Subgroups — C₁₃₉×#36029 #48030625

Order 35584.

3322 conjugacy classes of subgroups.

The subgroup lattice has 486 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×#520×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2619×C₁₃₉	C₂	1	3	yes	maximal, complemented
5	#2541×C₁₃₉	C₂	1	3	yes	maximal, complemented
6	#2535×C₁₃₉	C₂	1	3	yes	maximal, complemented
7	#2428×C₁₃₉	C₂	1	6	yes	maximal, complemented
8	#2416×C₁₃₉	C₂	1	6	yes	maximal, complemented
9	#2392×C₁₃₉	C₂	1	3	yes	maximal, complemented
10	#2351×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2341×C₁₃₉	C₂	1	2	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	6	yes	—
20	C₂×#121×C₁₃₉	C₂²	1	6	yes	—
21	C₂×#121×C₁₃₉	C₂²	1	12	yes	—
22	#520×C₁₃₉	—	2	8	no	—
23	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	6	yes	—
29	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
30	C₂×#117×C₁₃₉	C₂²	1	3	yes	—
31	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	3	yes	—
32	#398×C₁₃₉	C₂²	1	1	yes	characteristic
33	#397×C₁₃₉	C₂²	1	3	yes	—
34	#396×C₁₃₉	C₂²	1	6	yes	—
35	#394×C₁₃₉	C₂²	1	3	yes	—
36	#394×C₁₃₉	C₂²	1	6	yes	—
37	#394×C₁₃₉	C₂²	1	6	yes	—
38	#392×C₁₃₉	C₂²	1	6	yes	—
39	#392×C₁₃₉	C₂²	1	3	yes	—
40	#392×C₁₃₉	C₂²	1	6	yes	—
41	#390×C₁₃₉	C₂²	1	6	yes	—
42	#390×C₁₃₉	C₂²	1	6	yes	—
43	#389×C₁₃₉	C₂²	1	6	yes	—
44	#386×C₁₃₉	C₂²	1	12	yes	—
45	#382×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	6	yes	—
57	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
58	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
59	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
60	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
61	C₂²×D₄×C₁₃₉	C₂³	1	12	yes	—
62	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
63	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
64	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
65	#127×C₁₃₉	—	2	24	no	—
66	#127×C₁₃₉	—	2	12	no	—
67	#121×C₁₃₉	—	2	24	no	—
68	#121×C₁₃₉	—	2	24	no	—
69	#121×C₁₃₉	—	2	24	no	—
70	#121×C₁₃₉	—	4	24	no	—
71	C₄×Q₈×C₁₃₉	—	2	4	no	—
72	C₄×Q₈×C₁₃₉	—	2	8	no	—
73	C₄×Q₈×C₁₃₉	D₄	1	8	yes	complemented
74	C₄×D₄×C₁₃₉	—	2	24	no	—
75	C₄×D₄×C₁₃₉	—	2	12	no	—
76	C₄×D₄×C₁₃₉	—	2	12	no	—
77	C₄×D₄×C₁₃₉	—	2	12	no	—
78	#117×C₁₃₉	—	2	12	no	—
79	C₂×C₄⋊C₄×C₁₃₉	—	2	12	no	—
80	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
82	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
83	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
86	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
87	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
88	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
89	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
90	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
91	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
92	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
93	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
