Subgroups — C₁₃₉×#36429 #48031025

Order 35584.

5560 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#550×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	C₂×#548×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2847×C₁₃₉	C₂	1	3	yes	maximal, complemented
5	#2433×C₁₃₉	C₂	1	3	yes	maximal, complemented
6	#2431×C₁₃₉	C₂	1	6	yes	maximal, complemented
7	#2408×C₁₃₉	C₂	1	3	yes	maximal, complemented
8	#2407×C₁₃₉	C₂	1	6	yes	maximal, complemented
9	#2341×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	Q₈×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#120×C₁₃₉	C₂	1	3	yes	maximal, complemented
12	C₂²×#41×C₁₃₉	—	2	16	no	—
13	C₂²×#41×C₁₃₉	—	2	8	no	—
14	C₂²×#41×C₁₃₉	C₂²	1	6	yes	—
15	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
16	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
17	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₃₉	C₂²	1	3	yes	—
19	C₂⁴×C₄×C₁₃₉	C₂²	1	3	yes	—
20	#550×C₁₃₉	—	2	16	no	—
21	#548×C₁₃₉	—	2	8	no	—
22	C₂×#127×C₁₃₉	C₂²	1	6	yes	complemented
23	C₂×#124×C₁₃₉	C₂²	1	3	yes	complemented
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	3	yes	complemented
25	C₂×#121×C₁₃₉	C₂²	1	3	yes	—
26	C₂×#121×C₁₃₉	C₂²	1	6	yes	complemented
27	C₂×#121×C₁₃₉	C₂²	1	6	yes	complemented
28	C₂×#120×C₁₃₉	C₂²	1	3	yes	—
29	C₂×#120×C₁₃₉	C₂²	1	6	yes	—
30	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	complemented
31	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	6	yes	complemented
34	#394×C₁₃₉	C₂²	1	6	yes	complemented
35	#392×C₁₃₉	C₂²	1	12	yes	complemented
36	#392×C₁₃₉	C₂²	1	6	yes	complemented
37	#391×C₁₃₉	C₂²	1	6	yes	complemented
38	#390×C₁₃₉	C₂²	1	6	yes	complemented
39	#390×C₁₃₉	C₂²	1	6	yes	complemented
40	#386×C₁₃₉	C₂²	1	3	yes	—
41	#386×C₁₃₉	C₂²	1	6	yes	complemented
42	#386×C₁₃₉	C₂²	1	12	yes	complemented
43	#385×C₁₃₉	C₂²	1	1	yes	characteristic
44	#385×C₁₃₉	C₂²	1	6	yes	complemented
45	#380×C₁₃₉	C₂²	1	3	yes	—
46	#380×C₁₃₉	C₂²	1	6	yes	complemented
47	#379×C₁₃₉	C₂²	1	3	yes	—
48	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	3	yes	—
49	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	6	yes	complemented
50	C₂⁵×C₁₃₉	C₂³	1	3	yes	—
51	C₂×#41×C₁₃₉	—	2	128	no	—
52	C₂×#41×C₁₃₉	—	2	24	no	—
53	C₂×#41×C₁₃₉	—	2	8	no	—
54	C₂×#41×C₁₃₉	—	2	8	no	—
55	C₂×#41×C₁₃₉	—	2	4	no	—
56	C₂×#41×C₁₃₉	—	2	8	no	—
57	C₂×#41×C₁₃₉	—	2	24	no	—
58	C₂×#41×C₁₃₉	—	2	24	no	—
59	C₂×#41×C₁₃₉	D₄	1	16	yes	complemented
60	C₂²×Q₈×C₁₃₉	—	2	8	no	—
61	C₂²×Q₈×C₁₃₉	D₄	1	8	yes	complemented
62	C₂²×Q₈×C₁₃₉	C₂³	1	3	yes	—
63	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₃₉	—	2	24	no	—
65	C₂²×D₄×C₁₃₉	—	2	12	no	—
66	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
