Subgroups — C₁₃₉×#35676 #48030272

Order 35584.

5174 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×2₋¹⁺⁴×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#535×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	C₂²×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2436×C₁₃₉	C₂	1	8	yes	maximal, complemented
5	#2431×C₁₃₉	C₂	1	8	yes	maximal, complemented
6	#2404×C₁₃₉	C₂	1	8	yes	maximal, complemented
7	#2310×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2297×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	C₂×2₋¹⁺⁴×C₁₃₉	—	2	16	no	—
10	C₂×2₋¹⁺⁴×C₁₃₉	—	2	8	no	—
11	C₂²×#41×C₁₃₉	C₂²	1	4	yes	—
12	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
13	C₂²×#41×C₁₃₉	C₂²	1	4	yes	complemented
14	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂³×Q₈×C₁₃₉	C₂²	1	4	yes	complemented
16	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
17	#535×C₁₃₉	—	2	16	no	—
18	C₂×#127×C₁₃₉	C₂²	1	4	yes	—
19	C₂×#124×C₁₃₉	—	2	8	no	—
20	C₂×#124×C₁₃₉	C₂²	1	8	yes	—
21	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
22	C₂×#121×C₁₃₉	C₂²	1	8	yes	—
23	C₂×#120×C₁₃₉	C₂²	1	8	yes	—
24	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
26	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
27	#393×C₁₃₉	C₂²	1	16	yes	complemented
28	#392×C₁₃₉	C₂²	1	16	yes	complemented
29	#391×C₁₃₉	C₂²	1	4	yes	complemented
30	#391×C₁₃₉	C₂²	1	8	yes	complemented
31	#390×C₁₃₉	C₂²	1	4	yes	complemented
32	#386×C₁₃₉	C₂²	1	8	yes	—
33	#386×C₁₃₉	C₂²	1	32	yes	complemented
34	#381×C₁₃₉	C₂²	1	4	yes	—
35	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	8	yes	complemented
36	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
37	2₋¹⁺⁴×C₁₃₉	—	2	128	no	—
38	C₂×#41×C₁₃₉	—	2	16	no	—
39	C₂×#41×C₁₃₉	—	2	32	no	—
40	C₂×#41×C₁₃₉	—	2	16	no	—
41	C₂×#41×C₁₃₉	—	2	16	no	—
42	C₂×#41×C₁₃₉	—	2	8	no	—
43	C₂×#41×C₁₃₉	—	2	8	no	—
44	C₂×#41×C₁₃₉	—	2	16	no	—
45	C₂×#41×C₁₃₉	D₄	1	16	yes	complemented
46	C₂²×Q₈×C₁₃₉	—	2	16	no	—
47	C₂²×Q₈×C₁₃₉	—	2	16	no	—
48	C₂²×Q₈×C₁₃₉	—	2	8	no	—
49	C₂²×Q₈×C₁₃₉	—	2	16	no	—
50	C₂²×Q₈×C₁₃₉	D₄	1	8	yes	complemented
51	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
52	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
53	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
54	C₂²×D₄×C₁₃₉	—	2	4	no	—
55	C₂²×D₄×C₁₃₉	—	2	8	no	—
56	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
57	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
58	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
59	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
60	C₂²×D₄×C₁₃₉	C₂³	1	16	yes	—
61	C₂³×C₄×C₁₃₉	C₂³	1	8	yes	—
62	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
64	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
66	#127×C₁₃₉	—	2	16	no	—
67	#124×C₁₃₉	—	2	32	no	—
68	#124×C₁₃₉	—	2	16	no	—
69	#121×C₁₃₉	—	2	32	no	—
70	#120×C₁₃₉	—	2	32	no	—
71	#117×C₁₃₉	—	2	8	no	—
72	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
73	C₂×C₂²⋊C₄×C₁₃₉	—	2	16	no	—
74	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	16	yes	—
75	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
76	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	16	yes	—
