Subgroups — C₂×#2438×C₁₃₉ #48029327

Order 35584.

3006 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#117×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2438×C₁₃₉	C₂	1	16	yes	maximal, direct product factor
4	C₂×#400×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#398×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#398×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#395×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#391×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#389×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#387×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#387×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#385×C₁₃₉	C₂	1	1	yes	maximal, characteristic
13	C₂×#385×C₁₃₉	C₂	1	1	yes	maximal, characteristic
14	C₂×#381×C₁₃₉	C₂	1	1	yes	maximal, characteristic
15	C₂×#380×C₁₃₉	C₂	1	1	yes	maximal, characteristic
16	C₂²×#95×C₁₃₉	C₂	1	1	yes	maximal, characteristic
17	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
22	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	8	yes	—
23	C₂×#117×C₁₃₉	—	2	8	no	—
24	C₂×#117×C₁₃₉	C₂²	1	8	yes	—
25	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
42	#400×C₁₃₉	C₂²	1	8	yes	complemented
43	#398×C₁₃₉	C₂²	1	8	yes	complemented
44	#398×C₁₃₉	C₂²	1	8	yes	complemented
45	#395×C₁₃₉	C₂²	1	8	yes	complemented
46	#391×C₁₃₉	C₂²	1	8	yes	complemented
47	#389×C₁₃₉	C₂²	1	8	yes	complemented
48	#387×C₁₃₉	C₂²	1	8	yes	complemented
49	#387×C₁₃₉	C₂²	1	8	yes	complemented
50	#385×C₁₃₉	C₂²	1	8	yes	—
51	#385×C₁₃₉	C₂²	1	8	yes	—
52	#381×C₁₃₉	C₂²	1	8	yes	—
53	#380×C₁₃₉	C₂²	1	8	yes	—
54	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
55	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
56	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
57	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
58	C₂×#95×C₁₃₉	C₂²	1	8	yes	—
59	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
60	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
61	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
62	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
63	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
64	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
65	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
66	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
67	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
68	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
69	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₁₃₉	—	2	4	no	—
71	C₂²×Q₈×C₁₃₉	—	2	4	no	—
72	C₂²×Q₈×C₁₃₉	—	4	2	no	—
73	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
74	C₂³×C₄×C₁₃₉	—	2	4	no	—
75	C₂³×C₄×C₁₃₉	—	2	4	no	—
76	C₂³×C₄×C₁₃₉	—	2	4	no	—
77	C₂³×C₄×C₁₃₉	—	2	4	no	—
78	C₂³×C₄×C₁₃₉	—	2	4	no	—
79	C₂³×C₄×C₁₃₉	—	2	4	no	—
80	C₂³×C₄×C₁₃₉	—	4	2	no	—
81	C₂³×C₄×C₁₃₉	—	4	2	no	—
82	C₂³×C₄×C₁₃₉	Q₈	1	8	yes	complemented
83	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
92	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
98	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂²⋊Q₈×C₁₃₉	—	2	32	no	—
