Subgroups — C₁₃₉×#35618 #48030214

Order 35584.

2434 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#537×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#520×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2504×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2503×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2500×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2499×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2444×C₁₃₉	C₂	1	8	yes	maximal, complemented
8	#2421×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2420×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2317×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2311×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#382×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
17	#537×C₁₃₉	—	2	8	no	—
18	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
19	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
22	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
23	#520×C₁₃₉	—	2	8	no	—
24	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
27	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
30	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
33	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
34	#400×C₁₃₉	C₂²	1	8	yes	—
35	#397×C₁₃₉	C₂²	1	8	yes	—
36	#397×C₁₃₉	C₂²	1	8	yes	—
37	#394×C₁₃₉	C₂²	1	8	yes	—
38	#391×C₁₃₉	C₂²	1	2	yes	—
39	#391×C₁₃₉	C₂²	1	1	yes	characteristic
40	#391×C₁₃₉	C₂²	1	1	yes	characteristic
41	#391×C₁₃₉	C₂²	1	2	yes	—
42	#390×C₁₃₉	C₂²	1	2	yes	—
43	#390×C₁₃₉	C₂²	1	1	yes	characteristic
44	#390×C₁₃₉	C₂²	1	1	yes	characteristic
45	#390×C₁₃₉	C₂²	1	2	yes	—
46	#389×C₁₃₉	C₂²	1	4	yes	—
47	#388×C₁₃₉	C₂²	1	8	yes	—
48	#387×C₁₃₉	C₂²	1	8	yes	—
49	#386×C₁₃₉	C₂²	1	4	yes	—
50	#386×C₁₃₉	C₂²	1	4	yes	—
51	#386×C₁₃₉	C₂²	1	4	yes	—
52	#386×C₁₃₉	C₂²	1	8	yes	—
53	#385×C₁₃₉	C₂²	1	4	yes	—
54	#384×C₁₃₉	C₂²	1	2	yes	—
55	#382×C₁₃₉	C₂²	1	4	yes	—
56	#382×C₁₃₉	C₂²	1	2	yes	—
57	#382×C₁₃₉	C₂²	1	2	yes	—
58	#382×C₁₃₉	C₂²	1	2	yes	—
59	#381×C₁₃₉	C₂²	1	8	yes	—
60	#380×C₁₃₉	C₂²	1	4	yes	—
61	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
62	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
63	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
64	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
65	C₂×#41×C₁₃₉	—	2	4	no	—
66	C₂×#41×C₁₃₉	—	2	4	no	—
67	C₂×#41×C₁₃₉	—	2	4	no	—
68	C₂×#41×C₁₃₉	—	2	4	no	—
69	C₂×#41×C₁₃₉	—	2	4	no	—
70	C₂×#41×C₁₃₉	D₄	1	8	yes	—
71	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
74	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
76	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
78	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
80	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
81	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
82	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
83	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
84	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
85	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
86	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
87	#121×C₁₃₉	—	2	8	no	—
88	#121×C₁₃₉	—	2	16	no	—
89	#121×C₁₃₉	—	2	8	no	—
90	C₄×Q₈×C₁₃₉	—	2	8	no	—
91	C₄×D₄×C₁₃₉	—	2	8	no	—
92	C₄×D₄×C₁₃₉	—	2	16	no	—
93	#117×C₁₃₉	—	2	8	no	—
94	#117×C₁₃₉	—	2	4	no	—
95	#117×C₁₃₉	—	2	4	no	—
96	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
97	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
98	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