77	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	16	yes	—
78	C₂×C₄²×C₁₃₉	—	2	4	no	—
79	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
80	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
81	#95×C₁₃₉	C₂³	1	16	yes	—
82	#95×C₁₃₉	C₂³	1	16	yes	—
83	C₂⁴×C₁₃₉	—	2	4	no	—
84	C₂⁴×C₁₃₉	—	2	8	no	—
85	C₂⁴×C₁₃₉	—	4	8	no	—
86	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
87	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
88	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
89	#41×C₁₃₉	—	2	128	no	—
90	#41×C₁₃₉	—	2	128	no	—
91	#41×C₁₃₉	—	2	64	no	—
92	C₂×Q₈×C₁₃₉	—	2	128	no	—
93	C₂×Q₈×C₁₃₉	—	2	32	no	—
94	C₂×Q₈×C₁₃₉	—	2	8	no	—
95	C₂×Q₈×C₁₃₉	—	2	16	no	—
96	C₂×Q₈×C₁₃₉	—	2	4	no	—
97	C₂×Q₈×C₁₃₉	—	2	8	no	—
98	C₂×Q₈×C₁₃₉	—	2	8	no	—
99	C₂×Q₈×C₁₃₉	—	2	4	no	—
100	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
101	C₂×Q₈×C₁₃₉	C₂×D₄	1	16	yes	—
102	C₂×D₄×C₁₃₉	—	2	16	no	—
103	C₂×D₄×C₁₃₉	—	2	8	no	—
104	C₂×D₄×C₁₃₉	—	2	8	no	—
105	C₂×D₄×C₁₃₉	—	2	32	no	—
106	C₂×D₄×C₁₃₉	—	2	8	no	—
107	C₂×D₄×C₁₃₉	—	2	4	no	—
108	C₂×D₄×C₁₃₉	—	2	4	no	—
109	C₂×D₄×C₁₃₉	—	2	8	no	—
110	C₂×D₄×C₁₃₉	—	2	8	no	—
111	C₂×D₄×C₁₃₉	—	2	8	no	—
112	C₂×D₄×C₁₃₉	—	4	32	no	—
113	C₂×D₄×C₁₃₉	—	4	16	no	—
114	C₂×D₄×C₁₃₉	C₂×D₄	1	16	yes	—
115	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
116	C₂²×C₄×C₁₃₉	—	2	16	no	—
117	C₂²×C₄×C₁₃₉	—	2	8	no	—
118	C₂²×C₄×C₁₃₉	—	2	16	no	—
119	C₂²×C₄×C₁₃₉	—	2	16	no	—
120	C₂²×C₄×C₁₃₉	—	2	8	no	—
121	C₂²×C₄×C₁₃₉	—	2	8	no	—
122	C₂²×C₄×C₁₃₉	—	2	4	no	—
123	C₂²×C₄×C₁₃₉	—	4	4	no	—
124	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
125	C₂²×C₄×C₁₃₉	C₂×D₄	1	16	yes	—
126	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
128	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
129	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
133	C₄⋊C₄×C₁₃₉	—	2	8	no	—
134	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
135	C₂²⋊C₄×C₁₃₉	—	2	32	no	—
136	C₂²⋊C₄×C₁₃₉	—	2	32	no	—
137	C₂²⋊C₄×C₁₃₉	—	4	16	no	—
138	C₄²×C₁₃₉	—	2	8	no	—
139	C₄²×C₁₃₉	—	2	8	no	—
140	C₂³×C₁₃₉	—	2	4	no	—
141	C₂³×C₁₃₉	—	2	4	no	—
142	C₂³×C₁₃₉	—	2	4	no	—
143	C₂³×C₁₃₉	—	2	16	no	—
144	C₂³×C₁₃₉	—	2	4	no	—
145	C₂³×C₁₃₉	—	2	8	no	—
146	C₂³×C₁₃₉	—	2	16	no	—
147	C₂³×C₁₃₉	—	4	16	no	—
148	C₂³×C₁₃₉	—	4	8	no	—
149	C₂³×C₁₃₉	—	8	16	no	—
150	C₂³×C₁₃₉	C₂²×D₄	1	8	yes	—
151	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
152	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
153	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
154	Q₈×C₁₃₉	—	2	32	no	—
155	Q₈×C₁₃₉	—	2	16	no	—
156	Q₈×C₁₃₉	—	2	32	no	—
157	D₄×C₁₃₉	—	2	32	no	—
158	D₄×C₁₃₉	—	2	32	no	—
159	D₄×C₁₃₉	—	2	16	no	—
160	D₄×C₁₃₉	—	4	16	no	—
161	D₄×C₁₃₉	—	8	32	no	—
162	C₂×C₄×C₁₃₉	—	2	64	no	—
163	C₂×C₄×C₁₃₉	—	2	16	no	—
164	C₂×C₄×C₁₃₉	—	2	4	no	—
165	C₂×C₄×C₁₃₉	—	2	8	no	—
166	C₂×C₄×C₁₃₉	—	2	4	no	—
167	C₂×C₄×C₁₃₉	—	2	32	no	—
168	C₂×C₄×C₁₃₉	—	2	4	no	—
169	C₂×C₄×C₁₃₉	—	2	8	no	—
170	C₂×C₄×C₁₃₉	—	2	8	no	—
171	C₂×C₄×C₁₃₉	—	2	16	no	—
172	C₂×C₄×C₁₃₉	—	4	8	no	—
173	C₂×C₄×C₁₃₉	#120	1	16	yes	—
174	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
175	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
176	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
