Subgroups — C₁₃₉×#36415 #48031011

Order 35584.

2618 conjugacy classes of subgroups.

The subgroup lattice has 620 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×#547×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2862×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2850×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2563×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2557×C₁₃₉	C₂	1	8	yes	maximal, complemented
7	#2547×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2535×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2499×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2431×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2352×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	C₄×#127×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	#547×C₁₃₉	—	2	8	no	—
18	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
22	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
34	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
35	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
36	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
37	#397×C₁₃₉	C₂²	1	8	yes	—
38	#397×C₁₃₉	C₂²	1	4	yes	—
39	#393×C₁₃₉	C₂²	1	4	yes	—
40	#392×C₁₃₉	C₂²	1	8	yes	—
41	#391×C₁₃₉	C₂²	1	2	yes	—
42	#391×C₁₃₉	C₂²	1	2	yes	—
43	#391×C₁₃₉	C₂²	1	4	yes	—
44	#391×C₁₃₉	C₂²	1	2	yes	—
45	#390×C₁₃₉	C₂²	1	1	yes	characteristic
46	#390×C₁₃₉	C₂²	1	2	yes	—
47	#390×C₁₃₉	C₂²	1	4	yes	—
48	#390×C₁₃₉	C₂²	1	1	yes	characteristic
49	#388×C₁₃₉	C₂²	1	8	yes	—
50	#387×C₁₃₉	C₂²	1	8	yes	—
51	#386×C₁₃₉	C₂²	1	8	yes	—
52	#386×C₁₃₉	C₂²	1	8	yes	—
53	#386×C₁₃₉	C₂²	1	8	yes	—
54	#384×C₁₃₉	C₂²	1	1	yes	characteristic
55	#382×C₁₃₉	C₂²	1	4	yes	—
56	#382×C₁₃₉	C₂²	1	2	yes	—
57	#380×C₁₃₉	C₂²	1	4	yes	—
58	#380×C₁₃₉	C₂²	1	4	yes	—
59	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
60	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	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	8	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	2	yes	—
69	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
70	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
72	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
73	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
76	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
77	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
78	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
79	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
80	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
81	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
82	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
83	#127×C₁₃₉	—	2	4	no	—
84	#124×C₁₃₉	—	2	16	no	—
85	#124×C₁₃₉	—	4	4	no	—
86	#123×C₁₃₉	—	2	16	no	—
87	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
88	#121×C₁₃₉	—	2	8	no	—
89	#121×C₁₃₉	—	2	8	no	—
90	#121×C₁₃₉	—	2	8	no	—
91	C₄×D₄×C₁₃₉	—	2	4	no	—
92	C₄×D₄×C₁₃₉	—	2	4	no	—
93	C₄×D₄×C₁₃₉	—	2	8	no	—
94	C₄×D₄×C₁₃₉	—	2	16	no	—
95	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
96	#117×C₁₃₉	—	2	8	no	—
97	#117×C₁₃₉	—	2	8	no	—
98	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
99	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
110	C₂×C₂²⋊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	2	yes	—
120	C₂×C₄²×C₁₃₉	—	4	4	no	—
121	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
124	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
126	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
