Subgroups — #31817883

Order 17792.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17984869	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₈×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#22581596	C₂	1	1	yes	maximal, characteristic, complemented
4	#22581588	C₂	1	1	yes	maximal, characteristic, complemented
5	#22581203	C₂	1	1	yes	maximal, characteristic, complemented
6	#22581179	C₂	1	1	yes	maximal, characteristic, complemented
7	#22581165	C₂	1	1	yes	maximal, characteristic, complemented
8	#22581145	C₂	1	1	yes	maximal, characteristic, complemented
9	#22581102	C₂	1	1	yes	maximal, characteristic, complemented
10	#22581097	C₂	1	1	yes	maximal, characteristic, complemented
11	#22581085	C₂	1	1	yes	maximal, characteristic, complemented
12	#22581085	C₂	1	1	yes	maximal, characteristic, complemented
13	#22581066	C₂	1	1	yes	maximal, characteristic, complemented
14	#22581026	C₂	1	1	yes	maximal, characteristic, complemented
15	#496×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14555786	C₂²	1	1	yes	characteristic, complemented
17	C₂×D₄×D₁₃₉	—	2	1	no	—
18	C₂×D₄×D₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×D₄×D₁₃₉	C₂²	1	1	yes	characteristic, complemented
20	C₂×D₄×D₁₃₉	C₂²	1	1	yes	characteristic, complemented
21	#17984869	—	2	4	no	—
22	C₂×#14555772	C₂²	1	1	yes	characteristic, complemented
23	C₂×D₁₁₁₂	C₂²	1	1	yes	characteristic
24	C₂×#14555770	C₂²	1	1	yes	characteristic
25	C₂×#14555770	C₂²	1	1	yes	characteristic, complemented
26	C₂×#14555770	C₂²	1	1	yes	characteristic, complemented
27	D₈×D₁₃₉	—	2	4	no	—
28	C₂×#14555768	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₈×D₁₃₉	C₂²	1	1	yes	characteristic, complemented
30	#17984824	—	2	1	no	—
31	#17984818	C₂²	1	1	yes	characteristic, complemented
32	#17984815	—	2	1	no	—
33	#17984813	—	2	1	no	—
34	#17984813	C₂²	1	1	yes	characteristic
35	#17984813	C₂²	1	1	yes	characteristic, complemented
36	#17984813	C₂²	1	1	yes	characteristic, complemented
37	#17984812	—	2	1	no	—
38	#17984810	—	2	1	no	—
39	#17984810	—	2	1	no	—
40	C₄×D₅₅₆	C₂²	1	1	yes	characteristic
41	C₄×D₅₅₆	C₂²	1	1	yes	characteristic, complemented
42	C₄×D₅₅₆	C₂²	1	1	yes	characteristic, complemented
43	C₂²⋊C₄×D₁₃₉	—	2	1	no	—
44	#17984774	C₂²	1	1	yes	characteristic, complemented
45	C₄⋊(C₁₃₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
46	#17984766	C₂²	1	1	yes	characteristic, complemented
47	#17984764	C₂²	1	1	yes	characteristic, complemented
48	#17984764	C₂²	1	1	yes	characteristic, complemented
49	#17984763	C₂²	1	1	yes	characteristic, complemented
50	#17984763	C₂²	1	1	yes	characteristic, complemented
51	#17984763	C₂²	1	1	yes	characteristic, complemented