177	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
178	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
179	C₂²×C₁₃₉	—	2	4	no	—
180	C₂²×C₁₃₉	—	2	8	no	—
181	C₂²×C₁₃₉	—	2	8	no	—
182	C₂²×C₁₃₉	—	2	16	no	—
183	C₂²×C₁₃₉	—	4	8	no	—
184	C₂²×C₁₃₉	—	4	8	no	—
185	C₂²×C₁₃₉	—	4	4	no	—
186	C₂²×C₁₃₉	—	4	8	no	—
187	C₂²×C₁₃₉	—	4	16	no	—
188	C₂²×C₁₃₉	—	8	16	no	—
189	C₂²×C₁₃₉	C₂×#120	1	4	yes	—
190	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
191	C₂²×C₁₃₉	C₂³×D₄	1	2	yes	—
192	C₂²×C₁₃₉	#585	1	4	yes	—
193	C₄×C₁₃₉	—	2	8	no	—
194	C₄×C₁₃₉	—	2	8	no	—
195	C₄×C₁₃₉	—	4	4	no	—
196	C₄×C₁₃₉	—	4	8	no	—
197	C₄×C₁₃₉	C₂×#120	1	8	yes	—
198	C₂×C₁₃₉	—	2	4	no	—
199	C₂×C₁₃₉	—	4	8	no	—
200	C₂×C₁₃₉	—	8	4	no	—
201	C₂×C₁₃₉	C₂²×#120	1	1	yes	characteristic
202	C₂×C₁₃₉	#3487	1	2	yes	—
203	C₂×C₁₃₉	#3500	1	4	yes	—
204	#35676	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₁₃₉	#35676	1	1	yes	characteristic, direct product factor, Sylow
206	C₂²×2₋¹⁺⁴	C₂×C₁₃₉	1	1	yes	characteristic, complemented
207	C₂×#535	C₂×C₁₃₉	1	2	yes	complemented
208	C₂²×#124	C₂×C₁₃₉	1	1	yes	characteristic, complemented
209	#2436	C₂×C₁₃₉	1	8	yes	complemented
210	#2431	C₂×C₁₃₉	1	8	yes	complemented
211	#2404	C₂×C₁₃₉	1	8	yes	complemented
212	#2310	C₂×C₁₃₉	1	1	yes	characteristic, complemented
213	#2297	C₂×C₁₃₉	1	2	yes	complemented
214	C₂×2₋¹⁺⁴	—	2	16	no	—
215	C₂×2₋¹⁺⁴	—	2	8	no	—
216	C₂²×#41	C₂²×C₁₃₉	1	4	yes	—
217	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
218	C₂²×#41	C₂²×C₁₃₉	1	4	yes	complemented
219	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
220	C₂³×Q₈	C₂²×C₁₃₉	1	4	yes	complemented
221	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
222	#535	—	2	16	no	—
223	C₂×#127	C₂²×C₁₃₉	1	4	yes	—
224	C₂×#124	—	2	8	no	—
225	C₂×#124	C₂²×C₁₃₉	1	8	yes	—
226	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
227	C₂×#121	C₂²×C₁₃₉	1	8	yes	—
228	C₂×#120	C₂²×C₁₃₉	1	8	yes	—
229	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
230	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
231	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
232	#393	C₂²×C₁₃₉	1	16	yes	complemented
233	#392	C₂²×C₁₃₉	1	16	yes	complemented
234	#391	C₂²×C₁₃₉	1	8	yes	complemented
235	#391	C₂²×C₁₃₉	1	4	yes	complemented
236	#390	C₂²×C₁₃₉	1	4	yes	complemented
237	#386	C₂²×C₁₃₉	1	8	yes	—
238	#386	C₂²×C₁₃₉	1	32	yes	complemented
239	#381	C₂²×C₁₃₉	1	4	yes	—
240	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	8	yes	complemented
241	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
242	2₋¹⁺⁴	—	2	128	no	—
243	C₂×#41	—	2	16	no	—
244	C₂×#41	—	2	32	no	—
245	C₂×#41	—	2	16	no	—
246	C₂×#41	—	2	16	no	—
247	C₂×#41	—	2	8	no	—
248	C₂×#41	—	2	8	no	—
249	C₂×#41	—	2	16	no	—
250	C₂×#41	D₄×C₁₃₉	1	16	yes	complemented
251	C₂²×Q₈	—	2	16	no	—
252	C₂²×Q₈	—	2	16	no	—
253	C₂²×Q₈	—	2	8	no	—
254	C₂²×Q₈	—	2	16	no	—
255	C₂²×Q₈	D₄×C₁₃₉	1	8	yes	complemented
256	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
257	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
258	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
259	C₂²×D₄	—	2	4	no	—
260	C₂²×D₄	—	2	8	no	—
261	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
