Subgroups — C₁₃₉×#36412 #48031008

Order 35584.

2838 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#555×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#550×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2858×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2856×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2567×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2555×C₁₃₉	C₂	1	8	yes	maximal, complemented
7	#2541×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2500×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2431×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2428×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2363×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	C₄×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2297×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
16	#555×C₁₃₉	—	2	8	no	—
17	#550×C₁₃₉	—	2	8	no	—
18	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
23	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
25	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
26	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
27	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#121×C₁₃₉	C₂²	1	8	yes	—
31	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
37	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
38	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
39	#395×C₁₃₉	C₂²	1	4	yes	—
40	#394×C₁₃₉	C₂²	1	8	yes	—
41	#392×C₁₃₉	C₂²	1	4	yes	—
42	#392×C₁₃₉	C₂²	1	8	yes	—
43	#391×C₁₃₉	C₂²	1	1	yes	characteristic
44	#391×C₁₃₉	C₂²	1	2	yes	—
45	#390×C₁₃₉	C₂²	1	2	yes	—
46	#390×C₁₃₉	C₂²	1	2	yes	—
47	#390×C₁₃₉	C₂²	1	8	yes	—
48	#390×C₁₃₉	C₂²	1	1	yes	characteristic
49	#390×C₁₃₉	C₂²	1	4	yes	—
50	#390×C₁₃₉	C₂²	1	2	yes	—
51	#389×C₁₃₉	C₂²	1	4	yes	—
52	#388×C₁₃₉	C₂²	1	4	yes	—
53	#388×C₁₃₉	C₂²	1	8	yes	—
54	#386×C₁₃₉	C₂²	1	8	yes	—
55	#386×C₁₃₉	C₂²	1	8	yes	—
56	#384×C₁₃₉	C₂²	1	2	yes	—
57	#382×C₁₃₉	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
59	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
60	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
61	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
62	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	8	yes	—
63	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
64	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
65	C₂×#41×C₁₃₉	—	2	8	no	—
66	C₂×#41×C₁₃₉	—	2	8	no	—
67	C₂×#41×C₁₃₉	—	4	4	no	—
68	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
70	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
72	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
73	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
74	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
76	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
77	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
78	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
79	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
80	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
81	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
82	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
83	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
84	#127×C₁₃₉	—	2	8	no	—
85	#127×C₁₃₉	—	2	4	no	—
86	#127×C₁₃₉	—	4	4	no	—
87	#124×C₁₃₉	—	2	4	no	—
88	#124×C₁₃₉	—	2	16	no	—
89	#124×C₁₃₉	—	4	8	no	—
90	#121×C₁₃₉	—	2	8	no	—
91	#121×C₁₃₉	—	2	8	no	—
92	#121×C₁₃₉	—	2	8	no	—
93	#121×C₁₃₉	—	2	16	no	—
94	#121×C₁₃₉	—	2	16	no	—
95	#121×C₁₃₉	—	4	16	no	—
96	C₄×Q₈×C₁₃₉	—	2	4	no	—
97	C₄×D₄×C₁₃₉	—	2	8	no	—
98	C₄×D₄×C₁₃₉	—	2	8	no	—
99	C₄×D₄×C₁₃₉	—	2	4	no	—