52	(C₂×D₁₃₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	(C₂×D₁₃₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	C₂×SD₁₆×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×SD₁₆×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
56	C₂×D₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
57	C₂×D₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
58	#127×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
59	#124×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
60	#97×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₃₉	—	2	1	no	—
62	C₂³×D₁₃₉	—	2	1	no	—
63	C₂³×D₁₃₉	—	2	1	no	—
64	#14555786	—	2	2	no	—
65	#14555786	—	4	1	no	—
66	C₂×D₅₅₆	—	2	1	no	—
67	C₂×D₅₅₆	D₄	1	1	yes	characteristic
68	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
69	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
71	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
72	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
73	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
74	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
75	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
76	D₄×D₁₃₉	—	2	2	no	—
77	D₄×D₁₃₉	—	2	2	no	—
78	D₄×D₁₃₉	—	2	2	no	—
79	D₄×D₁₃₉	—	4	1	no	—
80	D₄×D₁₃₉	—	4	1	no	—
81	D₄×D₁₃₉	—	4	1	no	—
82	D₄×D₁₃₉	—	4	4	no	—
83	C₂×C₄×D₁₃₉	—	2	1	no	—
84	C₂×C₄×D₁₃₉	—	2	1	no	—
85	C₂×C₄×D₁₃₉	—	2	1	no	—
86	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
87	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
88	#14555772	—	2	2	no	—
89	D₁₁₁₂	D₄	1	4	yes	complemented
90	#14555770	—	2	2	no	—
91	#14555770	—	2	2	no	—
92	#14555770	—	2	2	no	—
93	#14555768	—	2	2	no	—
94	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
95	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
96	C₈×D₁₃₉	—	2	2	no	—
97	C₄⋊Dic₁₃₉	D₄	1	1	yes	characteristic
98	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
99	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
100	Dic₁₃₉⋊C₄	—	2	1	no	—
101	C₂²⋊Dic₁₃₉	—	2	1	no	—
102	C₂²⋊Dic₁₃₉	—	2	1	no	—
103	C₂²⋊Dic₁₃₉	—	2	1	no	—
104	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
105	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
106	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
107	(C₂×D₁₃₉)⋊C₄	D₄	1	1	yes	characteristic
108	(C₂×D₁₃₉)⋊C₄	D₄	1	1	yes	characteristic
109	C₂×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂×D₄×C₁₃₉	—	2	1	no	—
111	C₂×D₄×C₁₃₉	—	2	1	no	—
112	C₂×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
115	SD₁₆×C₁₃₉	—	2	2	no	—
116	SD₁₆×C₁₃₉	—	4	1	no	—
117	D₈×C₁₃₉	—	2	2	no	—
118	D₈×C₁₃₉	—	4	1	no	—
119	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
120	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
121	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
