₂)×C₁₃₉	—	2	12	no	—
36	H(5,𝔽₂)×C₁₃₉	—	2	24	no	—
37	H(5,𝔽₂)×C₁₃₉	—	2	24	no	—
38	H(5,𝔽₂)×C₁₃₉	—	2	12	no	—
39	H(5,𝔽₂)×C₁₃₉	—	2	24	no	—
40	H(5,𝔽₂)×C₁₃₉	—	2	12	no	—
41	H(5,𝔽₂)×C₁₃₉	—	2	6	no	—
42	H(5,𝔽₂)×C₁₃₉	—	2	3	no	—
43	H(5,𝔽₂)×C₁₃₉	—	2	6	no	—
44	H(5,𝔽₂)×C₁₃₉	—	2	12	no	—
45	H(5,𝔽₂)×C₁₃₉	D₄	1	4	yes	—
46	H(5,𝔽₂)×C₁₃₉	D₄	1	6	yes	complemented
47	C₂×#41×C₁₃₉	—	2	24	no	—
48	C₂×#41×C₁₃₉	—	2	12	no	—
49	C₂×#41×C₁₃₉	—	2	12	no	—
50	C₂×#41×C₁₃₉	—	2	24	no	—
51	C₂×#41×C₁₃₉	—	2	12	no	—
52	C₂×#41×C₁₃₉	—	2	3	no	—
53	C₂×#41×C₁₃₉	—	2	6	no	—
54	C₂×#41×C₁₃₉	—	2	6	no	—
55	C₂×#41×C₁₃₉	D₄	1	6	yes	complemented
56	C₂×#41×C₁₃₉	C₂³	1	3	yes	—
57	C₂×#41×C₁₃₉	C₂³	1	3	yes	—
58	C₂²×D₄×C₁₃₉	—	2	24	no	—
59	C₂²×D₄×C₁₃₉	—	2	12	no	—
60	C₂²×D₄×C₁₃₉	—	2	4	no	—
61	C₂²×D₄×C₁₃₉	—	2	6	no	—
62	C₂²×D₄×C₁₃₉	—	2	3	no	—
63	C₂²×D₄×C₁₃₉	D₄	1	6	yes	complemented
64	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic, complemented
66	AGL(1,ℤ/8)×C₁₃₉	—	2	12	no	—
67	C₂×SD₁₆×C₁₃₉	—	2	3	no	—
68	C₂×D₈×C₁₃₉	—	2	3	no	—
69	C₂×D₈×C₁₃₉	—	2	6	no	—
70	C₂×M₁₆×C₁₃₉	C₂³	1	3	yes	complemented
71	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic, complemented
72	#127×C₁₃₉	—	2	3	no	—
73	#124×C₁₃₉	—	2	3	no	—
74	#121×C₁₃₉	—	2	6	no	—
75	#120×C₁₃₉	—	2	6	no	—
76	#117×C₁₃₉	C₂³	1	3	yes	complemented
77	#104×C₁₃₉	—	2	12	no	—
78	#103×C₁₃₉	—	2	3	no	—
79	#102×C₁₃₉	—	2	3	no	—
80	#102×C₁₃₉	—	2	6	no	—
81	#101×C₁₃₉	—	2	3	no	—
82	#100×C₁₃₉	—	2	3	no	—
83	#99×C₁₃₉	—	2	6	no	—
84	C₂²⋊C₈×C₁₃₉	—	2	6	no	—
85	C₂⁴×C₁₃₉	—	2	8	no	—
86	C₂⁴×C₁₃₉	—	2	6	no	—
87	C₂⁴×C₁₃₉	—	2	1	no	—
88	C₂⁴×C₁₃₉	—	2	1	no	—
89	#41×C₁₃₉	—	2	24	no	—
90	#41×C₁₃₉	—	2	24	no	—
91	#41×C₁₃₉	—	2	48	no	—
92	#41×C₁₃₉	—	2	24	no	—
93	#41×C₁₃₉	—	2	24	no	—
94	#41×C₁₃₉	—	2	12	no	—
95	#41×C₁₃₉	—	2	12	no	—
96	#41×C₁₃₉	—	2	12	no	—
97	#41×C₁₃₉	—	2	4	no	—
98	#41×C₁₃₉	—	2	12	no	—
99	#41×C₁₃₉	—	2	12	no	—
100	#41×C₁₃₉	—	2	12	no	—