101	#117×C₁₃₉	—	2	32	no	—
102	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
103	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
104	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
105	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
106	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
107	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
108	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
109	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
110	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
111	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
112	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
125	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
126	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
127	C₂×C₂²⋊C₄×C₁₃₉	D₄	1	8	yes	—
128	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
132	C₂×C₄²×C₁₃₉	—	2	4	no	—
133	C₂×C₄²×C₁₃₉	—	2	4	no	—
134	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
135	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
136	#95×C₁₃₉	C₂³	1	4	yes	—
137	#95×C₁₃₉	C₂³	1	4	yes	—
138	#95×C₁₃₉	C₂³	1	4	yes	—
139	#95×C₁₃₉	C₂³	1	4	yes	—
140	#95×C₁₃₉	C₂³	1	4	yes	—
141	#95×C₁₃₉	C₂³	1	4	yes	—
142	#95×C₁₃₉	C₂³	1	4	yes	—
143	#95×C₁₃₉	C₂³	1	4	yes	—
144	#95×C₁₃₉	C₂³	1	4	yes	—
145	#95×C₁₃₉	C₂³	1	4	yes	—
146	#95×C₁₃₉	C₂³	1	4	yes	—
147	#95×C₁₃₉	C₂³	1	4	yes	—
148	#95×C₁₃₉	C₂³	1	4	yes	—
149	#95×C₁₃₉	C₂³	1	4	yes	—
150	C₂⁴×C₁₃₉	—	2	2	no	—
151	C₂⁴×C₁₃₉	—	2	2	no	—
152	C₂⁴×C₁₃₉	—	2	2	no	—
153	C₂⁴×C₁₃₉	—	2	2	no	—
154	C₂⁴×C₁₃₉	C₂×D₄	1	4	yes	—
155	C₂⁴×C₁₃₉	C₂×Q₈	1	4	yes	—
156	C₂⁴×C₁₃₉	#41	1	4	yes	—
157	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
158	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
159	C₂×Q₈×C₁₃₉	—	2	8	no	—
160	C₂×Q₈×C₁₃₉	—	2	8	no	—
161	C₂×Q₈×C₁₃₉	—	4	4	no	—
162	C₂×Q₈×C₁₃₉	—	4	16	no	—
163	C₂²×C₄×C₁₃₉	—	2	32	no	—
164	C₂²×C₄×C₁₃₉	—	2	2	no	—
165	C₂²×C₄×C₁₃₉	—	2	2	no	—
166	C₂²×C₄×C₁₃₉	—	2	2	no	—
167	C₂²×C₄×C₁₃₉	—	2	8	no	—
168	C₂²×C₄×C₁₃₉	—	2	2	no	—
169	C₂²×C₄×C₁₃₉	—	2	2	no	—
170	C₂²×C₄×C₁₃₉	—	2	2	no	—
171	C₂²×C₄×C₁₃₉	—	2	8	no	—
172	C₂²×C₄×C₁₃₉	—	2	2	no	—
173	C₂²×C₄×C₁₃₉	—	2	2	no	—
174	C₂²×C₄×C₁₃₉	—	2	2	no	—
175	C₂²×C₄×C₁₃₉	—	2	2	no	—
176	C₂²×C₄×C₁₃₉	—	2	2	no	—
177	C₂²×C₄×C₁₃₉	—	2	2	no	—
178	C₂²×C₄×C₁₃₉	—	2	2	no	—
179	C₂²×C₄×C₁₃₉	—	2	2	no	—
180	C₂²×C₄×C₁₃₉	—	2	2	no	—
181	C₂²×C₄×C₁₃₉	—	2	2	no	—
182	C₂²×C₄×C₁₃₉	—	2	2	no	—
183	C₂²×C₄×C₁₃₉	—	2	8	no	—
184	C₂²×C₄×C₁₃₉	—	2	2	no	—
185	C₂²×C₄×C₁₃₉	—	2	2	no	—
186	C₂²×C₄×C₁₃₉	—	2	2	no	—
187	C₂²×C₄×C₁₃₉	—	2	2	no	—
188	C₂²×C₄×C₁₃₉	—	2	2	no	—
189	C₂²×C₄×C₁₃₉	—	2	2	no	—
190	C₂²×C₄×C₁₃₉	—	2	2	no	—
191	C₂²×C₄×C₁₃₉	—	2	8	no	—
192	C₂²×C₄×C₁₃₉	—	2	2	no	—
193	C₂²×C₄×C₁₃₉	—	2	2	no	—
194	C₂²×C₄×C₁₃₉	—	2	2	no	—
195	C₂²×C₄×C₁₃₉	—	2	2	no	—
196	C₂²×C₄×C₁₃₉	—	2	2	no	—
197	C₂²×C₄×C₁₃₉	—	2	2	no	—
198	C₂²×C₄×C₁₃₉	—	2	2	no	—
199	C₂²×C₄×C₁₃₉	—	2	2	no	—
200	C₂²×C₄×C₁₃₉	—	2	2	no	—
201	C₂²×C₄×C₁₃₉	—	2	2	no	—
202	C₂²×C₄×C₁₃₉	—	2	2	no	—
203	C₂²×C₄×C₁₃₉	—	2	2	no	—
204	C₂²×C₄×C₁₃₉	—	2	8	no	—
205	C₂²×C₄×C₁₃₉	—	2	8	no	—
206	C₂²×C₄×C₁₃₉	—	4	4	no	—
207	C₂²×C₄×C₁₃₉	—	4	4	no	—