122	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
123	C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₂²×D₁₃₉	—	2	1	no	—
125	C₂²×D₁₃₉	—	2	1	no	—
126	C₂²×D₁₃₉	—	4	2	no	—
127	C₂²×D₁₃₉	—	4	2	no	—
128	C₂²×D₁₃₉	—	4	2	no	—
129	C₂²×D₁₃₉	—	4	2	no	—
130	C₂²×D₁₃₉	—	4	2	no	—
131	C₂²×D₁₃₉	—	4	2	no	—
132	C₂²×D₁₃₉	—	8	1	no	—
133	C₂²×D₁₃₉	—	8	1	no	—
134	C₂²×D₁₃₉	—	8	1	no	—
135	C₂²×D₁₃₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×D₁₃₉	C₂×D₄	1	1	yes	characteristic
137	D₅₅₆	—	2	2	no	—
138	D₅₅₆	—	2	1	no	—
139	D₅₅₆	—	2	1	no	—
140	D₅₅₆	—	4	2	no	—
141	D₅₅₆	C₂×D₄	1	2	yes	—
142	D₅₅₆	C₂×D₄	1	2	yes	complemented
143	C₂²⋊D₁₃₉	—	4	2	no	—
144	C₂²⋊D₁₃₉	—	4	2	no	—
145	C₂²⋊D₁₃₉	—	4	2	no	—
146	C₂²⋊D₁₃₉	—	4	2	no	—
147	C₂²⋊D₁₃₉	—	4	2	no	—
148	C₂²⋊D₁₃₉	—	8	1	no	—
149	C₂×Dic₁₃₉	—	2	1	no	—
150	C₂×Dic₁₃₉	—	2	1	no	—
151	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
152	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
153	C₄×D₁₃₉	—	2	1	no	—
154	C₄×D₁₃₉	—	2	1	no	—
155	C₄×D₁₃₉	—	2	1	no	—
156	C₄×D₁₃₉	—	2	1	no	—
157	C₄×D₁₃₉	—	4	2	no	—
158	C₄×D₁₃₉	—	4	2	no	—
159	C₄×D₁₃₉	—	8	1	no	—
160	C₁₃₉⋊C₈	—	2	1	no	—
161	C₁₃₉⋊C₈	—	2	1	no	—
162	C₂³×C₁₃₉	—	2	1	no	—
163	C₂³×C₁₃₉	—	2	1	no	—
164	C₂³×C₁₃₉	—	2	1	no	—
165	Q₈×C₁₃₉	—	2	1	no	—
166	Q₈×C₁₃₉	—	2	1	no	—
167	D₄×C₁₃₉	—	2	1	no	—
168	D₄×C₁₃₉	—	2	1	no	—
169	D₄×C₁₃₉	—	2	1	no	—
170	D₄×C₁₃₉	—	2	1	no	—
171	D₄×C₁₃₉	—	2	1	no	—
172	D₄×C₁₃₉	—	2	1	no	—
173	D₄×C₁₃₉	—	4	2	no	—
174	D₄×C₁₃₉	—	8	1	no	—
175	C₂×C₄×C₁₃₉	—	2	1	no	—
176	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
179	C₈×C₁₃₉	—	2	1	no	—
180	C₈×C₁₃₉	C₂×D₄	1	2	yes	complemented
181	C₂²×C₁₃₉	—	4	1	no	—
182	C₂²×C₁₃₉	—	4	1	no	—
183	C₂²×C₁₃₉	—	4	1	no	—
184	C₂²×C₁₃₉	—	4	1	no	—
185	C₂²×C₁₃₉	—	4	1	no	—
186	C₂²×C₁₃₉	—	4	1	no	—
187	C₂²×C₁₃₉	—	4	1	no	—
188	C₂²×C₁₃₉	—	4	1	no	—
189	C₂²×C₁₃₉	—	4	1	no	—
190	C₂²×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
191	C₂×D₁₃₉	—	2	1	no	—
192	C₂×D₁₃₉	—	2	1	no	—
193	C₂×D₁₃₉	—	2	1	no	—
194	C₂×D₁₃₉	—	2	2	no	—
195	C₂×D₁₃₉	—	2	2	no	—
196	C₂×D₁₃₉	—	2	1	no	—
197	C₂×D₁₃₉	—	2	1	no	—
198	C₂×D₁₃₉	—	4	1	no	—
199	C₂×D₁₃₉	—	4	1	no	—
200	C₂×D₁₃₉	—	4	1	no	—
201	C₂×D₁₃₉	—	4	1	no	—
202	C₂×D₁₃₉	—	8	4	no	—
203	C₂×D₁₃₉	—	8	4	no	—
204	C₂×D₁₃₉	—	8	4	no	—
205	C₂×D₁₃₉	AGL(1,ℤ/8)	1	2	yes	complemented
206	C₄×C₁₃₉	—	2	1	no	—
207	C₄×C₁₃₉	—	2	1	no	—
208	C₄×C₁₃₉	—	4	1	no	—
209	C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
210	C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
211	Dic₁₃₉	—	2	1	no	—
212	Dic₁₃₉	—	2	1	no	—
213	Dic₁₃₉	—	4	1	no	—
214	Dic₁₃₉	—	4	1	no	—
215	C₂×C₁₃₉	—	8	1	no	—
216	C₂×C₁₃₉	—	8	1	no	—
217	C₂×C₁₃₉	—	8	1	no	—
218	C₂×C₁₃₉	D₄²	1	1	yes	characteristic