100	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
101	#117×C₁₃₉	—	2	8	no	—
102	#117×C₁₃₉	—	2	8	no	—
103	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
109	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
113	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
116	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
117	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
118	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	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×C₄²×C₁₃₉	—	4	4	no	—
123	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
126	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
131	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
132	#95×C₁₃₉	C₂³	1	2	yes	—
133	#95×C₁₃₉	C₂³	1	8	yes	—
134	#95×C₁₃₉	C₂³	1	4	yes	—
135	#95×C₁₃₉	C₂³	1	4	yes	—
136	#95×C₁₃₉	C₂³	1	4	yes	—
137	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
138	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
139	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
140	#41×C₁₃₉	—	4	32	no	—
141	C₂×Q₈×C₁₃₉	—	2	2	no	—
142	C₂×Q₈×C₁₃₉	—	2	4	no	—
143	C₂×Q₈×C₁₃₉	—	2	2	no	—
144	C₂×Q₈×C₁₃₉	—	4	4	no	—
145	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
146	C₂×D₄×C₁₃₉	—	2	8	no	—
147	C₂×D₄×C₁₃₉	—	2	8	no	—
148	C₂×D₄×C₁₃₉	—	2	8	no	—
149	C₂×D₄×C₁₃₉	—	2	2	no	—
150	C₂×D₄×C₁₃₉	—	2	4	no	—
151	C₂×D₄×C₁₃₉	—	2	4	no	—
152	C₂×D₄×C₁₃₉	—	2	4	no	—
153	C₂×D₄×C₁₃₉	—	2	4	no	—
154	C₂×D₄×C₁₃₉	—	2	8	no	—
155	C₂×D₄×C₁₃₉	—	2	2	no	—
156	C₂×D₄×C₁₃₉	—	2	8	no	—
157	C₂×D₄×C₁₃₉	—	2	4	no	—
158	C₂×D₄×C₁₃₉	—	2	16	no	—
159	C₂×D₄×C₁₃₉	—	2	2	no	—
160	C₂×D₄×C₁₃₉	—	2	4	no	—
161	C₂×D₄×C₁₃₉	—	4	4	no	—
162	C₂×D₄×C₁₃₉	—	4	8	no	—
163	C₂×D₄×C₁₃₉	—	4	8	no	—
164	C₂×D₄×C₁₃₉	—	4	8	no	—
165	C₂×D₄×C₁₃₉	—	4	4	no	—
166	C₂×D₄×C₁₃₉	—	4	8	no	—
167	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
168	C₂²×C₄×C₁₃₉	—	2	4	no	—
169	C₂²×C₄×C₁₃₉	—	2	4	no	—
170	C₂²×C₄×C₁₃₉	—	2	4	no	—
171	C₂²×C₄×C₁₃₉	—	2	8	no	—
172	C₂²×C₄×C₁₃₉	—	2	8	no	—
173	C₂²×C₄×C₁₃₉	—	2	8	no	—
174	C₂²×C₄×C₁₃₉	—	2	8	no	—
175	C₂²×C₄×C₁₃₉	—	2	8	no	—
176	C₂²×C₄×C₁₃₉	—	4	4	no	—
177	C₂²×C₄×C₁₃₉	—	4	4	no	—
178	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
179	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
185	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
190	C₄⋊C₄×C₁₃₉	—	2	2	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	—	4	8	no	—
196	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
197	C₄⋊C₄×C₁₃₉	#41	1	8	yes	complemented
198	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
199	C₂²⋊C₄×C₁₃₉	—	2	8	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	—	2	16	no	—
204	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
205	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
206	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
207	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
208	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
209	C₄²×C₁₃₉	—	2	8	no	—
210	C₄²×C₁₃₉	—	2	4	no	—
211	C₄²×C₁₃₉	—	2	4	no	—
212	C₄²×C₁₃₉	—	2	2	no	—
213	C₄²×C₁₃₉	—	2	2	no	—
214	C₄²×C₁₃₉	—	2	4	no	—
215	C₄²×C₁₃₉	—	2	4	no	—
216	C₄²×C₁₃₉	—	4	4	no	—
217	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
218	C₂³×C₁₃₉	—	2	4	no	—
219	C₂³×C₁₃₉	—	2	2	no	—
220	C₂³×C₁₃₉	—	2	2	no	—
221	C₂³×C₁₃₉	—	2	4	no	—
222	C₂³×C₁₃₉	—	2	2	no	—
223	C₂³×C₁₃₉	—	2	4	no	—
224	C₂³×C₁₃₉	—	2	2	no	—
225	C₂³×C₁₃₉	—	2	8	no	—
226	C₂³×C₁₃₉	—	2	4	no	—
227	C₂³×C₁₃₉	—	2	4	no	—
228	C₂³×C₁₃₉	—	2	8	no	—
229	C₂³×C₁₃₉	—	2	4	no	—
230	C₂³×C₁₃₉	—	2	4	no	—
231	C₂³×C₁₃₉	—	2	2	no	—
232	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