101	#41×C₁₃₉	—	2	12	no	—
102	#41×C₁₃₉	—	2	12	no	—
103	#41×C₁₃₉	—	2	12	no	—
104	#41×C₁₃₉	—	2	6	no	—
105	#41×C₁₃₉	—	2	6	no	—
106	#41×C₁₃₉	—	2	6	no	—
107	#41×C₁₃₉	C₂×D₄	1	12	yes	—
108	C₂×Q₈×C₁₃₉	—	2	8	no	—
109	C₂×Q₈×C₁₃₉	—	2	6	no	—
110	C₂×Q₈×C₁₃₉	—	2	6	no	—
111	C₂×Q₈×C₁₃₉	—	2	12	no	—
112	C₂×Q₈×C₁₃₉	C₂×D₄	1	3	yes	—
113	C₂×Q₈×C₁₃₉	C₂×D₄	1	3	yes	—
114	C₂×D₄×C₁₃₉	—	2	24	no	—
115	C₂×D₄×C₁₃₉	—	2	48	no	—
116	C₂×D₄×C₁₃₉	—	2	24	no	—
117	C₂×D₄×C₁₃₉	—	2	24	no	—
118	C₂×D₄×C₁₃₉	—	2	24	no	—
119	C₂×D₄×C₁₃₉	—	2	48	no	—
120	C₂×D₄×C₁₃₉	—	2	24	no	—
121	C₂×D₄×C₁₃₉	—	2	6	no	—
122	C₂×D₄×C₁₃₉	—	2	6	no	—
123	C₂×D₄×C₁₃₉	—	2	12	no	—
124	C₂×D₄×C₁₃₉	—	2	12	no	—
125	C₂×D₄×C₁₃₉	—	2	6	no	—
126	C₂×D₄×C₁₃₉	—	2	3	no	—
127	C₂×D₄×C₁₃₉	—	2	12	no	—
128	C₂×D₄×C₁₃₉	—	2	12	no	—
129	C₂×D₄×C₁₃₉	—	2	12	no	—
130	C₂×D₄×C₁₃₉	—	2	6	no	—
131	C₂×D₄×C₁₃₉	—	2	3	no	—
132	C₂×D₄×C₁₃₉	—	2	3	no	—
133	C₂×D₄×C₁₃₉	—	2	3	no	—
134	C₂×D₄×C₁₃₉	—	4	6	no	—
135	C₂×D₄×C₁₃₉	C₂×D₄	1	6	yes	—
136	C₂×D₄×C₁₃₉	C₂×D₄	1	3	yes	—
137	C₂×D₄×C₁₃₉	C₂×D₄	1	3	yes	—
138	C₂×D₄×C₁₃₉	C₂×D₄	1	6	yes	—
139	C₂²×C₄×C₁₃₉	—	2	24	no	—
140	C₂²×C₄×C₁₃₉	—	2	12	no	—
141	C₂²×C₄×C₁₃₉	—	2	4	no	—
142	C₂²×C₄×C₁₃₉	—	2	6	no	—
143	C₂²×C₄×C₁₃₉	—	2	3	no	—
144	C₂²×C₄×C₁₃₉	C₂×D₄	1	6	yes	—
145	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
146	SD₁₆×C₁₃₉	—	4	6	no	—
147	D₈×C₁₃₉	—	4	4	no	—
148	D₈×C₁₃₉	—	4	6	no	—
149	M₁₆×C₁₃₉	—	2	6	no	—
150	C₂×C₈×C₁₃₉	—	2	3	no	—
151	C₂×C₈×C₁₃₉	—	2	3	no	—
152	C₄⋊C₄×C₁₃₉	—	2	3	no	—
153	C₂²⋊C₄×C₁₃₉	—	2	3	no	—
154	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
155	C₄²×C₁₃₉	—	2	3	no	—
156	C₂³×C₁₃₉	—	2	4	no	—
157	C₂³×C₁₃₉	—	2	24	no	—
158	C₂³×C₁₃₉	—	2	12	no	—
159	C₂³×C₁₃₉	—	2	6	no	—
160	C₂³×C₁₃₉	—	2	3	no	—
161	C₂³×C₁₃₉	—	4	3	no	—
162	C₂³×C₁₃₉	—	16	1	no	—
163	C₂³×C₁₃₉	—	16	1	no	—
164	C₂³×C₁₃₉	—	16	6	no	—
165	C₂³×C₁₃₉	—	16	8	no	—
166	C₂³×C₁₃₉	#120	1	6	yes	—
167	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
