Subgroups — C₁₃₉×#36125 #48030721

Order 35584.

3310 conjugacy classes of subgroups.

The subgroup lattice has 660 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×#547×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#532×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2858×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2850×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2546×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2541×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2464×C₁₃₉	C₂	1	8	yes	maximal, complemented
9	#2432×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2431×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2428×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2361×C₁₃₉	C₂	1	4	yes	maximal, complemented
13	C₄×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
16	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
17	#550×C₁₃₉	—	2	8	no	—
18	#547×C₁₃₉	—	2	8	no	—
19	#532×C₁₃₉	—	2	16	no	—
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
29	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
31	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#121×C₁₃₉	C₂²	1	8	yes	—
33	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
34	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
35	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	8	yes	—
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
42	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
43	#398×C₁₃₉	C₂²	1	4	yes	—
44	#394×C₁₃₉	C₂²	1	8	yes	—
45	#392×C₁₃₉	C₂²	1	4	yes	—
46	#392×C₁₃₉	C₂²	1	8	yes	—
47	#391×C₁₃₉	C₂²	1	2	yes	—
48	#391×C₁₃₉	C₂²	1	1	yes	characteristic
49	#390×C₁₃₉	C₂²	1	2	yes	—
50	#390×C₁₃₉	C₂²	1	1	yes	characteristic
51	#390×C₁₃₉	C₂²	1	4	yes	—
52	#390×C₁₃₉	C₂²	1	4	yes	—
53	#389×C₁₃₉	C₂²	1	4	yes	—
54	#388×C₁₃₉	C₂²	1	4	yes	—
55	#388×C₁₃₉	C₂²	1	8	yes	—
56	#386×C₁₃₉	C₂²	1	8	yes	—
57	#386×C₁₃₉	C₂²	1	8	yes	—
58	#385×C₁₃₉	C₂²	1	8	yes	—
59	#382×C₁₃₉	C₂²	1	1	yes	characteristic
60	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
61	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
62	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
63	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
64	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
65	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
66	C₂×#41×C₁₃₉	—	2	8	no	—
67	C₂×#41×C₁₃₉	—	2	8	no	—
68	C₂×#41×C₁₃₉	—	2	8	no	—
69	C₂×#41×C₁₃₉	—	2	8	no	—
70	C₂×#41×C₁₃₉	—	4	4	no	—
71	C₂×#41×C₁₃₉	—	4	4	no	—
72	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
73	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
75	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
76	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
77	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
78	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
79	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
82	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
84	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
85	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
86	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
87	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