67	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
68	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
69	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
70	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
71	C₂²×D₄×C₁₃₉	C₂³	1	12	yes	—
72	C₂³×C₄×C₁₃₉	—	2	12	no	—
73	C₂³×C₄×C₁₃₉	—	2	24	no	—
74	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
75	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
77	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
78	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
79	#127×C₁₃₉	—	2	24	no	—
80	#124×C₁₃₉	—	2	12	no	—
81	C₂²⋊Q₈×C₁₃₉	—	2	12	no	—
82	#121×C₁₃₉	—	2	24	no	—
83	#121×C₁₃₉	—	2	12	no	—
84	#121×C₁₃₉	—	2	24	no	—
85	#120×C₁₃₉	—	2	12	no	—
86	#120×C₁₃₉	—	4	12	no	—
87	C₄×Q₈×C₁₃₉	—	2	4	no	—
88	C₄×Q₈×C₁₃₉	—	2	8	no	—
89	C₄×D₄×C₁₃₉	—	2	12	no	—
90	C₄×D₄×C₁₃₉	—	2	24	no	—
91	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
92	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
94	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
95	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
97	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
98	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
99	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
100	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
101	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
102	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	12	yes	—
103	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
104	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
106	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
107	#95×C₁₃₉	C₂³	1	6	yes	—
108	#95×C₁₃₉	C₂³	1	2	yes	—
109	#95×C₁₃₉	C₂³	1	6	yes	—
110	#95×C₁₃₉	C₂³	1	6	yes	—
111	C₂⁴×C₁₃₉	—	2	12	no	—
112	C₂⁴×C₁₃₉	—	2	6	no	—
113	C₂⁴×C₁₃₉	—	2	6	no	—
114	C₂⁴×C₁₃₉	—	2	6	no	—
115	C₂⁴×C₁₃₉	—	4	6	no	—
116	C₂⁴×C₁₃₉	C₂⁴	1	3	yes	—
117	C₂⁴×C₁₃₉	C₂⁴	1	6	yes	—
118	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
119	#41×C₁₃₉	—	2	192	no	—
120	#41×C₁₃₉	—	2	64	no	—
121	#41×C₁₃₉	—	4	16	no	—
122	C₂×Q₈×C₁₃₉	—	2	32	no	—
123	C₂×Q₈×C₁₃₉	—	2	12	no	—
124	C₂×Q₈×C₁₃₉	C₂×D₄	1	12	yes	—
125	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
126	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
127	C₂×D₄×C₁₃₉	—	2	96	no	—
128	C₂×D₄×C₁₃₉	—	2	24	no	—
129	C₂×D₄×C₁₃₉	—	2	6	no	—
130	C₂×D₄×C₁₃₉	—	2	12	no	—
131	C₂×D₄×C₁₃₉	—	2	6	no	—
132	C₂×D₄×C₁₃₉	—	2	6	no	—
133	C₂×D₄×C₁₃₉	—	2	24	no	—
134	C₂×D₄×C₁₃₉	—	2	12	no	—
135	C₂×D₄×C₁₃₉	—	2	12	no	—
136	C₂×D₄×C₁₃₉	—	2	12	no	—
137	C₂×D₄×C₁₃₉	—	2	6	no	—
138	C₂×D₄×C₁₃₉	—	2	12	no	—
139	C₂×D₄×C₁₃₉	—	2	12	no	—
140	C₂×D₄×C₁₃₉	—	4	6	no	—
141	C₂×D₄×C₁₃₉	—	4	12	no	—
142	C₂×D₄×C₁₃₉	—	4	12	no	—
