Subgroups — C₁₃₉×#35903 #48030499

Order 35584.

3036 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2641×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2639×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2591×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2562×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2548×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2491×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2490×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2472×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2472×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2435×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2398×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#394×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2275×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×D₄×C₁₃₉	C₂²	1	2	yes	—
19	C₂³×D₄×C₁₃₉	C₂²	1	2	yes	—
20	#554×C₁₃₉	—	2	8	no	—
21	D₄²×C₁₃₉	—	2	8	no	—
22	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
25	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
26	C₂×#124×C₁₃₉	C₂²	1	2	yes	complemented
27	C₂×#124×C₁₃₉	C₂²	1	4	yes	complemented
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
29	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
30	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
31	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
33	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
34	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
41	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
42	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
43	#400×C₁₃₉	C₂²	1	2	yes	complemented
44	#400×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
45	#400×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
46	#397×C₁₃₉	C₂²	1	4	yes	complemented
47	#397×C₁₃₉	C₂²	1	2	yes	complemented
48	#394×C₁₃₉	C₂²	1	2	yes	—
49	#394×C₁₃₉	C₂²	1	1	yes	characteristic
50	#394×C₁₃₉	C₂²	1	1	yes	characteristic
51	#394×C₁₃₉	C₂²	1	2	yes	complemented
52	#394×C₁₃₉	C₂²	1	2	yes	complemented
53	#394×C₁₃₉	C₂²	1	2	yes	complemented
54	#394×C₁₃₉	C₂²	1	2	yes	complemented
55	#394×C₁₃₉	C₂²	1	4	yes	complemented
56	#394×C₁₃₉	C₂²	1	4	yes	complemented
57	#394×C₁₃₉	C₂²	1	4	yes	complemented
58	#393×C₁₃₉	C₂²	1	4	yes	complemented
59	#393×C₁₃₉	C₂²	1	2	yes	complemented
60	#390×C₁₃₉	C₂²	1	2	yes	complemented
61	#390×C₁₃₉	C₂²	1	2	yes	complemented
62	#390×C₁₃₉	C₂²	1	2	yes	complemented
63	#390×C₁₃₉	C₂²	1	2	yes	complemented
64	#390×C₁₃₉	C₂²	1	2	yes	complemented
65	#390×C₁₃₉	C₂²	1	4	yes	complemented
66	#388×C₁₃₉	C₂²	1	4	yes	complemented
67	#388×C₁₃₉	C₂²	1	4	yes	complemented
68	#388×C₁₃₉	C₂²	1	4	yes	complemented
69	#386×C₁₃₉	C₂²	1	4	yes	complemented
70	#386×C₁₃₉	C₂²	1	4	yes	complemented
71	#386×C₁₃₉	C₂²	1	4	yes	complemented
72	#386×C₁₃₉	C₂²	1	4	yes	complemented
73	#380×C₁₃₉	C₂²	1	2	yes	complemented
74	#380×C₁₃₉	C₂²	1	2	yes	complemented
75	#379×C₁₃₉	C₂²	1	4	yes	complemented
76	#379×C₁₃₉	C₂²	1	4	yes	complemented
77	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
78	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
79	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
80	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
81	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
83	#376×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
84	C₂×#95×C₁₃₉	C₂²	1	2	yes	complemented
85	C₂⁵×C₁₃₉	C₂³	1	4	yes	—
86	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₁₃₉	—	2	8	no	—
89	C₂²×D₄×C₁₃₉	—	2	8	no	—
90	C₂²×D₄×C₁₃₉	—	2	8	no	—
91	C₂²×D₄×C₁₃₉	—	2	8	no	—
92	C₂²×D₄×C₁₃₉	—	4	8	no	—