88	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
89	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
90	#127×C₁₃₉	—	2	8	no	—
91	#127×C₁₃₉	—	2	8	no	—
92	#127×C₁₃₉	—	2	4	no	—
93	#124×C₁₃₉	—	2	8	no	—
94	#124×C₁₃₉	—	4	4	no	—
95	#124×C₁₃₉	D₄	1	8	yes	complemented
96	#123×C₁₃₉	—	2	16	no	—
97	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
98	#121×C₁₃₉	—	2	8	no	—
99	#121×C₁₃₉	—	2	8	no	—
100	#121×C₁₃₉	—	2	16	no	—
101	#121×C₁₃₉	—	2	32	no	—
102	#121×C₁₃₉	—	2	16	no	—
103	C₄×Q₈×C₁₃₉	—	2	4	no	—
104	C₄×D₄×C₁₃₉	—	2	8	no	—
105	C₄×D₄×C₁₃₉	—	2	8	no	—
106	C₄×D₄×C₁₃₉	—	2	32	no	—
107	C₄×D₄×C₁₃₉	—	2	4	no	—
108	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
109	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
110	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
121	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
125	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
126	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₄²×C₁₃₉	—	2	8	no	—
130	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
131	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
138	#95×C₁₃₉	C₂³	1	2	yes	—
139	#95×C₁₃₉	C₂³	1	8	yes	—
140	#95×C₁₃₉	C₂³	1	4	yes	—
141	#95×C₁₃₉	C₂³	1	4	yes	—
142	#95×C₁₃₉	C₂³	1	4	yes	—
143	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
144	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
145	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
146	#41×C₁₃₉	—	4	32	no	—
147	#41×C₁₃₉	—	4	32	no	—
148	C₂×Q₈×C₁₃₉	—	2	2	no	—
149	C₂×Q₈×C₁₃₉	—	2	4	no	—
150	C₂×Q₈×C₁₃₉	—	2	4	no	—
151	C₂×Q₈×C₁₃₉	—	2	2	no	—
152	C₂×Q₈×C₁₃₉	—	2	4	no	—
153	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
154	C₂×D₄×C₁₃₉	—	2	16	no	—
155	C₂×D₄×C₁₃₉	—	2	8	no	—
156	C₂×D₄×C₁₃₉	—	2	8	no	—
157	C₂×D₄×C₁₃₉	—	2	8	no	—
158	C₂×D₄×C₁₃₉	—	2	8	no	—
159	C₂×D₄×C₁₃₉	—	2	2	no	—
160	C₂×D₄×C₁₃₉	—	2	4	no	—
161	C₂×D₄×C₁₃₉	—	2	8	no	—
162	C₂×D₄×C₁₃₉	—	2	4	no	—
163	C₂×D₄×C₁₃₉	—	2	4	no	—
164	C₂×D₄×C₁₃₉	—	2	4	no	—
165	C₂×D₄×C₁₃₉	—	2	4	no	—
166	C₂×D₄×C₁₃₉	—	2	16	no	—
167	C₂×D₄×C₁₃₉	—	2	8	no	—
168	C₂×D₄×C₁₃₉	—	2	2	no	—
169	C₂×D₄×C₁₃₉	—	2	4	no	—
170	C₂×D₄×C₁₃₉	—	4	8	no	—
171	C₂×D₄×C₁₃₉	—	4	4	no	—
172	C₂×D₄×C₁₃₉	—	4	4	no	—
173	C₂×D₄×C₁₃₉	—	4	4	no	—
174	C₂×D₄×C₁₃₉	—	4	8	no	—
175	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
176	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
177	C₂²×C₄×C₁₃₉	—	2	4	no	—
178	C₂²×C₄×C₁₃₉	—	2	4	no	—
179	C₂²×C₄×C₁₃₉	—	2	8	no	—
180	C₂²×C₄×C₁₃₉	—	2	8	no	—
181	C₂²×C₄×C₁₃₉	—	2	4	no	—
182	C₂²×C₄×C₁₃₉	—	2	8	no	—
183	C₂²×C₄×C₁₃₉	—	2	8	no	—
184	C₂²×C₄×C₁₃₉	—	2	8	no	—
185	C₂²×C₄×C₁₃₉	—	2	8	no	—
186	C₂²×C₄×C₁₃₉	—	2	8	no	—
187	C₂²×C₄×C₁₃₉	—	4	4	no	—
188	C₂²×C₄×C₁₃₉	—	4	4	no	—
189	C₂²×C₄×C₁₃₉	—	4	4	no	—
190	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
191	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
202	C₄⋊C₄×C₁₃₉	—	2	4	no	—
203	C₄⋊C₄×C₁₃₉	—	2	8	no	—
204	C₄⋊C₄×C₁₃₉	—	2	16	no	—
205	C₄⋊C₄×C₁₃₉	—	2	2	no	—
206	C₄⋊C₄×C₁₃₉	—	2	4	no	—
207	C₄⋊C₄×C₁₃₉	—	2	2	no	—
208	C₄⋊C₄×C₁₃₉	—	2	4	no	—
209	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
210	C₄⋊C₄×C₁₃₉	#41	1	8	yes	complemented
211	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
212	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