168	Q₈×C₁₃₉	—	2	12	no	—
169	Q₈×C₁₃₉	—	2	4	no	—
170	Q₈×C₁₃₉	—	2	3	no	—
171	Q₈×C₁₃₉	—	2	6	no	—
172	Q₈×C₁₃₉	#120	1	6	yes	—
173	D₄×C₁₃₉	—	2	24	no	—
174	D₄×C₁₃₉	—	2	24	no	—
175	D₄×C₁₃₉	—	2	12	no	—
176	D₄×C₁₃₉	—	2	12	no	—
177	D₄×C₁₃₉	—	2	24	no	—
178	D₄×C₁₃₉	—	2	12	no	—
179	D₄×C₁₃₉	—	2	12	no	—
180	D₄×C₁₃₉	—	2	6	no	—
181	D₄×C₁₃₉	—	2	6	no	—
182	D₄×C₁₃₉	—	2	3	no	—
183	D₄×C₁₃₉	—	4	1	no	—
184	D₄×C₁₃₉	—	4	3	no	—
185	D₄×C₁₃₉	—	16	6	no	—
186	D₄×C₁₃₉	#120	1	6	yes	—
187	D₄×C₁₃₉	#120	1	4	yes	—
188	C₂×C₄×C₁₃₉	—	2	12	no	—
189	C₂×C₄×C₁₃₉	—	2	24	no	—
190	C₂×C₄×C₁₃₉	—	2	24	no	—
191	C₂×C₄×C₁₃₉	—	2	12	no	—
192	C₂×C₄×C₁₃₉	—	2	3	no	—
193	C₂×C₄×C₁₃₉	—	2	12	no	—
194	C₂×C₄×C₁₃₉	—	2	6	no	—
195	C₂×C₄×C₁₃₉	—	2	6	no	—
196	C₂×C₄×C₁₃₉	—	4	3	no	—
197	C₂×C₄×C₁₃₉	#120	1	6	yes	—
198	C₂×C₄×C₁₃₉	C₂²×D₄	1	3	yes	—
199	C₂×C₄×C₁₃₉	C₂²×D₄	1	3	yes	—
200	C₈×C₁₃₉	—	4	1	no	—
201	C₈×C₁₃₉	—	4	3	no	—
202	C₂²×C₁₃₉	—	2	6	no	—
203	C₂²×C₁₃₉	—	2	4	no	—
204	C₂²×C₁₃₉	—	2	6	no	—
205	C₂²×C₁₃₉	—	4	1	no	—
206	C₂²×C₁₃₉	—	4	6	no	—
207	C₂²×C₁₃₉	—	8	6	no	—
208	C₂²×C₁₃₉	—	8	3	no	—
209	C₂²×C₁₃₉	—	8	6	no	—
210	C₂²×C₁₃₉	—	8	4	no	—
211	C₂²×C₁₃₉	—	8	24	no	—
212	C₂²×C₁₃₉	—	8	12	no	—
213	C₂²×C₁₃₉	—	8	1	no	—
214	C₂²×C₁₃₉	C₂×#120	1	3	yes	—
215	C₄×C₁₃₉	—	2	6	no	—
216	C₄×C₁₃₉	—	2	6	no	—
217	C₄×C₁₃₉	—	8	3	no	—
218	C₄×C₁₃₉	C₂×#120	1	3	yes	—
219	C₄×C₁₃₉	C₂×#120	1	1	yes	characteristic
220	C₂×C₁₃₉	—	2	3	no	—
221	C₂×C₁₃₉	—	4	6	no	—
222	C₂×C₁₃₉	—	4	4	no	—
223	C₂×C₁₃₉	—	4	6	no	—
224	C₂×C₁₃₉	—	16	1	no	—
225	C₂×C₁₃₉	#2846	1	1	yes	characteristic
226	#32894	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₁₃₉	#32894	1	1	yes	characteristic, direct product factor, Sylow
228	H(7,𝔽₂)	C₂×C₁₃₉	1	1	yes	characteristic, complemented
229	#3027	C₂×C₁₃₉	1	1	yes	characteristic, complemented
230	#3021	C₂×C₁₃₉	1	3	yes	complemented
231	#3008	C₂×C₁₃₉	1	3	yes	complemented