143	C₂×D₄×C₁₃₉	C₂×D₄	1	24	yes	—
144	C₂²×C₄×C₁₃₉	—	2	96	no	—
145	C₂²×C₄×C₁₃₉	—	2	2	no	—
146	C₂²×C₄×C₁₃₉	—	2	12	no	—
147	C₂²×C₄×C₁₃₉	—	2	4	no	—
148	C₂²×C₄×C₁₃₉	—	2	12	no	—
149	C₂²×C₄×C₁₃₉	—	2	12	no	—
150	C₂²×C₄×C₁₃₉	—	2	12	no	—
151	C₂²×C₄×C₁₃₉	—	2	12	no	—
152	C₂²×C₄×C₁₃₉	—	2	12	no	—
153	C₂²×C₄×C₁₃₉	—	2	12	no	—
154	C₂²×C₄×C₁₃₉	—	2	6	no	—
155	C₂²×C₄×C₁₃₉	C₂×D₄	1	12	yes	—
156	C₂²×C₄×C₁₃₉	C₂×D₄	1	24	yes	—
157	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
158	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
159	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
160	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
161	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
163	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
165	C₄⋊C₄×C₁₃₉	—	2	4	no	—
166	C₄⋊C₄×C₁₃₉	—	2	6	no	—
167	C₄⋊C₄×C₁₃₉	—	2	12	no	—
168	C₄⋊C₄×C₁₃₉	—	2	6	no	—
169	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
170	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
171	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
172	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
173	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
174	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
175	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
176	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
177	C₂²⋊C₄×C₁₃₉	—	4	12	no	—
178	C₂²⋊C₄×C₁₃₉	#41	1	4	yes	complemented
179	C₄²×C₁₃₉	—	2	6	no	—
180	C₄²×C₁₃₉	—	2	12	no	—
181	C₂³×C₁₃₉	—	2	2	no	—
182	C₂³×C₁₃₉	—	2	2	no	—
183	C₂³×C₁₃₉	—	2	24	no	—
184	C₂³×C₁₃₉	—	2	6	no	—
185	C₂³×C₁₃₉	—	2	6	no	—
186	C₂³×C₁₃₉	—	2	6	no	—
187	C₂³×C₁₃₉	—	2	6	no	—
188	C₂³×C₁₃₉	—	2	6	no	—
189	C₂³×C₁₃₉	—	2	6	no	—
190	C₂³×C₁₃₉	—	2	3	no	—
191	C₂³×C₁₃₉	—	2	6	no	—
192	C₂³×C₁₃₉	—	2	3	no	—
193	C₂³×C₁₃₉	—	2	3	no	—
194	C₂³×C₁₃₉	—	2	6	no	—
195	C₂³×C₁₃₉	—	4	24	no	—
196	C₂³×C₁₃₉	—	4	24	no	—
197	C₂³×C₁₃₉	—	4	12	no	—
198	C₂³×C₁₃₉	—	4	12	no	—
199	C₂³×C₁₃₉	C₂²×D₄	1	12	yes	—
200	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
201	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
202	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
203	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
204	Q₈×C₁₃₉	—	2	24	no	—
205	Q₈×C₁₃₉	#120	1	16	yes	complemented
206	D₄×C₁₃₉	—	2	48	no	—
207	D₄×C₁₃₉	—	2	48	no	—
208	D₄×C₁₃₉	—	4	24	no	—
209	D₄×C₁₃₉	—	4	12	no	—
210	D₄×C₁₃₉	—	4	12	no	—
211	D₄×C₁₃₉	—	8	24	no	—
212	C₂×C₄×C₁₃₉	—	2	8	no	—
213	C₂×C₄×C₁₃₉	—	2	48	no	—
214	C₂×C₄×C₁₃₉	—	2	2	no	—
215	C₂×C₄×C₁₃₉	—	2	2	no	—
216	C₂×C₄×C₁₃₉	—	2	2	no	—
217	C₂×C₄×C₁₃₉	—	2	6	no	—
218	C₂×C₄×C₁₃₉	—	2	2	no	—
219	C₂×C₄×C₁₃₉	—	2	24	no	—
220	C₂×C₄×C₁₃₉	—	2	48	no	—
221	C₂×C₄×C₁₃₉	—	2	1	no	—
222	C₂×C₄×C₁₃₉	—	2	3	no	—