94	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	12	yes	—
95	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
96	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
97	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
98	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
99	#95×C₁₃₉	C₂³	1	6	yes	—
100	#95×C₁₃₉	C₂³	1	3	yes	—
101	#95×C₁₃₉	C₂³	1	2	yes	—
102	#95×C₁₃₉	C₂³	1	1	yes	characteristic
103	#95×C₁₃₉	C₂³	1	6	yes	—
104	C₂⁴×C₁₃₉	C₂⁴	1	6	yes	—
105	C₂⁴×C₁₃₉	C₂⁴	1	3	yes	—
106	#41×C₁₃₉	—	2	32	no	—
107	#41×C₁₃₉	—	4	32	no	—
108	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
109	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
110	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
111	C₂×D₄×C₁₃₉	—	2	12	no	—
112	C₂×D₄×C₁₃₉	—	2	24	no	—
113	C₂×D₄×C₁₃₉	—	2	6	no	—
114	C₂×D₄×C₁₃₉	—	2	6	no	—
115	C₂×D₄×C₁₃₉	—	2	12	no	—
116	C₂×D₄×C₁₃₉	—	2	12	no	—
117	C₂×D₄×C₁₃₉	—	2	12	no	—
118	C₂×D₄×C₁₃₉	—	2	6	no	—
119	C₂×D₄×C₁₃₉	—	2	12	no	—
120	C₂×D₄×C₁₃₉	—	2	12	no	—
121	C₂×D₄×C₁₃₉	—	4	6	no	—
122	C₂×D₄×C₁₃₉	—	4	6	no	—
123	C₂×D₄×C₁₃₉	—	4	12	no	—
124	C₂×D₄×C₁₃₉	—	4	12	no	—
125	C₂×D₄×C₁₃₉	—	4	12	no	—
126	C₂×D₄×C₁₃₉	C₂×D₄	1	12	yes	—
127	C₂²×C₄×C₁₃₉	—	2	6	no	—
128	C₂²×C₄×C₁₃₉	—	2	6	no	—
129	C₂²×C₄×C₁₃₉	—	2	12	no	—
130	C₂²×C₄×C₁₃₉	—	2	12	no	—
131	C₂²×C₄×C₁₃₉	—	2	12	no	—
132	C₂²×C₄×C₁₃₉	—	2	12	no	—
133	C₂²×C₄×C₁₃₉	—	4	12	no	—
134	C₂²×C₄×C₁₃₉	C₂×D₄	1	12	yes	—
135	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
136	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
139	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
140	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
141	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
142	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
144	C₄⋊C₄×C₁₃₉	—	2	6	no	—
145	C₄⋊C₄×C₁₃₉	—	2	6	no	—
146	C₄⋊C₄×C₁₃₉	—	2	2	no	—
147	C₄⋊C₄×C₁₃₉	—	2	4	no	—
148	C₄⋊C₄×C₁₃₉	—	2	2	no	—
149	C₄⋊C₄×C₁₃₉	—	2	12	no	—
150	C₄⋊C₄×C₁₃₉	—	2	12	no	—
151	C₄⋊C₄×C₁₃₉	C₂×D₄	1	12	yes	—
152	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
153	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
154	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
155	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
156	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
157	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
158	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
159	C₂²⋊C₄×C₁₃₉	—	4	12	no	—
160	C₄²×C₁₃₉	—	2	6	no	—
161	C₄²×C₁₃₉	—	2	12	no	—
162	C₄²×C₁₃₉	C₂×D₄	1	12	yes	—
163	C₂³×C₁₃₉	—	2	3	no	—
164	C₂³×C₁₃₉	—	2	3	no	—
165	C₂³×C₁₃₉	—	2	6	no	—
166	C₂³×C₁₃₉	—	2	6	no	—
167	C₂³×C₁₃₉	—	2	6	no	—
168	C₂³×C₁₃₉	—	2	6	no	—
169	C₂³×C₁₃₉	—	2	6	no	—
170	C₂³×C₁₃₉	—	2	6	no	—
171	C₂³×C₁₃₉	—	2	6	no	—
172	C₂³×C₁₃₉	—	2	6	no	—
173	C₂³×C₁₃₉	—	2	6	no	—
174	C₂³×C₁₃₉	C₂²×D₄	1	6	yes	—