93	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
95	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
97	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
99	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
104	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
106	#127×C₁₃₉	—	2	4	no	—
107	#125×C₁₃₉	—	2	4	no	—
108	#125×C₁₃₉	—	2	4	no	—
109	#124×C₁₃₉	—	4	8	no	—
110	#124×C₁₃₉	—	4	4	no	—
111	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
112	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
113	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
114	#121×C₁₃₉	—	2	8	no	—
115	#121×C₁₃₉	—	2	8	no	—
116	#120×C₁₃₉	—	2	16	no	—
117	C₄×Q₈×C₁₃₉	—	2	4	no	—
118	C₄×D₄×C₁₃₉	—	2	4	no	—
119	C₄×D₄×C₁₃₉	—	2	4	no	—
120	C₄×D₄×C₁₃₉	—	2	8	no	—
121	C₄×D₄×C₁₃₉	—	2	4	no	—
122	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊C₄×C₁₃₉	—	4	8	no	—
138	C₂×C₂²⋊C₄×C₁₃₉	—	4	8	no	—
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
155	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
163	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
164	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
165	#95×C₁₃₉	C₂³	1	2	yes	—
166	#95×C₁₃₉	C₂³	1	2	yes	—
167	#95×C₁₃₉	C₂³	1	2	yes	—
168	#95×C₁₃₉	C₂³	1	4	yes	—
169	#95×C₁₃₉	C₂³	1	4	yes	—
170	#95×C₁₃₉	C₂³	1	2	yes	—
171	#95×C₁₃₉	C₂³	1	1	yes	characteristic
172	#95×C₁₃₉	C₂³	1	2	yes	—
173	#95×C₁₃₉	C₂³	1	1	yes	characteristic
174	#95×C₁₃₉	C₂³	1	2	yes	—
175	#95×C₁₃₉	C₂³	1	4	yes	—
176	C₂⁴×C₁₃₉	—	2	8	no	—
177	C₂⁴×C₁₃₉	—	2	8	no	—
178	C₂⁴×C₁₃₉	—	2	8	no	—
179	C₂⁴×C₁₃₉	—	2	8	no	—
180	C₂⁴×C₁₃₉	—	4	4	no	—
181	C₂⁴×C₁₃₉	—	4	4	no	—
182	C₂⁴×C₁₃₉	—	4	4	no	—
183	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
184	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
185	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
186	C₂×Q₈×C₁₃₉	—	2	2	no	—
187	C₂×Q₈×C₁₃₉	—	2	4	no	—
188	C₂×Q₈×C₁₃₉	—	2	2	no	—
189	C₂×Q₈×C₁₃₉	—	4	1	no	—
190	C₂×Q₈×C₁₃₉	—	4	4	no	—
191	C₂×D₄×C₁₃₉	—	2	4	no	—
192	C₂×D₄×C₁₃₉	—	2	8	no	—
193	C₂×D₄×C₁₃₉	—	2	8	no	—
194	C₂×D₄×C₁₃₉	—	2	8	no	—
195	C₂×D₄×C₁₃₉	—	2	8	no	—
196	C₂×D₄×C₁₃₉	—	2	2	no	—
197	C₂×D₄×C₁₃₉	—	2	8	no	—
198	C₂×D₄×C₁₃₉	—	2	4	no	—
199	C₂×D₄×C₁₃₉	—	2	4	no	—
200	C₂×D₄×C₁₃₉	—	2	4	no	—
201	C₂×D₄×C₁₃₉	—	2	4	no	—
202	C₂×D₄×C₁₃₉	—	2	4	no	—
203	C₂×D₄×C₁₃₉	—	4	4	no	—
204	C₂×D₄×C₁₃₉	—	4	4	no	—
205	C₂×D₄×C₁₃₉	—	4	2	no	—
206	C₂×D₄×C₁₃₉	—	4	2	no	—
207	C₂×D₄×C₁₃₉	—	4	32	no	—
208	C₂×D₄×C₁₃₉	—	4	32	no	—
209	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
210	C₂×D₄×C₁₃₉	#41	1	8	yes	—
211	C₂²×C₄×C₁₃₉	—	2	4	no	—
212	C₂²×C₄×C₁₃₉	—	2	4	no	—
213	C₂²×C₄×C₁₃₉	—	2	8	no	—
214	C₂²×C₄×C₁₃₉	—	2	4	no	—
215	C₂²×C₄×C₁₃₉	—	2	4	no	—
216	C₂²×C₄×C₁₃₉	—	2	4	no	—
217	C₂²×C₄×C₁₃₉	—	2	4	no	—
218	C₂²×C₄×C₁₃₉	—	4	2	no	—
219	C₂²×C₄×C₁₃₉	—	4	4	no	—
220	C₂²×C₄×C₁₃₉	—	4	4	no	—
221	C₂²×C₄×C₁₃₉	—	4	4	no	—
222	C₂²×C₄×C₁₃₉	—	4	4	no	—
223	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
224	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
235	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
238	C₄⋊C₄×C₁₃₉	—	2	2	no	—
239	C₄⋊C₄×C₁₃₉	—	2	4	no	—
240	C₄⋊C₄×C₁₃₉	—	2	4	no	—
241	C₄⋊C₄×C₁₃₉	—	2	4	no	—
242	C₄⋊C₄×C₁₃₉	—	2	2	no	—
243	C₄⋊C₄×C₁₃₉	—	2	2	no	—
244	C₄⋊C₄×C₁₃₉	—	2	2	no	—
245	C₄⋊C₄×C₁₃₉	—	2	2	no	—
246	C₄⋊C₄×C₁₃₉	—	2	2	no	—
247	C₄⋊C₄×C₁₃₉	—	2	4	no	—
248	C₄⋊C₄×C₁₃₉	—	2	4	no	—
249	C₄⋊C₄×C₁₃₉	—	2	4	no	—
250	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
251	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
252	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
253	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