99	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
109	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
111	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
115	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
116	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
117	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
119	C₂×C₄²×C₁₃₉	—	2	4	no	—
120	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
125	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
126	#95×C₁₃₉	C₂³	1	8	yes	—
127	#95×C₁₃₉	C₂³	1	4	yes	—
128	#95×C₁₃₉	C₂³	1	4	yes	—
129	#95×C₁₃₉	C₂³	1	8	yes	—
130	#95×C₁₃₉	C₂³	1	8	yes	—
131	#95×C₁₃₉	C₂³	1	4	yes	—
132	#95×C₁₃₉	C₂³	1	4	yes	—
133	#95×C₁₃₉	C₂³	1	8	yes	—
134	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
135	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
136	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
137	#41×C₁₃₉	—	2	32	no	—
138	#41×C₁₃₉	—	4	16	no	—
139	C₂×Q₈×C₁₃₉	—	2	2	no	—
140	C₂×Q₈×C₁₃₉	—	2	2	no	—
141	C₂×Q₈×C₁₃₉	—	2	2	no	—
142	C₂×Q₈×C₁₃₉	—	2	2	no	—
143	C₂×Q₈×C₁₃₉	—	2	2	no	—
144	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
145	C₂×D₄×C₁₃₉	—	2	4	no	—
146	C₂×D₄×C₁₃₉	—	2	4	no	—
147	C₂×D₄×C₁₃₉	—	2	4	no	—
148	C₂×D₄×C₁₃₉	—	2	4	no	—
149	C₂×D₄×C₁₃₉	—	2	4	no	—
150	C₂×D₄×C₁₃₉	—	2	8	no	—
151	C₂×D₄×C₁₃₉	—	2	2	no	—
152	C₂×D₄×C₁₃₉	—	2	2	no	—
153	C₂×D₄×C₁₃₉	—	2	2	no	—
154	C₂×D₄×C₁₃₉	—	2	2	no	—
155	C₂×D₄×C₁₃₉	—	2	2	no	—
156	C₂×D₄×C₁₃₉	—	4	8	no	—
157	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
158	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
159	C₂²×C₄×C₁₃₉	—	2	4	no	—
160	C₂²×C₄×C₁₃₉	—	2	4	no	—
161	C₂²×C₄×C₁₃₉	—	2	4	no	—
162	C₂²×C₄×C₁₃₉	—	2	8	no	—
163	C₂²×C₄×C₁₃₉	—	2	4	no	—
164	C₂²×C₄×C₁₃₉	—	2	4	no	—
165	C₂²×C₄×C₁₃₉	—	2	4	no	—
166	C₂²×C₄×C₁₃₉	—	2	4	no	—
167	C₂²×C₄×C₁₃₉	—	2	4	no	—
168	C₂²×C₄×C₁₃₉	—	4	2	no	—
169	C₂²×C₄×C₁₃₉	—	4	2	no	—
170	C₂²×C₄×C₁₃₉	—	4	4	no	—
171	C₂²×C₄×C₁₃₉	—	4	8	no	—
172	C₂²×C₄×C₁₃₉	—	4	4	no	—
173	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
174	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
175	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
176	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
177	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
188	C₄⋊C₄×C₁₃₉	—	2	2	no	—
189	C₄⋊C₄×C₁₃₉	—	2	4	no	—
190	C₄⋊C₄×C₁₃₉	—	2	8	no	—
191	C₄⋊C₄×C₁₃₉	—	2	4	no	—
192	C₄⋊C₄×C₁₃₉	—	2	4	no	—
193	C₄⋊C₄×C₁₃₉	—	2	4	no	—
194	C₄⋊C₄×C₁₃₉	—	2	2	no	—
195	C₄⋊C₄×C₁₃₉	—	2	8	no	—
196	C₄⋊C₄×C₁₃₉	—	2	4	no	—
197	C₄⋊C₄×C₁₃₉	—	4	8	no	—
198	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
199	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
200	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
201	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
202	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
203	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
204	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
205	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
206	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
207	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
208	C₄²×C₁₃₉	—	2	8	no	—
209	C₄²×C₁₃₉	—	2	4	no	—
210	C₄²×C₁₃₉	—	2	2	no	—
211	C₄²×C₁₃₉	—	2	2	no	—
212	C₄²×C₁₃₉	—	2	4	no	—
213	C₄²×C₁₃₉	—	2	4	no	—
214	C₂³×C₁₃₉	—	2	2	no	—
215	C₂³×C₁₃₉	—	2	2	no	—
216	C₂³×C₁₃₉	—	2	2	no	—
217	C₂³×C₁₃₉	—	2	2	no	—
218	C₂³×C₁₃₉	—	2	4	no	—
219	C₂³×C₁₃₉	—	2	4	no	—
220	C₂³×C₁₃₉	—	2	2	no	—
221	C₂³×C₁₃₉	—	2	2	no	—
222	C₂³×C₁₃₉	—	2	2	no	—
223	C₂³×C₁₃₉	—	2	4	no	—
224	C₂³×C₁₃₉	—	2	4	no	—
