Subgroups — C₁₃₉×#37258 #48031854

Order 35584.

2314 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#536×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2853×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2734×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2731×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2729×C₁₃₉	C₂	1	8	yes	maximal, complemented
7	#2614×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2484×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2413×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2406×C₁₃₉	C₂	1	2	yes	maximal
11	#2310×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
15	#536×C₁₃₉	—	2	8	no	—
16	C₂×C₄⋊Q₈×C₁₃₉	—	2	8	no	—
17	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
18	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
19	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
25	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
27	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
28	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
29	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
30	#400×C₁₃₉	C₂²	1	4	yes	—
31	#398×C₁₃₉	C₂²	1	8	yes	—
32	#398×C₁₃₉	C₂²	1	4	yes	—
33	#396×C₁₃₉	C₂²	1	8	yes	—
34	#395×C₁₃₉	C₂²	1	8	yes	—
35	#395×C₁₃₉	C₂²	1	4	yes	—
36	#394×C₁₃₉	C₂²	1	4	yes	—
37	#393×C₁₃₉	C₂²	1	8	yes	—
38	#391×C₁₃₉	C₂²	1	4	yes	—
39	#391×C₁₃₉	C₂²	1	4	yes	—
40	#389×C₁₃₉	C₂²	1	8	yes	—
41	#388×C₁₃₉	C₂²	1	8	yes	—
42	#388×C₁₃₉	C₂²	1	8	yes	—
43	#387×C₁₃₉	C₂²	1	8	yes	—
44	#387×C₁₃₉	C₂²	1	8	yes	—
45	#386×C₁₃₉	C₂²	1	4	yes	—
46	#385×C₁₃₉	C₂²	1	4	yes	—
47	#385×C₁₃₉	C₂²	1	8	yes	—
48	#381×C₁₃₉	C₂²	1	2	yes	—
49	#381×C₁₃₉	C₂²	1	2	yes	—
50	#381×C₁₃₉	C₂²	1	4	yes	—
51	C₂×#41×C₁₃₉	—	2	4	no	—
52	C₂×#41×C₁₃₉	—	4	4	no	—
53	C₂²×Q₈×C₁₃₉	—	2	4	no	—
54	C₂²×Q₈×C₁₃₉	—	4	4	no	—
55	C₂²×Q₈×C₁₃₉	—	4	4	no	—
56	C₂²×Q₈×C₁₃₉	D₄	1	8	yes	—
57	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
58	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
59	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
60	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
61	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
62	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
69	C₄⋊Q₈×C₁₃₉	—	2	16	no	—
70	C₄⋊Q₈×C₁₃₉	—	2	16	no	—
71	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
72	#124×C₁₃₉	—	2	8	no	—
73	#123×C₁₃₉	—	2	8	no	—
74	#123×C₁₃₉	—	2	8	no	—
75	#123×C₁₃₉	—	4	8	no	—
76	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
77	#117×C₁₃₉	—	2	4	no	—
78	#117×C₁₃₉	—	4	4	no	—
79	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
80	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
81	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
82	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
84	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
85	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
89	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
90	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
91	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
92	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
93	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
96	C₂×C₄²×C₁₃₉	—	2	4	no	—
97	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
98	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
99	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
100	#95×C₁₃₉	C₂³	1	8	yes	—
101	#95×C₁₃₉	C₂³	1	8	yes	—
102	#95×C₁₃₉	C₂³	1	8	yes	—
103	#95×C₁₃₉	C₂³	1	4	yes	—
104	#95×C₁₃₉	C₂³	1	8	yes	—
105	#95×C₁₃₉	C₂³	1	4	yes	—
106	#95×C₁₃₉	C₂³	1	8	yes	—
107	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
108	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
109	#41×C₁₃₉	—	4	16	no	—
110	C₂×Q₈×C₁₃₉	—	2	8	no	—
111	C₂×Q₈×C₁₃₉	—	2	2	no	—
112	C₂×Q₈×C₁₃₉	—	4	16	no	—
113	C₂×Q₈×C₁₃₉	—	4	2	no	—
114	C₂×Q₈×C₁₃₉	—	4	2	no	—
115	C₂×Q₈×C₁₃₉	—	4	2	no	—
116	C₂×Q₈×C₁₃₉	—	4	2	no	—
117	C₂×Q₈×C₁₃₉	—	4	4	no	—
118	C₂×Q₈×C₁₃₉	—	4	4	no	—
119	C₂×Q₈×C₁₃₉	—	4	2	no	—
120	C₂×Q₈×C₁₃₉	—	4	16	no	—
121	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
