Subgroups — C₁₃₉×#36049 #48030645

Order 35584.

2436 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#557×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#550×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2641×C₁₃₉	C₂	1	3	yes	maximal, complemented
4	#2562×C₁₃₉	C₂	1	3	yes	maximal, complemented
5	#2548×C₁₃₉	C₂	1	3	yes	maximal, complemented
6	#2491×C₁₃₉	C₂	1	6	yes	maximal, complemented
7	#2490×C₁₃₉	C₂	1	6	yes	maximal, complemented
8	#2398×C₁₃₉	C₂	1	3	yes	maximal, complemented
9	#2341×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2341×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2276×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
13	#557×C₁₃₉	—	2	8	no	—
14	#550×C₁₃₉	—	2	8	no	—
15	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	3	yes	—
16	C₂×#127×C₁₃₉	C₂²	1	3	yes	—
17	C₂×#125×C₁₃₉	C₂²	1	3	yes	—
18	C₂×#125×C₁₃₉	C₂²	1	3	yes	—
19	C₂×#124×C₁₃₉	C₂²	1	6	yes	—
20	C₂×#121×C₁₃₉	C₂²	1	6	yes	—
21	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₃₉	C₂²	1	3	yes	—
23	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
27	#400×C₁₃₉	C₂²	1	3	yes	—
28	#400×C₁₃₉	C₂²	1	1	yes	characteristic
29	#397×C₁₃₉	C₂²	1	6	yes	—
30	#394×C₁₃₉	C₂²	1	3	yes	—
31	#394×C₁₃₉	C₂²	1	6	yes	—
32	#394×C₁₃₉	C₂²	1	3	yes	—
33	#394×C₁₃₉	C₂²	1	12	yes	—
34	#393×C₁₃₉	C₂²	1	6	yes	—
35	#390×C₁₃₉	C₂²	1	6	yes	—
36	#390×C₁₃₉	C₂²	1	6	yes	—
37	#390×C₁₃₉	C₂²	1	6	yes	—
38	#390×C₁₃₉	C₂²	1	6	yes	—
39	#390×C₁₃₉	C₂²	1	6	yes	—
40	#388×C₁₃₉	C₂²	1	12	yes	—
41	#380×C₁₃₉	C₂²	1	6	yes	—
42	#380×C₁₃₉	C₂²	1	6	yes	—
43	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	3	yes	—
44	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	6	yes	—
45	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	6	yes	—
46	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	6	yes	—
47	#376×C₁₃₉	C₂²	1	3	yes	—
48	C₂×#41×C₁₃₉	—	2	8	no	—
49	C₂×#41×C₁₃₉	—	2	8	no	—
50	C₂×#41×C₁₃₉	—	2	8	no	—
51	C₂²×Q₈×C₁₃₉	C₂³	1	3	yes	—
52	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
54	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
55	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
56	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
57	C₄⋊Q₈×C₁₃₉	—	2	12	no	—
58	#127×C₁₃₉	—	2	12	no	—
59	#125×C₁₃₉	—	2	12	no	—
60	#125×C₁₃₉	—	2	12	no	—
61	#124×C₁₃₉	—	4	12	no	—
62	#121×C₁₃₉	—	2	24	no	—
63	C₄×Q₈×C₁₃₉	—	2	4	no	—
64	C₄×Q₈×C₁₃₉	—	2	4	no	—
65	C₄×Q₈×C₁₃₉	—	2	8	no	—
66	C₄×Q₈×C₁₃₉	—	2	12	no	—
67	C₄×Q₈×C₁₃₉	D₄	1	8	yes	—
68	C₄×D₄×C₁₃₉	—	2	12	no	—
69	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
70	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
73	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
74	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
75	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
76	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
77	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
78	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
79	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
80	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
81	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
82	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	12	yes	—