225	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
226	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
227	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
228	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
229	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
230	Q₈×C₁₃₉	—	2	8	no	—
231	Q₈×C₁₃₉	—	4	4	no	—
232	D₄×C₁₃₉	—	2	16	no	—
233	D₄×C₁₃₉	—	2	8	no	—
234	D₄×C₁₃₉	—	4	8	no	—
235	D₄×C₁₃₉	—	4	4	no	—
236	D₄×C₁₃₉	—	8	8	no	—
237	C₂×C₄×C₁₃₉	—	2	2	no	—
238	C₂×C₄×C₁₃₉	—	2	2	no	—
239	C₂×C₄×C₁₃₉	—	2	16	no	—
240	C₂×C₄×C₁₃₉	—	2	2	no	—
241	C₂×C₄×C₁₃₉	—	2	4	no	—
242	C₂×C₄×C₁₃₉	—	2	2	no	—
243	C₂×C₄×C₁₃₉	—	2	4	no	—
244	C₂×C₄×C₁₃₉	—	2	2	no	—
245	C₂×C₄×C₁₃₉	—	2	2	no	—
246	C₂×C₄×C₁₃₉	—	2	2	no	—
247	C₂×C₄×C₁₃₉	—	2	4	no	—
248	C₂×C₄×C₁₃₉	—	2	2	no	—
249	C₂×C₄×C₁₃₉	—	2	2	no	—
250	C₂×C₄×C₁₃₉	—	2	4	no	—
251	C₂×C₄×C₁₃₉	—	2	2	no	—
252	C₂×C₄×C₁₃₉	—	2	2	no	—
253	C₂×C₄×C₁₃₉	—	2	2	no	—
254	C₂×C₄×C₁₃₉	—	2	2	no	—
255	C₂×C₄×C₁₃₉	—	2	4	no	—
256	C₂×C₄×C₁₃₉	—	2	4	no	—
257	C₂×C₄×C₁₃₉	—	2	8	no	—
258	C₂×C₄×C₁₃₉	—	2	4	no	—
259	C₂×C₄×C₁₃₉	—	2	8	no	—
260	C₂×C₄×C₁₃₉	—	4	8	no	—
261	C₂×C₄×C₁₃₉	—	4	8	no	—
262	C₂×C₄×C₁₃₉	—	8	4	no	—
263	C₂×C₄×C₁₃₉	—	8	8	no	—
264	C₂×C₄×C₁₃₉	—	8	4	no	—
265	C₂×C₄×C₁₃₉	#123	1	16	yes	—
266	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
267	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
268	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
269	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
270	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
271	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
272	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
273	C₂²×C₁₃₉	—	2	4	no	—
274	C₂²×C₁₃₉	—	2	2	no	—
275	C₂²×C₁₃₉	—	2	2	no	—
276	C₂²×C₁₃₉	—	2	4	no	—
277	C₂²×C₁₃₉	—	2	4	no	—
278	C₂²×C₁₃₉	—	2	4	no	—
279	C₂²×C₁₃₉	—	2	4	no	—
280	C₂²×C₁₃₉	—	4	4	no	—
281	C₂²×C₁₃₉	—	4	4	no	—
282	C₂²×C₁₃₉	—	4	2	no	—
283	C₂²×C₁₃₉	—	4	4	no	—
284	C₂²×C₁₃₉	—	4	2	no	—
285	C₂²×C₁₃₉	—	4	2	no	—
286	C₂²×C₁₃₉	—	4	4	no	—
287	C₂²×C₁₃₉	C₂×#123	1	4	yes	—
288	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
289	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
290	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
291	C₂²×C₁₃₉	#585	1	2	yes	—
292	C₂²×C₁₃₉	#585	1	2	yes	—
293	C₄×C₁₃₉	—	2	4	no	—
294	C₄×C₁₃₉	—	4	2	no	—
295	C₄×C₁₃₉	—	4	2	no	—
296	C₄×C₁₃₉	—	4	2	no	—
297	C₄×C₁₃₉	—	4	2	no	—
298	C₄×C₁₃₉	—	4	4	no	—
299	C₄×C₁₃₉	—	4	2	no	—
300	C₄×C₁₃₉	—	4	4	no	—
301	C₄×C₁₃₉	—	4	4	no	—
302	C₄×C₁₃₉	C₂×#123	1	4	yes	—
303	C₄×C₁₃₉	C₂×#123	1	4	yes	—
304	C₂×C₁₃₉	—	2	4	no	—
305	C₂×C₁₃₉	—	4	4	no	—
306	C₂×C₁₃₉	—	8	2	no	—
307	C₂×C₁₃₉	C₂²×#123	1	1	yes	characteristic
308	C₂×C₁₃₉	#3493	1	2	yes	—
309	C₂×C₁₃₉	#3500	1	1	yes	characteristic
310	C₂×C₁₃₉	#3500	1	1	yes	characteristic
311	C₂×C₁₃₉	#3512	1	2	yes	—
312	#35618	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₁₃₉	#35618	1	1	yes	characteristic, direct product factor, Sylow
314	C₂×#537	C₂×C₁₃₉	1	1	yes	characteristic
315	C₂×#520	C₂×C₁₃₉	1	1	yes	characteristic, complemented
316	#2504	C₂×C₁₃₉	1	2	yes	complemented
317	#2503	C₂×C₁₃₉	1	2	yes	complemented
318	#2500	C₂×C₁₃₉	1	2	yes	complemented
319	#2499	C₂×C₁₃₉	1	2	yes	complemented
320	#2444	C₂×C₁₃₉	1	8	yes	complemented
321	#2421	C₂×C₁₃₉	1	4	yes	complemented
322	#2420	C₂×C₁₃₉	1	4	yes	complemented
323	#2317	C₂×C₁₃₉	1	1	yes	characteristic, complemented
324	#2311	C₂×C₁₃₉	1	1	yes	characteristic, complemented
325	#2297	C₂×C₁₃₉	1	1	yes	characteristic, complemented
326	#2297	C₂×C₁₃₉	1	1	yes	characteristic, complemented
