Subgroups — C₁₃₉×#35921 #48030517

Order 35584.

4618 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#546×C₁₃₉	C₂	1	3	yes	maximal, complemented
2	C₂×D₄²×C₁₃₉	C₂	1	3	yes	maximal, complemented
3	#2657×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2656×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2541×C₁₃₉	C₂	1	3	yes	maximal, complemented
6	#2540×C₁₃₉	C₂	1	3	yes	maximal, complemented
7	#2539×C₁₃₉	C₂	1	6	yes	maximal, complemented
8	#2433×C₁₃₉	C₂	1	6	yes	maximal, complemented
9	#2397×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#392×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2275×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₃₉	C₂²	1	3	yes	—
14	C₂³×D₄×C₁₃₉	C₂²	1	6	yes	complemented
15	#546×C₁₃₉	—	2	24	no	—
16	D₄²×C₁₃₉	—	2	24	no	—
17	C₂×#127×C₁₃₉	C₂²	1	3	yes	complemented
18	C₂×#127×C₁₃₉	C₂²	1	6	yes	complemented
19	C₂×#124×C₁₃₉	C₂²	1	3	yes	complemented
20	C₂×#123×C₁₃₉	C₂²	1	6	yes	complemented
21	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	3	yes	complemented
22	C₂×#121×C₁₃₉	C₂²	1	6	yes	complemented
23	C₂×#121×C₁₃₉	C₂²	1	6	yes	complemented
24	C₂×#121×C₁₃₉	C₂²	1	3	yes	complemented
25	C₂×#121×C₁₃₉	C₂²	1	6	yes	complemented
26	C₂×#120×C₁₃₉	C₂²	1	12	yes	complemented
27	C₂×#120×C₁₃₉	C₂²	1	6	yes	complemented
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
29	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	complemented
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	complemented
31	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	6	yes	complemented
32	#399×C₁₃₉	C₂²	1	3	yes	complemented
33	#399×C₁₃₉	C₂²	1	6	yes	complemented
34	#399×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
35	#392×C₁₃₉	C₂²	1	1	yes	characteristic
36	#392×C₁₃₉	C₂²	1	6	yes	complemented
37	#392×C₁₃₉	C₂²	1	6	yes	complemented
38	#392×C₁₃₉	C₂²	1	6	yes	complemented
39	#392×C₁₃₉	C₂²	1	6	yes	complemented
40	#392×C₁₃₉	C₂²	1	2	yes	complemented
41	#392×C₁₃₉	C₂²	1	3	yes	complemented
42	#390×C₁₃₉	C₂²	1	6	yes	complemented
43	#390×C₁₃₉	C₂²	1	12	yes	complemented
44	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	3	yes	complemented
45	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	6	yes	complemented
46	#376×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
47	C₂×#95×C₁₃₉	C₂²	1	2	yes	complemented
48	C₂⁵×C₁₃₉	C₂³	1	6	yes	—
49	C₂×#41×C₁₃₉	—	2	12	no	—
50	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₁₃₉	—	2	24	no	—
52	C₂²×D₄×C₁₃₉	—	2	12	no	—
53	C₂²×D₄×C₁₃₉	—	2	24	no	—
54	C₂²×D₄×C₁₃₉	—	4	24	no	—
55	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
56	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
57	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
58	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
59	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
60	C₂²×D₄×C₁₃₉	C₂³	1	12	yes	—
61	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
62	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
63	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