213	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
214	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
215	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
216	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
217	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
218	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
219	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	16	yes	—
220	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
221	C₄²×C₁₃₉	—	2	8	no	—
222	C₄²×C₁₃₉	—	2	4	no	—
223	C₄²×C₁₃₉	—	2	4	no	—
224	C₄²×C₁₃₉	—	2	4	no	—
225	C₄²×C₁₃₉	—	2	2	no	—
226	C₄²×C₁₃₉	—	4	2	no	—
227	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
228	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
229	C₂³×C₁₃₉	—	2	2	no	—
230	C₂³×C₁₃₉	—	2	2	no	—
231	C₂³×C₁₃₉	—	2	4	no	—
232	C₂³×C₁₃₉	—	2	4	no	—
233	C₂³×C₁₃₉	—	2	2	no	—
234	C₂³×C₁₃₉	—	2	2	no	—
235	C₂³×C₁₃₉	—	2	4	no	—
236	C₂³×C₁₃₉	—	2	4	no	—
237	C₂³×C₁₃₉	—	2	4	no	—
238	C₂³×C₁₃₉	—	2	4	no	—
239	C₂³×C₁₃₉	—	2	8	no	—
240	C₂³×C₁₃₉	—	2	4	no	—
241	C₂³×C₁₃₉	—	2	8	no	—
242	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
243	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
244	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
245	Q₈×C₁₃₉	—	2	8	no	—
246	Q₈×C₁₃₉	—	4	8	no	—
247	D₄×C₁₃₉	—	2	8	no	—
248	D₄×C₁₃₉	—	2	8	no	—
249	D₄×C₁₃₉	—	4	32	no	—
250	D₄×C₁₃₉	—	4	16	no	—
251	D₄×C₁₃₉	—	4	16	no	—
252	D₄×C₁₃₉	—	4	8	no	—
253	D₄×C₁₃₉	—	4	8	no	—
254	D₄×C₁₃₉	—	8	4	no	—
255	D₄×C₁₃₉	—	8	8	no	—
256	C₂×C₄×C₁₃₉	—	2	4	no	—
257	C₂×C₄×C₁₃₉	—	2	2	no	—
258	C₂×C₄×C₁₃₉	—	2	2	no	—
259	C₂×C₄×C₁₃₉	—	2	2	no	—
260	C₂×C₄×C₁₃₉	—	2	2	no	—
261	C₂×C₄×C₁₃₉	—	2	2	no	—
262	C₂×C₄×C₁₃₉	—	2	2	no	—
263	C₂×C₄×C₁₃₉	—	2	2	no	—
264	C₂×C₄×C₁₃₉	—	2	4	no	—
265	C₂×C₄×C₁₃₉	—	2	16	no	—
266	C₂×C₄×C₁₃₉	—	2	2	no	—
267	C₂×C₄×C₁₃₉	—	2	2	no	—
268	C₂×C₄×C₁₃₉	—	2	4	no	—
269	C₂×C₄×C₁₃₉	—	2	4	no	—
270	C₂×C₄×C₁₃₉	—	2	2	no	—
271	C₂×C₄×C₁₃₉	—	2	4	no	—
272	C₂×C₄×C₁₃₉	—	2	2	no	—
273	C₂×C₄×C₁₃₉	—	2	4	no	—
274	C₂×C₄×C₁₃₉	—	2	2	no	—
275	C₂×C₄×C₁₃₉	—	2	4	no	—
276	C₂×C₄×C₁₃₉	—	4	16	no	—
277	C₂×C₄×C₁₃₉	—	4	16	no	—
278	C₂×C₄×C₁₃₉	—	4	16	no	—
279	C₂×C₄×C₁₃₉	—	4	8	no	—
280	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
281	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
282	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
283	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
284	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
285	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
286	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
287	C₂×C₄×C₁₃₉	C₂×#41	1	8	yes	—
288	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
289	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
290	C₂²×C₁₃₉	—	2	4	no	—
291	C₂²×C₁₃₉	—	2	4	no	—
292	C₂²×C₁₃₉	—	2	4	no	—
293	C₂²×C₁₃₉	—	2	8	no	—
294	C₂²×C₁₃₉	—	2	4	no	—
295	C₂²×C₁₃₉	—	4	2	no	—
296	C₂²×C₁₃₉	—	4	4	no	—
297	C₂²×C₁₃₉	—	4	2	no	—
298	C₂²×C₁₃₉	—	4	4	no	—
299	C₂²×C₁₃₉	—	4	4	no	—
300	C₂²×C₁₃₉	—	4	4	no	—
301	C₂²×C₁₃₉	—	4	4	no	—
302	C₂²×C₁₃₉	—	4	8	no	—
303	C₂²×C₁₃₉	—	4	4	no	—
304	C₂²×C₁₃₉	—	4	8	no	—
305	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
306	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
307	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