219	C₂×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
220	C₂×C₁₃₉	#576	1	1	yes	characteristic
221	D₁₃₉	—	2	2	no	—
222	D₁₃₉	—	4	1	no	—
223	D₁₃₉	—	4	2	no	—
224	D₁₃₉	—	4	2	no	—
225	C₁₃₉	#3264	1	1	yes	characteristic, complemented, Sylow
226	#3264	—	139	1	no	maximal, Sylow
227	C₂×AGL(1,ℤ/8)	—	139	1	no	—
228	C₂²×D₈	—	139	1	no	—
229	#546	—	139	1	no	—
230	D₄²	—	139	1	no	—
231	#496	D₁₃₉	1	1	yes	characteristic, complemented
232	#469	—	139	1	no	—
233	#465	—	139	1	no	—
234	#463	—	139	1	no	—
235	#459	—	139	1	no	—
236	#450	—	139	1	no	—
237	#449	—	139	1	no	—
238	#447	—	139	1	no	—
239	#447	—	139	1	no	—
240	#442	—	139	1	no	—
241	#435	—	139	1	no	—
242	C₂×#41	—	139	1	no	—
243	C₂²×D₄	—	278	1	no	—
244	C₂²×D₄	—	139	1	no	—
245	C₂²×D₄	—	139	1	no	—
246	C₂²×D₄	—	139	1	no	—
247	AGL(1,ℤ/8)	—	278	4	no	—
248	C₂×SD₁₆	—	139	1	no	—
249	C₂×SD₁₆	C₂×D₁₃₉	1	1	yes	characteristic, complemented
250	C₂×SD₁₆	C₂×D₁₃₉	1	1	yes	characteristic, complemented
251	C₂×D₈	—	278	4	no	—
252	C₂×D₈	—	139	1	no	—
253	C₂×D₈	—	139	1	no	—
254	C₂×D₈	—	139	1	no	—
255	C₂×D₈	—	139	1	no	—
256	C₂×D₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
257	C₂×D₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
258	C₂×M₁₆	—	139	1	no	—
259	C₂²×C₈	—	139	1	no	—
260	#127	C₂×D₁₃₉	1	1	yes	characteristic, complemented
261	#124	C₂×D₁₃₉	1	1	yes	characteristic, complemented
262	#123	—	278	1	no	—
263	C₂²⋊Q₈	—	139	1	no	—
264	#121	—	278	1	no	—
265	#121	—	278	1	no	—
266	#121	—	139	1	no	—
267	#121	—	139	1	no	—
268	#121	—	139	1	no	—
269	#120	—	278	1	no	—
270	#120	—	278	1	no	—
271	#120	—	278	1	no	—
272	C₄×D₄	—	139	1	no	—
273	C₄×D₄	—	139	1	no	—
274	C₄×D₄	—	139	1	no	—
275	C₂×C₂²⋊C₄	—	278	1	no	—
276	#106	—	139	1	no	—
277	C₄⋊C₈	—	139	1	no	—
278	#103	—	139	1	no	—
279	#102	—	139	1	no	—
280	#102	—	139	1	no	—
281	#102	—	139	1	no	—
282	#102	—	139	1	no	—
283	#102	—	139	1	no	—
284	C₂²⋊C₈	—	139	1	no	—
285	C₂²⋊C₈	—	139	1	no	—
286	#97	C₂×D₁₃₉	1	1	yes	characteristic, complemented
287	C₂⁴	—	278	1	no	—
288	C₂⁴	—	278	1	no	—
289	C₂⁴	—	278	1	no	—
290	#41	—	278	2	no	—
291	#41	—	556	1	no	—
292	C₂×Q₈	C₂²×D₁₃₉	1	1	yes	characteristic
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	278	1	no	—
296	C₂×D₄	—	278	2	no	—
297	C₂×D₄	—	278	2	no	—
298	C₂×D₄	—	278	2	no	—
299	C₂×D₄	—	278	1	no	—
300	C₂×D₄	—	278	1	no	—
301	C₂×D₄	—	278	1	no	—
302	C₂×D₄	—	278	1	no	—
303	C₂×D₄	—	278	1	no	—
304	C₂×D₄	—	278	1	no	—
305	C₂×D₄	—	556	1	no	—
306	C₂×D₄	—	556	1	no	—
307	C₂×D₄	—	556	1	no	—
308	C₂×D₄	—	556	4	no	—
309	C₂×D₄	—	139	1	no	—
310	C₂×D₄	—	139	1	no	—
311	C₂×D₄	—	139	1	no	—
312	C₂×D₄	C₂²×D₁₃₉	1	1	yes	characteristic
313	C₂×D₄	C₂²×D₁₃₉	1	1	yes	characteristic
314	C₂×D₄	C₂²×D₁₃₉	1	1	yes	characteristic
315	C₂²×C₄	—	278	1	no	—
316	C₂²×C₄	—	278	1	no	—