64	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
66	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
68	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
69	#127×C₁₃₉	—	2	12	no	—
70	#127×C₁₃₉	—	4	12	no	—
71	#124×C₁₃₉	—	2	12	no	—
72	#123×C₁₃₉	—	2	24	no	—
73	C₂²⋊Q₈×C₁₃₉	—	2	12	no	—
74	#121×C₁₃₉	—	2	24	no	—
75	#121×C₁₃₉	—	2	24	no	—
76	#121×C₁₃₉	—	2	24	no	—
77	#121×C₁₃₉	—	2	12	no	—
78	#120×C₁₃₉	—	2	48	no	—
79	#120×C₁₃₉	—	2	24	no	—
80	C₄×D₄×C₁₃₉	—	2	12	no	—
81	C₄×D₄×C₁₃₉	—	2	12	no	—
82	C₄×D₄×C₁₃₉	D₄	1	24	yes	complemented
83	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
84	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
85	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
86	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
87	C₂×C₂²⋊C₄×C₁₃₉	—	2	24	no	—
88	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
89	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
90	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
91	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
92	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	12	yes	—
93	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
94	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
95	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
96	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
97	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
98	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
99	#95×C₁₃₉	C₂³	1	1	yes	characteristic
100	#95×C₁₃₉	C₂³	1	6	yes	—
101	#95×C₁₃₉	C₂³	1	3	yes	—
102	C₂⁴×C₁₃₉	—	2	12	no	—
103	C₂⁴×C₁₃₉	—	2	12	no	—
104	C₂⁴×C₁₃₉	—	2	24	no	—
105	C₂⁴×C₁₃₉	—	4	12	no	—
106	C₂⁴×C₁₃₉	—	4	6	no	—
107	C₂⁴×C₁₃₉	C₂⁴	1	6	yes	—
108	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
109	C₂⁴×C₁₃₉	C₂⁴	1	3	yes	—
110	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
111	#41×C₁₃₉	—	4	16	no	—
112	C₂×Q₈×C₁₃₉	—	2	6	no	—
113	C₂×D₄×C₁₃₉	—	2	12	no	—
114	C₂×D₄×C₁₃₉	—	2	24	no	—
115	C₂×D₄×C₁₃₉	—	2	12	no	—
116	C₂×D₄×C₁₃₉	—	2	12	no	—
117	C₂×D₄×C₁₃₉	—	2	6	no	—
118	C₂×D₄×C₁₃₉	—	2	24	no	—
119	C₂×D₄×C₁₃₉	—	2	6	no	—
120	C₂×D₄×C₁₃₉	—	2	6	no	—
121	C₂×D₄×C₁₃₉	—	2	24	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	12	no	—
126	C₂×D₄×C₁₃₉	—	2	12	no	—
127	C₂×D₄×C₁₃₉	—	4	12	no	—
128	C₂×D₄×C₁₃₉	—	4	12	no	—
129	C₂×D₄×C₁₃₉	—	4	3	no	—
130	C₂×D₄×C₁₃₉	—	4	6	no	—
131	C₂×D₄×C₁₃₉	—	4	12	no	—
132	C₂×D₄×C₁₃₉	—	4	6	no	—
133	C₂×D₄×C₁₃₉	—	4	96	no	—
134	C₂×D₄×C₁₃₉	—	4	48	no	—
135	C₂×D₄×C₁₃₉	C₂×D₄	1	12	yes	—
136	C₂²×C₄×C₁₃₉	—	2	12	no	—
137	C₂²×C₄×C₁₃₉	—	2	12	no	—
138	C₂²×C₄×C₁₃₉	—	2	6	no	—
139	C₂²×C₄×C₁₃₉	—	2	6	no	—
140	C₂²×C₄×C₁₃₉	—	4	12	no	—
141	C₂²×C₄×C₁₃₉	C₂×D₄	1	24	yes	complemented
142	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
143	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
145	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
146	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
147	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
148	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
149	C₄⋊C₄×C₁₃₉	—	2	6	no	—
150	C₄⋊C₄×C₁₃₉	—	2	6	no	—