254	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
255	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
256	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
257	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
258	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
259	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
260	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
261	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
262	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
263	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
264	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
265	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
266	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
267	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
268	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
269	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
270	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
271	C₄²×C₁₃₉	—	2	2	no	—
272	C₄²×C₁₃₉	—	2	2	no	—
273	C₄²×C₁₃₉	—	2	4	no	—
274	C₄²×C₁₃₉	—	4	2	no	—
275	C₄²×C₁₃₉	—	4	4	no	—
276	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
277	C₂³×C₁₃₉	—	2	2	no	—
278	C₂³×C₁₃₉	—	2	4	no	—
279	C₂³×C₁₃₉	—	2	2	no	—
280	C₂³×C₁₃₉	—	2	2	no	—
281	C₂³×C₁₃₉	—	2	2	no	—
282	C₂³×C₁₃₉	—	2	2	no	—
283	C₂³×C₁₃₉	—	2	2	no	—
284	C₂³×C₁₃₉	—	2	2	no	—
285	C₂³×C₁₃₉	—	2	2	no	—
286	C₂³×C₁₃₉	—	2	4	no	—
287	C₂³×C₁₃₉	—	2	4	no	—
288	C₂³×C₁₃₉	—	2	4	no	—
289	C₂³×C₁₃₉	—	2	4	no	—
290	C₂³×C₁₃₉	—	2	4	no	—
291	C₂³×C₁₃₉	—	2	4	no	—
292	C₂³×C₁₃₉	—	2	4	no	—
293	C₂³×C₁₃₉	—	4	16	no	—
294	C₂³×C₁₃₉	—	4	16	no	—
295	C₂³×C₁₃₉	—	4	16	no	—
296	C₂³×C₁₃₉	—	4	16	no	—
297	C₂³×C₁₃₉	—	8	8	no	—
298	C₂³×C₁₃₉	—	8	8	no	—
299	C₂³×C₁₃₉	—	8	8	no	—
300	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
301	C₂³×C₁₃₉	C₂×#41	1	8	yes	—
302	C₂³×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
303	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
304	Q₈×C₁₃₉	—	4	4	no	—
305	Q₈×C₁₃₉	—	8	4	no	—
306	D₄×C₁₃₉	—	2	8	no	—
307	D₄×C₁₃₉	—	4	16	no	—
308	D₄×C₁₃₉	—	4	8	no	—
309	D₄×C₁₃₉	—	4	16	no	—
310	D₄×C₁₃₉	—	4	8	no	—
311	D₄×C₁₃₉	—	8	4	no	—
312	D₄×C₁₃₉	#124	1	16	yes	complemented
313	C₂×C₄×C₁₃₉	—	2	1	no	—
314	C₂×C₄×C₁₃₉	—	2	1	no	—
315	C₂×C₄×C₁₃₉	—	2	4	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	1	no	—
318	C₂×C₄×C₁₃₉	—	2	1	no	—
319	C₂×C₄×C₁₃₉	—	2	1	no	—
320	C₂×C₄×C₁₃₉	—	2	1	no	—
321	C₂×C₄×C₁₃₉	—	2	1	no	—
322	C₂×C₄×C₁₃₉	—	2	2	no	—
323	C₂×C₄×C₁₃₉	—	2	2	no	—
324	C₂×C₄×C₁₃₉	—	2	2	no	—
325	C₂×C₄×C₁₃₉	—	2	2	no	—
326	C₂×C₄×C₁₃₉	—	2	2	no	—
327	C₂×C₄×C₁₃₉	—	2	4	no	—
328	C₂×C₄×C₁₃₉	—	2	2	no	—
329	C₂×C₄×C₁₃₉	—	2	2	no	—
330	C₂×C₄×C₁₃₉	—	2	2	no	—
331	C₂×C₄×C₁₃₉	—	2	4	no	—
332	C₂×C₄×C₁₃₉	—	2	4	no	—
333	C₂×C₄×C₁₃₉	—	2	2	no	—
334	C₂×C₄×C₁₃₉	—	2	2	no	—
335	C₂×C₄×C₁₃₉	—	2	2	no	—
336	C₂×C₄×C₁₃₉	—	2	4	no	—
337	C₂×C₄×C₁₃₉	—	2	2	no	—
338	C₂×C₄×C₁₃₉	—	2	2	no	—
339	C₂×C₄×C₁₃₉	—	2	1	no	—
340	C₂×C₄×C₁₃₉	—	2	2	no	—
341	C₂×C₄×C₁₃₉	—	2	2	no	—
342	C₂×C₄×C₁₃₉	—	2	1	no	—
343	C₂×C₄×C₁₃₉	—	4	8	no	—
344	C₂×C₄×C₁₃₉	—	4	8	no	—
345	C₂×C₄×C₁₃₉	—	4	8	no	—
346	C₂×C₄×C₁₃₉	—	8	4	no	—
347	C₂×C₄×C₁₃₉	—	8	8	no	—
348	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
349	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
350	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
351	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
352	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
353	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
354	C₂²×C₁₃₉	—	2	4	no	—
355	C₂²×C₁₃₉	—	2	4	no	—
356	C₂²×C₁₃₉	—	2	8	no	—
357	C₂²×C₁₃₉	—	2	8	no	—