122	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
123	C₂×D₄×C₁₃₉	—	2	4	no	—
124	C₂×D₄×C₁₃₉	—	2	8	no	—
125	C₂×D₄×C₁₃₉	—	2	2	no	—
126	C₂×D₄×C₁₃₉	—	4	2	no	—
127	C₂²×C₄×C₁₃₉	—	2	4	no	—
128	C₂²×C₄×C₁₃₉	—	2	4	no	—
129	C₂²×C₄×C₁₃₉	—	2	4	no	—
130	C₂²×C₄×C₁₃₉	—	2	4	no	—
131	C₂²×C₄×C₁₃₉	—	2	8	no	—
132	C₂²×C₄×C₁₃₉	—	2	4	no	—
133	C₂²×C₄×C₁₃₉	—	2	8	no	—
134	C₂²×C₄×C₁₃₉	—	2	4	no	—
135	C₂²×C₄×C₁₃₉	—	4	4	no	—
136	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
137	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
139	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
140	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
141	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
145	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
146	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
148	C₄⋊C₄×C₁₃₉	—	2	8	no	—
149	C₄⋊C₄×C₁₃₉	—	2	16	no	—
150	C₄⋊C₄×C₁₃₉	—	2	8	no	—
151	C₄⋊C₄×C₁₃₉	—	2	4	no	—
152	C₄⋊C₄×C₁₃₉	—	2	8	no	—
153	C₄⋊C₄×C₁₃₉	—	2	8	no	—
154	C₄⋊C₄×C₁₃₉	—	2	16	no	—
155	C₄⋊C₄×C₁₃₉	—	4	4	no	—
156	C₄⋊C₄×C₁₃₉	—	4	8	no	—
157	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
158	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
159	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
160	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
161	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
162	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
163	C₄²×C₁₃₉	—	2	8	no	—
164	C₄²×C₁₃₉	—	2	4	no	—
165	C₄²×C₁₃₉	—	4	4	no	—
166	C₂³×C₁₃₉	—	2	4	no	—
167	C₂³×C₁₃₉	—	2	2	no	—
168	C₂³×C₁₃₉	—	2	4	no	—
169	C₂³×C₁₃₉	—	2	8	no	—
170	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
171	C₂³×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
172	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
173	Q₈×C₁₃₉	—	4	8	no	—
174	Q₈×C₁₃₉	—	4	8	no	—
175	Q₈×C₁₃₉	—	4	16	no	—
176	Q₈×C₁₃₉	—	4	4	no	—
177	D₄×C₁₃₉	—	4	4	no	—
178	D₄×C₁₃₉	—	4	8	no	—
179	C₂×C₄×C₁₃₉	—	2	16	no	—
180	C₂×C₄×C₁₃₉	—	2	8	no	—
181	C₂×C₄×C₁₃₉	—	2	8	no	—
182	C₂×C₄×C₁₃₉	—	2	8	no	—
183	C₂×C₄×C₁₃₉	—	2	4	no	—
184	C₂×C₄×C₁₃₉	—	2	2	no	—
185	C₂×C₄×C₁₃₉	—	2	2	no	—
186	C₂×C₄×C₁₃₉	—	2	2	no	—
187	C₂×C₄×C₁₃₉	—	2	2	no	—
188	C₂×C₄×C₁₃₉	—	2	2	no	—
189	C₂×C₄×C₁₃₉	—	2	2	no	—
190	C₂×C₄×C₁₃₉	—	2	4	no	—
191	C₂×C₄×C₁₃₉	—	2	4	no	—
192	C₂×C₄×C₁₃₉	—	2	2	no	—
193	C₂×C₄×C₁₃₉	—	2	4	no	—
194	C₂×C₄×C₁₃₉	—	2	8	no	—
195	C₂×C₄×C₁₃₉	—	2	8	no	—
196	C₂×C₄×C₁₃₉	—	2	4	no	—
197	C₂×C₄×C₁₃₉	—	2	8	no	—
198	C₂×C₄×C₁₃₉	—	2	8	no	—
199	C₂×C₄×C₁₃₉	—	2	8	no	—
200	C₂×C₄×C₁₃₉	—	4	8	no	—
201	C₂×C₄×C₁₃₉	—	4	8	no	—
202	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
203	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
204	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
205	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
206	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	8	yes	—
207	C₂²×C₁₃₉	—	2	4	no	—
208	C₂²×C₁₃₉	—	2	8	no	—
209	C₂²×C₁₃₉	—	4	2	no	—
210	C₂²×C₁₃₉	—	4	4	no	—
211	C₂²×C₁₃₉	—	4	8	no	—
212	C₂²×C₁₃₉	#534	1	4	yes	—
213	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
214	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
215	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	4	yes	—
216	C₄×C₁₃₉	—	2	2	no	—
217	C₄×C₁₃₉	—	2	2	no	—
218	C₄×C₁₃₉	—	2	4	no	—
219	C₄×C₁₃₉	—	2	4	no	—
220	C₄×C₁₃₉	—	2	8	no	—
221	C₄×C₁₃₉	—	4	2	no	—
222	C₄×C₁₃₉	—	4	4	no	—
223	C₄×C₁₃₉	—	4	4	no	—
224	C₄×C₁₃₉	—	4	8	no	—
225	C₂×C₁₃₉	—	2	4	no	—
226	C₂×C₁₃₉	—	8	2	no	—
227	C₂×C₁₃₉	C₂×#534	1	1	yes	characteristic
228	C₂×C₁₃₉	#3486	1	2	yes	—
229	C₂×C₁₃₉	#3544	1	4	yes	—
230	#37258	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₁₃₉	#37258	1	1	yes	characteristic, direct product factor, Sylow
232	C₂×#536	C₂×C₁₃₉	1	1	yes	characteristic
233	C₂²×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
234	#2853	C₂×C₁₃₉	1	2	yes	complemented
235	#2734	C₂×C₁₃₉	1	4	yes	complemented
236	#2731	C₂×C₁₃₉	1	4	yes	complemented
237	#2729	C₂×C₁₃₉	1	8	yes	complemented
238	#2614	C₂×C₁₃₉	1	2	yes	complemented
239	#2484	C₂×C₁₃₉	1	2	yes	complemented
240	#2413	C₂×C₁₃₉	1	4	yes	complemented
241	#2406	C₂×C₁₃₉	1	2	yes	—
