Subgroups — C₁₃₉×#36455 #48031051

Order 35584.

3432 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#550×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#550×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×#41×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2856×C₁₃₉	C₂	1	3	yes	maximal, complemented
5	#2541×C₁₃₉	C₂	1	3	yes	maximal, complemented
6	#2537×C₁₃₉	C₂	1	3	yes	maximal, complemented
7	#2428×C₁₃₉	C₂	1	6	yes	maximal, complemented
8	#2414×C₁₃₉	C₂	1	6	yes	maximal, complemented
9	Q₈×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2341×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	C₄×#121×C₁₃₉	C₂	1	3	yes	maximal, complemented
12	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
13	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
14	#550×C₁₃₉	—	2	16	no	—
15	#550×C₁₃₉	—	2	8	no	—
16	C₂×#127×C₁₃₉	C₂²	1	3	yes	—
17	C₂×#127×C₁₃₉	C₂²	1	6	yes	—
18	C₂×#121×C₁₃₉	C₂²	1	6	yes	—
19	C₂×#121×C₁₃₉	C₂²	1	3	yes	—
20	C₂×#121×C₁₃₉	C₂²	1	6	yes	—
21	C₂×#121×C₁₃₉	C₂²	1	6	yes	—
22	C₂×#121×C₁₃₉	C₂²	1	6	yes	—
23	C₂×#121×C₁₃₉	C₂²	1	6	yes	—
24	C₄×#41×C₁₃₉	—	2	8	no	—
25	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
29	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	6	yes	—
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
32	C₂×#117×C₁₃₉	C₂²	1	3	yes	—
33	C₂²×C₄²×C₁₃₉	C₂²	1	3	yes	—
34	#394×C₁₃₉	C₂²	1	12	yes	—
35	#392×C₁₃₉	C₂²	1	12	yes	—
36	#390×C₁₃₉	C₂²	1	6	yes	—
37	#390×C₁₃₉	C₂²	1	3	yes	—
38	#390×C₁₃₉	C₂²	1	6	yes	—
39	#390×C₁₃₉	C₂²	1	6	yes	—
40	#389×C₁₃₉	C₂²	1	1	yes	characteristic
41	#389×C₁₃₉	C₂²	1	6	yes	—
42	#388×C₁₃₉	C₂²	1	6	yes	—
43	#386×C₁₃₉	C₂²	1	6	yes	—
44	#384×C₁₃₉	C₂²	1	3	yes	—
45	#380×C₁₃₉	C₂²	1	3	yes	—
46	#380×C₁₃₉	C₂²	1	6	yes	—
47	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	3	yes	—
48	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	6	yes	—
49	C₂×#41×C₁₃₉	—	2	4	no	—
50	C₂×#41×C₁₃₉	—	2	8	no	—
51	C₂×#41×C₁₃₉	—	2	8	no	—
52	C₂×#41×C₁₃₉	—	2	4	no	—
53	C₂×#41×C₁₃₉	—	2	8	no	—
54	C₂×#41×C₁₃₉	D₄	1	8	yes	complemented
55	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
57	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
58	C₂²×D₄×C₁₃₉	C₂³	1	6	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	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
63	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
64	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
65	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
66	#127×C₁₃₉	—	2	24	no	—
67	#127×C₁₃₉	—	2	12	no	—
68	#121×C₁₃₉	—	2	24	no	—
69	#121×C₁₃₉	—	2	24	no	—
70	#121×C₁₃₉	—	2	24	no	—
71	#121×C₁₃₉	—	2	12	no	—
72	#121×C₁₃₉	—	4	12	no	—
73	#121×C₁₃₉	—	4	12	no	—
74	C₄×Q₈×C₁₃₉	—	2	4	no	—
75	C₄×Q₈×C₁₃₉	—	2	8	no	—
76	C₄×Q₈×C₁₃₉	D₄	1	8	yes	complemented