327	C₂×#382	C₂×C₁₃₉	1	1	yes	characteristic, complemented
328	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
329	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
330	#537	—	2	8	no	—
331	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
332	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
333	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
334	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
335	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
336	#520	—	2	8	no	—
337	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
338	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
339	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
340	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
341	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
342	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
343	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
344	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
345	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
346	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
347	#400	C₂²×C₁₃₉	1	8	yes	—
348	#397	C₂²×C₁₃₉	1	8	yes	—
349	#397	C₂²×C₁₃₉	1	8	yes	—
350	#394	C₂²×C₁₃₉	1	8	yes	—
351	#391	C₂²×C₁₃₉	1	2	yes	—
352	#391	C₂²×C₁₃₉	1	2	yes	—
353	#391	C₂²×C₁₃₉	1	1	yes	characteristic
354	#391	C₂²×C₁₃₉	1	1	yes	characteristic
355	#390	C₂²×C₁₃₉	1	2	yes	—
356	#390	C₂²×C₁₃₉	1	2	yes	—
357	#390	C₂²×C₁₃₉	1	1	yes	characteristic
358	#390	C₂²×C₁₃₉	1	1	yes	characteristic
359	#389	C₂²×C₁₃₉	1	4	yes	—
360	#388	C₂²×C₁₃₉	1	8	yes	—
361	#387	C₂²×C₁₃₉	1	8	yes	—
362	#386	C₂²×C₁₃₉	1	4	yes	—
363	#386	C₂²×C₁₃₉	1	8	yes	—
364	#386	C₂²×C₁₃₉	1	4	yes	—
365	#386	C₂²×C₁₃₉	1	4	yes	—
366	#385	C₂²×C₁₃₉	1	4	yes	—
367	#384	C₂²×C₁₃₉	1	2	yes	—
368	#382	C₂²×C₁₃₉	1	2	yes	—
369	#382	C₂²×C₁₃₉	1	4	yes	—
370	#382	C₂²×C₁₃₉	1	2	yes	—
371	#382	C₂²×C₁₃₉	1	2	yes	—
372	#381	C₂²×C₁₃₉	1	8	yes	—
373	#380	C₂²×C₁₃₉	1	4	yes	—
374	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
375	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
376	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
377	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
378	C₂×#41	—	2	4	no	—
379	C₂×#41	—	2	4	no	—
380	C₂×#41	—	2	4	no	—
381	C₂×#41	—	2	4	no	—
382	C₂×#41	—	2	4	no	—
383	C₂×#41	D₄×C₁₃₉	1	8	yes	—
384	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
385	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
386	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
387	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
388	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
389	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
390	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
391	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
392	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
393	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
394	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
395	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
396	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
397	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
398	C₂²⋊Q₈	—	2	8	no	—
399	C₂²⋊Q₈	—	2	8	no	—
400	#121	—	2	8	no	—
401	#121	—	2	16	no	—
402	#121	—	2	8	no	—
403	C₄×Q₈	—	2	8	no	—
404	C₄×D₄	—	2	8	no	—
405	C₄×D₄	—	2	16	no	—
406	#117	—	2	8	no	—
407	#117	—	2	4	no	—
408	#117	—	2	4	no	—
409	C₂×C₄⋊C₄	—	2	8	no	—
410	C₂×C₄⋊C₄	—	2	4	no	—
411	C₂×C₄⋊C₄	—	2	4	no	—
412	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