233	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
234	Q₈×C₁₃₉	—	2	8	no	—
235	Q₈×C₁₃₉	—	8	4	no	—
236	D₄×C₁₃₉	—	2	8	no	—
237	D₄×C₁₃₉	—	4	16	no	—
238	D₄×C₁₃₉	—	4	8	no	—
239	D₄×C₁₃₉	—	4	4	no	—
240	D₄×C₁₃₉	—	4	8	no	—
241	D₄×C₁₃₉	—	8	4	no	—
242	D₄×C₁₃₉	—	8	16	no	—
243	D₄×C₁₃₉	—	8	8	no	—
244	D₄×C₁₃₉	—	8	8	no	—
245	C₂×C₄×C₁₃₉	—	2	2	no	—
246	C₂×C₄×C₁₃₉	—	2	2	no	—
247	C₂×C₄×C₁₃₉	—	2	2	no	—
248	C₂×C₄×C₁₃₉	—	2	2	no	—
249	C₂×C₄×C₁₃₉	—	2	4	no	—
250	C₂×C₄×C₁₃₉	—	2	2	no	—
251	C₂×C₄×C₁₃₉	—	2	2	no	—
252	C₂×C₄×C₁₃₉	—	2	4	no	—
253	C₂×C₄×C₁₃₉	—	2	2	no	—
254	C₂×C₄×C₁₃₉	—	2	16	no	—
255	C₂×C₄×C₁₃₉	—	2	2	no	—
256	C₂×C₄×C₁₃₉	—	2	2	no	—
257	C₂×C₄×C₁₃₉	—	2	4	no	—
258	C₂×C₄×C₁₃₉	—	2	2	no	—
259	C₂×C₄×C₁₃₉	—	2	2	no	—
260	C₂×C₄×C₁₃₉	—	2	4	no	—
261	C₂×C₄×C₁₃₉	—	2	2	no	—
262	C₂×C₄×C₁₃₉	—	2	8	no	—
263	C₂×C₄×C₁₃₉	—	2	4	no	—
264	C₂×C₄×C₁₃₉	—	4	16	no	—
265	C₂×C₄×C₁₃₉	—	4	16	no	—
266	C₂×C₄×C₁₃₉	—	4	8	no	—
267	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
268	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
269	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
270	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
271	C₂×C₄×C₁₃₉	C₂×#41	1	8	yes	—
272	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
273	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
274	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
275	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
276	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
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	4	no	—
285	C₂²×C₁₃₉	—	4	2	no	—
286	C₂²×C₁₃₉	—	4	4	no	—
287	C₂²×C₁₃₉	—	4	8	no	—
288	C₂²×C₁₃₉	—	4	4	no	—
289	C₂²×C₁₃₉	—	4	2	no	—
290	C₂²×C₁₃₉	—	4	4	no	—
291	C₂²×C₁₃₉	—	4	8	no	—
292	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
293	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
294	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
295	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
296	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
297	C₄×C₁₃₉	—	2	4	no	—
298	C₄×C₁₃₉	—	2	4	no	—
299	C₄×C₁₃₉	—	2	2	no	—
300	C₄×C₁₃₉	—	2	4	no	—
301	C₄×C₁₃₉	—	2	8	no	—
302	C₄×C₁₃₉	—	4	2	no	—
303	C₄×C₁₃₉	—	4	2	no	—
304	C₄×C₁₃₉	—	4	2	no	—
305	C₄×C₁₃₉	—	4	4	no	—
306	C₄×C₁₃₉	#532	1	4	yes	—
307	C₄×C₁₃₉	#546	1	4	yes	—
308	C₂×C₁₃₉	—	4	4	no	—
309	C₂×C₁₃₉	—	8	2	no	—
310	C₂×C₁₃₉	—	8	4	no	—
311	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
312	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
313	C₂×C₁₃₉	#3483	1	2	yes	—
314	C₂×C₁₃₉	#3498	1	1	yes	characteristic
315	C₂×C₁₃₉	#3519	1	2	yes	—
316	#36412	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
317	C₁₃₉	#36412	1	1	yes	characteristic, direct product factor, Sylow
318	C₂×#555	C₂×C₁₃₉	1	1	yes	characteristic, complemented
319	C₂×#550	C₂×C₁₃₉	1	1	yes	characteristic, complemented
320	#2858	C₂×C₁₃₉	1	1	yes	characteristic, complemented
321	#2856	C₂×C₁₃₉	1	2	yes	complemented
322	#2567	C₂×C₁₃₉	1	1	yes	characteristic, complemented
323	#2555	C₂×C₁₃₉	1	8	yes	complemented
324	#2541	C₂×C₁₃₉	1	1	yes	characteristic, complemented
325	#2500	C₂×C₁₃₉	1	2	yes	complemented
326	#2431	C₂×C₁₃₉	1	2	yes	complemented
327	#2428	C₂×C₁₃₉	1	4	yes	complemented
328	#2363	C₂×C₁₃₉	1	4	yes	complemented
329	C₄×#124	C₂×C₁₃₉	1	1	yes	characteristic, complemented
330	#2297	C₂×C₁₃₉	1	2	yes	complemented
331	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
332	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
333	#555	—	2	8	no	—
334	#550	—	2	8	no	—
335	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
336	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
