Subgroups — C₁₃₉×#37297 #48031893

Order 35584.

3114 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	C₂×#535×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2856×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2733×C₁₃₉	C₂	1	4	yes	maximal, complemented
4	#2679×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2669×C₁₃₉	C₂	1	8	yes	maximal, complemented
6	#2619×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2500×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2433×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₁₃₉	C₂²	1	2	yes	complemented
12	#535×C₁₃₉	—	2	16	no	—
13	C₂×#127×C₁₃₉	C₂²	1	4	yes	—
14	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
15	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
16	C₂×#124×C₁₃₉	C₂²	1	4	yes	complemented
17	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
18	C₂×#121×C₁₃₉	C₂²	1	4	yes	complemented
19	C₂×#121×C₁₃₉	C₂²	1	8	yes	complemented
20	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
21	C₂×#120×C₁₃₉	C₂²	1	4	yes	complemented
22	C₂×#120×C₁₃₉	C₂²	1	16	yes	complemented
23	C₂×#117×C₁₃₉	C₂²	1	2	yes	complemented
24	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
26	#394×C₁₃₉	C₂²	1	8	yes	complemented
27	#394×C₁₃₉	C₂²	1	16	yes	complemented
28	#392×C₁₃₉	C₂²	1	8	yes	complemented
29	#392×C₁₃₉	C₂²	1	16	yes	complemented
30	#391×C₁₃₉	C₂²	1	2	yes	complemented
31	#390×C₁₃₉	C₂²	1	2	yes	—
32	#390×C₁₃₉	C₂²	1	8	yes	complemented
33	#390×C₁₃₉	C₂²	1	4	yes	complemented
34	#390×C₁₃₉	C₂²	1	4	yes	complemented
35	#388×C₁₃₉	C₂²	1	16	yes	complemented
36	#386×C₁₃₉	C₂²	1	4	yes	complemented
37	#384×C₁₃₉	C₂²	1	2	yes	complemented
38	#382×C₁₃₉	C₂²	1	2	yes	complemented
39	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
40	C₂⁵×C₁₃₉	C₂³	1	4	yes	—
41	C₂×#41×C₁₃₉	—	4	2	no	—
42	C₂×#41×C₁₃₉	—	4	2	no	—
43	C₂×#41×C₁₃₉	D₄	1	8	yes	complemented
44	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃₉	—	2	8	no	—
46	C₂²×D₄×C₁₃₉	—	4	4	no	—
47	C₂²×D₄×C₁₃₉	—	4	4	no	—
48	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
49	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
50	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
51	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
52	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
53	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
54	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
55	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
59	#127×C₁₃₉	—	2	16	no	—
60	#127×C₁₃₉	—	4	4	no	—
61	#127×C₁₃₉	—	4	4	no	—
62	#124×C₁₃₉	—	2	16	no	—
63	#121×C₁₃₉	—	2	16	no	—
64	#121×C₁₃₉	—	2	16	no	—
65	#121×C₁₃₉	—	4	16	no	—
66	#120×C₁₃₉	—	2	16	no	—
67	#120×C₁₃₉	—	2	16	no	—
68	#120×C₁₃₉	—	4	32	no	—
69	#117×C₁₃₉	—	2	8	no	—
70	#117×C₁₃₉	—	4	2	no	—
71	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
72	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
74	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
75	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