129	#95×C₁₃₉	C₂³	1	2	yes	—
130	#95×C₁₃₉	C₂³	1	8	yes	—
131	#95×C₁₃₉	C₂³	1	8	yes	—
132	#95×C₁₃₉	C₂³	1	8	yes	—
133	#95×C₁₃₉	C₂³	1	4	yes	—
134	#95×C₁₃₉	C₂³	1	8	yes	—
135	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
136	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
137	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
138	#41×C₁₃₉	—	4	32	no	—
139	C₂×Q₈×C₁₃₉	—	2	4	no	—
140	C₂×Q₈×C₁₃₉	—	2	4	no	—
141	C₂×Q₈×C₁₃₉	—	2	4	no	—
142	C₂×Q₈×C₁₃₉	—	2	4	no	—
143	C₂×Q₈×C₁₃₉	—	4	4	no	—
144	C₂×D₄×C₁₃₉	—	2	8	no	—
145	C₂×D₄×C₁₃₉	—	2	8	no	—
146	C₂×D₄×C₁₃₉	—	2	8	no	—
147	C₂×D₄×C₁₃₉	—	2	8	no	—
148	C₂×D₄×C₁₃₉	—	2	2	no	—
149	C₂×D₄×C₁₃₉	—	2	2	no	—
150	C₂×D₄×C₁₃₉	—	2	4	no	—
151	C₂×D₄×C₁₃₉	—	2	8	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	—	4	4	no	—
156	C₂×D₄×C₁₃₉	—	4	4	no	—
157	C₂×D₄×C₁₃₉	—	4	8	no	—
158	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
159	C₂×D₄×C₁₃₉	#41	1	4	yes	—
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	8	no	—
165	C₂²×C₄×C₁₃₉	—	2	4	no	—
166	C₂²×C₄×C₁₃₉	—	2	8	no	—
167	C₂²×C₄×C₁₃₉	—	2	8	no	—
168	C₂²×C₄×C₁₃₉	—	2	8	no	—
169	C₂²×C₄×C₁₃₉	—	4	4	no	—
170	C₂²×C₄×C₁₃₉	—	4	4	no	—
171	C₂²×C₄×C₁₃₉	—	4	4	no	—
172	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
173	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
175	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
180	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
184	C₄⋊C₄×C₁₃₉	—	2	4	no	—
185	C₄⋊C₄×C₁₃₉	—	2	8	no	—
186	C₄⋊C₄×C₁₃₉	—	2	2	no	—
187	C₄⋊C₄×C₁₃₉	—	2	4	no	—
188	C₄⋊C₄×C₁₃₉	—	2	4	no	—
189	C₄⋊C₄×C₁₃₉	—	2	2	no	—
190	C₄⋊C₄×C₁₃₉	—	2	4	no	—
191	C₄⋊C₄×C₁₃₉	—	2	8	no	—
192	C₄⋊C₄×C₁₃₉	—	2	4	no	—
193	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
194	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
195	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
196	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
197	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
198	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
199	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
200	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
201	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
202	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
203	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
204	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
205	C₄²×C₁₃₉	—	2	8	no	—
206	C₄²×C₁₃₉	—	2	2	no	—
207	C₄²×C₁₃₉	—	2	2	no	—
208	C₄²×C₁₃₉	—	2	4	no	—
209	C₄²×C₁₃₉	—	4	4	no	—
210	C₄²×C₁₃₉	—	4	2	no	—
211	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
212	C₄²×C₁₃₉	#41	1	8	yes	complemented
213	C₂³×C₁₃₉	—	2	2	no	—
214	C₂³×C₁₃₉	—	2	4	no	—
215	C₂³×C₁₃₉	—	2	4	no	—
216	C₂³×C₁₃₉	—	2	2	no	—
217	C₂³×C₁₃₉	—	2	2	no	—
218	C₂³×C₁₃₉	—	2	2	no	—
219	C₂³×C₁₃₉	—	2	4	no	—
220	C₂³×C₁₃₉	—	2	4	no	—
221	C₂³×C₁₃₉	—	2	2	no	—
222	C₂³×C₁₃₉	—	2	4	no	—
223	C₂³×C₁₃₉	—	2	2	no	—
224	C₂³×C₁₃₉	—	2	2	no	—
225	C₂³×C₁₃₉	—	2	4	no	—
226	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
227	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
228	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
229	Q₈×C₁₃₉	—	4	8	no	—
230	Q₈×C₁₃₉	—	8	4	no	—
231	D₄×C₁₃₉	—	2	8	no	—
232	D₄×C₁₃₉	—	2	8	no	—
233	D₄×C₁₃₉	—	4	16	no	—
234	D₄×C₁₃₉	—	4	16	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	2	no	—
240	C₂×C₄×C₁₃₉	—	2	2	no	—
241	C₂×C₄×C₁₃₉	—	2	2	no	—
242	C₂×C₄×C₁₃₉	—	2	2	no	—
243	C₂×C₄×C₁₃₉	—	2	2	no	—
244	C₂×C₄×C₁₃₉	—	2	16	no	—
245	C₂×C₄×C₁₃₉	—	2	2	no	—
246	C₂×C₄×C₁₃₉	—	2	4	no	—