358	C₂²×C₁₃₉	—	2	4	no	—
359	C₂²×C₁₃₉	—	2	4	no	—
360	C₂²×C₁₃₉	—	2	4	no	—
361	C₂²×C₁₃₉	—	4	2	no	—
362	C₂²×C₁₃₉	—	4	2	no	—
363	C₂²×C₁₃₉	—	4	2	no	—
364	C₂²×C₁₃₉	—	4	2	no	—
365	C₂²×C₁₃₉	—	4	4	no	—
366	C₂²×C₁₃₉	—	4	4	no	—
367	C₂²×C₁₃₉	—	4	4	no	—
368	C₂²×C₁₃₉	—	4	4	no	—
369	C₂²×C₁₃₉	—	4	4	no	—
370	C₂²×C₁₃₉	—	4	4	no	—
371	C₂²×C₁₃₉	—	4	4	no	—
372	C₂²×C₁₃₉	—	8	32	no	—
373	C₂²×C₁₃₉	C₂×#124	1	8	yes	—
374	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
375	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
376	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
377	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂²×C₁₃₉	#585	1	1	yes	characteristic
379	C₄×C₁₃₉	—	2	2	no	—
380	C₄×C₁₃₉	—	2	4	no	—
381	C₄×C₁₃₉	—	2	2	no	—
382	C₄×C₁₃₉	—	2	2	no	—
383	C₄×C₁₃₉	—	4	2	no	—
384	C₄×C₁₃₉	—	4	1	no	—
385	C₄×C₁₃₉	—	4	2	no	—
386	C₄×C₁₃₉	—	4	1	no	—
387	C₄×C₁₃₉	—	4	2	no	—
388	C₄×C₁₃₉	—	4	1	no	—
389	C₄×C₁₃₉	—	4	2	no	—
390	C₄×C₁₃₉	—	4	4	no	—
391	C₄×C₁₃₉	—	4	2	no	—
392	C₄×C₁₃₉	C₂×#124	1	4	yes	—
393	C₂×C₁₃₉	—	2	8	no	—
394	C₂×C₁₃₉	—	4	4	no	—
395	C₂×C₁₃₉	—	8	4	no	—
396	C₂×C₁₃₉	C₂²×#124	1	1	yes	characteristic
397	C₂×C₁₃₉	#3484	1	1	yes	characteristic
398	C₂×C₁₃₉	#3488	1	1	yes	characteristic
399	C₂×C₁₃₉	#3513	1	2	yes	—
400	C₂×C₁₃₉	#3519	1	2	yes	—
401	#35903	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
402	C₁₃₉	#35903	1	1	yes	characteristic, direct product factor, Sylow
403	C₂×#554	C₂×C₁₃₉	1	1	yes	characteristic, complemented
404	C₂×D₄²	C₂×C₁₃₉	1	1	yes	characteristic
405	#2641	C₂×C₁₃₉	1	1	yes	characteristic, complemented
406	#2639	C₂×C₁₃₉	1	2	yes	complemented
407	#2591	C₂×C₁₃₉	1	2	yes	complemented
408	#2562	C₂×C₁₃₉	1	1	yes	characteristic, complemented
409	#2548	C₂×C₁₃₉	1	1	yes	characteristic, complemented
410	#2491	C₂×C₁₃₉	1	2	yes	complemented
411	#2490	C₂×C₁₃₉	1	2	yes	complemented
412	#2472	C₂×C₁₃₉	1	4	yes	complemented
413	#2472	C₂×C₁₃₉	1	4	yes	complemented
414	#2435	C₂×C₁₃₉	1	2	yes	complemented
415	#2398	C₂×C₁₃₉	1	1	yes	characteristic, complemented
416	C₂×#394	C₂×C₁₃₉	1	2	yes	complemented
417	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	2	yes	complemented
418	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	2	yes	complemented
419	#2275	C₂×C₁₃₉	1	1	yes	characteristic, complemented
420	C₂³×D₄	C₂²×C₁₃₉	1	2	yes	—
421	C₂³×D₄	C₂²×C₁₃₉	1	2	yes	—
422	#554	—	2	8	no	—
423	D₄²	—	2	8	no	—
424	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
425	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
426	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
427	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
428	C₂×#124	C₂²×C₁₃₉	1	4	yes	complemented
429	C₂×#124	C₂²×C₁₃₉	1	2	yes	complemented
430	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
431	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
432	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
433	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
434	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
435	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
436	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
437	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
438	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
439	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
440	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
441	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
442	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
443	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
444	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
445	#400	C₂²×C₁₃₉	1	2	yes	complemented