242	#2310	C₂×C₁₃₉	1	1	yes	characteristic, complemented
243	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
244	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
245	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
246	#536	—	2	8	no	—
247	C₂×C₄⋊Q₈	—	2	8	no	—
248	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
249	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
250	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
251	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
252	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
253	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
254	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
255	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
256	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
257	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
258	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
259	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
260	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
261	#400	C₂²×C₁₃₉	1	4	yes	—
262	#398	C₂²×C₁₃₉	1	8	yes	—
263	#398	C₂²×C₁₃₉	1	4	yes	—
264	#396	C₂²×C₁₃₉	1	8	yes	—
265	#395	C₂²×C₁₃₉	1	8	yes	—
266	#395	C₂²×C₁₃₉	1	4	yes	—
267	#394	C₂²×C₁₃₉	1	4	yes	—
268	#393	C₂²×C₁₃₉	1	8	yes	—
269	#391	C₂²×C₁₃₉	1	4	yes	—
270	#391	C₂²×C₁₃₉	1	4	yes	—
271	#389	C₂²×C₁₃₉	1	8	yes	—
272	#388	C₂²×C₁₃₉	1	8	yes	—
273	#388	C₂²×C₁₃₉	1	8	yes	—
274	#387	C₂²×C₁₃₉	1	8	yes	—
275	#387	C₂²×C₁₃₉	1	8	yes	—
276	#386	C₂²×C₁₃₉	1	4	yes	—
277	#385	C₂²×C₁₃₉	1	4	yes	—
278	#385	C₂²×C₁₃₉	1	8	yes	—
279	#381	C₂²×C₁₃₉	1	2	yes	—
280	#381	C₂²×C₁₃₉	1	2	yes	—
281	#381	C₂²×C₁₃₉	1	4	yes	—
282	C₂×#41	—	2	4	no	—
283	C₂×#41	—	4	4	no	—
284	C₂²×Q₈	—	2	4	no	—
285	C₂²×Q₈	—	4	4	no	—
286	C₂²×Q₈	—	4	4	no	—
287	C₂²×Q₈	D₄×C₁₃₉	1	8	yes	—
288	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
289	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
290	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
291	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
292	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
293	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
294	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
295	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
296	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
297	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
298	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
299	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
300	C₄⋊Q₈	—	2	16	no	—
301	C₄⋊Q₈	—	2	16	no	—
302	C₄⋊Q₈	—	2	8	no	—
303	#124	—	2	8	no	—
304	#123	—	2	8	no	—
305	#123	—	2	8	no	—
306	#123	—	4	8	no	—
307	C₂²⋊Q₈	—	2	16	no	—
308	#117	—	2	4	no	—
309	#117	—	4	4	no	—
310	C₂×C₄⋊C₄	—	2	8	no	—
311	C₂×C₄⋊C₄	—	2	8	no	—
312	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
314	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
318	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
320	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
321	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
322	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
323	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
324	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
325	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
326	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
327	C₂×C₄²	—	2	4	no	—
328	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
329	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
330	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
331	#95	C₂³×C₁₃₉	1	4	yes	—
332	#95	C₂³×C₁₃₉	1	4	yes	—
333	#95	C₂³×C₁₃₉	1	8	yes	—
334	#95	C₂³×C₁₃₉	1	8	yes	—
335	#95	C₂³×C₁₃₉	1	8	yes	—
336	#95	C₂³×C₁₃₉	1	8	yes	—
337	#95	C₂³×C₁₃₉	1	8	yes	—
338	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
339	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
340	#41	—	4	16	no	—
341	C₂×Q₈	—	2	8	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	4	16	no	—
344	C₂×Q₈	—	4	2	no	—
345	C₂×Q₈	—	4	2	no	—
346	C₂×Q₈	—	4	2	no	—
347	C₂×Q₈	—	4	2	no	—