175	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
176	Q₈×C₁₃₉	#121	1	16	yes	complemented
177	D₄×C₁₃₉	—	2	24	no	—
178	D₄×C₁₃₉	—	4	24	no	—
179	D₄×C₁₃₉	—	4	12	no	—
180	D₄×C₁₃₉	—	4	24	no	—
181	D₄×C₁₃₉	—	8	12	no	—
182	D₄×C₁₃₉	—	8	24	no	—
183	C₂×C₄×C₁₃₉	—	2	2	no	—
184	C₂×C₄×C₁₃₉	—	2	1	no	—
185	C₂×C₄×C₁₃₉	—	2	1	no	—
186	C₂×C₄×C₁₃₉	—	2	6	no	—
187	C₂×C₄×C₁₃₉	—	2	2	no	—
188	C₂×C₄×C₁₃₉	—	2	2	no	—
189	C₂×C₄×C₁₃₉	—	2	24	no	—
190	C₂×C₄×C₁₃₉	—	2	1	no	—
191	C₂×C₄×C₁₃₉	—	2	6	no	—
192	C₂×C₄×C₁₃₉	—	2	3	no	—
193	C₂×C₄×C₁₃₉	—	2	2	no	—
194	C₂×C₄×C₁₃₉	—	2	2	no	—
195	C₂×C₄×C₁₃₉	—	2	2	no	—
196	C₂×C₄×C₁₃₉	—	2	6	no	—
197	C₂×C₄×C₁₃₉	—	2	6	no	—
198	C₂×C₄×C₁₃₉	—	2	2	no	—
199	C₂×C₄×C₁₃₉	—	2	6	no	—
200	C₂×C₄×C₁₃₉	—	4	24	no	—
201	C₂×C₄×C₁₃₉	—	8	12	no	—
202	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
203	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
204	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
205	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
206	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
207	C₂×C₄×C₁₃₉	C₂×#41	1	6	yes	—
208	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
209	C₂²×C₁₃₉	—	2	6	no	—
210	C₂²×C₁₃₉	—	2	12	no	—
211	C₂²×C₁₃₉	—	4	3	no	—
212	C₂²×C₁₃₉	—	4	3	no	—
213	C₂²×C₁₃₉	—	4	6	no	—
214	C₂²×C₁₃₉	—	4	6	no	—
215	C₂²×C₁₃₉	—	4	6	no	—
216	C₂²×C₁₃₉	—	4	6	no	—
217	C₂²×C₁₃₉	—	4	6	no	—
218	C₂²×C₁₃₉	—	4	6	no	—
219	C₂²×C₁₃₉	—	4	6	no	—
220	C₂²×C₁₃₉	—	4	6	no	—
221	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
222	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
223	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
224	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
225	C₂²×C₁₃₉	#585	1	2	yes	—
226	C₄×C₁₃₉	—	2	2	no	—
227	C₄×C₁₃₉	—	2	2	no	—
228	C₄×C₁₃₉	—	2	4	no	—
229	C₄×C₁₃₉	—	2	6	no	—
230	C₄×C₁₃₉	—	4	2	no	—
231	C₄×C₁₃₉	—	4	1	no	—
232	C₄×C₁₃₉	—	4	6	no	—
233	C₄×C₁₃₉	—	4	3	no	—
234	C₄×C₁₃₉	C₂×#121	1	12	yes	—
235	C₂×C₁₃₉	—	4	6	no	—
236	C₂×C₁₃₉	—	8	6	no	—
237	C₂×C₁₃₉	C₂²×#121	1	1	yes	characteristic
238	C₂×C₁₃₉	#3487	1	1	yes	characteristic
239	C₂×C₁₃₉	#3488	1	2	yes	—
240	C₂×C₁₃₉	#3498	1	1	yes	characteristic
241	C₂×C₁₃₉	#3517	1	2	yes	—
242	#36029	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₁₃₉	#36029	1	1	yes	characteristic, direct product factor, Sylow
244	C₂×#550	C₂×C₁₃₉	1	2	yes	complemented
245	C₂×#550	C₂×C₁₃₉	1	1	yes	characteristic, complemented
246	C₂×#520	C₂×C₁₃₉	1	1	yes	characteristic, complemented
247	#2619	C₂×C₁₃₉	1	3	yes	complemented
248	#2541	C₂×C₁₃₉	1	3	yes	complemented
249	#2535	C₂×C₁₃₉	1	3	yes	complemented
250	#2428	C₂×C₁₃₉	1	6	yes	complemented
251	#2416	C₂×C₁₃₉	1	6	yes	complemented
252	#2392	C₂×C₁₃₉	1	3	yes	complemented
253	#2351	C₂×C₁₃₉	1	1	yes	characteristic, complemented
254	#2341	C₂×C₁₃₉	1	2	yes	complemented
255	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
256	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