308	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
309	C₂²×C₁₃₉	#585	1	2	yes	—
310	C₄×C₁₃₉	—	2	4	no	—
311	C₄×C₁₃₉	—	2	4	no	—
312	C₄×C₁₃₉	—	2	4	no	—
313	C₄×C₁₃₉	—	2	8	no	—
314	C₄×C₁₃₉	—	2	2	no	—
315	C₄×C₁₃₉	—	4	2	no	—
316	C₄×C₁₃₉	—	4	4	no	—
317	C₄×C₁₃₉	—	4	2	no	—
318	C₄×C₁₃₉	—	4	2	no	—
319	C₄×C₁₃₉	#532	1	4	yes	complemented
320	C₄×C₁₃₉	D₄²	1	4	yes	—
321	C₂×C₁₃₉	—	4	4	no	—
322	C₂×C₁₃₉	—	4	4	no	—
323	C₂×C₁₃₉	—	8	4	no	—
324	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
325	C₂×C₁₃₉	C₂×D₄²	1	1	yes	characteristic
326	C₂×C₁₃₉	D₄×#41	1	2	yes	—
327	C₂×C₁₃₉	#3500	1	1	yes	characteristic
328	C₂×C₁₃₉	#3517	1	2	yes	—
329	#36125	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
330	C₁₃₉	#36125	1	1	yes	characteristic, direct product factor, Sylow
331	C₂×#550	C₂×C₁₃₉	1	1	yes	characteristic, complemented
332	C₂×#547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
333	C₂×#532	C₂×C₁₃₉	1	2	yes	complemented
334	#2858	C₂×C₁₃₉	1	1	yes	characteristic, complemented
335	#2850	C₂×C₁₃₉	1	2	yes	complemented
336	#2546	C₂×C₁₃₉	1	1	yes	characteristic, complemented
337	#2541	C₂×C₁₃₉	1	1	yes	characteristic, complemented
338	#2464	C₂×C₁₃₉	1	8	yes	complemented
339	#2432	C₂×C₁₃₉	1	2	yes	complemented
340	#2431	C₂×C₁₃₉	1	2	yes	complemented
341	#2428	C₂×C₁₃₉	1	4	yes	complemented
342	#2361	C₂×C₁₃₉	1	4	yes	complemented
343	C₄×#124	C₂×C₁₃₉	1	1	yes	characteristic, complemented
344	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
345	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
346	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
347	#550	—	2	8	no	—
348	#547	—	2	8	no	—
349	#532	—	2	16	no	—
350	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
351	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
352	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
353	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
354	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
355	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
356	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
357	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
358	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
359	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
360	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
361	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
362	C₂×#121	C₂²×C₁₃₉	1	8	yes	—
363	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
364	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
365	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
366	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
367	C₂×C₄×D₄	C₂²×C₁₃₉	1	8	yes	—
368	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
369	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
370	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
371	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
372	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
373	#398	C₂²×C₁₃₉	1	4	yes	—
374	#394	C₂²×C₁₃₉	1	8	yes	—
375	#392	C₂²×C₁₃₉	1	8	yes	—
376	#392	C₂²×C₁₃₉	1	4	yes	—
377	#391	C₂²×C₁₃₉	1	2	yes	—
378	#391	C₂²×C₁₃₉	1	1	yes	characteristic
379	#390	C₂²×C₁₃₉	1	2	yes	—
380	#390	C₂²×C₁₃₉	1	4	yes	—