76	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
77	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
78	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	16	yes	—
79	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
80	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	16	yes	—
81	C₂×C₄²×C₁₃₉	—	4	2	no	—
82	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
83	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
84	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
85	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
86	#95×C₁₃₉	C₂³	1	8	yes	—
87	#95×C₁₃₉	C₂³	1	8	yes	—
88	C₂⁴×C₁₃₉	—	2	8	no	—
89	C₂⁴×C₁₃₉	—	4	4	no	—
90	C₂⁴×C₁₃₉	—	4	4	no	—
91	C₂⁴×C₁₃₉	—	4	16	no	—
92	C₂⁴×C₁₃₉	C₂⁴	1	8	yes	—
93	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
94	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
95	#41×C₁₃₉	—	4	16	no	—
96	C₂×Q₈×C₁₃₉	—	4	1	no	—
97	C₂×Q₈×C₁₃₉	—	4	1	no	—
98	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
99	C₂×D₄×C₁₃₉	—	2	16	no	—
100	C₂×D₄×C₁₃₉	—	2	16	no	—
101	C₂×D₄×C₁₃₉	—	2	8	no	—
102	C₂×D₄×C₁₃₉	—	2	8	no	—
103	C₂×D₄×C₁₃₉	—	2	8	no	—
104	C₂×D₄×C₁₃₉	—	2	8	no	—
105	C₂×D₄×C₁₃₉	—	2	16	no	—
106	C₂×D₄×C₁₃₉	—	4	4	no	—
107	C₂×D₄×C₁₃₉	—	4	4	no	—
108	C₂×D₄×C₁₃₉	—	4	1	no	—
109	C₂×D₄×C₁₃₉	—	4	1	no	—
110	C₂×D₄×C₁₃₉	—	4	2	no	—
111	C₂×D₄×C₁₃₉	—	4	2	no	—
112	C₂×D₄×C₁₃₉	—	4	32	no	—
113	C₂×D₄×C₁₃₉	—	4	16	no	—
114	C₂×D₄×C₁₃₉	—	4	16	no	—
115	C₂×D₄×C₁₃₉	—	4	8	no	—
116	C₂×D₄×C₁₃₉	—	4	16	no	—
117	C₂×D₄×C₁₃₉	—	4	8	no	—
118	C₂×D₄×C₁₃₉	—	4	8	no	—
119	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
120	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
121	C₂²×C₄×C₁₃₉	—	2	2	no	—
122	C₂²×C₄×C₁₃₉	—	2	2	no	—
123	C₂²×C₄×C₁₃₉	—	2	4	no	—
124	C₂²×C₄×C₁₃₉	—	2	4	no	—
125	C₂²×C₄×C₁₃₉	—	2	8	no	—
126	C₂²×C₄×C₁₃₉	—	4	2	no	—
127	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
128	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
131	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
132	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
133	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
135	C₄⋊C₄×C₁₃₉	—	2	8	no	—
136	C₄⋊C₄×C₁₃₉	—	4	2	no	—
137	C₄⋊C₄×C₁₃₉	—	4	8	no	—
138	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
139	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
140	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
141	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
142	C₂²⋊C₄×C₁₃₉	—	2	32	no	—
143	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
144	C₂²⋊C₄×C₁₃₉	—	4	16	no	—
145	C₄²×C₁₃₉	—	2	8	no	—
146	C₄²×C₁₃₉	—	2	4	no	—
147	C₄²×C₁₃₉	—	2	4	no	—
148	C₄²×C₁₃₉	—	4	2	no	—
149	C₂³×C₁₃₉	—	2	8	no	—
150	C₂³×C₁₃₉	—	2	1	no	—
151	C₂³×C₁₃₉	—	2	1	no	—
152	C₂³×C₁₃₉	—	2	4	no	—
153	C₂³×C₁₃₉	—	2	2	no	—
154	C₂³×C₁₃₉	—	2	2	no	—
155	C₂³×C₁₃₉	—	2	8	no	—
156	C₂³×C₁₃₉	—	2	16	no	—
157	C₂³×C₁₃₉	—	2	16	no	—
158	C₂³×C₁₃₉	—	2	8	no	—
159	C₂³×C₁₃₉	—	2	8	no	—
160	C₂³×C₁₃₉	—	4	16	no	—
161	C₂³×C₁₃₉	—	8	16	no	—
162	C₂³×C₁₃₉	—	8	16	no	—
163	C₂³×C₁₃₉	—	8	16	no	—