337	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
338	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
339	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
340	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
341	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
342	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
343	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
344	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
345	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
346	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
347	C₂×#121	C₂²×C₁₃₉	1	8	yes	—
348	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
349	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
350	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
351	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
352	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
353	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
354	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
355	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
356	#395	C₂²×C₁₃₉	1	4	yes	—
357	#394	C₂²×C₁₃₉	1	8	yes	—
358	#392	C₂²×C₁₃₉	1	8	yes	—
359	#392	C₂²×C₁₃₉	1	4	yes	—
360	#391	C₂²×C₁₃₉	1	2	yes	—
361	#391	C₂²×C₁₃₉	1	1	yes	characteristic
362	#390	C₂²×C₁₃₉	1	1	yes	characteristic
363	#390	C₂²×C₁₃₉	1	2	yes	—
364	#390	C₂²×C₁₃₉	1	8	yes	—
365	#390	C₂²×C₁₃₉	1	4	yes	—
366	#390	C₂²×C₁₃₉	1	2	yes	—
367	#390	C₂²×C₁₃₉	1	2	yes	—
368	#389	C₂²×C₁₃₉	1	4	yes	—
369	#388	C₂²×C₁₃₉	1	8	yes	—
370	#388	C₂²×C₁₃₉	1	4	yes	—
371	#386	C₂²×C₁₃₉	1	8	yes	—
372	#386	C₂²×C₁₃₉	1	8	yes	—
373	#384	C₂²×C₁₃₉	1	2	yes	—
374	#382	C₂²×C₁₃₉	1	1	yes	characteristic
375	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
376	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
377	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
378	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	8	yes	—
379	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
380	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
381	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
382	C₂×#41	—	2	8	no	—
383	C₂×#41	—	2	8	no	—
384	C₂×#41	—	4	4	no	—
385	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
386	C₂²×Q₈	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	2	yes	—
390	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
391	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
392	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
393	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
394	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
395	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
396	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
397	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
398	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
399	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
400	C₄⋊Q₈	—	2	4	no	—
401	#127	—	2	8	no	—
402	#127	—	2	4	no	—
403	#127	—	4	4	no	—
404	#124	—	2	4	no	—
405	#124	—	2	16	no	—
406	#124	—	4	8	no	—
407	#121	—	2	8	no	—
408	#121	—	2	8	no	—
409	#121	—	2	8	no	—
410	#121	—	2	16	no	—
411	#121	—	2	16	no	—
412	#121	—	4	16	no	—
413	C₄×Q₈	—	2	4	no	—
414	C₄×D₄	—	2	8	no	—
415	C₄×D₄	—	2	8	no	—
416	C₄×D₄	—	2	4	no	—
417	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
418	#117	—	2	8	no	—
419	#117	—	2	8	no	—
420	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
423	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
425	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