381	#390	C₂²×C₁₃₉	1	4	yes	—
382	#390	C₂²×C₁₃₉	1	1	yes	characteristic
383	#389	C₂²×C₁₃₉	1	4	yes	—
384	#388	C₂²×C₁₃₉	1	8	yes	—
385	#388	C₂²×C₁₃₉	1	4	yes	—
386	#386	C₂²×C₁₃₉	1	8	yes	—
387	#386	C₂²×C₁₃₉	1	8	yes	—
388	#385	C₂²×C₁₃₉	1	8	yes	—
389	#382	C₂²×C₁₃₉	1	1	yes	characteristic
390	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
391	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
392	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
393	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
394	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
395	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
396	C₂×#41	—	2	8	no	—
397	C₂×#41	—	2	8	no	—
398	C₂×#41	—	2	8	no	—
399	C₂×#41	—	2	8	no	—
400	C₂×#41	—	4	4	no	—
401	C₂×#41	—	4	4	no	—
402	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
403	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
404	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
405	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
406	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
407	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
408	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
409	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
410	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
411	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
412	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
413	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
414	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
415	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
416	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
417	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
418	C₄⋊Q₈	—	2	8	no	—
419	C₄⋊Q₈	—	2	4	no	—
420	#127	—	2	8	no	—
421	#127	—	2	8	no	—
422	#127	—	2	4	no	—
423	#124	—	2	8	no	—
424	#124	—	4	4	no	—
425	#124	D₄×C₁₃₉	1	8	yes	complemented
426	#123	—	2	16	no	—
427	C₂²⋊Q₈	—	2	8	no	—
428	#121	—	2	8	no	—
429	#121	—	2	8	no	—
430	#121	—	2	16	no	—
431	#121	—	2	32	no	—
432	#121	—	2	16	no	—
433	C₄×Q₈	—	2	4	no	—
434	C₄×D₄	—	2	8	no	—
435	C₄×D₄	—	2	8	no	—
436	C₄×D₄	—	2	32	no	—
437	C₄×D₄	—	2	4	no	—
438	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
439	C₂×C₄⋊C₄	—	2	8	no	—
440	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
441	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
442	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
443	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
459	C₂×C₄²	—	2	8	no	—
460	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
461	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
462	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
463	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
465	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
466	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
467	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
468	#95	C₂³×C₁₃₉	1	4	yes	—
469	#95	C₂³×C₁₃₉	1	2	yes	—
470	#95	C₂³×C₁₃₉	1	4	yes	—
471	#95	C₂³×C₁₃₉	1	4	yes	—
472	#95	C₂³×C₁₃₉	1	8	yes	—
473	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
474	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
475	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