208	C₂²×C₄×C₁₃₉	—	4	16	no	—
209	C₂²×C₄×C₁₃₉	—	4	16	no	—
210	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
211	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
212	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
213	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
214	C₂²×C₄×C₁₃₉	C₂×Q₈	1	16	yes	complemented
215	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
216	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
217	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₁₃₉	C₂⁴	1	2	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	2	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
231	C₄⋊C₄×C₁₃₉	—	2	8	no	—
232	C₄⋊C₄×C₁₃₉	—	2	8	no	—
233	C₄⋊C₄×C₁₃₉	—	2	8	no	—
234	C₄⋊C₄×C₁₃₉	—	2	8	no	—
235	C₄⋊C₄×C₁₃₉	—	2	8	no	—
236	C₄⋊C₄×C₁₃₉	—	2	8	no	—
237	C₄⋊C₄×C₁₃₉	—	2	8	no	—
238	C₄⋊C₄×C₁₃₉	—	2	8	no	—
239	C₄⋊C₄×C₁₃₉	—	4	4	no	—
240	C₄⋊C₄×C₁₃₉	—	4	4	no	—
241	C₄⋊C₄×C₁₃₉	—	4	4	no	—
242	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
243	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
244	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
245	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	16	yes	—
246	C₄²×C₁₃₉	—	2	8	no	—
247	C₄²×C₁₃₉	—	2	8	no	—
248	C₂³×C₁₃₉	—	2	8	no	—
249	C₂³×C₁₃₉	—	2	8	no	—
250	C₂³×C₁₃₉	—	2	8	no	—
251	C₂³×C₁₃₉	—	2	8	no	—
252	C₂³×C₁₃₉	—	2	8	no	—
253	C₂³×C₁₃₉	—	2	8	no	—
254	C₂³×C₁₃₉	—	2	2	no	—
255	C₂³×C₁₃₉	—	2	2	no	—
256	C₂³×C₁₃₉	—	2	2	no	—
257	C₂³×C₁₃₉	—	2	2	no	—
258	C₂³×C₁₃₉	C₂²⋊Q₈	1	16	yes	—
259	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
260	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
261	C₂³×C₁₃₉	C₂²×Q₈	1	4	yes	—
262	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
263	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
264	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
265	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
266	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
267	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
268	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
269	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
270	Q₈×C₁₃₉	—	4	16	no	—
271	C₂×C₄×C₁₃₉	—	2	8	no	—
272	C₂×C₄×C₁₃₉	—	2	8	no	—
273	C₂×C₄×C₁₃₉	—	2	32	no	—
274	C₂×C₄×C₁₃₉	—	2	8	no	—
275	C₂×C₄×C₁₃₉	—	2	8	no	—
276	C₂×C₄×C₁₃₉	—	2	8	no	—
277	C₂×C₄×C₁₃₉	—	2	8	no	—
278	C₂×C₄×C₁₃₉	—	2	2	no	—
279	C₂×C₄×C₁₃₉	—	2	2	no	—
280	C₂×C₄×C₁₃₉	—	2	2	no	—
281	C₂×C₄×C₁₃₉	—	2	2	no	—
282	C₂×C₄×C₁₃₉	—	2	2	no	—
283	C₂×C₄×C₁₃₉	—	2	2	no	—
284	C₂×C₄×C₁₃₉	—	2	2	no	—
285	C₂×C₄×C₁₃₉	—	2	2	no	—
286	C₂×C₄×C₁₃₉	—	2	2	no	—
287	C₂×C₄×C₁₃₉	—	2	2	no	—
288	C₂×C₄×C₁₃₉	—	2	2	no	—
289	C₂×C₄×C₁₃₉	—	2	2	no	—
290	C₂×C₄×C₁₃₉	—	2	2	no	—
291	C₂×C₄×C₁₃₉	—	2	2	no	—
292	C₂×C₄×C₁₃₉	—	2	2	no	—
293	C₂×C₄×C₁₃₉	—	2	2	no	—
294	C₂×C₄×C₁₃₉	—	2	2	no	—
295	C₂×C₄×C₁₃₉	—	2	2	no	—
296	C₂×C₄×C₁₃₉	—	2	2	no	—
297	C₂×C₄×C₁₃₉	—	2	2	no	—
298	C₂×C₄×C₁₃₉	—	2	2	no	—
299	C₂×C₄×C₁₃₉	—	2	2	no	—
300	C₂×C₄×C₁₃₉	—	2	2	no	—
301	C₂×C₄×C₁₃₉	—	2	2	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	2	2	no	—
304	C₂×C₄×C₁₃₉	—	2	2	no	—
305	C₂×C₄×C₁₃₉	—	2	2	no	—