151	C₄⋊C₄×C₁₃₉	—	2	12	no	—
152	C₄⋊C₄×C₁₃₉	C₂×D₄	1	12	yes	complemented
153	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
154	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
155	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
156	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
157	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
158	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
159	C₂²⋊C₄×C₁₃₉	—	2	24	no	—
160	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
161	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	24	yes	complemented
162	C₄²×C₁₃₉	—	4	6	no	—
163	C₄²×C₁₃₉	C₂×D₄	1	12	yes	complemented
164	C₂³×C₁₃₉	—	2	6	no	—
165	C₂³×C₁₃₉	—	2	2	no	—
166	C₂³×C₁₃₉	—	2	3	no	—
167	C₂³×C₁₃₉	—	2	6	no	—
168	C₂³×C₁₃₉	—	2	6	no	—
169	C₂³×C₁₃₉	—	2	3	no	—
170	C₂³×C₁₃₉	—	2	6	no	—
171	C₂³×C₁₃₉	—	2	3	no	—
172	C₂³×C₁₃₉	—	2	12	no	—
173	C₂³×C₁₃₉	—	2	3	no	—
174	C₂³×C₁₃₉	—	2	12	no	—
175	C₂³×C₁₃₉	—	2	6	no	—
176	C₂³×C₁₃₉	—	2	1	no	—
177	C₂³×C₁₃₉	—	2	6	no	—
178	C₂³×C₁₃₉	—	4	48	no	—
179	C₂³×C₁₃₉	—	4	24	no	—
180	C₂³×C₁₃₉	—	4	24	no	—
181	C₂³×C₁₃₉	—	8	12	no	—
182	C₂³×C₁₃₉	—	8	24	no	—
183	C₂³×C₁₃₉	C₂²×D₄	1	12	yes	—
184	C₂³×C₁₃₉	H(5,𝔽₂)	1	6	yes	—
185	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
186	Q₈×C₁₃₉	—	4	4	no	—
187	D₄×C₁₃₉	—	2	24	no	—
188	D₄×C₁₃₉	—	4	12	no	—
189	D₄×C₁₃₉	—	4	48	no	—
190	D₄×C₁₃₉	—	4	24	no	—
191	D₄×C₁₃₉	—	4	24	no	—
192	D₄×C₁₃₉	—	4	8	no	—
193	D₄×C₁₃₉	—	4	12	no	—
194	D₄×C₁₃₉	—	8	12	no	—
195	D₄×C₁₃₉	—	8	12	no	—
196	D₄×C₁₃₉	#127	1	16	yes	complemented
197	C₂×C₄×C₁₃₉	—	2	3	no	—
198	C₂×C₄×C₁₃₉	—	2	12	no	—
199	C₂×C₄×C₁₃₉	—	2	6	no	—
200	C₂×C₄×C₁₃₉	—	2	3	no	—
201	C₂×C₄×C₁₃₉	—	2	3	no	—
202	C₂×C₄×C₁₃₉	—	2	6	no	—
203	C₂×C₄×C₁₃₉	—	2	6	no	—
204	C₂×C₄×C₁₃₉	—	2	3	no	—
205	C₂×C₄×C₁₃₉	—	4	24	no	—
206	C₂×C₄×C₁₃₉	—	4	8	no	—
207	C₂×C₄×C₁₃₉	—	4	12	no	—
208	C₂×C₄×C₁₃₉	—	4	4	no	—
209	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
210	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
211	C₂×C₄×C₁₃₉	C₂²×D₄	1	12	yes	—
212	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
213	C₂²×C₁₃₉	—	2	12	no	—
214	C₂²×C₁₃₉	—	2	12	no	—
215	C₂²×C₁₃₉	—	2	12	no	—
216	C₂²×C₁₃₉	—	2	6	no	—
217	C₂²×C₁₃₉	—	4	3	no	—
218	C₂²×C₁₃₉	—	4	3	no	—
219	C₂²×C₁₃₉	—	4	6	no	—
220	C₂²×C₁₃₉	—	4	1	no	—
221	C₂²×C₁₃₉	—	4	6	no	—
222	C₂²×C₁₃₉	—	4	12	no	—
223	C₂²×C₁₃₉	—	4	3	no	—
224	C₂²×C₁₃₉	—	4	6	no	—
225	C₂²×C₁₃₉	—	4	3	no	—
226	C₂²×C₁₃₉	—	4	12	no	—
227	C₂²×C₁₃₉	—	4	6	no	—
228	C₂²×C₁₃₉	—	8	48	no	—
229	C₂²×C₁₃₉	C₂×#127	1	8	yes	—
230	C₂²×C₁₃₉	C₂³×D₄	1	3	yes	—
231	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	3	yes	—
232	C₂²×C₁₃₉	#585	1	1	yes	characteristic
233	C₄×C₁₃₉	—	2	6	no	—
234	C₄×C₁₃₉	—	2	12	no	—
235	C₄×C₁₃₉	—	2	6	no	—
236	C₄×C₁₃₉	—	4	1	no	—
237	C₄×C₁₃₉	—	4	3	no	—
238	C₄×C₁₃₉	—	4	2	no	—
239	C₄×C₁₃₉	C₂×#127	1	4	yes	—
240	C₂×C₁₃₉	—	2	8	no	—
241	C₂×C₁₃₉	—	4	6	no	—
242	C₂×C₁₃₉	—	8	1	no	—
243	C₂×C₁₃₉	—	8	6	no	—
244	C₂×C₁₃₉	C₂²×#127	1	1	yes	characteristic
245	C₂×C₁₃₉	#3484	1	3	yes	—
246	C₂×C₁₃₉	#3488	1	3	yes	—
247	#35921	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