247	C₂×C₄×C₁₃₉	—	2	2	no	—
248	C₂×C₄×C₁₃₉	—	2	4	no	—
249	C₂×C₄×C₁₃₉	—	2	4	no	—
250	C₂×C₄×C₁₃₉	—	2	4	no	—
251	C₂×C₄×C₁₃₉	—	2	4	no	—
252	C₂×C₄×C₁₃₉	—	2	4	no	—
253	C₂×C₄×C₁₃₉	—	2	4	no	—
254	C₂×C₄×C₁₃₉	—	2	4	no	—
255	C₂×C₄×C₁₃₉	—	2	4	no	—
256	C₂×C₄×C₁₃₉	—	2	8	no	—
257	C₂×C₄×C₁₃₉	—	4	16	no	—
258	C₂×C₄×C₁₃₉	—	4	16	no	—
259	C₂×C₄×C₁₃₉	—	4	8	no	—
260	C₂×C₄×C₁₃₉	—	4	8	no	—
261	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
262	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
263	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
264	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
265	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
266	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
267	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
268	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
269	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
270	C₂²×C₁₃₉	—	2	4	no	—
271	C₂²×C₁₃₉	—	2	4	no	—
272	C₂²×C₁₃₉	—	2	4	no	—
273	C₂²×C₁₃₉	—	2	8	no	—
274	C₂²×C₁₃₉	—	2	4	no	—
275	C₂²×C₁₃₉	—	4	2	no	—
276	C₂²×C₁₃₉	—	4	4	no	—
277	C₂²×C₁₃₉	—	4	2	no	—
278	C₂²×C₁₃₉	—	4	4	no	—
279	C₂²×C₁₃₉	—	4	4	no	—
280	C₂²×C₁₃₉	—	4	2	no	—
281	C₂²×C₁₃₉	—	4	2	no	—
282	C₂²×C₁₃₉	—	4	4	no	—
283	C₂²×C₁₃₉	—	4	2	no	—
284	C₂²×C₁₃₉	—	4	4	no	—
285	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
286	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
287	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
288	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
289	C₂²×C₁₃₉	#585	1	2	yes	—
290	C₄×C₁₃₉	—	2	4	no	—
291	C₄×C₁₃₉	—	2	4	no	—
292	C₄×C₁₃₉	—	2	2	no	—
293	C₄×C₁₃₉	—	2	4	no	—
294	C₄×C₁₃₉	—	4	2	no	—
295	C₄×C₁₃₉	—	4	2	no	—
296	C₄×C₁₃₉	—	4	4	no	—
297	C₄×C₁₃₉	—	4	4	no	—
298	C₄×C₁₃₉	—	4	4	no	—
299	C₄×C₁₃₉	#532	1	4	yes	—
300	C₄×C₁₃₉	#546	1	4	yes	—
301	C₂×C₁₃₉	—	4	4	no	—
302	C₂×C₁₃₉	—	4	4	no	—
303	C₂×C₁₃₉	—	8	2	no	—
304	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
305	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
306	C₂×C₁₃₉	#3475	1	2	yes	—
307	C₂×C₁₃₉	#3500	1	1	yes	characteristic
308	C₂×C₁₃₉	#3506	1	2	yes	—
309	#36415	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
310	C₁₃₉	#36415	1	1	yes	characteristic, direct product factor, Sylow
311	C₂×#555	C₂×C₁₃₉	1	1	yes	characteristic, complemented
312	C₂×#547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
313	#2862	C₂×C₁₃₉	1	1	yes	characteristic, complemented
314	#2850	C₂×C₁₃₉	1	2	yes	complemented
315	#2563	C₂×C₁₃₉	1	1	yes	characteristic, complemented
316	#2557	C₂×C₁₃₉	1	8	yes	complemented
317	#2547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
318	#2535	C₂×C₁₃₉	1	4	yes	complemented
319	#2499	C₂×C₁₃₉	1	2	yes	complemented
320	#2431	C₂×C₁₃₉	1	2	yes	complemented
321	#2352	C₂×C₁₃₉	1	4	yes	complemented
322	C₄×#127	C₂×C₁₃₉	1	1	yes	characteristic, complemented
323	#2297	C₂×C₁₃₉	1	2	yes	complemented
324	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
325	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
326	#555	—	2	8	no	—
327	#547	—	2	8	no	—
328	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
329	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
330	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
331	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
332	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
333	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
334	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
335	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