223	C₂×C₄×C₁₃₉	—	2	6	no	—
224	C₂×C₄×C₁₃₉	—	2	2	no	—
225	C₂×C₄×C₁₃₉	—	2	1	no	—
226	C₂×C₄×C₁₃₉	—	2	3	no	—
227	C₂×C₄×C₁₃₉	—	2	6	no	—
228	C₂×C₄×C₁₃₉	—	2	3	no	—
229	C₂×C₄×C₁₃₉	—	2	2	no	—
230	C₂×C₄×C₁₃₉	—	2	6	no	—
231	C₂×C₄×C₁₃₉	—	4	12	no	—
232	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
233	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
234	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
235	C₂×C₄×C₁₃₉	C₂²×D₄	1	12	yes	—
236	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	complemented
237	C₂²×C₁₃₉	—	2	2	no	—
238	C₂²×C₁₃₉	—	2	4	no	—
239	C₂²×C₁₃₉	—	2	2	no	—
240	C₂²×C₁₃₉	—	2	4	no	—
241	C₂²×C₁₃₉	—	2	12	no	—
242	C₂²×C₁₃₉	—	2	12	no	—
243	C₂²×C₁₃₉	—	2	12	no	—
244	C₂²×C₁₃₉	—	4	48	no	—
245	C₂²×C₁₃₉	—	4	6	no	—
246	C₂²×C₁₃₉	—	4	6	no	—
247	C₂²×C₁₃₉	—	4	6	no	—
248	C₂²×C₁₃₉	—	4	6	no	—
249	C₂²×C₁₃₉	—	4	3	no	—
250	C₂²×C₁₃₉	—	4	3	no	—
251	C₂²×C₁₃₉	—	4	6	no	—
252	C₂²×C₁₃₉	—	4	3	no	—
253	C₂²×C₁₃₉	—	4	6	no	—
254	C₂²×C₁₃₉	#550	1	4	yes	complemented
255	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
256	C₂²×C₁₃₉	C₂³×D₄	1	2	yes	—
257	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
258	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
259	C₂²×C₁₃₉	#585	1	2	yes	—
260	C₄×C₁₃₉	—	2	4	no	—
261	C₄×C₁₃₉	—	2	6	no	—
262	C₄×C₁₃₉	—	2	4	no	—
263	C₄×C₁₃₉	—	4	1	no	—
264	C₄×C₁₃₉	—	4	3	no	—
265	C₄×C₁₃₉	—	4	1	no	—
266	C₄×C₁₃₉	—	4	6	no	—
267	C₄×C₁₃₉	C₂×#120	1	12	yes	—
268	C₂×C₁₃₉	—	2	4	no	—
269	C₂×C₁₃₉	—	4	12	no	—
270	C₂×C₁₃₉	—	8	3	no	—
271	C₂×C₁₃₉	C₂²×#120	1	1	yes	characteristic
272	C₂×C₁₃₉	C₂×#550	1	1	yes	characteristic
273	C₂×C₁₃₉	D₄×#41	1	2	yes	—
274	C₂×C₁₃₉	#3487	1	1	yes	characteristic
275	C₂×C₁₃₉	#3488	1	2	yes	—
276	#36429	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
277	C₁₃₉	#36429	1	1	yes	characteristic, direct product factor, Sylow
278	C₂³×#41	C₂×C₁₃₉	1	1	yes	characteristic, complemented
279	C₂×#550	C₂×C₁₃₉	1	2	yes	complemented
280	C₂×#548	C₂×C₁₃₉	1	1	yes	characteristic, complemented
281	#2847	C₂×C₁₃₉	1	3	yes	complemented
282	#2433	C₂×C₁₃₉	1	3	yes	complemented
283	#2431	C₂×C₁₃₉	1	6	yes	complemented
284	#2408	C₂×C₁₃₉	1	3	yes	complemented
285	#2407	C₂×C₁₃₉	1	6	yes	complemented
286	#2341	C₂×C₁₃₉	1	2	yes	complemented
287	Q₈×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
288	C₄×#120	C₂×C₁₃₉	1	3	yes	complemented
289	C₂²×#41	—	2	16	no	—
290	C₂²×#41	—	2	8	no	—
291	C₂²×#41	C₂²×C₁₃₉	1	6	yes	—
292	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
293	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
294	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
295	C₂³×D₄	C₂²×C₁₃₉	1	3	yes	—
296	C₂⁴×C₄	C₂²×C₁₃₉	1	3	yes	—
297	#550	—	2	16	no	—
298	#548	—	2	8	no	—
299	C₂×#127	C₂²×C₁₃₉	1	6	yes	complemented