413	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
415	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
416	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
417	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
418	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
420	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
421	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
432	C₂×C₄²	—	2	4	no	—
433	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
434	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
435	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
436	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
437	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
438	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
439	#95	C₂³×C₁₃₉	1	8	yes	—
440	#95	C₂³×C₁₃₉	1	8	yes	—
441	#95	C₂³×C₁₃₉	1	4	yes	—
442	#95	C₂³×C₁₃₉	1	4	yes	—
443	#95	C₂³×C₁₃₉	1	4	yes	—
444	#95	C₂³×C₁₃₉	1	4	yes	—
445	#95	C₂³×C₁₃₉	1	8	yes	—
446	#95	C₂³×C₁₃₉	1	8	yes	—
447	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
448	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
449	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
450	#41	—	2	32	no	—
451	#41	—	4	16	no	—
452	C₂×Q₈	—	2	2	no	—
453	C₂×Q₈	—	2	2	no	—
454	C₂×Q₈	—	2	2	no	—
455	C₂×Q₈	—	2	2	no	—
456	C₂×Q₈	—	2	2	no	—
457	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
458	C₂×D₄	—	2	4	no	—
459	C₂×D₄	—	2	4	no	—
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	2	4	no	—
462	C₂×D₄	—	2	4	no	—
463	C₂×D₄	—	2	8	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	4	8	no	—
470	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
471	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	8	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	4	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	4	2	no	—
482	C₂²×C₄	—	4	2	no	—
483	C₂²×C₄	—	4	4	no	—
484	C₂²×C₄	—	4	8	no	—
485	C₂²×C₄	—	4	4	no	—
486	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
487	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
488	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
489	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
490	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
491	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
492	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
493	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
494	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
495	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
496	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
497	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
498	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
499	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
500	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	4	no	—
503	C₄⋊C₄	—	2	8	no	—
504	C₄⋊C₄	—	2	4	no	—
505	C₄⋊C₄	—	2	4	no	—
506	C₄⋊C₄	—	2	4	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	8	no	—
509	C₄⋊C₄	—	2	4	no	—
510	C₄⋊C₄	—	4	8	no	—
511	C₂²⋊C₄	—	2	8	no	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	2	8	no	—
514	C₂²⋊C₄	—	2	4	no	—
515	C₂²⋊C₄	—	2	8	no	—
516	C₂²⋊C₄	—	4	4	no	—
517	C₂²⋊C₄	—	4	8	no	—
518	C₂²⋊C₄	—	4	4	no	—
519	C₂²⋊C₄	—	4	4	no	—
520	C₂²⋊C₄	—	4	4	no	—
521	C₄²	—	2	8	no	—
522	C₄²	—	2	4	no	—
523	C₄²	—	2	2	no	—
524	C₄²	—	2	2	no	—
525	C₄²	—	2	4	no	—
526	C₄²	—	2	4	no	—
527	C₂³	—	2	2	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	2	no	—
530	C₂³	—	2	2	no	—
531	C₂³	—	2	4	no	—
532	C₂³	—	2	4	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	4	no	—