83	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
84	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	12	yes	—
85	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
86	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
87	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
88	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
89	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
90	#95×C₁₃₉	C₂³	1	2	yes	—
91	#95×C₁₃₉	C₂³	1	6	yes	—
92	#95×C₁₃₉	C₂³	1	6	yes	—
93	#95×C₁₃₉	C₂³	1	1	yes	characteristic
94	#95×C₁₃₉	C₂³	1	3	yes	—
95	#95×C₁₃₉	C₂³	1	2	yes	—
96	#95×C₁₃₉	C₂³	1	6	yes	—
97	C₂⁴×C₁₃₉	C₂⁴	1	6	yes	—
98	#41×C₁₃₉	—	4	32	no	—
99	C₂×Q₈×C₁₃₉	—	2	6	no	—
100	C₂×Q₈×C₁₃₉	—	2	6	no	—
101	C₂×Q₈×C₁₃₉	—	4	3	no	—
102	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
103	C₂×Q₈×C₁₃₉	#41	1	8	yes	—
104	C₂×D₄×C₁₃₉	—	2	6	no	—
105	C₂×D₄×C₁₃₉	—	2	12	no	—
106	C₂×D₄×C₁₃₉	—	2	12	no	—
107	C₂×D₄×C₁₃₉	—	2	12	no	—
108	C₂×D₄×C₁₃₉	—	2	12	no	—
109	C₂×D₄×C₁₃₉	—	4	6	no	—
110	C₂×D₄×C₁₃₉	—	4	6	no	—
111	C₂×D₄×C₁₃₉	—	4	6	no	—
112	C₂²×C₄×C₁₃₉	—	2	12	no	—
113	C₂²×C₄×C₁₃₉	—	2	12	no	—
114	C₂²×C₄×C₁₃₉	—	2	12	no	—
115	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
116	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
118	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
119	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
120	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
121	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
122	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
123	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
124	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
125	C₄⋊C₄×C₁₃₉	—	2	2	no	—
126	C₄⋊C₄×C₁₃₉	—	2	2	no	—
127	C₄⋊C₄×C₁₃₉	—	2	6	no	—
128	C₄⋊C₄×C₁₃₉	—	2	6	no	—
129	C₄⋊C₄×C₁₃₉	—	2	6	no	—
130	C₄⋊C₄×C₁₃₉	—	2	6	no	—
131	C₄⋊C₄×C₁₃₉	—	2	12	no	—
132	C₄⋊C₄×C₁₃₉	—	2	12	no	—
133	C₄⋊C₄×C₁₃₉	C₂×D₄	1	12	yes	—
134	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
135	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
136	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
137	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
138	C₂²⋊C₄×C₁₃₉	—	4	12	no	—
139	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
140	C₂²⋊C₄×C₁₃₉	—	4	12	no	—
141	C₄²×C₁₃₉	—	2	6	no	—
142	C₄²×C₁₃₉	—	2	6	no	—
143	C₄²×C₁₃₉	—	2	12	no	—
144	C₄²×C₁₃₉	—	4	6	no	—
145	C₄²×C₁₃₉	C₂×D₄	1	12	yes	—
146	C₂³×C₁₃₉	—	2	6	no	—
147	C₂³×C₁₃₉	—	2	6	no	—
148	C₂³×C₁₃₉	—	2	6	no	—
149	C₂³×C₁₃₉	—	2	6	no	—
150	C₂³×C₁₃₉	—	2	6	no	—
151	C₂³×C₁₃₉	—	2	6	no	—
152	C₂³×C₁₃₉	—	2	6	no	—
153	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
154	Q₈×C₁₃₉	—	4	12	no	—
155	Q₈×C₁₃₉	#124	1	16	yes	complemented
156	D₄×C₁₃₉	—	4	12	no	—
157	D₄×C₁₃₉	—	4	24	no	—
158	D₄×C₁₃₉	—	8	12	no	—
159	C₂×C₄×C₁₃₉	—	2	1	no	—
160	C₂×C₄×C₁₃₉	—	2	3	no	—
161	C₂×C₄×C₁₃₉	—	2	2	no	—
162	C₂×C₄×C₁₃₉	—	2	3	no	—
163	C₂×C₄×C₁₃₉	—	2	1	no	—
164	C₂×C₄×C₁₃₉	—	2	1	no	—
165	C₂×C₄×C₁₃₉	—	2	3	no	—
166	C₂×C₄×C₁₃₉	—	2	3	no	—
167	C₂×C₄×C₁₃₉	—	2	2	no	—
168	C₂×C₄×C₁₃₉	—	2	2	no	—
169	C₂×C₄×C₁₃₉	—	2	6	no	—
170	C₂×C₄×C₁₃₉	—	2	2	no	—
171	C₂×C₄×C₁₃₉	—	2	2	no	—
172	C₂×C₄×C₁₃₉	—	2	6	no	—
173	C₂×C₄×C₁₃₉	—	2	3	no	—
174	C₂×C₄×C₁₃₉	—	2	2	no	—
175	C₂×C₄×C₁₃₉	—	2	6	no	—