336	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
337	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
338	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
339	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
340	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
341	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
342	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
343	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
344	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
345	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
346	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
347	#397	C₂²×C₁₃₉	1	8	yes	—
348	#397	C₂²×C₁₃₉	1	4	yes	—
349	#393	C₂²×C₁₃₉	1	4	yes	—
350	#392	C₂²×C₁₃₉	1	8	yes	—
351	#391	C₂²×C₁₃₉	1	2	yes	—
352	#391	C₂²×C₁₃₉	1	2	yes	—
353	#391	C₂²×C₁₃₉	1	4	yes	—
354	#391	C₂²×C₁₃₉	1	2	yes	—
355	#390	C₂²×C₁₃₉	1	1	yes	characteristic
356	#390	C₂²×C₁₃₉	1	1	yes	characteristic
357	#390	C₂²×C₁₃₉	1	4	yes	—
358	#390	C₂²×C₁₃₉	1	2	yes	—
359	#388	C₂²×C₁₃₉	1	8	yes	—
360	#387	C₂²×C₁₃₉	1	8	yes	—
361	#386	C₂²×C₁₃₉	1	8	yes	—
362	#386	C₂²×C₁₃₉	1	8	yes	—
363	#386	C₂²×C₁₃₉	1	8	yes	—
364	#384	C₂²×C₁₃₉	1	1	yes	characteristic
365	#382	C₂²×C₁₃₉	1	2	yes	—
366	#382	C₂²×C₁₃₉	1	4	yes	—
367	#380	C₂²×C₁₃₉	1	4	yes	—
368	#380	C₂²×C₁₃₉	1	4	yes	—
369	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
370	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
371	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	8	yes	—
372	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
373	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
374	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
375	C₂×#41	—	2	8	no	—
376	C₂×#41	—	2	8	no	—
377	C₂×#41	—	4	4	no	—
378	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
379	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
380	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
381	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
382	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
383	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
384	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
385	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
386	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
387	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
388	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
389	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
390	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
391	C₄⋊Q₈	—	2	4	no	—
392	C₄⋊Q₈	—	2	4	no	—
393	#127	—	2	4	no	—
394	#124	—	2	16	no	—
395	#124	—	4	4	no	—
396	#123	—	2	16	no	—
397	C₂²⋊Q₈	—	2	8	no	—
398	#121	—	2	8	no	—
399	#121	—	2	8	no	—
400	#121	—	2	8	no	—
401	C₄×D₄	—	2	4	no	—
402	C₄×D₄	—	2	4	no	—
403	C₄×D₄	—	2	8	no	—
404	C₄×D₄	—	2	16	no	—
405	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
406	#117	—	2	8	no	—
407	#117	—	2	8	no	—
408	C₂×C₄⋊C₄	—	2	8	no	—
409	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
410	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
411	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
413	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
414	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
416	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
417	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
418	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