537	C₂³	—	2	4	no	—
538	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
539	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
540	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
541	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
542	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
543	Q₈	—	2	8	no	—
544	Q₈	—	4	4	no	—
545	D₄	—	2	16	no	—
546	D₄	—	2	8	no	—
547	D₄	—	4	8	no	—
548	D₄	—	4	4	no	—
549	D₄	—	8	8	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	16	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	8	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	8	no	—
573	C₂×C₄	—	4	8	no	—
574	C₂×C₄	—	4	8	no	—
575	C₂×C₄	—	8	4	no	—
576	C₂×C₄	—	8	8	no	—
577	C₂×C₄	—	8	4	no	—
578	C₂×C₄	#123×C₁₃₉	1	16	yes	—
579	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
580	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
581	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
582	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
583	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
584	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
585	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
586	C₂²	—	2	4	no	—
587	C₂²	—	2	2	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	4	no	—
590	C₂²	—	2	4	no	—
591	C₂²	—	2	4	no	—
592	C₂²	—	2	4	no	—
593	C₂²	—	4	4	no	—
594	C₂²	—	4	4	no	—
595	C₂²	—	4	2	no	—
596	C₂²	—	4	4	no	—
597	C₂²	—	4	2	no	—
598	C₂²	—	4	2	no	—
599	C₂²	—	4	4	no	—
600	C₂²	C₂×#123×C₁₃₉	1	4	yes	—
601	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
602	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
603	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
604	C₂²	#585×C₁₃₉	1	2	yes	—
605	C₂²	#585×C₁₃₉	1	2	yes	—
606	C₄	—	2	4	no	—
607	C₄	—	4	2	no	—
608	C₄	—	4	2	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	4	no	—
611	C₄	—	4	2	no	—
612	C₄	—	4	4	no	—
613	C₄	—	4	2	no	—
614	C₄	—	4	4	no	—
615	C₄	C₂×#123×C₁₃₉	1	4	yes	—
616	C₄	C₂×#123×C₁₃₉	1	4	yes	—
617	C₂	—	2	4	no	—
618	C₂	—	4	4	no	—
619	C₂	—	8	2	no	—
620	C₂	C₂²×#123×C₁₃₉	1	1	yes	characteristic
621	C₂	#3493×C₁₃₉	1	2	yes	—
622	C₂	#3500×C₁₃₉	1	1	yes	characteristic
623	C₂	#3500×C₁₃₉	1	1	yes	characteristic
624	C₂	#3512×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#537×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
2. C₂×#520×C₁₃₉	C₂	semidirect
3. #2504×C₁₃₉	C₂	semidirect
4. #2503×C₁₃₉	C₂	semidirect
5. #2500×C₁₃₉	C₂	semidirect
6. #2499×C₁₃₉	C₂	semidirect
7. #2444×C₁₃₉	C₂	semidirect
8. #2421×C₁₃₉	C₂	semidirect
9. #2420×C₁₃₉	C₂	semidirect
10. #2317×C₁₃₉	C₂	semidirect
11. #2311×C₁₃₉	C₂	semidirect
12. #2297×C₁₃₉	C₂	semidirect
13. #2297×C₁₃₉	C₂	semidirect
14. C₂×#382×C₁₃₉	C₂	semidirect
312. #35618	C₁₃₉	direct (N × H)
313. C₁₃₉	#35618	direct (N × H)
315. C₂×#520	C₂×C₁₃₉	semidirect
316. #2504	C₂×C₁₃₉	semidirect
317. #2503	C₂×C₁₃₉	semidirect
318. #2500	C₂×C₁₃₉	semidirect
319. #2499	C₂×C₁₃₉	semidirect
320. #2444	C₂×C₁₃₉	semidirect
321. #2421	C₂×C₁₃₉	semidirect
322. #2420	C₂×C₁₃₉	semidirect
323. #2317	C₂×C₁₃₉	semidirect
324. #2311	C₂×C₁₃₉	semidirect
325. #2297	C₂×C₁₃₉	semidirect
326. #2297	C₂×C₁₃₉	semidirect
327. C₂×#382	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#537×C₁₃₉	2
C₂×#520×C₁₃₉	2
#2504×C₁₃₉	2
#2503×C₁₃₉	2
#2500×C₁₃₉	2
#2499×C₁₃₉	2
#2444×C₁₃₉	2
#2421×C₁₃₉	2
#2420×C₁₃₉	2
#2317×C₁₃₉	2
#2311×C₁₃₉	2
#2297×C₁₃₉	2
C₂×#382×C₁₃₉	2
#35618	139

Subgroups — C139×#35618 #48030214

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35618 #48030214