257	#550	—	2	16	no	—
258	#550	—	2	8	no	—
259	C₂×#127	C₂²×C₁₃₉	1	3	yes	—
260	C₂×#127	C₂²×C₁₃₉	1	6	yes	—
261	C₂×#121	C₂²×C₁₃₉	1	6	yes	—
262	C₂×#121	C₂²×C₁₃₉	1	6	yes	—
263	C₂×#121	C₂²×C₁₃₉	1	6	yes	—
264	C₂×#121	C₂²×C₁₃₉	1	12	yes	—
265	#520	—	2	8	no	—
266	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
267	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
268	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
269	C₂×C₄×D₄	C₂²×C₁₃₉	1	6	yes	—
270	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
271	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
272	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
273	C₂×#117	C₂²×C₁₃₉	1	3	yes	—
274	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	3	yes	—
275	#398	C₂²×C₁₃₉	1	1	yes	characteristic
276	#397	C₂²×C₁₃₉	1	3	yes	—
277	#396	C₂²×C₁₃₉	1	6	yes	—
278	#394	C₂²×C₁₃₉	1	3	yes	—
279	#394	C₂²×C₁₃₉	1	6	yes	—
280	#394	C₂²×C₁₃₉	1	6	yes	—
281	#392	C₂²×C₁₃₉	1	6	yes	—
282	#392	C₂²×C₁₃₉	1	6	yes	—
283	#392	C₂²×C₁₃₉	1	3	yes	—
284	#390	C₂²×C₁₃₉	1	6	yes	—
285	#390	C₂²×C₁₃₉	1	6	yes	—
286	#389	C₂²×C₁₃₉	1	6	yes	—
287	#386	C₂²×C₁₃₉	1	12	yes	—
288	#382	C₂²×C₁₃₉	1	3	yes	—
289	#380	C₂²×C₁₃₉	1	6	yes	—
290	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	3	yes	—
291	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	—
292	C₂×#41	—	2	4	no	—
293	C₂×#41	—	2	8	no	—
294	C₂×#41	—	2	8	no	—
295	C₂×#41	—	2	4	no	—
296	C₂×#41	—	2	8	no	—
297	C₂×#41	D₄×C₁₃₉	1	8	yes	complemented
298	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
299	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
300	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
301	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
302	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
303	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
304	C₂²×D₄	C₂³×C₁₃₉	1	12	yes	—
305	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
306	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
307	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
308	#127	—	2	24	no	—
309	#127	—	2	12	no	—
310	#121	—	2	24	no	—
311	#121	—	2	24	no	—
312	#121	—	2	24	no	—
313	#121	—	4	24	no	—
314	C₄×Q₈	—	2	4	no	—
315	C₄×Q₈	—	2	8	no	—
316	C₄×Q₈	D₄×C₁₃₉	1	8	yes	complemented
317	C₄×D₄	—	2	24	no	—
318	C₄×D₄	—	2	12	no	—
319	C₄×D₄	—	2	12	no	—
320	C₄×D₄	—	2	12	no	—
321	#117	—	2	12	no	—
322	C₂×C₄⋊C₄	—	2	12	no	—
323	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
324	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
325	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
329	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
330	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
331	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
332	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
333	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