446	#400	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
447	#400	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
448	#397	C₂²×C₁₃₉	1	4	yes	complemented
449	#397	C₂²×C₁₃₉	1	2	yes	complemented
450	#394	C₂²×C₁₃₉	1	2	yes	—
451	#394	C₂²×C₁₃₉	1	1	yes	characteristic
452	#394	C₂²×C₁₃₉	1	1	yes	characteristic
453	#394	C₂²×C₁₃₉	1	2	yes	complemented
454	#394	C₂²×C₁₃₉	1	2	yes	complemented
455	#394	C₂²×C₁₃₉	1	2	yes	complemented
456	#394	C₂²×C₁₃₉	1	2	yes	complemented
457	#394	C₂²×C₁₃₉	1	4	yes	complemented
458	#394	C₂²×C₁₃₉	1	4	yes	complemented
459	#394	C₂²×C₁₃₉	1	4	yes	complemented
460	#393	C₂²×C₁₃₉	1	4	yes	complemented
461	#393	C₂²×C₁₃₉	1	2	yes	complemented
462	#390	C₂²×C₁₃₉	1	2	yes	complemented
463	#390	C₂²×C₁₃₉	1	2	yes	complemented
464	#390	C₂²×C₁₃₉	1	2	yes	complemented
465	#390	C₂²×C₁₃₉	1	2	yes	complemented
466	#390	C₂²×C₁₃₉	1	4	yes	complemented
467	#390	C₂²×C₁₃₉	1	2	yes	complemented
468	#388	C₂²×C₁₃₉	1	4	yes	complemented
469	#388	C₂²×C₁₃₉	1	4	yes	complemented
470	#388	C₂²×C₁₃₉	1	4	yes	complemented
471	#386	C₂²×C₁₃₉	1	4	yes	complemented
472	#386	C₂²×C₁₃₉	1	4	yes	complemented
473	#386	C₂²×C₁₃₉	1	4	yes	complemented
474	#386	C₂²×C₁₃₉	1	4	yes	complemented
475	#380	C₂²×C₁₃₉	1	2	yes	complemented
476	#380	C₂²×C₁₃₉	1	2	yes	complemented
477	#379	C₂²×C₁₃₉	1	4	yes	complemented
478	#379	C₂²×C₁₃₉	1	4	yes	complemented
479	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
480	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
481	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
482	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
483	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
484	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
485	#376	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
486	C₂×#95	C₂²×C₁₃₉	1	2	yes	complemented
487	C₂⁵	C₂³×C₁₃₉	1	4	yes	—
488	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
489	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
490	C₂²×D₄	—	2	8	no	—
491	C₂²×D₄	—	2	8	no	—
492	C₂²×D₄	—	2	8	no	—
493	C₂²×D₄	—	2	8	no	—
494	C₂²×D₄	—	4	8	no	—
495	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
496	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
497	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
498	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
499	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
500	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
501	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
502	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
503	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
504	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
505	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
506	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
507	C₄⋊Q₈	—	2	4	no	—
508	#127	—	2	4	no	—
509	#125	—	2	4	no	—
510	#125	—	2	4	no	—
511	#124	—	4	8	no	—
512	#124	—	4	4	no	—
513	C₂²⋊Q₈	—	2	8	no	—
514	C₂²⋊Q₈	—	2	8	no	—
515	C₂²⋊Q₈	—	2	8	no	—
516	#121	—	2	8	no	—
517	#121	—	2	8	no	—
518	#120	—	2	16	no	—
519	C₄×Q₈	—	2	4	no	—
520	C₄×D₄	—	2	4	no	—
521	C₄×D₄	—	2	4	no	—
522	C₄×D₄	—	2	8	no	—
523	C₄×D₄	—	2	4	no	—
524	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
525	C₂×C₄⋊C₄	—	2	8	no	—
526	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
535	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	—	4	8	no	—
540	C₂×C₂²⋊C₄	—	4	8	no	—
541	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
561	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
562	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