306	C₂×C₄×C₁₃₉	—	2	2	no	—
307	C₂×C₄×C₁₃₉	—	2	2	no	—
308	C₂×C₄×C₁₃₉	—	2	2	no	—
309	C₂×C₄×C₁₃₉	—	2	2	no	—
310	C₂×C₄×C₁₃₉	—	2	2	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	2	no	—
313	C₂×C₄×C₁₃₉	—	2	2	no	—
314	C₂×C₄×C₁₃₉	—	4	16	no	—
315	C₂×C₄×C₁₃₉	—	4	16	no	—
316	C₂×C₄×C₁₃₉	—	4	4	no	—
317	C₂×C₄×C₁₃₉	—	4	4	no	—
318	C₂×C₄×C₁₃₉	—	4	4	no	—
319	C₂×C₄×C₁₃₉	—	4	4	no	—
320	C₂×C₄×C₁₃₉	—	4	4	no	—
321	C₂×C₄×C₁₃₉	—	4	4	no	—
322	C₂×C₄×C₁₃₉	—	4	4	no	—
323	C₂×C₄×C₁₃₉	—	4	4	no	—
324	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
325	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
326	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
327	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
328	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
329	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
330	C₂²×C₁₃₉	—	2	4	no	—
331	C₂²×C₁₃₉	—	2	4	no	—
332	C₂²×C₁₃₉	—	2	32	no	—
333	C₂²×C₁₃₉	—	2	4	no	—
334	C₂²×C₁₃₉	—	2	4	no	—
335	C₂²×C₁₃₉	—	2	4	no	—
336	C₂²×C₁₃₉	—	2	4	no	—
337	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	8	yes	—
338	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	4	yes	—
339	C₂²×C₁₃₉	#533	1	4	yes	—
340	C₂²×C₁₃₉	#544	1	4	yes	—
341	C₂²×C₁₃₉	#546	1	4	yes	—
342	C₂²×C₁₃₉	#547	1	4	yes	—
343	C₂²×C₁₃₉	#551	1	4	yes	—
344	C₂²×C₁₃₉	#552	1	4	yes	—
345	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
346	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
347	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
348	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
349	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
350	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
351	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
352	C₄×C₁₃₉	—	2	4	no	—
353	C₄×C₁₃₉	—	2	4	no	—
354	C₄×C₁₃₉	—	2	4	no	—
355	C₄×C₁₃₉	—	2	4	no	—
356	C₄×C₁₃₉	—	2	4	no	—
357	C₄×C₁₃₉	—	2	4	no	—
358	C₄×C₁₃₉	—	4	2	no	—
359	C₄×C₁₃₉	—	4	2	no	—
360	C₄×C₁₃₉	—	4	2	no	—
361	C₄×C₁₃₉	—	4	2	no	—
362	C₄×C₁₃₉	—	4	2	no	—
363	C₄×C₁₃₉	—	4	2	no	—
364	C₄×C₁₃₉	—	4	2	no	—
365	C₄×C₁₃₉	—	4	2	no	—
366	C₂×C₁₃₉	—	2	8	no	—
367	C₂×C₁₃₉	#2438	1	8	yes	direct product factor
368	C₂×C₁₃₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
369	C₂×C₁₃₉	C₂×#533	1	1	yes	characteristic
370	C₂×C₁₃₉	C₂×#544	1	1	yes	characteristic
371	C₂×C₁₃₉	C₂×#546	1	1	yes	characteristic
372	C₂×C₁₃₉	C₂×#547	1	1	yes	characteristic
373	C₂×C₁₃₉	C₂×#551	1	1	yes	characteristic
374	C₂×C₁₃₉	C₂×#552	1	1	yes	characteristic
375	C₂×#2438	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
376	C₁₃₉	C₂×#2438	1	1	yes	characteristic, direct product factor, Sylow
377	C₂²×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic
378	C₂²×#117	C₂×C₁₃₉	1	1	yes	characteristic
379	#2438	C₂×C₁₃₉	1	16	yes	direct product factor
380	C₂×#400	C₂×C₁₃₉	1	1	yes	characteristic, complemented
381	C₂×#398	C₂×C₁₃₉	1	1	yes	characteristic, complemented
382	C₂×#398	C₂×C₁₃₉	1	1	yes	characteristic, complemented
383	C₂×#395	C₂×C₁₃₉	1	1	yes	characteristic, complemented
384	C₂×#391	C₂×C₁₃₉	1	1	yes	characteristic, complemented
385	C₂×#389	C₂×C₁₃₉	1	1	yes	characteristic, complemented