248	C₁₃₉	#35921	1	1	yes	characteristic, direct product factor, Sylow
249	C₂×#546	C₂×C₁₃₉	1	3	yes	complemented
250	C₂×D₄²	C₂×C₁₃₉	1	3	yes	complemented
251	#2657	C₂×C₁₃₉	1	1	yes	characteristic, complemented
252	#2656	C₂×C₁₃₉	1	2	yes	complemented
253	#2541	C₂×C₁₃₉	1	3	yes	complemented
254	#2540	C₂×C₁₃₉	1	3	yes	complemented
255	#2539	C₂×C₁₃₉	1	6	yes	complemented
256	#2433	C₂×C₁₃₉	1	6	yes	complemented
257	#2397	C₂×C₁₃₉	1	1	yes	characteristic, complemented
258	C₂×#392	C₂×C₁₃₉	1	2	yes	complemented
259	#2275	C₂×C₁₃₉	1	1	yes	characteristic, complemented
260	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
261	C₂³×D₄	C₂²×C₁₃₉	1	3	yes	—
262	C₂³×D₄	C₂²×C₁₃₉	1	6	yes	complemented
263	#546	—	2	24	no	—
264	D₄²	—	2	24	no	—
265	C₂×#127	C₂²×C₁₃₉	1	3	yes	complemented
266	C₂×#127	C₂²×C₁₃₉	1	6	yes	complemented
267	C₂×#124	C₂²×C₁₃₉	1	3	yes	complemented
268	C₂×#123	C₂²×C₁₃₉	1	6	yes	complemented
269	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	3	yes	complemented
270	C₂×#121	C₂²×C₁₃₉	1	6	yes	complemented
271	C₂×#121	C₂²×C₁₃₉	1	6	yes	complemented
272	C₂×#121	C₂²×C₁₃₉	1	6	yes	complemented
273	C₂×#121	C₂²×C₁₃₉	1	3	yes	complemented
274	C₂×#120	C₂²×C₁₃₉	1	6	yes	complemented
275	C₂×#120	C₂²×C₁₃₉	1	12	yes	complemented
276	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
277	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	complemented
278	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	complemented
279	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	complemented
280	#399	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
281	#399	C₂²×C₁₃₉	1	3	yes	complemented
282	#399	C₂²×C₁₃₉	1	6	yes	complemented
283	#392	C₂²×C₁₃₉	1	1	yes	characteristic
284	#392	C₂²×C₁₃₉	1	2	yes	complemented
285	#392	C₂²×C₁₃₉	1	6	yes	complemented
286	#392	C₂²×C₁₃₉	1	6	yes	complemented
287	#392	C₂²×C₁₃₉	1	3	yes	complemented
288	#392	C₂²×C₁₃₉	1	6	yes	complemented
289	#392	C₂²×C₁₃₉	1	6	yes	complemented
290	#390	C₂²×C₁₃₉	1	12	yes	complemented
291	#390	C₂²×C₁₃₉	1	6	yes	complemented
292	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	3	yes	complemented
293	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	complemented
294	#376	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
295	C₂×#95	C₂²×C₁₃₉	1	2	yes	complemented
296	C₂⁵	C₂³×C₁₃₉	1	6	yes	—
297	C₂×#41	—	2	12	no	—
298	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
299	C₂²×D₄	—	2	24	no	—
300	C₂²×D₄	—	2	12	no	—
301	C₂²×D₄	—	2	24	no	—
302	C₂²×D₄	—	4	24	no	—
303	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
304	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
305	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
306	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
307	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
308	C₂²×D₄	C₂³×C₁₃₉	1	12	yes	—
309	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
310	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
311	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