317	C₂²×C₄	—	278	1	no	—
318	C₂²×C₄	—	139	1	no	—
319	C₂²×C₄	—	139	1	no	—
320	SD₁₆	—	2	2	no	—
321	SD₁₆	—	4	1	no	—
322	SD₁₆	—	278	2	no	—
323	D₈	—	2	2	no	—
324	D₈	—	4	1	no	—
325	D₈	—	278	2	no	—
326	D₈	—	278	2	no	—
327	D₈	—	278	2	no	—
328	D₈	—	139	4	no	—
329	M₁₆	—	278	2	no	—
330	C₂×C₈	—	278	2	no	—
331	C₂×C₈	—	139	1	no	—
332	C₂×C₈	—	139	1	no	—
333	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
334	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
335	C₄⋊C₄	—	278	1	no	—
336	C₄⋊C₄	—	139	1	no	—
337	C₄⋊C₄	—	139	1	no	—
338	C₄⋊C₄	—	139	1	no	—
339	C₂²⋊C₄	—	2	1	no	—
340	C₂²⋊C₄	—	2	1	no	—
341	C₂²⋊C₄	—	278	1	no	—
342	C₂²⋊C₄	—	278	1	no	—
343	C₂²⋊C₄	—	278	1	no	—
344	C₂²⋊C₄	—	278	1	no	—
345	C₂²⋊C₄	—	278	1	no	—
346	C₂²⋊C₄	—	278	1	no	—
347	C₂²⋊C₄	—	139	1	no	—
348	C₂²⋊C₄	—	139	1	no	—
349	C₄²	C₂²×D₁₃₉	1	1	yes	characteristic
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	278	1	no	—
354	C₂³	—	278	1	no	—
355	C₂³	—	556	2	no	—
356	C₂³	—	556	2	no	—
357	C₂³	—	556	2	no	—
358	C₂³	—	556	2	no	—
359	C₂³	—	556	2	no	—
360	C₂³	—	556	2	no	—
361	C₂³	—	1112	1	no	—
362	C₂³	—	1112	1	no	—
363	C₂³	—	1112	1	no	—
364	C₂³	—	139	1	no	—
365	C₂³	—	139	1	no	—
366	Q₈	—	2	1	no	—
367	Q₈	—	2	1	no	—
368	D₄	—	2	1	no	—
369	D₄	—	2	1	no	—
370	D₄	—	2	1	no	—
371	D₄	—	2	1	no	—
372	D₄	—	2	1	no	—
373	D₄	—	2	1	no	—
374	D₄	—	4	2	no	—
375	D₄	—	8	1	no	—
376	D₄	—	278	2	no	—
377	D₄	—	278	1	no	—
378	D₄	—	278	1	no	—
379	D₄	—	556	2	no	—
380	D₄	—	556	2	no	—
381	D₄	—	556	2	no	—
382	D₄	—	556	2	no	—
383	D₄	—	556	2	no	—
384	D₄	—	556	2	no	—
385	D₄	—	1112	1	no	—
386	D₄	—	139	2	no	—
387	D₄	—	139	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	278	1	no	—
390	C₂×C₄	—	278	1	no	—
391	C₂×C₄	—	278	1	no	—
392	C₂×C₄	—	278	1	no	—
393	C₂×C₄	—	278	1	no	—
394	C₂×C₄	—	278	1	no	—
395	C₂×C₄	—	556	2	no	—
396	C₂×C₄	—	556	2	no	—
397	C₂×C₄	—	1112	1	no	—
398	C₂×C₄	—	139	1	no	—
399	C₂×C₄	—	139	1	no	—
400	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
401	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
402	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
403	C₈	—	2	1	no	—
404	C₈	—	278	1	no	—
405	C₈	—	278	1	no	—
406	C₈	D₄×D₁₃₉	1	2	yes	complemented
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	278	1	no	—
417	C₂²	—	278	1	no	—
418	C₂²	—	278	1	no	—
419	C₂²	—	278	2	no	—
420	C₂²	—	278	2	no	—
421	C₂²	—	278	1	no	—
422	C₂²	—	278	1	no	—
423	C₂²	—	556	1	no	—
424	C₂²	—	556	1	no	—
425	C₂²	—	556	1	no	—
426	C₂²	—	556	1	no	—
427	C₂²	—	1112	4	no	—
428	C₂²	—	1112	4	no	—
429	C₂²	—	1112	4	no	—
430	C₂²	—	139	2	no	—
431	C₂²	C₂×D₄×D₁₃₉	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	4	1	no	—
435	C₄	—	278	1	no	—
436	C₄	—	278	1	no	—
437	C₄	—	556	1	no	—
438	C₄	—	556	1	no	—