164	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
165	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
166	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
167	Q₈×C₁₃₉	—	4	4	no	—
168	D₄×C₁₃₉	—	4	8	no	—
169	D₄×C₁₃₉	—	4	4	no	—
170	D₄×C₁₃₉	—	4	16	no	—
171	D₄×C₁₃₉	—	4	16	no	—
172	D₄×C₁₃₉	—	8	16	no	—
173	D₄×C₁₃₉	—	8	16	no	—
174	D₄×C₁₃₉	—	8	16	no	—
175	D₄×C₁₃₉	—	8	16	no	—
176	C₂×C₄×C₁₃₉	—	2	4	no	—
177	C₂×C₄×C₁₃₉	—	2	1	no	—
178	C₂×C₄×C₁₃₉	—	2	4	no	—
179	C₂×C₄×C₁₃₉	—	2	1	no	—
180	C₂×C₄×C₁₃₉	—	2	2	no	—
181	C₂×C₄×C₁₃₉	—	2	2	no	—
182	C₂×C₄×C₁₃₉	—	2	16	no	—
183	C₂×C₄×C₁₃₉	—	2	8	no	—
184	C₂×C₄×C₁₃₉	—	2	8	no	—
185	C₂×C₄×C₁₃₉	—	2	4	no	—
186	C₂×C₄×C₁₃₉	—	2	8	no	—
187	C₂×C₄×C₁₃₉	—	2	16	no	—
188	C₂×C₄×C₁₃₉	—	4	8	no	—
189	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
190	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
191	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
192	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	8	yes	—
193	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
194	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
195	C₂²×C₁₃₉	—	2	4	no	—
196	C₂²×C₁₃₉	—	2	2	no	—
197	C₂²×C₁₃₉	—	2	4	no	—
198	C₂²×C₁₃₉	—	2	8	no	—
199	C₂²×C₁₃₉	—	4	2	no	—
200	C₂²×C₁₃₉	—	4	4	no	—
201	C₂²×C₁₃₉	—	4	2	no	—
202	C₂²×C₁₃₉	—	4	4	no	—
203	C₂²×C₁₃₉	—	4	8	no	—
204	C₂²×C₁₃₉	—	4	8	no	—
205	C₂²×C₁₃₉	—	4	8	no	—
206	C₂²×C₁₃₉	—	4	16	no	—
207	C₂²×C₁₃₉	—	4	16	no	—
208	C₂²×C₁₃₉	—	8	32	no	—
209	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
210	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
211	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
212	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	4	yes	—
213	C₄×C₁₃₉	—	2	4	no	—
214	C₄×C₁₃₉	—	2	2	no	—
215	C₄×C₁₃₉	—	2	8	no	—
216	C₄×C₁₃₉	—	4	8	no	—
217	C₄×C₁₃₉	—	4	4	no	—
218	C₄×C₁₃₉	#534	1	4	yes	—
219	C₂×C₁₃₉	—	4	2	no	—
220	C₂×C₁₃₉	—	4	4	no	—
221	C₂×C₁₃₉	—	8	8	no	—
222	C₂×C₁₃₉	C₂×#534	1	1	yes	characteristic
223	C₂×C₁₃₉	#3498	1	2	yes	—
224	C₂×C₁₃₉	#3537	1	2	yes	—
225	C₂×C₁₃₉	#3549	1	2	yes	—
226	#37297	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₁₃₉	#37297	1	1	yes	characteristic, direct product factor, Sylow
228	C₂×#535	C₂×C₁₃₉	1	2	yes	complemented
229	#2856	C₂×C₁₃₉	1	2	yes	complemented
230	#2733	C₂×C₁₃₉	1	4	yes	complemented
231	#2679	C₂×C₁₃₉	1	4	yes	complemented
232	#2669	C₂×C₁₃₉	1	8	yes	complemented
233	#2619	C₂×C₁₃₉	1	2	yes	complemented
234	#2500	C₂×C₁₃₉	1	4	yes	complemented
235	#2433	C₂×C₁₃₉	1	4	yes	complemented
236	#2297	C₂×C₁₃₉	1	1	yes	characteristic, complemented
237	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
238	C₂³×D₄	C₂²×C₁₃₉	1	2	yes	complemented
239	#535	—	2	16	no	—
240	C₂×#127	C₂²×C₁₃₉	1	4	yes	—
241	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
242	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
243	C₂×#124	C₂²×C₁₃₉	1	4	yes	complemented
244	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
245	C₂×#121	C₂²×C₁₃₉	1	4	yes	complemented
246	C₂×#121	C₂²×C₁₃₉	1	8	yes	complemented