312	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
313	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
314	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
315	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
316	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
317	#127	—	2	12	no	—
318	#127	—	4	12	no	—
319	#124	—	2	12	no	—
320	#123	—	2	24	no	—
321	C₂²⋊Q₈	—	2	12	no	—
322	#121	—	2	24	no	—
323	#121	—	2	24	no	—
324	#121	—	2	24	no	—
325	#121	—	2	12	no	—
326	#120	—	2	48	no	—
327	#120	—	2	24	no	—
328	C₄×D₄	—	2	12	no	—
329	C₄×D₄	—	2	12	no	—
330	C₄×D₄	D₄×C₁₃₉	1	24	yes	complemented
331	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
332	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
333	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
334	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
335	C₂×C₂²⋊C₄	—	2	24	no	—
336	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
337	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
338	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
339	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
340	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
341	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
342	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	12	yes	—
343	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
344	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
345	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
346	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
347	#95	C₂³×C₁₃₉	1	1	yes	characteristic
348	#95	C₂³×C₁₃₉	1	6	yes	—
349	#95	C₂³×C₁₃₉	1	3	yes	—
350	C₂⁴	—	2	12	no	—
351	C₂⁴	—	2	12	no	—
352	C₂⁴	—	2	24	no	—
353	C₂⁴	—	4	12	no	—
354	C₂⁴	—	4	6	no	—
355	C₂⁴	C₂⁴×C₁₃₉	1	6	yes	—
356	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
357	C₂⁴	C₂⁴×C₁₃₉	1	3	yes	—
358	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
359	#41	—	4	16	no	—
360	C₂×Q₈	—	2	6	no	—
361	C₂×D₄	—	2	12	no	—
362	C₂×D₄	—	2	24	no	—
363	C₂×D₄	—	2	12	no	—
364	C₂×D₄	—	2	12	no	—
365	C₂×D₄	—	2	6	no	—
366	C₂×D₄	—	2	24	no	—
367	C₂×D₄	—	2	6	no	—
368	C₂×D₄	—	2	6	no	—
369	C₂×D₄	—	2	24	no	—
370	C₂×D₄	—	2	6	no	—
371	C₂×D₄	—	2	12	no	—
372	C₂×D₄	—	2	12	no	—
373	C₂×D₄	—	2	12	no	—
374	C₂×D₄	—	2	12	no	—
375	C₂×D₄	—	4	12	no	—
376	C₂×D₄	—	4	12	no	—
377	C₂×D₄	—	4	3	no	—
378	C₂×D₄	—	4	6	no	—
379	C₂×D₄	—	4	12	no	—
380	C₂×D₄	—	4	6	no	—
381	C₂×D₄	—	4	96	no	—
382	C₂×D₄	—	4	48	no	—
383	C₂×D₄	C₂×D₄×C₁₃₉	1	12	yes	—
384	C₂²×C₄	—	2	12	no	—
385	C₂²×C₄	—	2	12	no	—
386	C₂²×C₄	—	2	6	no	—
387	C₂²×C₄	—	2	6	no	—
388	C₂²×C₄	—	4	12	no	—
389	C₂²×C₄	C₂×D₄×C₁₃₉	1	24	yes	complemented
390	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
391	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
392	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
393	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
394	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
395	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
396	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
397	C₄⋊C₄	—	2	6	no	—