300	C₂×#124	C₂²×C₁₃₉	1	3	yes	complemented
301	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	3	yes	complemented
302	C₂×#121	C₂²×C₁₃₉	1	3	yes	—
303	C₂×#121	C₂²×C₁₃₉	1	6	yes	complemented
304	C₂×#121	C₂²×C₁₃₉	1	6	yes	complemented
305	C₂×#120	C₂²×C₁₃₉	1	3	yes	—
306	C₂×#120	C₂²×C₁₃₉	1	6	yes	—
307	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	complemented
308	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
309	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
310	C₂×C₄×D₄	C₂²×C₁₃₉	1	6	yes	complemented
311	#394	C₂²×C₁₃₉	1	6	yes	complemented
312	#392	C₂²×C₁₃₉	1	12	yes	complemented
313	#392	C₂²×C₁₃₉	1	6	yes	complemented
314	#391	C₂²×C₁₃₉	1	6	yes	complemented
315	#390	C₂²×C₁₃₉	1	6	yes	complemented
316	#390	C₂²×C₁₃₉	1	6	yes	complemented
317	#386	C₂²×C₁₃₉	1	3	yes	—
318	#386	C₂²×C₁₃₉	1	12	yes	complemented
319	#386	C₂²×C₁₃₉	1	6	yes	complemented
320	#385	C₂²×C₁₃₉	1	1	yes	characteristic
321	#385	C₂²×C₁₃₉	1	6	yes	complemented
322	#380	C₂²×C₁₃₉	1	3	yes	—
323	#380	C₂²×C₁₃₉	1	6	yes	complemented
324	#379	C₂²×C₁₃₉	1	3	yes	—
325	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	3	yes	—
326	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	complemented
327	C₂⁵	C₂³×C₁₃₉	1	3	yes	—
328	C₂×#41	—	2	128	no	—
329	C₂×#41	—	2	24	no	—
330	C₂×#41	—	2	8	no	—
331	C₂×#41	—	2	8	no	—
332	C₂×#41	—	2	4	no	—
333	C₂×#41	—	2	8	no	—
334	C₂×#41	—	2	24	no	—
335	C₂×#41	—	2	24	no	—
336	C₂×#41	D₄×C₁₃₉	1	16	yes	complemented
337	C₂²×Q₈	—	2	8	no	—
338	C₂²×Q₈	D₄×C₁₃₉	1	8	yes	complemented
339	C₂²×Q₈	C₂³×C₁₃₉	1	3	yes	—
340	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
341	C₂²×D₄	—	2	24	no	—
342	C₂²×D₄	—	2	12	no	—
343	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
344	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
345	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
346	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
347	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
348	C₂²×D₄	C₂³×C₁₃₉	1	12	yes	—
349	C₂³×C₄	—	2	12	no	—
350	C₂³×C₄	—	2	24	no	—
351	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
352	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
353	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
354	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
355	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
356	#127	—	2	24	no	—
357	#124	—	2	12	no	—
358	C₂²⋊Q₈	—	2	12	no	—
359	#121	—	2	24	no	—
360	#121	—	2	12	no	—
361	#121	—	2	24	no	—
362	#120	—	2	12	no	—
363	#120	—	4	12	no	—
364	C₄×Q₈	—	2	4	no	—
365	C₄×Q₈	—	2	8	no	—
366	C₄×D₄	—	2	12	no	—
367	C₄×D₄	—	2	24	no	—
368	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