386	C₂×#387	C₂×C₁₃₉	1	1	yes	characteristic, complemented
387	C₂×#387	C₂×C₁₃₉	1	1	yes	characteristic, complemented
388	C₂×#385	C₂×C₁₃₉	1	1	yes	characteristic
389	C₂×#385	C₂×C₁₃₉	1	1	yes	characteristic
390	C₂×#381	C₂×C₁₃₉	1	1	yes	characteristic
391	C₂×#380	C₂×C₁₃₉	1	1	yes	characteristic
392	C₂²×#95	C₂×C₁₃₉	1	1	yes	characteristic
393	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
394	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
395	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
396	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
397	C₂×C₂²⋊Q₈	—	2	8	no	—
398	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	8	yes	—
399	C₂×#117	—	2	8	no	—
400	C₂×#117	C₂²×C₁₃₉	1	8	yes	—
401	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
402	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
403	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
404	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
405	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
406	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
407	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
408	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
409	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
410	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
411	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
412	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
413	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
414	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
415	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
416	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
417	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
418	#400	C₂²×C₁₃₉	1	8	yes	complemented
419	#398	C₂²×C₁₃₉	1	8	yes	complemented
420	#398	C₂²×C₁₃₉	1	8	yes	complemented
421	#395	C₂²×C₁₃₉	1	8	yes	complemented
422	#391	C₂²×C₁₃₉	1	8	yes	complemented
423	#389	C₂²×C₁₃₉	1	8	yes	complemented
424	#387	C₂²×C₁₃₉	1	8	yes	complemented
425	#387	C₂²×C₁₃₉	1	8	yes	complemented
426	#385	C₂²×C₁₃₉	1	8	yes	—
427	#385	C₂²×C₁₃₉	1	8	yes	—
428	#381	C₂²×C₁₃₉	1	8	yes	—
429	#380	C₂²×C₁₃₉	1	8	yes	—
430	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
431	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
432	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
433	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
434	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
435	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
436	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
437	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
438	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
439	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
440	C₂×#95	C₂²×C₁₃₉	1	8	yes	—
441	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
442	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
443	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
444	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
445	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