232	#1795	C₂×C₁₃₉	1	3	yes	complemented
233	#1794	C₂×C₁₃₉	1	3	yes	complemented
234	#1791	C₂×C₁₃₉	1	1	yes	characteristic, complemented
235	#585	—	2	6	no	—
236	#585	—	2	6	no	—
237	#585	C₂²×C₁₃₉	1	3	yes	—
238	#585	C₂²×C₁₃₉	1	1	yes	characteristic
239	C₂×H(5,𝔽₂)	—	2	4	no	—
240	C₂×H(5,𝔽₂)	—	2	6	no	—
241	C₂×H(5,𝔽₂)	—	2	6	no	—
242	C₂×H(5,𝔽₂)	C₂²×C₁₃₉	1	3	yes	—
243	C₂×AGL(1,ℤ/8)	C₂²×C₁₃₉	1	3	yes	complemented
244	C₂²×D₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
245	#535	C₂²×C₁₃₉	1	3	yes	complemented
246	B(4,𝔽₂)	—	2	4	no	—
247	#454	—	2	6	no	—
248	#453	—	2	6	no	—
249	#449	—	2	6	no	—
250	#447	—	2	6	no	—
251	#421	C₂²×C₁₃₉	1	6	yes	complemented
252	#418	C₂²×C₁₃₉	1	3	yes	complemented
253	#416	C₂²×C₁₃₉	1	3	yes	complemented
254	#413	C₂²×C₁₃₉	1	3	yes	complemented
255	#410	C₂²×C₁₃₉	1	3	yes	complemented
256	#408	C₂²×C₁₃₉	1	3	yes	complemented
257	2₋¹⁺⁴	—	2	4	no	—
258	2₋¹⁺⁴	—	2	12	no	—
259	2₋¹⁺⁴	—	2	3	no	—
260	2₋¹⁺⁴	—	2	6	no	—
261	2₋¹⁺⁴	D₄×C₁₃₉	1	6	yes	complemented
262	H(5,𝔽₂)	—	2	12	no	—
263	H(5,𝔽₂)	—	2	24	no	—
264	H(5,𝔽₂)	—	2	24	no	—
265	H(5,𝔽₂)	—	2	12	no	—
266	H(5,𝔽₂)	—	2	24	no	—
267	H(5,𝔽₂)	—	2	12	no	—
268	H(5,𝔽₂)	—	2	6	no	—
269	H(5,𝔽₂)	—	2	3	no	—
270	H(5,𝔽₂)	—	2	6	no	—
271	H(5,𝔽₂)	—	2	12	no	—
272	H(5,𝔽₂)	D₄×C₁₃₉	1	4	yes	—
273	H(5,𝔽₂)	D₄×C₁₃₉	1	6	yes	complemented
274	C₂×#41	—	2	24	no	—
275	C₂×#41	—	2	12	no	—
276	C₂×#41	—	2	12	no	—
277	C₂×#41	—	2	24	no	—
278	C₂×#41	—	2	12	no	—
279	C₂×#41	—	2	3	no	—
280	C₂×#41	—	2	6	no	—
281	C₂×#41	—	2	6	no	—
282	C₂×#41	D₄×C₁₃₉	1	6	yes	complemented
283	C₂×#41	C₂³×C₁₃₉	1	3	yes	—
284	C₂×#41	C₂³×C₁₃₉	1	3	yes	—
285	C₂²×D₄	—	2	24	no	—
286	C₂²×D₄	—	2	12	no	—
287	C₂²×D₄	—	2	4	no	—
288	C₂²×D₄	—	2	6	no	—
289	C₂²×D₄	—	2	3	no	—
290	C₂²×D₄	D₄×C₁₃₉	1	6	yes	complemented
291	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
292	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic, complemented