398	C₄⋊C₄	—	2	6	no	—
399	C₄⋊C₄	—	2	12	no	—
400	C₄⋊C₄	C₂×D₄×C₁₃₉	1	12	yes	complemented
401	C₂²⋊C₄	—	2	6	no	—
402	C₂²⋊C₄	—	2	12	no	—
403	C₂²⋊C₄	—	2	12	no	—
404	C₂²⋊C₄	—	2	12	no	—
405	C₂²⋊C₄	—	2	12	no	—
406	C₂²⋊C₄	—	2	6	no	—
407	C₂²⋊C₄	—	2	24	no	—
408	C₂²⋊C₄	—	2	12	no	—
409	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	24	yes	complemented
410	C₄²	—	4	6	no	—
411	C₄²	C₂×D₄×C₁₃₉	1	12	yes	complemented
412	C₂³	—	2	6	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	3	no	—
415	C₂³	—	2	6	no	—
416	C₂³	—	2	6	no	—
417	C₂³	—	2	3	no	—
418	C₂³	—	2	6	no	—
419	C₂³	—	2	3	no	—
420	C₂³	—	2	12	no	—
421	C₂³	—	2	3	no	—
422	C₂³	—	2	12	no	—
423	C₂³	—	2	6	no	—
424	C₂³	—	2	1	no	—
425	C₂³	—	2	6	no	—
426	C₂³	—	4	48	no	—
427	C₂³	—	4	24	no	—
428	C₂³	—	4	24	no	—
429	C₂³	—	8	12	no	—
430	C₂³	—	8	24	no	—
431	C₂³	C₂²×D₄×C₁₃₉	1	12	yes	—
432	C₂³	H(5,𝔽₂)×C₁₃₉	1	6	yes	—
433	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
434	Q₈	—	4	4	no	—
435	D₄	—	2	24	no	—
436	D₄	—	4	48	no	—
437	D₄	—	4	12	no	—
438	D₄	—	4	24	no	—
439	D₄	—	4	24	no	—
440	D₄	—	4	8	no	—
441	D₄	—	4	12	no	—
442	D₄	—	8	12	no	—
443	D₄	—	8	12	no	—
444	D₄	#127×C₁₃₉	1	16	yes	complemented
445	C₂×C₄	—	2	3	no	—
446	C₂×C₄	—	2	12	no	—
447	C₂×C₄	—	2	6	no	—
448	C₂×C₄	—	2	3	no	—
449	C₂×C₄	—	2	3	no	—
450	C₂×C₄	—	2	6	no	—
451	C₂×C₄	—	2	6	no	—
452	C₂×C₄	—	2	3	no	—
453	C₂×C₄	—	4	24	no	—
454	C₂×C₄	—	4	8	no	—
455	C₂×C₄	—	4	12	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
458	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
459	C₂×C₄	C₂²×D₄×C₁₃₉	1	12	yes	—
460	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
461	C₂²	—	2	12	no	—
462	C₂²	—	2	12	no	—
463	C₂²	—	2	12	no	—
464	C₂²	—	2	6	no	—
465	C₂²	—	4	3	no	—
466	C₂²	—	4	3	no	—
467	C₂²	—	4	6	no	—
468	C₂²	—	4	1	no	—
469	C₂²	—	4	6	no	—
470	C₂²	—	4	12	no	—
471	C₂²	—	4	3	no	—
472	C₂²	—	4	6	no	—
473	C₂²	—	4	3	no	—
474	C₂²	—	4	12	no	—
475	C₂²	—	4	6	no	—
476	C₂²	—	8	48	no	—
477	C₂²	C₂×#127×C₁₃₉	1	8	yes	—
478	C₂²	C₂³×D₄×C₁₃₉	1	3	yes	—
479	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	3	yes	—
480	C₂²	#585×C₁₃₉	1	1	yes	characteristic
481	C₄	—	2	6	no	—
482	C₄	—	2	12	no	—
483	C₄	—	2	6	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	3	no	—
486	C₄	—	4	2	no	—
487	C₄	C₂×#127×C₁₃₉	1	4	yes	—
488	C₂	—	2	8	no	—
489	C₂	—	4	6	no	—
490	C₂	—	8	6	no	—
491	C₂	—	8	1	no	—
492	C₂	C₂²×#127×C₁₃₉	1	1	yes	characteristic
493	C₂	#3484×C₁₃₉	1	3	yes	—
494	C₂	#3488×C₁₃₉	1	3	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#546×C₁₃₉	C₂	semidirect
2. C₂×D₄²×C₁₃₉	C₂	semidirect
3. #2657×C₁₃₉	C₂	semidirect
4. #2656×C₁₃₉	C₂	semidirect
5. #2541×C₁₃₉	C₂	semidirect
6. #2540×C₁₃₉	C₂	semidirect
7. #2539×C₁₃₉	C₂	semidirect
8. #2433×C₁₃₉	C₂	semidirect
9. #2397×C₁₃₉	C₂	semidirect
10. C₂×#392×C₁₃₉	C₂	semidirect
11. #2275×C₁₃₉	C₂	semidirect
14. C₂³×D₄×C₁₃₉	C₂²	semidirect
17. C₂×#127×C₁₃₉	C₂²	semidirect
18. C₂×#127×C₁₃₉	C₂²	semidirect
19. C₂×#124×C₁₃₉	C₂²	semidirect
20. C₂×#123×C₁₃₉	C₂²	semidirect
21. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
22. C₂×#121×C₁₃₉	C₂²	semidirect