334	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
335	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
336	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
337	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	12	yes	—
338	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
339	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
340	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
341	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
342	#95	C₂³×C₁₃₉	1	2	yes	—
343	#95	C₂³×C₁₃₉	1	6	yes	—
344	#95	C₂³×C₁₃₉	1	1	yes	characteristic
345	#95	C₂³×C₁₃₉	1	3	yes	—
346	#95	C₂³×C₁₃₉	1	6	yes	—
347	C₂⁴	C₂⁴×C₁₃₉	1	6	yes	—
348	C₂⁴	C₂⁴×C₁₃₉	1	3	yes	—
349	#41	—	2	32	no	—
350	#41	—	4	32	no	—
351	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
352	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
353	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
354	C₂×D₄	—	2	12	no	—
355	C₂×D₄	—	2	24	no	—
356	C₂×D₄	—	2	6	no	—
357	C₂×D₄	—	2	6	no	—
358	C₂×D₄	—	2	12	no	—
359	C₂×D₄	—	2	12	no	—
360	C₂×D₄	—	2	12	no	—
361	C₂×D₄	—	2	6	no	—
362	C₂×D₄	—	2	12	no	—
363	C₂×D₄	—	2	12	no	—
364	C₂×D₄	—	4	6	no	—
365	C₂×D₄	—	4	6	no	—
366	C₂×D₄	—	4	12	no	—
367	C₂×D₄	—	4	12	no	—
368	C₂×D₄	—	4	12	no	—
369	C₂×D₄	C₂×D₄×C₁₃₉	1	12	yes	—
370	C₂²×C₄	—	2	6	no	—
371	C₂²×C₄	—	2	6	no	—
372	C₂²×C₄	—	2	12	no	—
373	C₂²×C₄	—	2	12	no	—
374	C₂²×C₄	—	2	12	no	—
375	C₂²×C₄	—	2	12	no	—
376	C₂²×C₄	—	4	12	no	—
377	C₂²×C₄	C₂×D₄×C₁₃₉	1	12	yes	—
378	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
379	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
380	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
381	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
382	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
383	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
384	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
385	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
386	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
387	C₄⋊C₄	—	2	6	no	—
388	C₄⋊C₄	—	2	6	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	12	no	—
393	C₄⋊C₄	—	2	12	no	—
394	C₄⋊C₄	C₂×D₄×C₁₃₉	1	12	yes	—
395	C₂²⋊C₄	—	2	12	no	—
396	C₂²⋊C₄	—	2	6	no	—
397	C₂²⋊C₄	—	2	6	no	—
398	C₂²⋊C₄	—	2	12	no	—
399	C₂²⋊C₄	—	2	12	no	—
400	C₂²⋊C₄	—	2	12	no	—
401	C₂²⋊C₄	—	4	6	no	—
402	C₂²⋊C₄	—	4	12	no	—
403	C₄²	—	2	6	no	—
404	C₄²	—	2	12	no	—
405	C₄²	C₂×D₄×C₁₃₉	1	12	yes	—
406	C₂³	—	2	3	no	—
407	C₂³	—	2	3	no	—
408	C₂³	—	2	6	no	—
409	C₂³	—	2	6	no	—
410	C₂³	—	2	6	no	—
411	C₂³	—	2	6	no	—
412	C₂³	—	2	6	no	—
413	C₂³	—	2	6	no	—
414	C₂³	—	2	6	no	—
415	C₂³	—	2	6	no	—
416	C₂³	—	2	6	no	—
417	C₂³	C₂²×D₄×C₁₃₉	1	6	yes	—
418	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
419	Q₈	#121×C₁₃₉	1	16	yes	complemented
420	D₄	—	2	24	no	—
421	D₄	—	4	24	no	—
422	D₄	—	4	12	no	—
423	D₄	—	4	24	no	—
424	D₄	—	8	12	no	—