293	AGL(1,ℤ/8)	—	2	12	no	—
294	C₂×SD₁₆	—	2	3	no	—
295	C₂×D₈	—	2	6	no	—
296	C₂×D₈	—	2	3	no	—
297	C₂×M₁₆	C₂³×C₁₃₉	1	3	yes	complemented
298	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic, complemented
299	#127	—	2	3	no	—
300	#124	—	2	3	no	—
301	#121	—	2	6	no	—
302	#120	—	2	6	no	—
303	#117	C₂³×C₁₃₉	1	3	yes	complemented
304	#104	—	2	12	no	—
305	#103	—	2	3	no	—
306	#102	—	2	3	no	—
307	#102	—	2	6	no	—
308	#101	—	2	3	no	—
309	#100	—	2	3	no	—
310	#99	—	2	6	no	—
311	C₂²⋊C₈	—	2	6	no	—
312	C₂⁴	—	2	8	no	—
313	C₂⁴	—	2	6	no	—
314	C₂⁴	—	2	1	no	—
315	C₂⁴	—	2	1	no	—
316	#41	—	2	24	no	—
317	#41	—	2	24	no	—
318	#41	—	2	48	no	—
319	#41	—	2	24	no	—
320	#41	—	2	24	no	—
321	#41	—	2	12	no	—
322	#41	—	2	12	no	—
323	#41	—	2	12	no	—
324	#41	—	2	4	no	—
325	#41	—	2	12	no	—
326	#41	—	2	12	no	—
327	#41	—	2	12	no	—
328	#41	—	2	12	no	—
329	#41	—	2	12	no	—
330	#41	—	2	12	no	—
331	#41	—	2	6	no	—
332	#41	—	2	6	no	—
333	#41	—	2	6	no	—
334	#41	C₂×D₄×C₁₃₉	1	12	yes	—
335	C₂×Q₈	—	2	8	no	—
336	C₂×Q₈	—	2	6	no	—
337	C₂×Q₈	—	2	6	no	—
338	C₂×Q₈	—	2	12	no	—
339	C₂×Q₈	C₂×D₄×C₁₃₉	1	3	yes	—
340	C₂×Q₈	C₂×D₄×C₁₃₉	1	3	yes	—
341	C₂×D₄	—	2	24	no	—
342	C₂×D₄	—	2	48	no	—
343	C₂×D₄	—	2	24	no	—
344	C₂×D₄	—	2	24	no	—
345	C₂×D₄	—	2	24	no	—
346	C₂×D₄	—	2	48	no	—
347	C₂×D₄	—	2	24	no	—
348	C₂×D₄	—	2	6	no	—
349	C₂×D₄	—	2	6	no	—
350	C₂×D₄	—	2	12	no	—
351	C₂×D₄	—	2	12	no	—
352	C₂×D₄	—	2	6	no	—
353	C₂×D₄	—	2	3	no	—
354	C₂×D₄	—	2	12	no	—
355	C₂×D₄	—	2	12	no	—
356	C₂×D₄	—	2	12	no	—
357	C₂×D₄	—	2	6	no	—
358	C₂×D₄	—	2	3	no	—
359	C₂×D₄	—	2	3	no	—
360	C₂×D₄	—	2	3	no	—
361	C₂×D₄	—	4	6	no	—
362	C₂×D₄	C₂×D₄×C₁₃₉	1	6	yes	—
363	C₂×D₄	C₂×D₄×C₁₃₉	1	3	yes	—
364	C₂×D₄	C₂×D₄×C₁₃₉	1	3	yes	—
365	C₂×D₄	C₂×D₄×C₁₃₉	1	6	yes	—
366	C₂²×C₄	—	2	24	no	—
367	C₂²×C₄	—	2	12	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	6	no	—
370	C₂²×C₄	—	2	3	no	—
371	C₂²×C₄	C₂×D₄×C₁₃₉	1	6	yes	—