348	C₂×Q₈	—	4	4	no	—
349	C₂×Q₈	—	4	4	no	—
350	C₂×Q₈	—	4	2	no	—
351	C₂×Q₈	—	4	16	no	—
352	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
353	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	8	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	8	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	4	4	no	—
367	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
368	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
369	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
370	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
371	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
372	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
373	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
374	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
375	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
376	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
377	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
378	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
379	C₄⋊C₄	—	2	8	no	—
380	C₄⋊C₄	—	2	16	no	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	8	no	—
385	C₄⋊C₄	—	2	16	no	—
386	C₄⋊C₄	—	4	4	no	—
387	C₄⋊C₄	—	4	8	no	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	2	8	no	—
390	C₂²⋊C₄	—	2	8	no	—
391	C₂²⋊C₄	—	2	8	no	—
392	C₂²⋊C₄	—	2	16	no	—
393	C₂²⋊C₄	—	4	8	no	—
394	C₄²	—	2	8	no	—
395	C₄²	—	2	4	no	—
396	C₄²	—	4	4	no	—
397	C₂³	—	2	4	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	4	no	—
400	C₂³	—	2	8	no	—
401	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
402	C₂³	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
403	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
404	Q₈	—	4	8	no	—
405	Q₈	—	4	8	no	—
406	Q₈	—	4	16	no	—
407	Q₈	—	4	4	no	—
408	D₄	—	4	4	no	—
409	D₄	—	4	8	no	—
410	C₂×C₄	—	2	16	no	—
411	C₂×C₄	—	2	8	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	8	no	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	8	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	8	no	—
431	C₂×C₄	—	4	8	no	—
432	C₂×C₄	—	4	8	no	—
433	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
434	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
435	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
436	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
437	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	8	yes	—
438	C₂²	—	2	8	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	4	8	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	4	no	—
443	C₂²	#534×C₁₃₉	1	4	yes	—
444	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
445	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
446	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	4	yes	—
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	4	no	—
450	C₄	—	2	4	no	—
451	C₄	—	2	8	no	—
452	C₄	—	4	8	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	4	no	—
455	C₄	—	4	4	no	—
456	C₂	—	2	4	no	—
457	C₂	—	8	2	no	—
458	C₂	C₂×#534×C₁₃₉	1	1	yes	characteristic
459	C₂	#3486×C₁₃₉	1	2	yes	—
460	C₂	#3544×C₁₃₉	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×#41×C₁₃₉	C₂²
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. C₂²×C₄⋊Q₈×C₁₃₉	C₂	semidirect
3. #2853×C₁₃₉	C₂	semidirect
4. #2734×C₁₃₉	C₂	semidirect
5. #2731×C₁₃₉	C₂	semidirect
6. #2729×C₁₃₉	C₂	semidirect
7. #2614×C₁₃₉	C₂	semidirect
8. #2484×C₁₃₉	C₂	semidirect
9. #2413×C₁₃₉	C₂	semidirect
11. #2310×C₁₃₉	C₂	semidirect
230. #37258	C₁₃₉	direct (N × H)
231. C₁₃₉	#37258	direct (N × H)
233. C₂²×C₄⋊Q₈	C₂×C₁₃₉	semidirect
234. #2853	C₂×C₁₃₉	semidirect
235. #2734	C₂×C₁₃₉	semidirect
236. #2731	C₂×C₁₃₉	semidirect
237. #2729	C₂×C₁₃₉	semidirect
238. #2614	C₂×C₁₃₉	semidirect
239. #2484	C₂×C₁₃₉	semidirect
240. #2413	C₂×C₁₃₉	semidirect
242. #2310	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×#536×C₁₃₉	2
C₂²×C₄⋊Q₈×C₁₃₉	2
#2853×C₁₃₉	2
#2734×C₁₃₉	2
#2731×C₁₃₉	2
#2729×C₁₃₉	2
#2614×C₁₃₉	2
#2484×C₁₃₉	2
#2413×C₁₃₉	2
#2406×C₁₃₉	2
#2310×C₁₃₉	2
#37258	139

Subgroups — C139×#37258 #48031854

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37258 #48031854