371	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
373	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
376	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	12	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
382	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
383	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
384	#95	C₂³×C₁₃₉	1	6	yes	—
385	#95	C₂³×C₁₃₉	1	2	yes	—
386	#95	C₂³×C₁₃₉	1	6	yes	—
387	#95	C₂³×C₁₃₉	1	6	yes	—
388	C₂⁴	—	2	12	no	—
389	C₂⁴	—	2	6	no	—
390	C₂⁴	—	2	6	no	—
391	C₂⁴	—	2	6	no	—
392	C₂⁴	—	4	6	no	—
393	C₂⁴	C₂⁴×C₁₃₉	1	3	yes	—
394	C₂⁴	C₂⁴×C₁₃₉	1	6	yes	—
395	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
396	#41	—	2	192	no	—
397	#41	—	2	64	no	—
398	#41	—	4	16	no	—
399	C₂×Q₈	—	2	32	no	—
400	C₂×Q₈	—	2	12	no	—
401	C₂×Q₈	C₂×D₄×C₁₃₉	1	12	yes	—
402	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
403	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
404	C₂×D₄	—	2	96	no	—
405	C₂×D₄	—	2	24	no	—
406	C₂×D₄	—	2	6	no	—
407	C₂×D₄	—	2	12	no	—
408	C₂×D₄	—	2	6	no	—
409	C₂×D₄	—	2	6	no	—
410	C₂×D₄	—	2	24	no	—
411	C₂×D₄	—	2	12	no	—
412	C₂×D₄	—	2	12	no	—
413	C₂×D₄	—	2	12	no	—
414	C₂×D₄	—	2	6	no	—
415	C₂×D₄	—	2	12	no	—
416	C₂×D₄	—	2	12	no	—
417	C₂×D₄	—	4	6	no	—
418	C₂×D₄	—	4	12	no	—
419	C₂×D₄	—	4	12	no	—
420	C₂×D₄	C₂×D₄×C₁₃₉	1	24	yes	—
421	C₂²×C₄	—	2	96	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	12	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	12	no	—
426	C₂²×C₄	—	2	12	no	—
427	C₂²×C₄	—	2	12	no	—
428	C₂²×C₄	—	2	12	no	—
429	C₂²×C₄	—	2	12	no	—
430	C₂²×C₄	—	2	12	no	—
431	C₂²×C₄	—	2	6	no	—
432	C₂²×C₄	C₂×D₄×C₁₃₉	1	12	yes	—
433	C₂²×C₄	C₂×D₄×C₁₃₉	1	24	yes	—
434	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
435	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
436	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
437	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
438	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
439	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
440	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
441	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	6	no	—
444	C₄⋊C₄	—	2	12	no	—
445	C₄⋊C₄	—	2	6	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	12	no	—
448	C₂²⋊C₄	—	2	6	no	—
449	C₂²⋊C₄	—	2	12	no	—
450	C₂²⋊C₄	—	2	6	no	—
451	C₂²⋊C₄	—	2	12	no	—
452	C₂²⋊C₄	—	2	12	no	—
453	C₂²⋊C₄	—	4	6	no	—
454	C₂²⋊C₄	—	4	12	no	—
455	C₂²⋊C₄	#41×C₁₃₉	1	4	yes	complemented
456	C₄²	—	2	6	no	—
457	C₄²	—	2	12	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	24	no	—
461	C₂³	—	2	6	no	—
462	C₂³	—	2	6	no	—
463	C₂³	—	2	6	no	—
464	C₂³	—	2	6	no	—
465	C₂³	—	2	6	no	—
466	C₂³	—	2	6	no	—
467	C₂³	—	2	3	no	—
468	C₂³	—	2	6	no	—