176	C₂×C₄×C₁₃₉	—	2	6	no	—
177	C₂×C₄×C₁₃₉	—	2	2	no	—
178	C₂×C₄×C₁₃₉	—	2	2	no	—
179	C₂×C₄×C₁₃₉	—	2	3	no	—
180	C₂×C₄×C₁₃₉	—	4	24	no	—
181	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
182	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
183	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
184	C₂×C₄×C₁₃₉	C₂×#41	1	12	yes	—
185	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
186	C₂²×C₁₃₉	—	4	6	no	—
187	C₂²×C₁₃₉	—	4	6	no	—
188	C₂²×C₁₃₉	—	4	6	no	—
189	C₂²×C₁₃₉	—	4	6	no	—
190	C₂²×C₁₃₉	—	4	6	no	—
191	C₂²×C₁₃₉	—	4	6	no	—
192	C₂²×C₁₃₉	—	4	6	no	—
193	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
194	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
195	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
196	C₂²×C₁₃₉	#585	1	2	yes	—
197	C₂²×C₁₃₉	#585	1	1	yes	characteristic
198	C₄×C₁₃₉	—	2	2	no	—
199	C₄×C₁₃₉	—	2	6	no	—
200	C₄×C₁₃₉	—	2	2	no	—
201	C₄×C₁₃₉	—	4	2	no	—
202	C₄×C₁₃₉	—	4	1	no	—
203	C₄×C₁₃₉	—	4	3	no	—
204	C₄×C₁₃₉	—	4	3	no	—
205	C₄×C₁₃₉	—	4	6	no	—
206	C₄×C₁₃₉	—	4	2	no	—
207	C₄×C₁₃₉	C₂×#124	1	12	yes	—
208	C₂×C₁₃₉	—	8	6	no	—
209	C₂×C₁₃₉	C₂²×#124	1	1	yes	characteristic
210	C₂×C₁₃₉	#3487	1	1	yes	characteristic
211	C₂×C₁₃₉	#3488	1	1	yes	characteristic
212	C₂×C₁₃₉	#3517	1	2	yes	—
213	C₂×C₁₃₉	#3524	1	2	yes	—
214	#36049	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₁₃₉	#36049	1	1	yes	characteristic, direct product factor, Sylow
216	C₂×#557	C₂×C₁₃₉	1	1	yes	characteristic, complemented
217	C₂×#550	C₂×C₁₃₉	1	1	yes	characteristic
218	#2641	C₂×C₁₃₉	1	3	yes	complemented
219	#2562	C₂×C₁₃₉	1	3	yes	complemented
220	#2548	C₂×C₁₃₉	1	3	yes	complemented
221	#2491	C₂×C₁₃₉	1	6	yes	complemented
222	#2490	C₂×C₁₃₉	1	6	yes	complemented
223	#2398	C₂×C₁₃₉	1	3	yes	complemented
224	#2341	C₂×C₁₃₉	1	2	yes	complemented
225	#2341	C₂×C₁₃₉	1	2	yes	complemented
226	#2276	C₂×C₁₃₉	1	1	yes	characteristic, complemented
227	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
228	#557	—	2	8	no	—
229	#550	—	2	8	no	—
230	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	3	yes	—
231	C₂×#127	C₂²×C₁₃₉	1	3	yes	—
232	C₂×#125	C₂²×C₁₃₉	1	3	yes	—
233	C₂×#125	C₂²×C₁₃₉	1	3	yes	—
234	C₂×#124	C₂²×C₁₃₉	1	6	yes	—
235	C₂×#121	C₂²×C₁₃₉	1	6	yes	—
236	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
237	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
238	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
239	C₂×C₄×Q₈	C₂²×C₁₃₉	1	3	yes	—
240	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
241	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
242	#400	C₂²×C₁₃₉	1	3	yes	—
243	#400	C₂²×C₁₃₉	1	1	yes	characteristic
244	#397	C₂²×C₁₃₉	1	6	yes	—
245	#394	C₂²×C₁₃₉	1	6	yes	—
246	#394	C₂²×C₁₃₉	1	3	yes	—
247	#394	C₂²×C₁₃₉	1	12	yes	—
248	#394	C₂²×C₁₃₉	1	3	yes	—
249	#393	C₂²×C₁₃₉	1	6	yes	—
250	#390	C₂²×C₁₃₉	1	6	yes	—
251	#390	C₂²×C₁₃₉	1	6	yes	—
252	#390	C₂²×C₁₃₉	1	6	yes	—
253	#390	C₂²×C₁₃₉	1	6	yes	—
254	#390	C₂²×C₁₃₉	1	6	yes	—
255	#388	C₂²×C₁₃₉	1	12	yes	—
256	#380	C₂²×C₁₃₉	1	6	yes	—
257	#380	C₂²×C₁₃₉	1	6	yes	—
258	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	3	yes	—
259	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	6	yes	—
260	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	—