446	C₂²×Q₈	—	2	4	no	—
447	C₂²×Q₈	—	2	4	no	—
448	C₂²×Q₈	—	4	2	no	—
449	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
450	C₂³×C₄	—	2	4	no	—
451	C₂³×C₄	—	2	4	no	—
452	C₂³×C₄	—	2	4	no	—
453	C₂³×C₄	—	2	4	no	—
454	C₂³×C₄	—	2	4	no	—
455	C₂³×C₄	—	2	4	no	—
456	C₂³×C₄	—	4	2	no	—
457	C₂³×C₄	—	4	2	no	—
458	C₂³×C₄	Q₈×C₁₃₉	1	8	yes	complemented
459	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
460	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
461	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
462	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
463	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
464	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
465	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
466	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
467	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
468	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
469	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
470	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
471	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
474	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
475	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
476	C₂²⋊Q₈	—	2	32	no	—
477	#117	—	2	32	no	—
478	C₂×C₄⋊C₄	—	2	4	no	—
479	C₂×C₄⋊C₄	—	2	4	no	—
480	C₂×C₄⋊C₄	—	2	4	no	—
481	C₂×C₄⋊C₄	—	2	4	no	—
482	C₂×C₄⋊C₄	—	2	4	no	—
483	C₂×C₄⋊C₄	—	2	4	no	—
484	C₂×C₄⋊C₄	—	2	4	no	—
485	C₂×C₄⋊C₄	—	2	4	no	—
486	C₂×C₄⋊C₄	—	4	2	no	—
487	C₂×C₄⋊C₄	—	4	2	no	—
488	C₂×C₄⋊C₄	—	4	2	no	—
489	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
490	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
491	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
492	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
493	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
494	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
495	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
496	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
497	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
498	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
499	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
500	C₂×C₂²⋊C₄	—	2	4	no	—
501	C₂×C₂²⋊C₄	—	2	4	no	—
502	C₂×C₂²⋊C₄	—	2	4	no	—
503	C₂×C₂²⋊C₄	D₄×C₁₃₉	1	8	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
508	C₂×C₄²	—	2	4	no	—
509	C₂×C₄²	—	2	4	no	—
510	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
511	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
512	#95	C₂³×C₁₃₉	1	4	yes	—
513	#95	C₂³×C₁₃₉	1	4	yes	—
514	#95	C₂³×C₁₃₉	1	4	yes	—
515	#95	C₂³×C₁₃₉	1	4	yes	—
516	#95	C₂³×C₁₃₉	1	4	yes	—
517	#95	C₂³×C₁₃₉	1	4	yes	—
518	#95	C₂³×C₁₃₉	1	4	yes	—
519	#95	C₂³×C₁₃₉	1	4	yes	—
520	#95	C₂³×C₁₃₉	1	4	yes	—
521	#95	C₂³×C₁₃₉	1	4	yes	—
522	#95	C₂³×C₁₃₉	1	4	yes	—
523	#95	C₂³×C₁₃₉	1	4	yes	—
524	#95	C₂³×C₁₃₉	1	4	yes	—
525	#95	C₂³×C₁₃₉	1	4	yes	—
526	C₂⁴	—	2	2	no	—
527	C₂⁴	—	2	2	no	—
528	C₂⁴	—	2	2	no	—
529	C₂⁴	—	2	2	no	—
530	C₂⁴	C₂×D₄×C₁₃₉	1	4	yes	—
531	C₂⁴	C₂×Q₈×C₁₃₉	1	4	yes	—
532	C₂⁴	#41×C₁₃₉	1	4	yes	—