262	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
263	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
264	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
265	C₂²×D₄	C₂³×C₁₃₉	1	16	yes	—
266	C₂³×C₄	C₂³×C₁₃₉	1	8	yes	—
267	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
268	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
269	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
270	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
271	#127	—	2	16	no	—
272	#124	—	2	32	no	—
273	#124	—	2	16	no	—
274	#121	—	2	32	no	—
275	#120	—	2	32	no	—
276	#117	—	2	8	no	—
277	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
278	C₂×C₂²⋊C₄	—	2	16	no	—
279	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	16	yes	—
280	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
281	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	16	yes	—
282	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	16	yes	—
283	C₂×C₄²	—	2	4	no	—
284	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
285	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
286	#95	C₂³×C₁₃₉	1	16	yes	—
287	#95	C₂³×C₁₃₉	1	16	yes	—
288	C₂⁴	—	2	4	no	—
289	C₂⁴	—	2	8	no	—
290	C₂⁴	—	4	8	no	—
291	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
292	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
293	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
294	#41	—	2	128	no	—
295	#41	—	2	128	no	—
296	#41	—	2	64	no	—
297	C₂×Q₈	—	2	128	no	—
298	C₂×Q₈	—	2	32	no	—
299	C₂×Q₈	—	2	8	no	—
300	C₂×Q₈	—	2	16	no	—
301	C₂×Q₈	—	2	4	no	—
302	C₂×Q₈	—	2	8	no	—
303	C₂×Q₈	—	2	8	no	—
304	C₂×Q₈	—	2	4	no	—
305	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
306	C₂×Q₈	C₂×D₄×C₁₃₉	1	16	yes	—
307	C₂×D₄	—	2	16	no	—
308	C₂×D₄	—	2	8	no	—
309	C₂×D₄	—	2	8	no	—
310	C₂×D₄	—	2	32	no	—
311	C₂×D₄	—	2	8	no	—
312	C₂×D₄	—	2	4	no	—
313	C₂×D₄	—	2	4	no	—
314	C₂×D₄	—	2	8	no	—
315	C₂×D₄	—	2	8	no	—
316	C₂×D₄	—	2	8	no	—
317	C₂×D₄	—	4	32	no	—
318	C₂×D₄	—	4	16	no	—
319	C₂×D₄	C₂×D₄×C₁₃₉	1	16	yes	—
320	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
321	C₂²×C₄	—	2	16	no	—
322	C₂²×C₄	—	2	8	no	—
323	C₂²×C₄	—	2	16	no	—
324	C₂²×C₄	—	2	16	no	—
325	C₂²×C₄	—	2	8	no	—
326	C₂²×C₄	—	2	8	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	4	4	no	—
329	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
330	C₂²×C₄	C₂×D₄×C₁₃₉	1	16	yes	—
331	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
332	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
333	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
334	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
335	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
336	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
337	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
338	C₄⋊C₄	—	2	8	no	—
339	C₂²⋊C₄	—	2	8	no	—
340	C₂²⋊C₄	—	2	32	no	—
341	C₂²⋊C₄	—	2	32	no	—
342	C₂²⋊C₄	—	4	16	no	—
343	C₄²	—	2	8	no	—
344	C₄²	—	2	8	no	—
345	C₂³	—	2	4	no	—
346	C₂³	—	2	4	no	—
347	C₂³	—	2	4	no	—
348	C₂³	—	2	16	no	—
349	C₂³	—	2	4	no	—
350	C₂³	—	2	8	no	—
351	C₂³	—	2	16	no	—
352	C₂³	—	4	16	no	—
353	C₂³	—	4	8	no	—
354	C₂³	—	8	16	no	—