77	C₄×D₄×C₁₃₉	—	2	24	no	—
78	C₄×D₄×C₁₃₉	—	2	12	no	—
79	C₄×D₄×C₁₃₉	—	2	12	no	—
80	C₄×D₄×C₁₃₉	—	2	12	no	—
81	#117×C₁₃₉	—	2	12	no	—
82	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
83	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
86	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
87	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
88	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
89	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
91	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
92	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	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	12	yes	—
97	C₂×C₄²×C₁₃₉	—	2	12	no	—
98	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
100	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
101	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
102	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
103	#95×C₁₃₉	C₂³	1	2	yes	—
104	#95×C₁₃₉	C₂³	1	6	yes	—
105	#95×C₁₃₉	C₂³	1	6	yes	—
106	C₂⁴×C₁₃₉	C₂⁴	1	6	yes	—
107	C₂⁴×C₁₃₉	C₂⁴	1	3	yes	—
108	#41×C₁₃₉	—	2	32	no	—
109	#41×C₁₃₉	—	4	32	no	—
110	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
111	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
112	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
113	C₂×D₄×C₁₃₉	—	2	12	no	—
114	C₂×D₄×C₁₃₉	—	2	24	no	—
115	C₂×D₄×C₁₃₉	—	2	6	no	—
116	C₂×D₄×C₁₃₉	—	2	6	no	—
117	C₂×D₄×C₁₃₉	—	2	12	no	—
118	C₂×D₄×C₁₃₉	—	2	12	no	—
119	C₂×D₄×C₁₃₉	—	2	12	no	—
120	C₂×D₄×C₁₃₉	—	2	6	no	—
121	C₂×D₄×C₁₃₉	—	2	12	no	—
122	C₂×D₄×C₁₃₉	—	2	6	no	—
123	C₂×D₄×C₁₃₉	—	2	12	no	—
124	C₂×D₄×C₁₃₉	—	2	6	no	—
125	C₂×D₄×C₁₃₉	—	4	6	no	—
126	C₂×D₄×C₁₃₉	—	4	6	no	—
127	C₂×D₄×C₁₃₉	—	4	12	no	—
128	C₂×D₄×C₁₃₉	—	4	12	no	—
129	C₂×D₄×C₁₃₉	—	4	6	no	—
130	C₂×D₄×C₁₃₉	C₂×D₄	1	12	yes	—
131	C₂²×C₄×C₁₃₉	—	2	6	no	—
132	C₂²×C₄×C₁₃₉	—	2	6	no	—
133	C₂²×C₄×C₁₃₉	—	2	6	no	—
134	C₂²×C₄×C₁₃₉	—	2	6	no	—
135	C₂²×C₄×C₁₃₉	—	2	12	no	—
136	C₂²×C₄×C₁₃₉	—	2	12	no	—
137	C₂²×C₄×C₁₃₉	—	2	6	no	—
138	C₂²×C₄×C₁₃₉	—	2	12	no	—
139	C₂²×C₄×C₁₃₉	—	2	6	no	—
140	C₂²×C₄×C₁₃₉	—	2	6	no	—
141	C₂²×C₄×C₁₃₉	—	4	3	no	—
142	C₂²×C₄×C₁₃₉	C₂×D₄	1	12	yes	—
143	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
145	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
146	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
147	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
148	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
150	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
151	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
152	C₄⋊C₄×C₁₃₉	—	2	6	no	—
153	C₄⋊C₄×C₁₃₉	—	2	4	no	—
154	C₄⋊C₄×C₁₃₉	—	2	2	no	—
155	C₄⋊C₄×C₁₃₉	—	2	12	no	—
156	C₄⋊C₄×C₁₃₉	—	2	6	no	—
157	C₄⋊C₄×C₁₃₉	—	4	6	no	—
158	C₄⋊C₄×C₁₃₉	C₂×D₄	1	12	yes	—