564	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
565	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
566	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
567	#95	C₂³×C₁₃₉	1	1	yes	characteristic
568	#95	C₂³×C₁₃₉	1	4	yes	—
569	#95	C₂³×C₁₃₉	1	2	yes	—
570	#95	C₂³×C₁₃₉	1	2	yes	—
571	#95	C₂³×C₁₃₉	1	1	yes	characteristic
572	#95	C₂³×C₁₃₉	1	2	yes	—
573	#95	C₂³×C₁₃₉	1	2	yes	—
574	#95	C₂³×C₁₃₉	1	2	yes	—
575	#95	C₂³×C₁₃₉	1	2	yes	—
576	#95	C₂³×C₁₃₉	1	4	yes	—
577	#95	C₂³×C₁₃₉	1	4	yes	—
578	C₂⁴	—	2	8	no	—
579	C₂⁴	—	2	8	no	—
580	C₂⁴	—	2	8	no	—
581	C₂⁴	—	2	8	no	—
582	C₂⁴	—	4	4	no	—
583	C₂⁴	—	4	4	no	—
584	C₂⁴	—	4	4	no	—
585	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
586	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
587	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
588	C₂×Q₈	—	2	2	no	—
589	C₂×Q₈	—	2	4	no	—
590	C₂×Q₈	—	2	2	no	—
591	C₂×Q₈	—	4	1	no	—
592	C₂×Q₈	—	4	4	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	8	no	—
595	C₂×D₄	—	2	8	no	—
596	C₂×D₄	—	2	8	no	—
597	C₂×D₄	—	2	8	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	8	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	4	4	no	—
606	C₂×D₄	—	4	4	no	—
607	C₂×D₄	—	4	2	no	—
608	C₂×D₄	—	4	2	no	—
609	C₂×D₄	—	4	32	no	—
610	C₂×D₄	—	4	32	no	—
611	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
612	C₂×D₄	#41×C₁₃₉	1	8	yes	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	8	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	2	4	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	4	2	no	—
621	C₂²×C₄	—	4	4	no	—
622	C₂²×C₄	—	4	4	no	—
623	C₂²×C₄	—	4	4	no	—
624	C₂²×C₄	—	4	4	no	—
625	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
626	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
630	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
631	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
632	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
633	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
636	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
637	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	8	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	8	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	8	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	8	no	—
663	C₂²⋊C₄	—	4	4	no	—
664	C₂²⋊C₄	—	4	4	no	—
665	C₂²⋊C₄	—	4	4	no	—
666	C₂²⋊C₄	—	4	4	no	—
667	C₂²⋊C₄	—	4	4	no	—
668	C₂²⋊C₄	—	4	2	no	—
669	C₂²⋊C₄	—	4	4	no	—
670	C₂²⋊C₄	—	4	4	no	—
671	C₂²⋊C₄	—	4	4	no	—
672	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
673	C₄²	—	2	2	no	—
674	C₄²	—	2	2	no	—
675	C₄²	—	2	4	no	—
676	C₄²	—	4	2	no	—
677	C₄²	—	4	4	no	—
678	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	4	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	4	no	—
689	C₂³	—	2	4	no	—
690	C₂³	—	2	4	no	—
691	C₂³	—	2	4	no	—
692	C₂³	—	2	4	no	—
693	C₂³	—	2	4	no	—
694	C₂³	—	2	4	no	—
695	C₂³	—	4	16	no	—
696	C₂³	—	4	16	no	—
697	C₂³	—	4	16	no	—
698	C₂³	—	4	16	no	—
699	C₂³	—	8	8	no	—
700	C₂³	—	8	8	no	—
701	C₂³	—	8	8	no	—
702	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
703	C₂³	C₂×#41×C₁₃₉	1	8	yes	—
704	C₂³	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
705	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
706	Q₈	—	4	4	no	—
707	Q₈	—	8	4	no	—
708	D₄	—	2	8	no	—
709	D₄	—	4	16	no	—
710	D₄	—	4	8	no	—
711	D₄	—	4	16	no	—
712	D₄	—	4	8	no	—
713	D₄	—	8	4	no	—
714	D₄	#124×C₁₃₉	1	16	yes	complemented
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	4	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	4	no	—
734	C₂×C₄	—	2	4	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	4	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	4	8	no	—