439	C₄	C₂×D₄×D₁₃₉	1	1	yes	characteristic
440	C₄	#17984887	1	1	yes	characteristic
441	C₂	—	8	1	no	—
442	C₂	—	8	1	no	—
443	C₂	—	8	1	no	—
444	C₂	—	278	2	no	—
445	C₂	—	556	1	no	—
446	C₂	—	556	2	no	—
447	C₂	—	556	2	no	—
448	C₂	#22581588	1	1	yes	characteristic
449	C₂	AGL(1,ℤ/8)×D₁₃₉	1	1	yes	characteristic
450	C₂	#22581757	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₃₉
commutator, cosocle	C₂×C₄×C₁₃₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₃₉
Fitting	#496×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂²×D₄
hypercenter	#496	D₁₃₉
hypocenter	C₁₃₉	#3264
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #496

Complements

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

N	H ≅ G/N	type
1. C₂×#17984869	C₂	semidirect
2. C₂×D₈×D₁₃₉	C₂	semidirect
3. #22581596	C₂	semidirect
4. #22581588	C₂	semidirect
5. #22581203	C₂	semidirect
6. #22581179	C₂	semidirect
7. #22581165	C₂	semidirect
8. #22581145	C₂	semidirect
9. #22581102	C₂	semidirect
10. #22581097	C₂	semidirect
11. #22581085	C₂	semidirect
12. #22581085	C₂	semidirect
13. #22581066	C₂	semidirect
14. #22581026	C₂	semidirect
15. #496×C₁₃₉	C₂	semidirect
16. C₂×#14555786	C₂²	semidirect
19. C₂×D₄×D₁₃₉	C₂²	semidirect
20. C₂×D₄×D₁₃₉	C₂²	semidirect
22. C₂×#14555772	C₂²	semidirect
25. C₂×#14555770	C₂²	semidirect
26. C₂×#14555770	C₂²	semidirect
28. C₂×#14555768	C₂²	semidirect
29. C₂×C₈×D₁₃₉	C₂²	semidirect
31. #17984818	C₂²	semidirect
35. #17984813	C₂²	semidirect
36. #17984813	C₂²	semidirect
41. C₄×D₅₅₆	C₂²	semidirect
42. C₄×D₅₅₆	C₂²	semidirect
44. #17984774	C₂²	semidirect
45. C₄⋊(C₁₃₉⋊C₈)	C₂²	semidirect
46. #17984766	C₂²	semidirect
47. #17984764	C₂²	semidirect
48. #17984764	C₂²	semidirect
49. #17984763	C₂²	semidirect
50. #17984763	C₂²	semidirect
51. #17984763	C₂²	semidirect
52. (C₂×D₁₃₉)⋊C₈	C₂²	semidirect
53. (C₂×D₁₃₉)⋊C₈	C₂²	semidirect
54. C₂×SD₁₆×C₁₃₉	C₂²	semidirect
55. C₂×SD₁₆×C₁₃₉	C₂²	semidirect
56. C₂×D₈×C₁₃₉	C₂²	semidirect
57. C₂×D₈×C₁₃₉	C₂²	semidirect
58. #127×C₁₃₉	C₂²	semidirect
59. #124×C₁₃₉	C₂²	semidirect
60. #97×C₁₃₉	C₂²	semidirect
89. D₁₁₁₂	D₄	semidirect
142. D₅₅₆	C₂×D₄	semidirect
180. C₈×C₁₃₉	C₂×D₄	semidirect
205. C₂×D₁₃₉	AGL(1,ℤ/8)	semidirect
225. C₁₃₉	#3264	semidirect
231. #496	D₁₃₉	semidirect
249. C₂×SD₁₆	C₂×D₁₃₉	semidirect
250. C₂×SD₁₆	C₂×D₁₃₉	semidirect
256. C₂×D₈	C₂×D₁₃₉	semidirect
257. C₂×D₈	C₂×D₁₃₉	semidirect
260. #127	C₂×D₁₃₉	semidirect
261. #124	C₂×D₁₃₉	semidirect
286. #97	C₂×D₁₃₉	semidirect
406. C₈	D₄×D₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17984869	2
C₂×D₈×D₁₃₉	2
#22581596	2
#22581588	2
#22581203	2
#22581179	2
#22581165	2
#22581145	2
#22581102	2
#22581097	2
#22581085	2
#22581066	2
#22581026	2
#496×C₁₃₉	2
#3264	139