419	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	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	4	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	8	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
430	C₂×C₄²	—	4	4	no	—
431	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
432	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
433	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
434	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
436	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
437	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
438	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
439	#95	C₂³×C₁₃₉	1	4	yes	—
440	#95	C₂³×C₁₃₉	1	2	yes	—
441	#95	C₂³×C₁₃₉	1	8	yes	—
442	#95	C₂³×C₁₃₉	1	8	yes	—
443	#95	C₂³×C₁₃₉	1	8	yes	—
444	#95	C₂³×C₁₃₉	1	8	yes	—
445	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
446	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
447	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
448	#41	—	4	32	no	—
449	C₂×Q₈	—	2	4	no	—
450	C₂×Q₈	—	2	4	no	—
451	C₂×Q₈	—	2	4	no	—
452	C₂×Q₈	—	2	4	no	—
453	C₂×Q₈	—	4	4	no	—
454	C₂×D₄	—	2	8	no	—
455	C₂×D₄	—	2	8	no	—
456	C₂×D₄	—	2	8	no	—
457	C₂×D₄	—	2	8	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	2	8	no	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	4	4	no	—
466	C₂×D₄	—	4	4	no	—
467	C₂×D₄	—	4	8	no	—
468	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
469	C₂×D₄	#41×C₁₃₉	1	4	yes	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	4	no	—
472	C₂²×C₄	—	2	8	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	8	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	8	no	—
477	C₂²×C₄	—	2	8	no	—
478	C₂²×C₄	—	2	8	no	—
479	C₂²×C₄	—	4	4	no	—
480	C₂²×C₄	—	4	4	no	—
481	C₂²×C₄	—	4	4	no	—
482	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
483	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
484	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
485	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
486	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
487	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
488	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
489	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
490	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
491	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
492	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
493	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	2	8	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	4	no	—
498	C₄⋊C₄	—	2	4	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	4	no	—
501	C₄⋊C₄	—	2	8	no	—
502	C₄⋊C₄	—	2	4	no	—
503	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
504	C₂²⋊C₄	—	2	8	no	—
505	C₂²⋊C₄	—	2	8	no	—
506	C₂²⋊C₄	—	2	8	no	—
507	C₂²⋊C₄	—	2	4	no	—
508	C₂²⋊C₄	—	2	4	no	—
509	C₂²⋊C₄	—	2	8	no	—
510	C₂²⋊C₄	—	2	8	no	—
511	C₂²⋊C₄	—	2	8	no	—
512	C₂²⋊C₄	—	4	8	no	—
513	C₂²⋊C₄	—	4	8	no	—
514	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
515	C₄²	—	2	8	no	—
516	C₄²	—	2	2	no	—
517	C₄²	—	2	2	no	—
518	C₄²	—	2	4	no	—
519	C₄²	—	4	4	no	—
520	C₄²	—	4	2	no	—
521	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
522	C₄²	#41×C₁₃₉	1	8	yes	complemented
523	C₂³	—	2	2	no	—
524	C₂³	—	2	4	no	—
525	C₂³	—	2	4	no	—
526	C₂³	—	2	2	no	—
527	C₂³	—	2	2	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	4	no	—
530	C₂³	—	2	4	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	4	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	4	no	—
536	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