247	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
248	C₂×#120	C₂²×C₁₃₉	1	4	yes	complemented
249	C₂×#120	C₂²×C₁₃₉	1	16	yes	complemented
250	C₂×#117	C₂²×C₁₃₉	1	2	yes	complemented
251	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
252	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
253	#394	C₂²×C₁₃₉	1	8	yes	complemented
254	#394	C₂²×C₁₃₉	1	16	yes	complemented
255	#392	C₂²×C₁₃₉	1	8	yes	complemented
256	#392	C₂²×C₁₃₉	1	16	yes	complemented
257	#391	C₂²×C₁₃₉	1	2	yes	complemented
258	#390	C₂²×C₁₃₉	1	2	yes	—
259	#390	C₂²×C₁₃₉	1	8	yes	complemented
260	#390	C₂²×C₁₃₉	1	4	yes	complemented
261	#390	C₂²×C₁₃₉	1	4	yes	complemented
262	#388	C₂²×C₁₃₉	1	16	yes	complemented
263	#386	C₂²×C₁₃₉	1	4	yes	complemented
264	#384	C₂²×C₁₃₉	1	2	yes	complemented
265	#382	C₂²×C₁₃₉	1	2	yes	complemented
266	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
267	C₂⁵	C₂³×C₁₃₉	1	4	yes	—
268	C₂×#41	—	4	2	no	—
269	C₂×#41	—	4	2	no	—
270	C₂×#41	D₄×C₁₃₉	1	8	yes	complemented
271	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
272	C₂²×D₄	—	2	8	no	—
273	C₂²×D₄	—	4	4	no	—
274	C₂²×D₄	—	4	4	no	—
275	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
276	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
277	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
278	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
279	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
280	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
281	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
282	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
283	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
284	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
285	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
286	#127	—	2	16	no	—
287	#127	—	4	4	no	—
288	#127	—	4	4	no	—
289	#124	—	2	16	no	—
290	#121	—	2	16	no	—
291	#121	—	2	16	no	—
292	#121	—	4	16	no	—
293	#120	—	2	16	no	—
294	#120	—	2	16	no	—
295	#120	—	4	32	no	—
296	#117	—	2	8	no	—
297	#117	—	4	2	no	—
298	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
299	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
301	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
302	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
303	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
304	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
305	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	16	yes	—
306	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
307	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	16	yes	—
308	C₂×C₄²	—	4	2	no	—
309	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
310	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
311	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
312	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
313	#95	C₂³×C₁₃₉	1	8	yes	—
314	#95	C₂³×C₁₃₉	1	8	yes	—
315	C₂⁴	—	2	8	no	—
316	C₂⁴	—	4	4	no	—
317	C₂⁴	—	4	4	no	—
318	C₂⁴	—	4	16	no	—
319	C₂⁴	C₂⁴×C₁₃₉	1	8	yes	—
320	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