533	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
534	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
535	C₂×Q₈	—	2	8	no	—
536	C₂×Q₈	—	2	8	no	—
537	C₂×Q₈	—	4	4	no	—
538	C₂×Q₈	—	4	16	no	—
539	C₂²×C₄	—	2	32	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	8	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	8	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	8	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	8	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	8	no	—
581	C₂²×C₄	—	2	8	no	—
582	C₂²×C₄	—	4	4	no	—
583	C₂²×C₄	—	4	4	no	—
584	C₂²×C₄	—	4	16	no	—
585	C₂²×C₄	—	4	16	no	—
586	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
587	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
588	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
589	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
590	C₂²×C₄	C₂×Q₈×C₁₃₉	1	16	yes	complemented
591	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
592	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
593	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
600	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
607	C₄⋊C₄	—	2	8	no	—
608	C₄⋊C₄	—	2	8	no	—
609	C₄⋊C₄	—	2	8	no	—
610	C₄⋊C₄	—	2	8	no	—
611	C₄⋊C₄	—	2	8	no	—
612	C₄⋊C₄	—	2	8	no	—
613	C₄⋊C₄	—	2	8	no	—
614	C₄⋊C₄	—	2	8	no	—
615	C₄⋊C₄	—	4	4	no	—
616	C₄⋊C₄	—	4	4	no	—
617	C₄⋊C₄	—	4	4	no	—
618	C₂²⋊C₄	—	2	8	no	—
619	C₂²⋊C₄	—	2	8	no	—
620	C₂²⋊C₄	—	2	8	no	—
621	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	16	yes	—
622	C₄²	—	2	8	no	—
623	C₄²	—	2	8	no	—
624	C₂³	—	2	8	no	—
625	C₂³	—	2	8	no	—
626	C₂³	—	2	8	no	—
627	C₂³	—	2	8	no	—
628	C₂³	—	2	8	no	—
629	C₂³	—	2	8	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	C₂²⋊Q₈×C₁₃₉	1	16	yes	—
635	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
636	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
637	C₂³	C₂²×Q₈×C₁₃₉	1	4	yes	—
638	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
639	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
640	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
641	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
642	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
643	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
644	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
645	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
646	Q₈	—	4	16	no	—
647	C₂×C₄	—	2	8	no	—
648	C₂×C₄	—	2	8	no	—
649	C₂×C₄	—	2	32	no	—
650	C₂×C₄	—	2	8	no	—
651	C₂×C₄	—	2	8	no	—
652	C₂×C₄	—	2	8	no	—
653	C₂×C₄	—	2	8	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	4	16	no	—
691	C₂×C₄	—	4	16	no	—
692	C₂×C₄	—	4	4	no	—
693	C₂×C₄	—	4	4	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
701	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
702	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
703	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
704	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
705	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
706	C₂²	—	2	4	no	—
707	C₂²	—	2	4	no	—
708	C₂²	—	2	32	no	—
709	C₂²	—	2	4	no	—