476	#41	—	4	32	no	—
477	#41	—	4	32	no	—
478	C₂×Q₈	—	2	2	no	—
479	C₂×Q₈	—	2	4	no	—
480	C₂×Q₈	—	2	4	no	—
481	C₂×Q₈	—	2	2	no	—
482	C₂×Q₈	—	2	4	no	—
483	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
484	C₂×D₄	—	2	16	no	—
485	C₂×D₄	—	2	8	no	—
486	C₂×D₄	—	2	8	no	—
487	C₂×D₄	—	2	8	no	—
488	C₂×D₄	—	2	8	no	—
489	C₂×D₄	—	2	2	no	—
490	C₂×D₄	—	2	4	no	—
491	C₂×D₄	—	2	8	no	—
492	C₂×D₄	—	2	4	no	—
493	C₂×D₄	—	2	4	no	—
494	C₂×D₄	—	2	4	no	—
495	C₂×D₄	—	2	4	no	—
496	C₂×D₄	—	2	16	no	—
497	C₂×D₄	—	2	8	no	—
498	C₂×D₄	—	2	2	no	—
499	C₂×D₄	—	2	4	no	—
500	C₂×D₄	—	4	8	no	—
501	C₂×D₄	—	4	4	no	—
502	C₂×D₄	—	4	4	no	—
503	C₂×D₄	—	4	4	no	—
504	C₂×D₄	—	4	8	no	—
505	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
506	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
507	C₂²×C₄	—	2	4	no	—
508	C₂²×C₄	—	2	4	no	—
509	C₂²×C₄	—	2	8	no	—
510	C₂²×C₄	—	2	8	no	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	2	8	no	—
513	C₂²×C₄	—	2	8	no	—
514	C₂²×C₄	—	2	8	no	—
515	C₂²×C₄	—	2	8	no	—
516	C₂²×C₄	—	2	8	no	—
517	C₂²×C₄	—	4	4	no	—
518	C₂²×C₄	—	4	4	no	—
519	C₂²×C₄	—	4	4	no	—
520	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
521	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
522	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
523	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
524	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
525	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
526	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
527	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
528	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
530	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
531	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
532	C₄⋊C₄	—	2	4	no	—
533	C₄⋊C₄	—	2	8	no	—
534	C₄⋊C₄	—	2	16	no	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
540	C₄⋊C₄	#41×C₁₃₉	1	8	yes	complemented
541	C₂²⋊C₄	—	2	8	no	—
542	C₂²⋊C₄	—	2	8	no	—
543	C₂²⋊C₄	—	2	16	no	—
544	C₂²⋊C₄	—	2	4	no	—
545	C₂²⋊C₄	—	2	8	no	—
546	C₂²⋊C₄	—	2	16	no	—
547	C₂²⋊C₄	—	4	4	no	—
548	C₂²⋊C₄	—	4	8	no	—
549	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	16	yes	—
550	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
551	C₄²	—	2	8	no	—
552	C₄²	—	2	4	no	—
553	C₄²	—	2	4	no	—
554	C₄²	—	2	4	no	—
555	C₄²	—	2	2	no	—
556	C₄²	—	4	2	no	—
557	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
558	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
559	C₂³	—	2	2	no	—
560	C₂³	—	2	2	no	—
561	C₂³	—	2	4	no	—
562	C₂³	—	2	4	no	—
563	C₂³	—	2	2	no	—
564	C₂³	—	2	2	no	—
565	C₂³	—	2	4	no	—
566	C₂³	—	2	4	no	—
567	C₂³	—	2	4	no	—
568	C₂³	—	2	4	no	—
569	C₂³	—	2	8	no	—
570	C₂³	—	2	4	no	—
571	C₂³	—	2	8	no	—
572	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
573	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
574	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
575	Q₈	—	2	8	no	—
576	Q₈	—	4	8	no	—
577	D₄	—	2	8	no	—
578	D₄	—	2	8	no	—
579	D₄	—	4	16	no	—
580	D₄	—	4	32	no	—
581	D₄	—	4	16	no	—
582	D₄	—	4	8	no	—
583	D₄	—	4	8	no	—
584	D₄	—	8	4	no	—
585	D₄	—	8	8	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	4	no	—
595	C₂×C₄	—	2	16	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	4	16	no	—