425	D₄	—	8	24	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	6	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	24	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	6	no	—
435	C₂×C₄	—	2	3	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	6	no	—
440	C₂×C₄	—	2	6	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	6	no	—
443	C₂×C₄	—	4	24	no	—
444	C₂×C₄	—	8	12	no	—
445	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
446	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
447	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
448	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
449	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
450	C₂×C₄	C₂×#41×C₁₃₉	1	6	yes	—
451	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
452	C₂²	—	2	6	no	—
453	C₂²	—	2	12	no	—
454	C₂²	—	4	3	no	—
455	C₂²	—	4	3	no	—
456	C₂²	—	4	6	no	—
457	C₂²	—	4	6	no	—
458	C₂²	—	4	6	no	—
459	C₂²	—	4	6	no	—
460	C₂²	—	4	6	no	—
461	C₂²	—	4	6	no	—
462	C₂²	—	4	6	no	—
463	C₂²	—	4	6	no	—
464	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
465	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
466	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
467	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
468	C₂²	#585×C₁₃₉	1	2	yes	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	4	no	—
472	C₄	—	2	6	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	6	no	—
476	C₄	—	4	3	no	—
477	C₄	C₂×#121×C₁₃₉	1	12	yes	—
478	C₂	—	4	6	no	—
479	C₂	—	8	6	no	—
480	C₂	C₂²×#121×C₁₃₉	1	1	yes	characteristic
481	C₂	#3487×C₁₃₉	1	1	yes	characteristic
482	C₂	#3488×C₁₃₉	1	2	yes	—
483	C₂	#3498×C₁₃₉	1	1	yes	characteristic
484	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×#550×C₁₃₉	C₂	semidirect
3. C₂×#520×C₁₃₉	C₂	semidirect
4. #2619×C₁₃₉	C₂	semidirect
5. #2541×C₁₃₉	C₂	semidirect
6. #2535×C₁₃₉	C₂	semidirect
7. #2428×C₁₃₉	C₂	semidirect
8. #2416×C₁₃₉	C₂	semidirect
9. #2392×C₁₃₉	C₂	semidirect
10. #2351×C₁₃₉	C₂	semidirect
11. #2341×C₁₃₉	C₂	semidirect
54. C₂×#41×C₁₃₉	D₄	semidirect
73. C₄×Q₈×C₁₃₉	D₄	semidirect
176. Q₈×C₁₃₉	#121	semidirect
242. #36029	C₁₃₉	direct (N × H)
243. C₁₃₉	#36029	direct (N × H)
244. C₂×#550	C₂×C₁₃₉	semidirect
245. C₂×#550	C₂×C₁₃₉	semidirect
246. C₂×#520	C₂×C₁₃₉	semidirect
247. #2619	C₂×C₁₃₉	semidirect
248. #2541	C₂×C₁₃₉	semidirect
249. #2535	C₂×C₁₃₉	semidirect
250. #2428	C₂×C₁₃₉	semidirect
251. #2416	C₂×C₁₃₉	semidirect
252. #2392	C₂×C₁₃₉	semidirect
253. #2351	C₂×C₁₃₉	semidirect
254. #2341	C₂×C₁₃₉	semidirect
297. C₂×#41	D₄×C₁₃₉	semidirect
316. C₄×Q₈	D₄×C₁₃₉	semidirect
419. Q₈	#121×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×#520×C₁₃₉	2
#2619×C₁₃₉	2
#2541×C₁₃₉	2
#2535×C₁₃₉	2
#2428×C₁₃₉	2
#2416×C₁₃₉	2
#2392×C₁₃₉	2
#2351×C₁₃₉	2
#2341×C₁₃₉	2
#36029	139

Subgroups — C139×#36029 #48030625

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36029 #48030625