710	C₂²	—	2	4	no	—
711	C₂²	—	2	4	no	—
712	C₂²	—	2	4	no	—
713	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	8	yes	—
714	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	4	yes	—
715	C₂²	#533×C₁₃₉	1	4	yes	—
716	C₂²	#544×C₁₃₉	1	4	yes	—
717	C₂²	#546×C₁₃₉	1	4	yes	—
718	C₂²	#547×C₁₃₉	1	4	yes	—
719	C₂²	#551×C₁₃₉	1	4	yes	—
720	C₂²	#552×C₁₃₉	1	4	yes	—
721	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
722	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
723	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
724	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
725	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
726	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
727	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
728	C₄	—	2	4	no	—
729	C₄	—	2	4	no	—
730	C₄	—	2	4	no	—
731	C₄	—	2	4	no	—
732	C₄	—	2	4	no	—
733	C₄	—	2	4	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₂	—	2	8	no	—
743	C₂	#2438×C₁₃₉	1	8	yes	direct product factor
744	C₂	C₂²×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
745	C₂	C₂×#533×C₁₃₉	1	1	yes	characteristic
746	C₂	C₂×#544×C₁₃₉	1	1	yes	characteristic
747	C₂	C₂×#546×C₁₃₉	1	1	yes	characteristic
748	C₂	C₂×#547×C₁₃₉	1	1	yes	characteristic
749	C₂	C₂×#551×C₁₃₉	1	1	yes	characteristic
750	C₂	C₂×#552×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂⁵×C₁₃₉	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. #2438×C₁₃₉	C₂	direct (N × H)
4. C₂×#400×C₁₃₉	C₂	semidirect
5. C₂×#398×C₁₃₉	C₂	semidirect
6. C₂×#398×C₁₃₉	C₂	semidirect
7. C₂×#395×C₁₃₉	C₂	semidirect
8. C₂×#391×C₁₃₉	C₂	semidirect
9. C₂×#389×C₁₃₉	C₂	semidirect
10. C₂×#387×C₁₃₉	C₂	semidirect
11. C₂×#387×C₁₃₉	C₂	semidirect
42. #400×C₁₃₉	C₂²	semidirect
43. #398×C₁₃₉	C₂²	semidirect
44. #398×C₁₃₉	C₂²	semidirect
45. #395×C₁₃₉	C₂²	semidirect
46. #391×C₁₃₉	C₂²	semidirect
47. #389×C₁₃₉	C₂²	semidirect
48. #387×C₁₃₉	C₂²	semidirect
49. #387×C₁₃₉	C₂²	semidirect
82. C₂³×C₄×C₁₃₉	Q₈	semidirect
214. C₂²×C₄×C₁₃₉	C₂×Q₈	semidirect
367. C₂×C₁₃₉	#2438	direct (N × H)
375. C₂×#2438	C₁₃₉	direct (N × H)
376. C₁₃₉	C₂×#2438	direct (N × H)
379. #2438	C₂×C₁₃₉	direct (N × H)
380. C₂×#400	C₂×C₁₃₉	semidirect
381. C₂×#398	C₂×C₁₃₉	semidirect
382. C₂×#398	C₂×C₁₃₉	semidirect
383. C₂×#395	C₂×C₁₃₉	semidirect
384. C₂×#391	C₂×C₁₃₉	semidirect
385. C₂×#389	C₂×C₁₃₉	semidirect
386. C₂×#387	C₂×C₁₃₉	semidirect
387. C₂×#387	C₂×C₁₃₉	semidirect
418. #400	C₂²×C₁₃₉	semidirect
419. #398	C₂²×C₁₃₉	semidirect
420. #398	C₂²×C₁₃₉	semidirect
421. #395	C₂²×C₁₃₉	semidirect
422. #391	C₂²×C₁₃₉	semidirect
423. #389	C₂²×C₁₃₉	semidirect
424. #387	C₂²×C₁₃₉	semidirect
425. #387	C₂²×C₁₃₉	semidirect
458. C₂³×C₄	Q₈×C₁₃₉	semidirect
590. C₂²×C₄	C₂×Q₈×C₁₃₉	semidirect
743. C₂	#2438×C₁₃₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊Q₈×C₁₃₉	2
C₂²×#117×C₁₃₉	2
#2438×C₁₃₉	2
C₂×#400×C₁₃₉	2
C₂×#398×C₁₃₉	2
C₂×#395×C₁₃₉	2
C₂×#391×C₁₃₉	2
C₂×#389×C₁₃₉	2
C₂×#387×C₁₃₉	2
C₂×#385×C₁₃₉	2
C₂×#381×C₁₃₉	2
C₂×#380×C₁₃₉	2
C₂²×#95×C₁₃₉	2
C₂×#2438	139

Subgroups — C2×#2438×C139 #48029327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2438×C₁₃₉ #48029327