607	C₂×C₄	—	4	16	no	—
608	C₂×C₄	—	4	16	no	—
609	C₂×C₄	—	4	8	no	—
610	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
611	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
612	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
613	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
614	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
615	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
616	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
617	C₂×C₄	C₂×#41×C₁₃₉	1	8	yes	—
618	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
619	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
620	C₂²	—	2	4	no	—
621	C₂²	—	2	4	no	—
622	C₂²	—	2	4	no	—
623	C₂²	—	2	8	no	—
624	C₂²	—	2	4	no	—
625	C₂²	—	4	2	no	—
626	C₂²	—	4	4	no	—
627	C₂²	—	4	2	no	—
628	C₂²	—	4	4	no	—
629	C₂²	—	4	4	no	—
630	C₂²	—	4	4	no	—
631	C₂²	—	4	4	no	—
632	C₂²	—	4	8	no	—
633	C₂²	—	4	4	no	—
634	C₂²	—	4	8	no	—
635	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
636	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
637	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
638	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
639	C₂²	#585×C₁₃₉	1	2	yes	—
640	C₄	—	2	4	no	—
641	C₄	—	2	4	no	—
642	C₄	—	2	4	no	—
643	C₄	—	2	8	no	—
644	C₄	—	2	2	no	—
645	C₄	—	4	2	no	—
646	C₄	—	4	4	no	—
647	C₄	—	4	2	no	—
648	C₄	—	4	2	no	—
649	C₄	#532×C₁₃₉	1	4	yes	complemented
650	C₄	D₄²×C₁₃₉	1	4	yes	—
651	C₂	—	4	4	no	—
652	C₂	—	4	4	no	—
653	C₂	—	8	4	no	—
654	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
655	C₂	C₂×D₄²×C₁₃₉	1	1	yes	characteristic
656	C₂	D₄×#41×C₁₃₉	1	2	yes	—
657	C₂	#3500×C₁₃₉	1	1	yes	characteristic
658	C₂	#3517×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×#550×C₁₃₉	C₂	semidirect
2. C₂×#547×C₁₃₉	C₂	semidirect
3. C₂×#532×C₁₃₉	C₂	semidirect
4. #2858×C₁₃₉	C₂	semidirect
5. #2850×C₁₃₉	C₂	semidirect
6. #2546×C₁₃₉	C₂	semidirect
7. #2541×C₁₃₉	C₂	semidirect
8. #2464×C₁₃₉	C₂	semidirect
9. #2432×C₁₃₉	C₂	semidirect
10. #2431×C₁₃₉	C₂	semidirect
11. #2428×C₁₃₉	C₂	semidirect
12. #2361×C₁₃₉	C₂	semidirect
13. C₄×#124×C₁₃₉	C₂	semidirect
14. C₄²×D₄×C₁₃₉	C₂	semidirect
95. #124×C₁₃₉	D₄	semidirect
108. C₄×D₄×C₁₃₉	D₄	semidirect
210. C₄⋊C₄×C₁₃₉	#41	semidirect
319. C₄×C₁₃₉	#532	semidirect
329. #36125	C₁₃₉	direct (N × H)
330. C₁₃₉	#36125	direct (N × H)
331. C₂×#550	C₂×C₁₃₉	semidirect
332. C₂×#547	C₂×C₁₃₉	semidirect
333. C₂×#532	C₂×C₁₃₉	semidirect
334. #2858	C₂×C₁₃₉	semidirect
335. #2850	C₂×C₁₃₉	semidirect
336. #2546	C₂×C₁₃₉	semidirect
337. #2541	C₂×C₁₃₉	semidirect
338. #2464	C₂×C₁₃₉	semidirect
339. #2432	C₂×C₁₃₉	semidirect
340. #2431	C₂×C₁₃₉	semidirect
341. #2428	C₂×C₁₃₉	semidirect
342. #2361	C₂×C₁₃₉	semidirect
343. C₄×#124	C₂×C₁₃₉	semidirect
344. C₄²×D₄	C₂×C₁₃₉	semidirect
425. #124	D₄×C₁₃₉	semidirect
438. C₄×D₄	D₄×C₁₃₉	semidirect
540. C₄⋊C₄	#41×C₁₃₉	semidirect
649. C₄	#532×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×#547×C₁₃₉	2
C₂×#532×C₁₃₉	2
#2858×C₁₃₉	2
#2850×C₁₃₉	2
#2546×C₁₃₉	2
#2541×C₁₃₉	2
#2464×C₁₃₉	2
#2432×C₁₃₉	2
#2431×C₁₃₉	2
#2428×C₁₃₉	2
#2361×C₁₃₉	2
C₄×#124×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36125	139

Subgroups — C139×#36125 #48030721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36125 #48030721