159	C₄⋊C₄×C₁₃₉	#41	1	4	yes	complemented
160	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
161	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
162	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
163	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
164	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
165	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
166	C₂²⋊C₄×C₁₃₉	—	4	12	no	—
167	C₄²×C₁₃₉	—	2	2	no	—
168	C₄²×C₁₃₉	—	2	6	no	—
169	C₄²×C₁₃₉	—	2	6	no	—
170	C₄²×C₁₃₉	—	2	12	no	—
171	C₄²×C₁₃₉	C₂×D₄	1	12	yes	—
172	C₂³×C₁₃₉	—	2	3	no	—
173	C₂³×C₁₃₉	—	2	3	no	—
174	C₂³×C₁₃₉	—	2	3	no	—
175	C₂³×C₁₃₉	—	2	3	no	—
176	C₂³×C₁₃₉	—	2	3	no	—
177	C₂³×C₁₃₉	—	2	3	no	—
178	C₂³×C₁₃₉	—	2	6	no	—
179	C₂³×C₁₃₉	—	2	6	no	—
180	C₂³×C₁₃₉	—	2	6	no	—
181	C₂³×C₁₃₉	—	2	6	no	—
182	C₂³×C₁₃₉	—	2	6	no	—
183	C₂³×C₁₃₉	—	2	6	no	—
184	C₂³×C₁₃₉	—	2	6	no	—
185	C₂³×C₁₃₉	C₂²×D₄	1	6	yes	—
186	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
187	Q₈×C₁₃₉	#121	1	16	yes	complemented
188	D₄×C₁₃₉	—	2	24	no	—
189	D₄×C₁₃₉	—	4	24	no	—
190	D₄×C₁₃₉	—	4	24	no	—
191	D₄×C₁₃₉	—	4	12	no	—
192	D₄×C₁₃₉	—	8	12	no	—
193	D₄×C₁₃₉	—	8	24	no	—
194	C₂×C₄×C₁₃₉	—	2	1	no	—
195	C₂×C₄×C₁₃₉	—	2	1	no	—
196	C₂×C₄×C₁₃₉	—	2	2	no	—
197	C₂×C₄×C₁₃₉	—	2	1	no	—
198	C₂×C₄×C₁₃₉	—	2	3	no	—
199	C₂×C₄×C₁₃₉	—	2	1	no	—
200	C₂×C₄×C₁₃₉	—	2	3	no	—
201	C₂×C₄×C₁₃₉	—	2	2	no	—
202	C₂×C₄×C₁₃₉	—	2	24	no	—
203	C₂×C₄×C₁₃₉	—	2	3	no	—
204	C₂×C₄×C₁₃₉	—	2	6	no	—
205	C₂×C₄×C₁₃₉	—	2	2	no	—
206	C₂×C₄×C₁₃₉	—	2	2	no	—
207	C₂×C₄×C₁₃₉	—	2	3	no	—
208	C₂×C₄×C₁₃₉	—	2	2	no	—
209	C₂×C₄×C₁₃₉	—	2	6	no	—
210	C₂×C₄×C₁₃₉	—	2	3	no	—
211	C₂×C₄×C₁₃₉	—	2	6	no	—
212	C₂×C₄×C₁₃₉	—	4	12	no	—
213	C₂×C₄×C₁₃₉	—	4	24	no	—
214	C₂×C₄×C₁₃₉	—	4	12	no	—
215	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
216	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
217	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
218	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
219	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
221	C₂×C₄×C₁₃₉	C₂×#41	1	6	yes	—
222	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
223	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
224	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
225	C₂²×C₁₃₉	—	2	6	no	—
226	C₂²×C₁₃₉	—	2	6	no	—
227	C₂²×C₁₃₉	—	2	6	no	—
228	C₂²×C₁₃₉	—	4	3	no	—
229	C₂²×C₁₃₉	—	4	3	no	—
230	C₂²×C₁₃₉	—	4	3	no	—
231	C₂²×C₁₃₉	—	4	3	no	—
232	C₂²×C₁₃₉	—	4	6	no	—
233	C₂²×C₁₃₉	—	4	6	no	—
234	C₂²×C₁₃₉	—	4	6	no	—
235	C₂²×C₁₃₉	—	4	6	no	—
236	C₂²×C₁₃₉	—	4	6	no	—
237	C₂²×C₁₃₉	—	4	6	no	—
238	C₂²×C₁₃₉	—	4	6	no	—
239	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
240	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
241	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