426	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	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	2	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
439	C₂×C₄²	—	4	4	no	—
440	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
441	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
442	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
443	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
444	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
445	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
446	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
447	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
448	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
449	#95	C₂³×C₁₃₉	1	4	yes	—
450	#95	C₂³×C₁₃₉	1	4	yes	—
451	#95	C₂³×C₁₃₉	1	2	yes	—
452	#95	C₂³×C₁₃₉	1	4	yes	—
453	#95	C₂³×C₁₃₉	1	8	yes	—
454	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
455	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
456	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
457	#41	—	4	32	no	—
458	C₂×Q₈	—	2	2	no	—
459	C₂×Q₈	—	2	4	no	—
460	C₂×Q₈	—	2	2	no	—
461	C₂×Q₈	—	4	4	no	—
462	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
463	C₂×D₄	—	2	8	no	—
464	C₂×D₄	—	2	8	no	—
465	C₂×D₄	—	2	8	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	4	no	—
468	C₂×D₄	—	2	4	no	—
469	C₂×D₄	—	2	4	no	—
470	C₂×D₄	—	2	4	no	—
471	C₂×D₄	—	2	8	no	—
472	C₂×D₄	—	2	2	no	—
473	C₂×D₄	—	2	8	no	—
474	C₂×D₄	—	2	4	no	—
475	C₂×D₄	—	2	16	no	—
476	C₂×D₄	—	2	2	no	—
477	C₂×D₄	—	2	4	no	—
478	C₂×D₄	—	4	4	no	—
479	C₂×D₄	—	4	8	no	—
480	C₂×D₄	—	4	8	no	—
481	C₂×D₄	—	4	8	no	—
482	C₂×D₄	—	4	4	no	—
483	C₂×D₄	—	4	8	no	—
484	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	4	no	—
487	C₂²×C₄	—	2	4	no	—
488	C₂²×C₄	—	2	8	no	—
489	C₂²×C₄	—	2	8	no	—
490	C₂²×C₄	—	2	8	no	—
491	C₂²×C₄	—	2	8	no	—
492	C₂²×C₄	—	2	8	no	—
493	C₂²×C₄	—	4	4	no	—
494	C₂²×C₄	—	4	4	no	—
495	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
496	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
497	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
498	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
499	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
500	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
501	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
502	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
503	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
504	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
505	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
506	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	4	no	—
509	C₄⋊C₄	—	2	4	no	—
510	C₄⋊C₄	—	2	4	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	4	8	no	—
513	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
514	C₄⋊C₄	#41×C₁₃₉	1	8	yes	complemented
515	C₂²⋊C₄	—	2	8	no	—
516	C₂²⋊C₄	—	2	8	no	—
517	C₂²⋊C₄	—	2	8	no	—
518	C₂²⋊C₄	—	2	4	no	—
519	C₂²⋊C₄	—	2	8	no	—
520	C₂²⋊C₄	—	2	16	no	—
521	C₂²⋊C₄	—	2	8	no	—
522	C₂²⋊C₄	—	2	8	no	—
523	C₂²⋊C₄	—	2	16	no	—
524	C₂²⋊C₄	—	4	8	no	—
525	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
526	C₄²	—	2	8	no	—
527	C₄²	—	2	4	no	—
528	C₄²	—	2	4	no	—
529	C₄²	—	2	2	no	—
530	C₄²	—	2	2	no	—
531	C₄²	—	2	4	no	—
532	C₄²	—	2	4	no	—
533	C₄²	—	4	4	no	—
534	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	2	no	—
538	C₂³	—	2	4	no	—
539	C₂³	—	2	2	no	—
540	C₂³	—	2	4	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	8	no	—
543	C₂³	—	2	4	no	—
544	C₂³	—	2	4	no	—
545	C₂³	—	2	8	no	—
546	C₂³	—	2	4	no	—
547	C₂³	—	2	4	no	—
548	C₂³	—	2	2	no	—
549	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