261	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	—
262	#376	C₂²×C₁₃₉	1	3	yes	—
263	C₂×#41	—	2	8	no	—
264	C₂×#41	—	2	8	no	—
265	C₂×#41	—	2	8	no	—
266	C₂²×Q₈	C₂³×C₁₃₉	1	3	yes	—
267	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
268	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
269	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
270	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
271	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
272	C₄⋊Q₈	—	2	12	no	—
273	#127	—	2	12	no	—
274	#125	—	2	12	no	—
275	#125	—	2	12	no	—
276	#124	—	4	12	no	—
277	#121	—	2	24	no	—
278	C₄×Q₈	—	2	4	no	—
279	C₄×Q₈	—	2	4	no	—
280	C₄×Q₈	—	2	8	no	—
281	C₄×Q₈	—	2	12	no	—
282	C₄×Q₈	D₄×C₁₃₉	1	8	yes	—
283	C₄×D₄	—	2	12	no	—
284	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
287	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
288	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
291	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
292	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
293	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
294	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
295	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	12	yes	—
296	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
297	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
298	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
299	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	12	yes	—
300	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
301	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
302	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
303	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
304	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
305	#95	C₂³×C₁₃₉	1	1	yes	characteristic
306	#95	C₂³×C₁₃₉	1	6	yes	—
307	#95	C₂³×C₁₃₉	1	3	yes	—
308	#95	C₂³×C₁₃₉	1	2	yes	—
309	#95	C₂³×C₁₃₉	1	2	yes	—
310	#95	C₂³×C₁₃₉	1	6	yes	—
311	#95	C₂³×C₁₃₉	1	6	yes	—
312	C₂⁴	C₂⁴×C₁₃₉	1	6	yes	—
313	#41	—	4	32	no	—
314	C₂×Q₈	—	2	6	no	—
315	C₂×Q₈	—	2	6	no	—
316	C₂×Q₈	—	4	3	no	—
317	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
318	C₂×Q₈	#41×C₁₃₉	1	8	yes	—
319	C₂×D₄	—	2	6	no	—
320	C₂×D₄	—	2	12	no	—
321	C₂×D₄	—	2	12	no	—
322	C₂×D₄	—	2	12	no	—
323	C₂×D₄	—	2	12	no	—
324	C₂×D₄	—	4	6	no	—
325	C₂×D₄	—	4	6	no	—
326	C₂×D₄	—	4	6	no	—
327	C₂²×C₄	—	2	12	no	—
328	C₂²×C₄	—	2	12	no	—
329	C₂²×C₄	—	2	12	no	—
330	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
331	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
332	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
333	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
334	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
335	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
336	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
337	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
338	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
339	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	6	no	—
343	C₄⋊C₄	—	2	6	no	—
344	C₄⋊C₄	—	2	6	no	—
345	C₄⋊C₄	—	2	6	no	—
346	C₄⋊C₄	—	2	12	no	—
347	C₄⋊C₄	—	2	12	no	—
348	C₄⋊C₄	C₂×D₄×C₁₃₉	1	12	yes	—
349	C₂²⋊C₄	—	2	12	no	—