537	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
538	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
539	Q₈	—	4	8	no	—
540	Q₈	—	8	4	no	—
541	D₄	—	2	8	no	—
542	D₄	—	2	8	no	—
543	D₄	—	4	16	no	—
544	D₄	—	4	16	no	—
545	D₄	—	4	4	no	—
546	D₄	—	8	8	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	16	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	8	no	—
567	C₂×C₄	—	4	16	no	—
568	C₂×C₄	—	4	16	no	—
569	C₂×C₄	—	4	8	no	—
570	C₂×C₄	—	4	8	no	—
571	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
572	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
573	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
574	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
575	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
576	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
577	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
578	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
579	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
580	C₂²	—	2	4	no	—
581	C₂²	—	2	4	no	—
582	C₂²	—	2	4	no	—
583	C₂²	—	2	8	no	—
584	C₂²	—	2	4	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	4	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	4	4	no	—
589	C₂²	—	4	4	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	4	4	no	—
593	C₂²	—	4	2	no	—
594	C₂²	—	4	4	no	—
595	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
596	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
597	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
598	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
599	C₂²	#585×C₁₃₉	1	2	yes	—
600	C₄	—	2	4	no	—
601	C₄	—	2	4	no	—
602	C₄	—	2	2	no	—
603	C₄	—	2	4	no	—
604	C₄	—	4	2	no	—
605	C₄	—	4	2	no	—
606	C₄	—	4	4	no	—
607	C₄	—	4	4	no	—
608	C₄	—	4	4	no	—
609	C₄	#532×C₁₃₉	1	4	yes	—
610	C₄	#546×C₁₃₉	1	4	yes	—
611	C₂	—	4	4	no	—
612	C₂	—	4	4	no	—
613	C₂	—	8	2	no	—
614	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
615	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
616	C₂	#3475×C₁₃₉	1	2	yes	—
617	C₂	#3500×C₁₃₉	1	1	yes	characteristic
618	C₂	#3506×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×#547×C₁₃₉	C₂	semidirect
3. #2862×C₁₃₉	C₂	semidirect
4. #2850×C₁₃₉	C₂	semidirect
5. #2563×C₁₃₉	C₂	semidirect
6. #2557×C₁₃₉	C₂	semidirect
7. #2547×C₁₃₉	C₂	semidirect
8. #2535×C₁₃₉	C₂	semidirect
9. #2499×C₁₃₉	C₂	semidirect
10. #2431×C₁₃₉	C₂	semidirect
11. #2352×C₁₃₉	C₂	semidirect
12. C₄×#127×C₁₃₉	C₂	semidirect
13. #2297×C₁₃₉	C₂	semidirect
14. C₄²×D₄×C₁₃₉	C₂	semidirect
95. C₄×D₄×C₁₃₉	D₄	semidirect
212. C₄²×C₁₃₉	#41	semidirect
309. #36415	C₁₃₉	direct (N × H)
310. C₁₃₉	#36415	direct (N × H)
311. C₂×#555	C₂×C₁₃₉	semidirect
312. C₂×#547	C₂×C₁₃₉	semidirect
313. #2862	C₂×C₁₃₉	semidirect
314. #2850	C₂×C₁₃₉	semidirect
315. #2563	C₂×C₁₃₉	semidirect
316. #2557	C₂×C₁₃₉	semidirect
317. #2547	C₂×C₁₃₉	semidirect
318. #2535	C₂×C₁₃₉	semidirect
319. #2499	C₂×C₁₃₉	semidirect
320. #2431	C₂×C₁₃₉	semidirect
321. #2352	C₂×C₁₃₉	semidirect
322. C₄×#127	C₂×C₁₃₉	semidirect
323. #2297	C₂×C₁₃₉	semidirect
324. C₄²×D₄	C₂×C₁₃₉	semidirect
405. C₄×D₄	D₄×C₁₃₉	semidirect
522. C₄²	#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×#547×C₁₃₉	2
#2862×C₁₃₉	2
#2850×C₁₃₉	2
#2563×C₁₃₉	2
#2557×C₁₃₉	2
#2547×C₁₃₉	2
#2535×C₁₃₉	2
#2499×C₁₃₉	2
#2431×C₁₃₉	2
#2352×C₁₃₉	2
C₄×#127×C₁₃₉	2
#2297×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36415	139

Subgroups — C139×#36415 #48031011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36415 #48031011