321	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
322	#41	—	4	16	no	—
323	C₂×Q₈	—	4	1	no	—
324	C₂×Q₈	—	4	1	no	—
325	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
326	C₂×D₄	—	2	16	no	—
327	C₂×D₄	—	2	16	no	—
328	C₂×D₄	—	2	8	no	—
329	C₂×D₄	—	2	8	no	—
330	C₂×D₄	—	2	8	no	—
331	C₂×D₄	—	2	8	no	—
332	C₂×D₄	—	2	16	no	—
333	C₂×D₄	—	4	4	no	—
334	C₂×D₄	—	4	4	no	—
335	C₂×D₄	—	4	1	no	—
336	C₂×D₄	—	4	1	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	32	no	—
340	C₂×D₄	—	4	16	no	—
341	C₂×D₄	—	4	16	no	—
342	C₂×D₄	—	4	8	no	—
343	C₂×D₄	—	4	16	no	—
344	C₂×D₄	—	4	8	no	—
345	C₂×D₄	—	4	8	no	—
346	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
347	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	8	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
355	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
356	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
357	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
358	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
359	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
360	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
361	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
362	C₄⋊C₄	—	2	8	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₄⋊C₄	—	4	8	no	—
365	C₂²⋊C₄	—	2	8	no	—
366	C₂²⋊C₄	—	2	16	no	—
367	C₂²⋊C₄	—	2	16	no	—
368	C₂²⋊C₄	—	2	16	no	—
369	C₂²⋊C₄	—	2	32	no	—
370	C₂²⋊C₄	—	4	2	no	—
371	C₂²⋊C₄	—	4	16	no	—
372	C₄²	—	2	8	no	—
373	C₄²	—	2	4	no	—
374	C₄²	—	2	4	no	—
375	C₄²	—	4	2	no	—
376	C₂³	—	2	8	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	1	no	—
379	C₂³	—	2	4	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	8	no	—
383	C₂³	—	2	16	no	—
384	C₂³	—	2	16	no	—
385	C₂³	—	2	8	no	—
386	C₂³	—	2	8	no	—
387	C₂³	—	4	16	no	—
388	C₂³	—	8	16	no	—
389	C₂³	—	8	16	no	—
390	C₂³	—	8	16	no	—
391	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
392	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
393	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
394	Q₈	—	4	4	no	—
395	D₄	—	4	8	no	—
396	D₄	—	4	4	no	—
397	D₄	—	4	16	no	—
398	D₄	—	4	16	no	—
399	D₄	—	8	16	no	—
400	D₄	—	8	16	no	—
401	D₄	—	8	16	no	—
402	D₄	—	8	16	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	16	no	—
410	C₂×C₄	—	2	8	no	—
411	C₂×C₄	—	2	8	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	16	no	—
415	C₂×C₄	—	4	8	no	—
416	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
417	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
418	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
419	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	8	yes	—
420	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
421	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
422	C₂²	—	2	4	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	4	no	—
425	C₂²	—	2	8	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	4	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	16	no	—
431	C₂²	—	4	16	no	—
432	C₂²	—	4	8	no	—