242	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
243	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
244	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
245	C₂²×C₁₃₉	#585	1	1	yes	characteristic
246	C₄×C₁₃₉	—	2	2	no	—
247	C₄×C₁₃₉	—	2	4	no	—
248	C₄×C₁₃₉	—	2	2	no	—
249	C₄×C₁₃₉	—	2	6	no	—
250	C₄×C₁₃₉	—	4	2	no	—
251	C₄×C₁₃₉	—	4	3	no	—
252	C₄×C₁₃₉	—	4	6	no	—
253	C₄×C₁₃₉	C₂×#121	1	12	yes	—
254	C₄×C₁₃₉	#550	1	4	yes	complemented
255	C₂×C₁₃₉	—	4	6	no	—
256	C₂×C₁₃₉	—	8	6	no	—
257	C₂×C₁₃₉	C₂²×#121	1	1	yes	characteristic
258	C₂×C₁₃₉	C₂×#550	1	1	yes	characteristic
259	C₂×C₁₃₉	D₄×#41	1	1	yes	characteristic
260	C₂×C₁₃₉	#3483	1	1	yes	characteristic
261	C₂×C₁₃₉	#3488	1	1	yes	characteristic
262	C₂×C₁₃₉	#3498	1	1	yes	characteristic
263	C₂×C₁₃₉	#3517	1	1	yes	characteristic
264	#36455	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₁₃₉	#36455	1	1	yes	characteristic, direct product factor, Sylow
266	C₂×#550	C₂×C₁₃₉	1	2	yes	complemented
267	C₂×#550	C₂×C₁₃₉	1	1	yes	characteristic, complemented
268	C₂×C₄×#41	C₂×C₁₃₉	1	1	yes	characteristic, complemented
269	#2856	C₂×C₁₃₉	1	3	yes	complemented
270	#2541	C₂×C₁₃₉	1	3	yes	complemented
271	#2537	C₂×C₁₃₉	1	3	yes	complemented
272	#2428	C₂×C₁₃₉	1	6	yes	complemented
273	#2414	C₂×C₁₃₉	1	6	yes	complemented
274	Q₈×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
275	#2341	C₂×C₁₃₉	1	2	yes	complemented
276	C₄×#121	C₂×C₁₃₉	1	3	yes	complemented
277	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
278	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
279	#550	—	2	16	no	—
280	#550	—	2	8	no	—
281	C₂×#127	C₂²×C₁₃₉	1	3	yes	—
282	C₂×#127	C₂²×C₁₃₉	1	6	yes	—
283	C₂×#121	C₂²×C₁₃₉	1	6	yes	—
284	C₂×#121	C₂²×C₁₃₉	1	6	yes	—
285	C₂×#121	C₂²×C₁₃₉	1	6	yes	—
286	C₂×#121	C₂²×C₁₃₉	1	3	yes	—
287	C₂×#121	C₂²×C₁₃₉	1	6	yes	—
288	C₂×#121	C₂²×C₁₃₉	1	6	yes	—
289	C₄×#41	—	2	8	no	—
290	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
291	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
292	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
293	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
294	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
295	C₂×C₄×D₄	C₂²×C₁₃₉	1	6	yes	—
296	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
297	C₂×#117	C₂²×C₁₃₉	1	3	yes	—
298	C₂²×C₄²	C₂²×C₁₃₉	1	3	yes	—
299	#394	C₂²×C₁₃₉	1	12	yes	—
300	#392	C₂²×C₁₃₉	1	12	yes	—
301	#390	C₂²×C₁₃₉	1	6	yes	—
302	#390	C₂²×C₁₃₉	1	6	yes	—
303	#390	C₂²×C₁₃₉	1	3	yes	—
304	#390	C₂²×C₁₃₉	1	6	yes	—
305	#389	C₂²×C₁₃₉	1	6	yes	—
306	#389	C₂²×C₁₃₉	1	1	yes	characteristic
307	#388	C₂²×C₁₃₉	1	6	yes	—
308	#386	C₂²×C₁₃₉	1	6	yes	—
309	#384	C₂²×C₁₃₉	1	3	yes	—
310	#380	C₂²×C₁₃₉	1	6	yes	—
311	#380	C₂²×C₁₃₉	1	3	yes	—
312	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	3	yes	—