372	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
373	SD₁₆	—	4	6	no	—
374	D₈	—	4	4	no	—
375	D₈	—	4	6	no	—
376	M₁₆	—	2	6	no	—
377	C₂×C₈	—	2	3	no	—
378	C₂×C₈	—	2	3	no	—
379	C₄⋊C₄	—	2	3	no	—
380	C₂²⋊C₄	—	2	3	no	—
381	C₂²⋊C₄	—	4	6	no	—
382	C₄²	—	2	3	no	—
383	C₂³	—	2	4	no	—
384	C₂³	—	2	24	no	—
385	C₂³	—	2	12	no	—
386	C₂³	—	2	6	no	—
387	C₂³	—	2	3	no	—
388	C₂³	—	4	3	no	—
389	C₂³	—	16	1	no	—
390	C₂³	—	16	1	no	—
391	C₂³	—	16	6	no	—
392	C₂³	—	16	8	no	—
393	C₂³	#120×C₁₃₉	1	6	yes	—
394	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
395	Q₈	—	2	12	no	—
396	Q₈	—	2	4	no	—
397	Q₈	—	2	3	no	—
398	Q₈	—	2	6	no	—
399	Q₈	#120×C₁₃₉	1	6	yes	—
400	D₄	—	2	24	no	—
401	D₄	—	2	24	no	—
402	D₄	—	2	12	no	—
403	D₄	—	2	12	no	—
404	D₄	—	2	24	no	—
405	D₄	—	2	12	no	—
406	D₄	—	2	12	no	—
407	D₄	—	2	6	no	—
408	D₄	—	2	6	no	—
409	D₄	—	2	3	no	—
410	D₄	—	4	1	no	—
411	D₄	—	4	3	no	—
412	D₄	—	16	6	no	—
413	D₄	#120×C₁₃₉	1	6	yes	—
414	D₄	#120×C₁₃₉	1	4	yes	—
415	C₂×C₄	—	2	12	no	—
416	C₂×C₄	—	2	24	no	—
417	C₂×C₄	—	2	24	no	—
418	C₂×C₄	—	2	12	no	—
419	C₂×C₄	—	2	3	no	—
420	C₂×C₄	—	2	12	no	—
421	C₂×C₄	—	2	6	no	—
422	C₂×C₄	—	2	6	no	—
423	C₂×C₄	—	4	3	no	—
424	C₂×C₄	#120×C₁₃₉	1	6	yes	—
425	C₂×C₄	C₂²×D₄×C₁₃₉	1	3	yes	—
426	C₂×C₄	C₂²×D₄×C₁₃₉	1	3	yes	—
427	C₈	—	4	1	no	—
428	C₈	—	4	3	no	—
429	C₂²	—	2	6	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	6	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	6	no	—
434	C₂²	—	8	6	no	—
435	C₂²	—	8	3	no	—
436	C₂²	—	8	6	no	—
437	C₂²	—	8	4	no	—
438	C₂²	—	8	24	no	—
439	C₂²	—	8	12	no	—
440	C₂²	—	8	1	no	—
441	C₂²	C₂×#120×C₁₃₉	1	3	yes	—
442	C₄	—	2	6	no	—
443	C₄	—	2	6	no	—
444	C₄	—	8	3	no	—
445	C₄	C₂×#120×C₁₃₉	1	3	yes	—
446	C₄	C₂×#120×C₁₃₉	1	1	yes	characteristic
447	C₂	—	2	3	no	—
448	C₂	—	4	6	no	—
449	C₂	—	4	4	no	—
450	C₂	—	4	6	no	—
451	C₂	—	16	1	no	—
452	C₂	#2846×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃₉	#2846