550	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
551	Q₈	—	2	8	no	—
552	Q₈	—	8	4	no	—
553	D₄	—	2	8	no	—
554	D₄	—	4	16	no	—
555	D₄	—	4	8	no	—
556	D₄	—	4	8	no	—
557	D₄	—	4	4	no	—
558	D₄	—	8	4	no	—
559	D₄	—	8	16	no	—
560	D₄	—	8	8	no	—
561	D₄	—	8	8	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	16	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	8	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	4	16	no	—
582	C₂×C₄	—	4	16	no	—
583	C₂×C₄	—	4	8	no	—
584	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
585	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
586	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
587	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
588	C₂×C₄	C₂×#41×C₁₃₉	1	8	yes	—
589	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
590	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
591	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
592	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
593	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
594	C₂²	—	2	4	no	—
595	C₂²	—	2	4	no	—
596	C₂²	—	2	4	no	—
597	C₂²	—	4	4	no	—
598	C₂²	—	4	4	no	—
599	C₂²	—	4	2	no	—
600	C₂²	—	4	4	no	—
601	C₂²	—	4	4	no	—
602	C₂²	—	4	2	no	—
603	C₂²	—	4	4	no	—
604	C₂²	—	4	8	no	—
605	C₂²	—	4	4	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	4	no	—
608	C₂²	—	4	8	no	—
609	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
610	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
611	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
612	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
613	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
614	C₄	—	2	4	no	—
615	C₄	—	2	4	no	—
616	C₄	—	2	2	no	—
617	C₄	—	2	4	no	—
618	C₄	—	2	8	no	—
619	C₄	—	4	2	no	—
620	C₄	—	4	2	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	4	no	—
623	C₄	#532×C₁₃₉	1	4	yes	—
624	C₄	#546×C₁₃₉	1	4	yes	—
625	C₂	—	4	4	no	—
626	C₂	—	8	2	no	—
627	C₂	—	8	4	no	—
628	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
629	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
630	C₂	#3483×C₁₃₉	1	2	yes	—
631	C₂	#3498×C₁₃₉	1	1	yes	characteristic
632	C₂	#3519×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×#555×C₁₃₉	C₂	semidirect
2. C₂×#550×C₁₃₉	C₂	semidirect
3. #2858×C₁₃₉	C₂	semidirect
4. #2856×C₁₃₉	C₂	semidirect
5. #2567×C₁₃₉	C₂	semidirect
6. #2555×C₁₃₉	C₂	semidirect
7. #2541×C₁₃₉	C₂	semidirect
8. #2500×C₁₃₉	C₂	semidirect
9. #2431×C₁₃₉	C₂	semidirect
10. #2428×C₁₃₉	C₂	semidirect
11. #2363×C₁₃₉	C₂	semidirect
12. C₄×#124×C₁₃₉	C₂	semidirect
13. #2297×C₁₃₉	C₂	semidirect
14. C₄²×D₄×C₁₃₉	C₂	semidirect
100. C₄×D₄×C₁₃₉	D₄	semidirect
197. C₄⋊C₄×C₁₃₉	#41	semidirect
316. #36412	C₁₃₉	direct (N × H)
317. C₁₃₉	#36412	direct (N × H)
318. C₂×#555	C₂×C₁₃₉	semidirect
319. C₂×#550	C₂×C₁₃₉	semidirect
320. #2858	C₂×C₁₃₉	semidirect
321. #2856	C₂×C₁₃₉	semidirect
322. #2567	C₂×C₁₃₉	semidirect
323. #2555	C₂×C₁₃₉	semidirect
324. #2541	C₂×C₁₃₉	semidirect
325. #2500	C₂×C₁₃₉	semidirect
326. #2431	C₂×C₁₃₉	semidirect
327. #2428	C₂×C₁₃₉	semidirect
328. #2363	C₂×C₁₃₉	semidirect
329. C₄×#124	C₂×C₁₃₉	semidirect
330. #2297	C₂×C₁₃₉	semidirect
331. C₄²×D₄	C₂×C₁₃₉	semidirect
417. C₄×D₄	D₄×C₁₃₉	semidirect
514. C₄⋊C₄	#41×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#555×C₁₃₉	2
C₂×#550×C₁₃₉	2
#2858×C₁₃₉	2
#2856×C₁₃₉	2
#2567×C₁₃₉	2
#2555×C₁₃₉	2
#2541×C₁₃₉	2
#2500×C₁₃₉	2
#2431×C₁₃₉	2
#2428×C₁₃₉	2
#2363×C₁₃₉	2
C₄×#124×C₁₃₉	2
#2297×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36412	139

Subgroups — C139×#36412 #48031008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36412 #48031008