313	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	—
314	C₂×#41	—	2	4	no	—
315	C₂×#41	—	2	8	no	—
316	C₂×#41	—	2	8	no	—
317	C₂×#41	—	2	4	no	—
318	C₂×#41	—	2	8	no	—
319	C₂×#41	D₄×C₁₃₉	1	8	yes	complemented
320	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
321	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
322	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
323	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
324	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
325	C₂²×D₄	C₂³×C₁₃₉	1	12	yes	—
326	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
327	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
328	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
329	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
330	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
331	#127	—	2	24	no	—
332	#127	—	2	12	no	—
333	#121	—	2	24	no	—
334	#121	—	2	24	no	—
335	#121	—	2	24	no	—
336	#121	—	2	12	no	—
337	#121	—	4	12	no	—
338	#121	—	4	12	no	—
339	C₄×Q₈	—	2	4	no	—
340	C₄×Q₈	—	2	8	no	—
341	C₄×Q₈	D₄×C₁₃₉	1	8	yes	complemented
342	C₄×D₄	—	2	24	no	—
343	C₄×D₄	—	2	12	no	—
344	C₄×D₄	—	2	12	no	—
345	C₄×D₄	—	2	12	no	—
346	#117	—	2	12	no	—
347	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
348	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
350	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
351	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
352	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
353	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
354	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
355	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
360	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
361	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	12	yes	—
362	C₂×C₄²	—	2	12	no	—
363	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
364	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
365	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
366	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
368	#95	C₂³×C₁₃₉	1	2	yes	—
369	#95	C₂³×C₁₃₉	1	6	yes	—
370	#95	C₂³×C₁₃₉	1	6	yes	—
371	C₂⁴	C₂⁴×C₁₃₉	1	6	yes	—
372	C₂⁴	C₂⁴×C₁₃₉	1	3	yes	—
373	#41	—	2	32	no	—
374	#41	—	4	32	no	—
375	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
376	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
377	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
378	C₂×D₄	—	2	12	no	—
379	C₂×D₄	—	2	24	no	—
380	C₂×D₄	—	2	6	no	—
381	C₂×D₄	—	2	6	no	—
382	C₂×D₄	—	2	12	no	—
383	C₂×D₄	—	2	12	no	—
384	C₂×D₄	—	2	12	no	—
385	C₂×D₄	—	2	6	no	—
386	C₂×D₄	—	2	12	no	—
387	C₂×D₄	—	2	6	no	—
388	C₂×D₄	—	2	12	no	—
389	C₂×D₄	—	2	6	no	—
390	C₂×D₄	—	4	6	no	—
391	C₂×D₄	—	4	6	no	—