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. H(7,𝔽₂)×C₁₃₉	C₂	semidirect
2. #3027×C₁₃₉	C₂	semidirect
3. #3021×C₁₃₉	C₂	semidirect
4. #3008×C₁₃₉	C₂	semidirect
5. #1795×C₁₃₉	C₂	semidirect
6. #1794×C₁₃₉	C₂	semidirect
7. #1791×C₁₃₉	C₂	semidirect
16. C₂×AGL(1,ℤ/8)×C₁₃₉	C₂²	semidirect
17. C₂²×D₈×C₁₃₉	C₂²	semidirect
18. #535×C₁₃₉	C₂²	semidirect
24. #421×C₁₃₉	C₂²	semidirect
25. #418×C₁₃₉	C₂²	semidirect
26. #416×C₁₃₉	C₂²	semidirect
27. #413×C₁₃₉	C₂²	semidirect
28. #410×C₁₃₉	C₂²	semidirect
29. #408×C₁₃₉	C₂²	semidirect
34. 2₋¹⁺⁴×C₁₃₉	D₄	semidirect
46. H(5,𝔽₂)×C₁₃₉	D₄	semidirect
55. C₂×#41×C₁₃₉	D₄	semidirect
63. C₂²×D₄×C₁₃₉	D₄	semidirect
65. C₂²×D₄×C₁₃₉	C₂³	semidirect
70. C₂×M₁₆×C₁₃₉	C₂³	semidirect
71. C₂²×C₈×C₁₃₉	C₂³	semidirect
76. #117×C₁₃₉	C₂³	semidirect
226. #32894	C₁₃₉	direct (N × H)
227. C₁₃₉	#32894	direct (N × H)
228. H(7,𝔽₂)	C₂×C₁₃₉	semidirect
229. #3027	C₂×C₁₃₉	semidirect
230. #3021	C₂×C₁₃₉	semidirect
231. #3008	C₂×C₁₃₉	semidirect
232. #1795	C₂×C₁₃₉	semidirect
233. #1794	C₂×C₁₃₉	semidirect
234. #1791	C₂×C₁₃₉	semidirect
243. C₂×AGL(1,ℤ/8)	C₂²×C₁₃₉	semidirect
244. C₂²×D₈	C₂²×C₁₃₉	semidirect
245. #535	C₂²×C₁₃₉	semidirect
251. #421	C₂²×C₁₃₉	semidirect
252. #418	C₂²×C₁₃₉	semidirect
253. #416	C₂²×C₁₃₉	semidirect
254. #413	C₂²×C₁₃₉	semidirect
255. #410	C₂²×C₁₃₉	semidirect
256. #408	C₂²×C₁₃₉	semidirect
261. 2₋¹⁺⁴	D₄×C₁₃₉	semidirect
273. H(5,𝔽₂)	D₄×C₁₃₉	semidirect
282. C₂×#41	D₄×C₁₃₉	semidirect
290. C₂²×D₄	D₄×C₁₃₉	semidirect
292. C₂²×D₄	C₂³×C₁₃₉	semidirect
297. C₂×M₁₆	C₂³×C₁₃₉	semidirect
298. C₂²×C₈	C₂³×C₁₃₉	semidirect
303. #117	C₂³×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
H(7,𝔽₂)×C₁₃₉	2
#3027×C₁₃₉	2
#3021×C₁₃₉	2
#3008×C₁₃₉	2
#1795×C₁₃₉	2
#1794×C₁₃₉	2
#1791×C₁₃₉	2
#32894	139

Subgroups — C139×#32894 #48027490

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#32894 #48027490