746	C₂×C₄	—	4	8	no	—
747	C₂×C₄	—	4	8	no	—
748	C₂×C₄	—	8	4	no	—
749	C₂×C₄	—	8	8	no	—
750	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
751	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
752	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
753	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
754	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
755	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
756	C₂²	—	2	4	no	—
757	C₂²	—	2	4	no	—
758	C₂²	—	2	8	no	—
759	C₂²	—	2	8	no	—
760	C₂²	—	2	4	no	—
761	C₂²	—	2	4	no	—
762	C₂²	—	2	4	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	4	no	—
768	C₂²	—	4	4	no	—
769	C₂²	—	4	4	no	—
770	C₂²	—	4	4	no	—
771	C₂²	—	4	4	no	—
772	C₂²	—	4	4	no	—
773	C₂²	—	4	4	no	—
774	C₂²	—	8	32	no	—
775	C₂²	C₂×#124×C₁₃₉	1	8	yes	—
776	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
777	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
778	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
779	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
780	C₂²	#585×C₁₃₉	1	1	yes	characteristic
781	C₄	—	2	2	no	—
782	C₄	—	2	4	no	—
783	C₄	—	2	2	no	—
784	C₄	—	2	2	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	1	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	1	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	1	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	4	no	—
794	C₄	C₂×#124×C₁₃₉	1	4	yes	—
795	C₂	—	2	8	no	—
796	C₂	—	4	4	no	—
797	C₂	—	8	4	no	—
798	C₂	C₂²×#124×C₁₃₉	1	1	yes	characteristic
799	C₂	#3484×C₁₃₉	1	1	yes	characteristic
800	C₂	#3488×C₁₃₉	1	1	yes	characteristic
801	C₂	#3513×C₁₃₉	1	2	yes	—
802	C₂	#3519×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×D₄²×C₁₃₉	C₂
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×#554×C₁₃₉	C₂	semidirect
3. #2641×C₁₃₉	C₂	semidirect
4. #2639×C₁₃₉	C₂	semidirect
5. #2591×C₁₃₉	C₂	semidirect
6. #2562×C₁₃₉	C₂	semidirect
7. #2548×C₁₃₉	C₂	semidirect
8. #2491×C₁₃₉	C₂	semidirect
9. #2490×C₁₃₉	C₂	semidirect
10. #2472×C₁₃₉	C₂	semidirect
11. #2472×C₁₃₉	C₂	semidirect
12. #2435×C₁₃₉	C₂	semidirect
13. #2398×C₁₃₉	C₂	semidirect
14. C₂×#394×C₁₃₉	C₂	semidirect
15. D₄×C₂²⋊C₄×C₁₃₉	C₂	semidirect
16. D₄×C₂²⋊C₄×C₁₃₉	C₂	semidirect
17. #2275×C₁₃₉	C₂	semidirect
22. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
24. C₂×#125×C₁₃₉	C₂²	semidirect
25. C₂×#125×C₁₃₉	C₂²	semidirect
26. C₂×#124×C₁₃₉	C₂²	semidirect
27. C₂×#124×C₁₃₉	C₂²	semidirect
28. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
29. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
30. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
34. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
40. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
41. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
42. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
43. #400×C₁₃₉	C₂²	semidirect
44. #400×C₁₃₉	C₂²	semidirect
45. #400×C₁₃₉	C₂²	semidirect
46. #397×C₁₃₉	C₂²	semidirect
47. #397×C₁₃₉	C₂²	semidirect
51. #394×C₁₃₉	C₂²	semidirect
52. #394×C₁₃₉	C₂²	semidirect
53. #394×C₁₃₉	C₂²	semidirect
54. #394×C₁₃₉	C₂²	semidirect
55. #394×C₁₃₉	C₂²	semidirect
56. #394×C₁₃₉	C₂²	semidirect
57. #394×C₁₃₉	C₂²	semidirect
58. #393×C₁₃₉	C₂²	semidirect
59. #393×C₁₃₉	C₂²	semidirect
60. #390×C₁₃₉	C₂²	semidirect
61. #390×C₁₃₉	C₂²	semidirect
62. #390×C₁₃₉	C₂²	semidirect
63. #390×C₁₃₉	C₂²	semidirect
64. #390×C₁₃₉	C₂²	semidirect
65. #390×C₁₃₉	C₂²	semidirect
66. #388×C₁₃₉	C₂²	semidirect
67. #388×C₁₃₉	C₂²	semidirect
68. #388×C₁₃₉	C₂²	semidirect
69. #386×C₁₃₉	C₂²	semidirect