355	C₂³	C₂²×D₄×C₁₃₉	1	8	yes	—
356	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
357	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
358	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
359	Q₈	—	2	32	no	—
360	Q₈	—	2	16	no	—
361	Q₈	—	2	32	no	—
362	D₄	—	2	32	no	—
363	D₄	—	2	32	no	—
364	D₄	—	2	16	no	—
365	D₄	—	4	16	no	—
366	D₄	—	8	32	no	—
367	C₂×C₄	—	2	64	no	—
368	C₂×C₄	—	2	16	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	8	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	32	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	2	16	no	—
377	C₂×C₄	—	4	8	no	—
378	C₂×C₄	#120×C₁₃₉	1	16	yes	—
379	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
380	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
381	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
382	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
383	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
384	C₂²	—	2	4	no	—
385	C₂²	—	2	8	no	—
386	C₂²	—	2	8	no	—
387	C₂²	—	2	16	no	—
388	C₂²	—	4	8	no	—
389	C₂²	—	4	8	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	4	8	no	—
392	C₂²	—	4	16	no	—
393	C₂²	—	8	16	no	—
394	C₂²	C₂×#120×C₁₃₉	1	4	yes	—
395	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
396	C₂²	C₂³×D₄×C₁₃₉	1	2	yes	—
397	C₂²	#585×C₁₃₉	1	4	yes	—
398	C₄	—	2	8	no	—
399	C₄	—	2	8	no	—
400	C₄	—	4	4	no	—
401	C₄	—	4	8	no	—
402	C₄	C₂×#120×C₁₃₉	1	8	yes	—
403	C₂	—	2	4	no	—
404	C₂	—	4	8	no	—
405	C₂	—	8	4	no	—
406	C₂	C₂²×#120×C₁₃₉	1	1	yes	characteristic
407	C₂	#3487×C₁₃₉	1	2	yes	—
408	C₂	#3500×C₁₃₉	1	4	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. C₂²×2₋¹⁺⁴×C₁₃₉	C₂	semidirect
2. C₂×#535×C₁₃₉	C₂	semidirect
3. C₂²×#124×C₁₃₉	C₂	semidirect
4. #2436×C₁₃₉	C₂	semidirect
5. #2431×C₁₃₉	C₂	semidirect
6. #2404×C₁₃₉	C₂	semidirect
7. #2310×C₁₃₉	C₂	semidirect
8. #2297×C₁₃₉	C₂	semidirect
13. C₂²×#41×C₁₃₉	C₂²	semidirect
15. C₂³×Q₈×C₁₃₉	C₂²	semidirect
27. #393×C₁₃₉	C₂²	semidirect
28. #392×C₁₃₉	C₂²	semidirect
29. #391×C₁₃₉	C₂²	semidirect
30. #391×C₁₃₉	C₂²	semidirect
31. #390×C₁₃₉	C₂²	semidirect
33. #386×C₁₃₉	C₂²	semidirect
35. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
45. C₂×#41×C₁₃₉	D₄	semidirect
50. C₂²×Q₈×C₁₃₉	D₄	semidirect
204. #35676	C₁₃₉	direct (N × H)
205. C₁₃₉	#35676	direct (N × H)
206. C₂²×2₋¹⁺⁴	C₂×C₁₃₉	semidirect
207. C₂×#535	C₂×C₁₃₉	semidirect
208. C₂²×#124	C₂×C₁₃₉	semidirect
209. #2436	C₂×C₁₃₉	semidirect
210. #2431	C₂×C₁₃₉	semidirect
211. #2404	C₂×C₁₃₉	semidirect
212. #2310	C₂×C₁₃₉	semidirect
213. #2297	C₂×C₁₃₉	semidirect
218. C₂²×#41	C₂²×C₁₃₉	semidirect
220. C₂³×Q₈	C₂²×C₁₃₉	semidirect
232. #393	C₂²×C₁₃₉	semidirect
233. #392	C₂²×C₁₃₉	semidirect
234. #391	C₂²×C₁₃₉	semidirect
235. #391	C₂²×C₁₃₉	semidirect
236. #390	C₂²×C₁₃₉	semidirect
238. #386	C₂²×C₁₃₉	semidirect
240. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
250. C₂×#41	D₄×C₁₃₉	semidirect
255. C₂²×Q₈	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×2₋¹⁺⁴×C₁₃₉	2
C₂×#535×C₁₃₉	2
C₂²×#124×C₁₃₉	2
#2436×C₁₃₉	2
#2431×C₁₃₉	2
#2404×C₁₃₉	2
#2310×C₁₃₉	2
#2297×C₁₃₉	2
#35676	139

Subgroups — C139×#35676 #48030272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35676 #48030272