350	C₂²⋊C₄	—	2	12	no	—
351	C₂²⋊C₄	—	4	6	no	—
352	C₂²⋊C₄	—	4	6	no	—
353	C₂²⋊C₄	—	4	12	no	—
354	C₂²⋊C₄	—	4	6	no	—
355	C₂²⋊C₄	—	4	12	no	—
356	C₄²	—	2	6	no	—
357	C₄²	—	2	6	no	—
358	C₄²	—	2	12	no	—
359	C₄²	—	4	6	no	—
360	C₄²	C₂×D₄×C₁₃₉	1	12	yes	—
361	C₂³	—	2	6	no	—
362	C₂³	—	2	6	no	—
363	C₂³	—	2	6	no	—
364	C₂³	—	2	6	no	—
365	C₂³	—	2	6	no	—
366	C₂³	—	2	6	no	—
367	C₂³	—	2	6	no	—
368	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
369	Q₈	—	4	12	no	—
370	Q₈	#124×C₁₃₉	1	16	yes	complemented
371	D₄	—	4	12	no	—
372	D₄	—	4	24	no	—
373	D₄	—	8	12	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	3	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	3	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	3	no	—
381	C₂×C₄	—	2	3	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	6	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	6	no	—
388	C₂×C₄	—	2	3	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	6	no	—
391	C₂×C₄	—	2	6	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	3	no	—
395	C₂×C₄	—	4	24	no	—
396	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
397	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
398	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
399	C₂×C₄	C₂×#41×C₁₃₉	1	12	yes	—
400	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
401	C₂²	—	4	6	no	—
402	C₂²	—	4	6	no	—
403	C₂²	—	4	6	no	—
404	C₂²	—	4	6	no	—
405	C₂²	—	4	6	no	—
406	C₂²	—	4	6	no	—
407	C₂²	—	4	6	no	—
408	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
409	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
410	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
411	C₂²	#585×C₁₃₉	1	2	yes	—
412	C₂²	#585×C₁₃₉	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	2	6	no	—
415	C₄	—	2	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	3	no	—
419	C₄	—	4	3	no	—
420	C₄	—	4	6	no	—
421	C₄	—	4	2	no	—
422	C₄	C₂×#124×C₁₃₉	1	12	yes	—
423	C₂	—	8	6	no	—
424	C₂	C₂²×#124×C₁₃₉	1	1	yes	characteristic
425	C₂	#3487×C₁₃₉	1	1	yes	characteristic
426	C₂	#3488×C₁₃₉	1	1	yes	characteristic
427	C₂	#3517×C₁₃₉	1	2	yes	—
428	C₂	#3524×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#550×C₁₃₉	C₂
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×#557×C₁₃₉	C₂	semidirect
3. #2641×C₁₃₉	C₂	semidirect
4. #2562×C₁₃₉	C₂	semidirect
5. #2548×C₁₃₉	C₂	semidirect
6. #2491×C₁₃₉	C₂	semidirect
7. #2490×C₁₃₉	C₂	semidirect
8. #2398×C₁₃₉	C₂	semidirect
9. #2341×C₁₃₉	C₂	semidirect
10. #2341×C₁₃₉	C₂	semidirect
11. #2276×C₁₃₉	C₂	semidirect
155. Q₈×C₁₃₉	#124	semidirect
214. #36049	C₁₃₉	direct (N × H)
215. C₁₃₉	#36049	direct (N × H)
216. C₂×#557	C₂×C₁₃₉	semidirect
218. #2641	C₂×C₁₃₉	semidirect
219. #2562	C₂×C₁₃₉	semidirect
220. #2548	C₂×C₁₃₉	semidirect
221. #2491	C₂×C₁₃₉	semidirect
222. #2490	C₂×C₁₃₉	semidirect
223. #2398	C₂×C₁₃₉	semidirect
224. #2341	C₂×C₁₃₉	semidirect
225. #2341	C₂×C₁₃₉	semidirect
226. #2276	C₂×C₁₃₉	semidirect
370. Q₈	#124×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#557×C₁₃₉	2
C₂×#550×C₁₃₉	2
#2641×C₁₃₉	2
#2562×C₁₃₉	2
#2548×C₁₃₉	2
#2491×C₁₃₉	2
#2490×C₁₃₉	2
#2398×C₁₃₉	2
#2341×C₁₃₉	2
#2276×C₁₃₉	2
#36049	139

Subgroups — C139×#36049 #48030645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36049 #48030645