23. C₂×#121×C₁₃₉	C₂²	semidirect
24. C₂×#121×C₁₃₉	C₂²	semidirect
25. C₂×#121×C₁₃₉	C₂²	semidirect
26. C₂×#120×C₁₃₉	C₂²	semidirect
27. C₂×#120×C₁₃₉	C₂²	semidirect
29. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
30. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
31. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
32. #399×C₁₃₉	C₂²	semidirect
33. #399×C₁₃₉	C₂²	semidirect
34. #399×C₁₃₉	C₂²	semidirect
36. #392×C₁₃₉	C₂²	semidirect
37. #392×C₁₃₉	C₂²	semidirect
38. #392×C₁₃₉	C₂²	semidirect
39. #392×C₁₃₉	C₂²	semidirect
40. #392×C₁₃₉	C₂²	semidirect
41. #392×C₁₃₉	C₂²	semidirect
42. #390×C₁₃₉	C₂²	semidirect
43. #390×C₁₃₉	C₂²	semidirect
44. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
45. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
46. #376×C₁₃₉	C₂²	semidirect
47. C₂×#95×C₁₃₉	C₂²	semidirect
82. C₄×D₄×C₁₃₉	D₄	semidirect
141. C₂²×C₄×C₁₃₉	C₂×D₄	semidirect
152. C₄⋊C₄×C₁₃₉	C₂×D₄	semidirect
161. C₂²⋊C₄×C₁₃₉	C₂×D₄	semidirect
163. C₄²×C₁₃₉	C₂×D₄	semidirect
196. D₄×C₁₃₉	#127	semidirect
247. #35921	C₁₃₉	direct (N × H)
248. C₁₃₉	#35921	direct (N × H)
249. C₂×#546	C₂×C₁₃₉	semidirect
250. C₂×D₄²	C₂×C₁₃₉	semidirect
251. #2657	C₂×C₁₃₉	semidirect
252. #2656	C₂×C₁₃₉	semidirect
253. #2541	C₂×C₁₃₉	semidirect
254. #2540	C₂×C₁₃₉	semidirect
255. #2539	C₂×C₁₃₉	semidirect
256. #2433	C₂×C₁₃₉	semidirect
257. #2397	C₂×C₁₃₉	semidirect
258. C₂×#392	C₂×C₁₃₉	semidirect
259. #2275	C₂×C₁₃₉	semidirect
262. C₂³×D₄	C₂²×C₁₃₉	semidirect
265. C₂×#127	C₂²×C₁₃₉	semidirect
266. C₂×#127	C₂²×C₁₃₉	semidirect
267. C₂×#124	C₂²×C₁₃₉	semidirect
268. C₂×#123	C₂²×C₁₃₉	semidirect
269. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
270. C₂×#121	C₂²×C₁₃₉	semidirect
271. C₂×#121	C₂²×C₁₃₉	semidirect
272. C₂×#121	C₂²×C₁₃₉	semidirect
273. C₂×#121	C₂²×C₁₃₉	semidirect
274. C₂×#120	C₂²×C₁₃₉	semidirect
275. C₂×#120	C₂²×C₁₃₉	semidirect
277. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
278. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
279. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
280. #399	C₂²×C₁₃₉	semidirect
281. #399	C₂²×C₁₃₉	semidirect
282. #399	C₂²×C₁₃₉	semidirect
284. #392	C₂²×C₁₃₉	semidirect
285. #392	C₂²×C₁₃₉	semidirect
286. #392	C₂²×C₁₃₉	semidirect
287. #392	C₂²×C₁₃₉	semidirect
288. #392	C₂²×C₁₃₉	semidirect
289. #392	C₂²×C₁₃₉	semidirect
290. #390	C₂²×C₁₃₉	semidirect
291. #390	C₂²×C₁₃₉	semidirect
292. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
293. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
294. #376	C₂²×C₁₃₉	semidirect
295. C₂×#95	C₂²×C₁₃₉	semidirect
330. C₄×D₄	D₄×C₁₃₉	semidirect
389. C₂²×C₄	C₂×D₄×C₁₃₉	semidirect
400. C₄⋊C₄	C₂×D₄×C₁₃₉	semidirect
409. C₂²⋊C₄	C₂×D₄×C₁₃₉	semidirect
411. C₄²	C₂×D₄×C₁₃₉	semidirect
444. D₄	#127×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#546×C₁₃₉	2
C₂×D₄²×C₁₃₉	2
#2657×C₁₃₉	2
#2656×C₁₃₉	2
#2541×C₁₃₉	2
#2540×C₁₃₉	2
#2539×C₁₃₉	2
#2433×C₁₃₉	2
#2397×C₁₃₉	2
C₂×#392×C₁₃₉	2
#2275×C₁₃₉	2
#35921	139

Subgroups — C139×#35921 #48030517

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35921 #48030517