433	C₂²	—	4	8	no	—
434	C₂²	—	4	8	no	—
435	C₂²	—	8	32	no	—
436	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
437	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
438	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	4	yes	—
439	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
440	C₄	—	2	8	no	—
441	C₄	—	2	4	no	—
442	C₄	—	2	2	no	—
443	C₄	—	4	4	no	—
444	C₄	—	4	8	no	—
445	C₄	#534×C₁₃₉	1	4	yes	—
446	C₂	—	4	4	no	—
447	C₂	—	4	2	no	—
448	C₂	—	8	8	no	—
449	C₂	C₂×#534×C₁₃₉	1	1	yes	characteristic
450	C₂	#3498×C₁₃₉	1	2	yes	—
451	C₂	#3537×C₁₃₉	1	2	yes	—
452	C₂	#3549×C₁₃₉	1	2	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×#535×C₁₃₉	C₂	semidirect
2. #2856×C₁₃₉	C₂	semidirect
3. #2733×C₁₃₉	C₂	semidirect
4. #2679×C₁₃₉	C₂	semidirect
5. #2669×C₁₃₉	C₂	semidirect
6. #2619×C₁₃₉	C₂	semidirect
7. #2500×C₁₃₉	C₂	semidirect
8. #2433×C₁₃₉	C₂	semidirect
9. #2297×C₁₃₉	C₂	semidirect
11. C₂³×D₄×C₁₃₉	C₂²	semidirect
16. C₂×#124×C₁₃₉	C₂²	semidirect
18. C₂×#121×C₁₃₉	C₂²	semidirect
19. C₂×#121×C₁₃₉	C₂²	semidirect
21. C₂×#120×C₁₃₉	C₂²	semidirect
22. C₂×#120×C₁₃₉	C₂²	semidirect
23. C₂×#117×C₁₃₉	C₂²	semidirect
24. C₂×#117×C₁₃₉	C₂²	semidirect
25. C₂²×C₄²×C₁₃₉	C₂²	semidirect
26. #394×C₁₃₉	C₂²	semidirect
27. #394×C₁₃₉	C₂²	semidirect
28. #392×C₁₃₉	C₂²	semidirect
29. #392×C₁₃₉	C₂²	semidirect
30. #391×C₁₃₉	C₂²	semidirect
32. #390×C₁₃₉	C₂²	semidirect
33. #390×C₁₃₉	C₂²	semidirect
34. #390×C₁₃₉	C₂²	semidirect
35. #388×C₁₃₉	C₂²	semidirect
36. #386×C₁₃₉	C₂²	semidirect
37. #384×C₁₃₉	C₂²	semidirect
38. #382×C₁₃₉	C₂²	semidirect
39. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
43. C₂×#41×C₁₃₉	D₄	semidirect
226. #37297	C₁₃₉	direct (N × H)
227. C₁₃₉	#37297	direct (N × H)
228. C₂×#535	C₂×C₁₃₉	semidirect
229. #2856	C₂×C₁₃₉	semidirect
230. #2733	C₂×C₁₃₉	semidirect
231. #2679	C₂×C₁₃₉	semidirect
232. #2669	C₂×C₁₃₉	semidirect
233. #2619	C₂×C₁₃₉	semidirect
234. #2500	C₂×C₁₃₉	semidirect
235. #2433	C₂×C₁₃₉	semidirect
236. #2297	C₂×C₁₃₉	semidirect
238. C₂³×D₄	C₂²×C₁₃₉	semidirect
243. C₂×#124	C₂²×C₁₃₉	semidirect
245. C₂×#121	C₂²×C₁₃₉	semidirect
246. C₂×#121	C₂²×C₁₃₉	semidirect
248. C₂×#120	C₂²×C₁₃₉	semidirect
249. C₂×#120	C₂²×C₁₃₉	semidirect
250. C₂×#117	C₂²×C₁₃₉	semidirect
251. C₂×#117	C₂²×C₁₃₉	semidirect
252. C₂²×C₄²	C₂²×C₁₃₉	semidirect
253. #394	C₂²×C₁₃₉	semidirect
254. #394	C₂²×C₁₃₉	semidirect
255. #392	C₂²×C₁₃₉	semidirect
256. #392	C₂²×C₁₃₉	semidirect
257. #391	C₂²×C₁₃₉	semidirect
259. #390	C₂²×C₁₃₉	semidirect
260. #390	C₂²×C₁₃₉	semidirect
261. #390	C₂²×C₁₃₉	semidirect
262. #388	C₂²×C₁₃₉	semidirect
263. #386	C₂²×C₁₃₉	semidirect
264. #384	C₂²×C₁₃₉	semidirect
265. #382	C₂²×C₁₃₉	semidirect
266. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
270. C₂×#41	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#535×C₁₃₉	2
#2856×C₁₃₉	2
#2733×C₁₃₉	2
#2679×C₁₃₉	2
#2669×C₁₃₉	2
#2619×C₁₃₉	2
#2500×C₁₃₉	2
#2433×C₁₃₉	2
#2297×C₁₃₉	2
#37297	139

Subgroups — C139×#37297 #48031893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37297 #48031893