469	C₂³	—	2	3	no	—
470	C₂³	—	2	3	no	—
471	C₂³	—	2	6	no	—
472	C₂³	—	4	24	no	—
473	C₂³	—	4	24	no	—
474	C₂³	—	4	12	no	—
475	C₂³	—	4	12	no	—
476	C₂³	C₂²×D₄×C₁₃₉	1	12	yes	—
477	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
478	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
479	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
480	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
481	Q₈	—	2	24	no	—
482	Q₈	#120×C₁₃₉	1	16	yes	complemented
483	D₄	—	2	48	no	—
484	D₄	—	2	48	no	—
485	D₄	—	4	24	no	—
486	D₄	—	4	12	no	—
487	D₄	—	4	12	no	—
488	D₄	—	8	24	no	—
489	C₂×C₄	—	2	8	no	—
490	C₂×C₄	—	2	48	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	6	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	24	no	—
497	C₂×C₄	—	2	48	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	3	no	—
500	C₂×C₄	—	2	6	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	3	no	—
504	C₂×C₄	—	2	6	no	—
505	C₂×C₄	—	2	3	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	6	no	—
508	C₂×C₄	—	4	12	no	—
509	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
510	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
511	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
512	C₂×C₄	C₂²×D₄×C₁₃₉	1	12	yes	—
513	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	complemented
514	C₂²	—	2	2	no	—
515	C₂²	—	2	4	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	2	4	no	—
518	C₂²	—	2	12	no	—
519	C₂²	—	2	12	no	—
520	C₂²	—	2	12	no	—
521	C₂²	—	4	48	no	—
522	C₂²	—	4	6	no	—
523	C₂²	—	4	6	no	—
524	C₂²	—	4	6	no	—
525	C₂²	—	4	6	no	—
526	C₂²	—	4	3	no	—
527	C₂²	—	4	3	no	—
528	C₂²	—	4	6	no	—
529	C₂²	—	4	3	no	—
530	C₂²	—	4	6	no	—
531	C₂²	#550×C₁₃₉	1	4	yes	complemented
532	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
533	C₂²	C₂³×D₄×C₁₃₉	1	2	yes	—
534	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
535	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
536	C₂²	#585×C₁₃₉	1	2	yes	—
537	C₄	—	2	4	no	—
538	C₄	—	2	6	no	—
539	C₄	—	2	4	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	3	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	6	no	—
544	C₄	C₂×#120×C₁₃₉	1	12	yes	—
545	C₂	—	2	4	no	—
546	C₂	—	4	12	no	—
547	C₂	—	8	3	no	—
548	C₂	C₂²×#120×C₁₃₉	1	1	yes	characteristic
549	C₂	C₂×#550×C₁₃₉	1	1	yes	characteristic
550	C₂	D₄×#41×C₁₃₉	1	2	yes	—
551	C₂	#3487×C₁₃₉	1	1	yes	characteristic
552	C₂	#3488×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. C₂³×#41×C₁₃₉	C₂	semidirect
2. C₂×#550×C₁₃₉	C₂	semidirect
3. C₂×#548×C₁₃₉	C₂	semidirect
4. #2847×C₁₃₉	C₂	semidirect
5. #2433×C₁₃₉	C₂	semidirect
6. #2431×C₁₃₉	C₂	semidirect
7. #2408×C₁₃₉	C₂	semidirect
8. #2407×C₁₃₉	C₂	semidirect
9. #2341×C₁₃₉	C₂	semidirect