392	C₂×D₄	—	4	12	no	—
393	C₂×D₄	—	4	12	no	—
394	C₂×D₄	—	4	6	no	—
395	C₂×D₄	C₂×D₄×C₁₃₉	1	12	yes	—
396	C₂²×C₄	—	2	6	no	—
397	C₂²×C₄	—	2	6	no	—
398	C₂²×C₄	—	2	6	no	—
399	C₂²×C₄	—	2	6	no	—
400	C₂²×C₄	—	2	12	no	—
401	C₂²×C₄	—	2	12	no	—
402	C₂²×C₄	—	2	6	no	—
403	C₂²×C₄	—	2	12	no	—
404	C₂²×C₄	—	2	6	no	—
405	C₂²×C₄	—	2	6	no	—
406	C₂²×C₄	—	4	3	no	—
407	C₂²×C₄	C₂×D₄×C₁₃₉	1	12	yes	—
408	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
409	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
410	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
411	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
412	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
413	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
414	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
415	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
416	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
417	C₄⋊C₄	—	2	6	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	12	no	—
421	C₄⋊C₄	—	2	6	no	—
422	C₄⋊C₄	—	4	6	no	—
423	C₄⋊C₄	C₂×D₄×C₁₃₉	1	12	yes	—
424	C₄⋊C₄	#41×C₁₃₉	1	4	yes	complemented
425	C₂²⋊C₄	—	2	12	no	—
426	C₂²⋊C₄	—	2	12	no	—
427	C₂²⋊C₄	—	2	12	no	—
428	C₂²⋊C₄	—	2	12	no	—
429	C₂²⋊C₄	—	2	12	no	—
430	C₂²⋊C₄	—	2	12	no	—
431	C₂²⋊C₄	—	4	12	no	—
432	C₄²	—	2	2	no	—
433	C₄²	—	2	6	no	—
434	C₄²	—	2	6	no	—
435	C₄²	—	2	12	no	—
436	C₄²	C₂×D₄×C₁₃₉	1	12	yes	—
437	C₂³	—	2	3	no	—
438	C₂³	—	2	3	no	—
439	C₂³	—	2	3	no	—
440	C₂³	—	2	3	no	—
441	C₂³	—	2	3	no	—
442	C₂³	—	2	3	no	—
443	C₂³	—	2	6	no	—
444	C₂³	—	2	6	no	—
445	C₂³	—	2	6	no	—
446	C₂³	—	2	6	no	—
447	C₂³	—	2	6	no	—
448	C₂³	—	2	6	no	—
449	C₂³	—	2	6	no	—
450	C₂³	C₂²×D₄×C₁₃₉	1	6	yes	—
451	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
452	Q₈	#121×C₁₃₉	1	16	yes	complemented
453	D₄	—	2	24	no	—
454	D₄	—	4	24	no	—
455	D₄	—	4	24	no	—
456	D₄	—	4	12	no	—
457	D₄	—	8	12	no	—
458	D₄	—	8	24	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	3	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	3	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	24	no	—
468	C₂×C₄	—	2	3	no	—
469	C₂×C₄	—	2	6	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	3	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	6	no	—
475	C₂×C₄	—	2	3	no	—
476	C₂×C₄	—	2	6	no	—
477	C₂×C₄	—	4	12	no	—
478	C₂×C₄	—	4	24	no	—
479	C₂×C₄	—	4	12	no	—
480	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
481	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
482	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
483	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
484	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
485	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
486	C₂×C₄	C₂×#41×C₁₃₉	1	6	yes	—