70. #386×C₁₃₉	C₂²	semidirect
71. #386×C₁₃₉	C₂²	semidirect
72. #386×C₁₃₉	C₂²	semidirect
73. #380×C₁₃₉	C₂²	semidirect
74. #380×C₁₃₉	C₂²	semidirect
75. #379×C₁₃₉	C₂²	semidirect
76. #379×C₁₃₉	C₂²	semidirect
77. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
78. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
79. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
80. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
81. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
82. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
83. #376×C₁₃₉	C₂²	semidirect
84. C₂×#95×C₁₃₉	C₂²	semidirect
312. D₄×C₁₃₉	#124	semidirect
401. #35903	C₁₃₉	direct (N × H)
402. C₁₃₉	#35903	direct (N × H)
403. C₂×#554	C₂×C₁₃₉	semidirect
405. #2641	C₂×C₁₃₉	semidirect
406. #2639	C₂×C₁₃₉	semidirect
407. #2591	C₂×C₁₃₉	semidirect
408. #2562	C₂×C₁₃₉	semidirect
409. #2548	C₂×C₁₃₉	semidirect
410. #2491	C₂×C₁₃₉	semidirect
411. #2490	C₂×C₁₃₉	semidirect
412. #2472	C₂×C₁₃₉	semidirect
413. #2472	C₂×C₁₃₉	semidirect
414. #2435	C₂×C₁₃₉	semidirect
415. #2398	C₂×C₁₃₉	semidirect
416. C₂×#394	C₂×C₁₃₉	semidirect
417. D₄×C₂²⋊C₄	C₂×C₁₃₉	semidirect
418. D₄×C₂²⋊C₄	C₂×C₁₃₉	semidirect
419. #2275	C₂×C₁₃₉	semidirect
424. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
426. C₂×#125	C₂²×C₁₃₉	semidirect
427. C₂×#125	C₂²×C₁₃₉	semidirect
428. C₂×#124	C₂²×C₁₃₉	semidirect
429. C₂×#124	C₂²×C₁₃₉	semidirect
430. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
431. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
432. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
436. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
442. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
443. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
444. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
445. #400	C₂²×C₁₃₉	semidirect
446. #400	C₂²×C₁₃₉	semidirect
447. #400	C₂²×C₁₃₉	semidirect
448. #397	C₂²×C₁₃₉	semidirect
449. #397	C₂²×C₁₃₉	semidirect
453. #394	C₂²×C₁₃₉	semidirect
454. #394	C₂²×C₁₃₉	semidirect
455. #394	C₂²×C₁₃₉	semidirect
456. #394	C₂²×C₁₃₉	semidirect
457. #394	C₂²×C₁₃₉	semidirect
458. #394	C₂²×C₁₃₉	semidirect
459. #394	C₂²×C₁₃₉	semidirect
460. #393	C₂²×C₁₃₉	semidirect
461. #393	C₂²×C₁₃₉	semidirect
462. #390	C₂²×C₁₃₉	semidirect
463. #390	C₂²×C₁₃₉	semidirect
464. #390	C₂²×C₁₃₉	semidirect
465. #390	C₂²×C₁₃₉	semidirect
466. #390	C₂²×C₁₃₉	semidirect
467. #390	C₂²×C₁₃₉	semidirect
468. #388	C₂²×C₁₃₉	semidirect
469. #388	C₂²×C₁₃₉	semidirect
470. #388	C₂²×C₁₃₉	semidirect
471. #386	C₂²×C₁₃₉	semidirect
472. #386	C₂²×C₁₃₉	semidirect
473. #386	C₂²×C₁₃₉	semidirect
474. #386	C₂²×C₁₃₉	semidirect
475. #380	C₂²×C₁₃₉	semidirect
476. #380	C₂²×C₁₃₉	semidirect
477. #379	C₂²×C₁₃₉	semidirect
478. #379	C₂²×C₁₃₉	semidirect
479. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
480. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
481. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
482. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
483. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
484. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
485. #376	C₂²×C₁₃₉	semidirect
486. C₂×#95	C₂²×C₁₃₉	semidirect
714. D₄	#124×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#554×C₁₃₉	2
C₂×D₄²×C₁₃₉	2
#2641×C₁₃₉	2
#2639×C₁₃₉	2
#2591×C₁₃₉	2
#2562×C₁₃₉	2
#2548×C₁₃₉	2
#2491×C₁₃₉	2
#2490×C₁₃₉	2
#2472×C₁₃₉	2
#2435×C₁₃₉	2
#2398×C₁₃₉	2
C₂×#394×C₁₃₉	2
D₄×C₂²⋊C₄×C₁₃₉	2
#2275×C₁₃₉	2
#35903	139

Subgroups — C139×#35903 #48030499

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35903 #48030499