10. Q₈×C₂²⋊C₄×C₁₃₉	C₂	semidirect
11. C₄×#120×C₁₃₉	C₂	semidirect
16. C₂²×#41×C₁₃₉	C₂²	semidirect
22. C₂×#127×C₁₃₉	C₂²	semidirect
23. C₂×#124×C₁₃₉	C₂²	semidirect
24. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
26. C₂×#121×C₁₃₉	C₂²	semidirect
27. C₂×#121×C₁₃₉	C₂²	semidirect
30. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
31. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
33. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
34. #394×C₁₃₉	C₂²	semidirect
35. #392×C₁₃₉	C₂²	semidirect
36. #392×C₁₃₉	C₂²	semidirect
37. #391×C₁₃₉	C₂²	semidirect
38. #390×C₁₃₉	C₂²	semidirect
39. #390×C₁₃₉	C₂²	semidirect
41. #386×C₁₃₉	C₂²	semidirect
42. #386×C₁₃₉	C₂²	semidirect
44. #385×C₁₃₉	C₂²	semidirect
46. #380×C₁₃₉	C₂²	semidirect
49. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
59. C₂×#41×C₁₃₉	D₄	semidirect
61. C₂²×Q₈×C₁₃₉	D₄	semidirect
178. C₂²⋊C₄×C₁₃₉	#41	semidirect
205. Q₈×C₁₃₉	#120	semidirect
236. C₂×C₄×C₁₃₉	C₂×#41	semidirect
254. C₂²×C₁₃₉	#550	semidirect
276. #36429	C₁₃₉	direct (N × H)
277. C₁₃₉	#36429	direct (N × H)
278. C₂³×#41	C₂×C₁₃₉	semidirect
279. C₂×#550	C₂×C₁₃₉	semidirect
280. C₂×#548	C₂×C₁₃₉	semidirect
281. #2847	C₂×C₁₃₉	semidirect
282. #2433	C₂×C₁₃₉	semidirect
283. #2431	C₂×C₁₃₉	semidirect
284. #2408	C₂×C₁₃₉	semidirect
285. #2407	C₂×C₁₃₉	semidirect
286. #2341	C₂×C₁₃₉	semidirect
287. Q₈×C₂²⋊C₄	C₂×C₁₃₉	semidirect
288. C₄×#120	C₂×C₁₃₉	semidirect
293. C₂²×#41	C₂²×C₁₃₉	semidirect
299. C₂×#127	C₂²×C₁₃₉	semidirect
300. C₂×#124	C₂²×C₁₃₉	semidirect
301. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
303. C₂×#121	C₂²×C₁₃₉	semidirect
304. C₂×#121	C₂²×C₁₃₉	semidirect
307. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
308. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
310. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
311. #394	C₂²×C₁₃₉	semidirect
312. #392	C₂²×C₁₃₉	semidirect
313. #392	C₂²×C₁₃₉	semidirect
314. #391	C₂²×C₁₃₉	semidirect
315. #390	C₂²×C₁₃₉	semidirect
316. #390	C₂²×C₁₃₉	semidirect
318. #386	C₂²×C₁₃₉	semidirect
319. #386	C₂²×C₁₃₉	semidirect
321. #385	C₂²×C₁₃₉	semidirect
323. #380	C₂²×C₁₃₉	semidirect
326. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
336. C₂×#41	D₄×C₁₃₉	semidirect
338. C₂²×Q₈	D₄×C₁₃₉	semidirect
455. C₂²⋊C₄	#41×C₁₃₉	semidirect
482. Q₈	#120×C₁₃₉	semidirect
513. C₂×C₄	C₂×#41×C₁₃₉	semidirect
531. C₂²	#550×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂³×#41×C₁₃₉	2
C₂×#550×C₁₃₉	2
C₂×#548×C₁₃₉	2
#2847×C₁₃₉	2
#2433×C₁₃₉	2
#2431×C₁₃₉	2
#2408×C₁₃₉	2
#2407×C₁₃₉	2
#2341×C₁₃₉	2
Q₈×C₂²⋊C₄×C₁₃₉	2
C₄×#120×C₁₃₉	2
#36429	139

Subgroups — C139×#36429 #48031025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36429 #48031025