487	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
488	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
489	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
490	C₂²	—	2	6	no	—
491	C₂²	—	2	6	no	—
492	C₂²	—	2	6	no	—
493	C₂²	—	4	3	no	—
494	C₂²	—	4	3	no	—
495	C₂²	—	4	3	no	—
496	C₂²	—	4	3	no	—
497	C₂²	—	4	6	no	—
498	C₂²	—	4	6	no	—
499	C₂²	—	4	6	no	—
500	C₂²	—	4	6	no	—
501	C₂²	—	4	6	no	—
502	C₂²	—	4	6	no	—
503	C₂²	—	4	6	no	—
504	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
505	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
506	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
507	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
508	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
509	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
510	C₂²	#585×C₁₃₉	1	1	yes	characteristic
511	C₄	—	2	2	no	—
512	C₄	—	2	4	no	—
513	C₄	—	2	2	no	—
514	C₄	—	2	6	no	—
515	C₄	—	4	2	no	—
516	C₄	—	4	3	no	—
517	C₄	—	4	6	no	—
518	C₄	C₂×#121×C₁₃₉	1	12	yes	—
519	C₄	#550×C₁₃₉	1	4	yes	complemented
520	C₂	—	4	6	no	—
521	C₂	—	8	6	no	—
522	C₂	C₂²×#121×C₁₃₉	1	1	yes	characteristic
523	C₂	C₂×#550×C₁₃₉	1	1	yes	characteristic
524	C₂	D₄×#41×C₁₃₉	1	1	yes	characteristic
525	C₂	#3483×C₁₃₉	1	1	yes	characteristic
526	C₂	#3488×C₁₃₉	1	1	yes	characteristic
527	C₂	#3498×C₁₃₉	1	1	yes	characteristic
528	C₂	#3517×C₁₃₉	1	1	yes	characteristic

	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×#550×C₁₃₉	C₂	semidirect
2. C₂×#550×C₁₃₉	C₂	semidirect
3. C₂×C₄×#41×C₁₃₉	C₂	semidirect
4. #2856×C₁₃₉	C₂	semidirect
5. #2541×C₁₃₉	C₂	semidirect
6. #2537×C₁₃₉	C₂	semidirect
7. #2428×C₁₃₉	C₂	semidirect
8. #2414×C₁₃₉	C₂	semidirect
9. Q₈×C₄⋊C₄×C₁₃₉	C₂	semidirect
10. #2341×C₁₃₉	C₂	semidirect
11. C₄×#121×C₁₃₉	C₂	semidirect
54. C₂×#41×C₁₃₉	D₄	semidirect
76. C₄×Q₈×C₁₃₉	D₄	semidirect
159. C₄⋊C₄×C₁₃₉	#41	semidirect
187. Q₈×C₁₃₉	#121	semidirect
254. C₄×C₁₃₉	#550	semidirect
264. #36455	C₁₃₉	direct (N × H)
265. C₁₃₉	#36455	direct (N × H)
266. C₂×#550	C₂×C₁₃₉	semidirect
267. C₂×#550	C₂×C₁₃₉	semidirect
268. C₂×C₄×#41	C₂×C₁₃₉	semidirect
269. #2856	C₂×C₁₃₉	semidirect
270. #2541	C₂×C₁₃₉	semidirect
271. #2537	C₂×C₁₃₉	semidirect
272. #2428	C₂×C₁₃₉	semidirect
273. #2414	C₂×C₁₃₉	semidirect
274. Q₈×C₄⋊C₄	C₂×C₁₃₉	semidirect
275. #2341	C₂×C₁₃₉	semidirect
276. C₄×#121	C₂×C₁₃₉	semidirect
319. C₂×#41	D₄×C₁₃₉	semidirect
341. C₄×Q₈	D₄×C₁₃₉	semidirect
424. C₄⋊C₄	#41×C₁₃₉	semidirect
452. Q₈	#121×C₁₃₉	semidirect
519. C₄	#550×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#550×C₁₃₉	2
C₂×C₄×#41×C₁₃₉	2
#2856×C₁₃₉	2
#2541×C₁₃₉	2
#2537×C₁₃₉	2
#2428×C₁₃₉	2
#2414×C₁₃₉	2
Q₈×C₄⋊C₄×C₁₃₉	2
#2341×C₁₃₉	2
C₄×#121×C₁₃₉	2
#36455	139

Subgroups — C139×#36455 #48031051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36455 #48031051