Subgroups — #31817901

Order 17792.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 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×SD₁₆×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#22581615	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×D₅₅₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#22581342	C₂	1	1	yes	maximal, characteristic, complemented
6	#22581200	C₂	1	1	yes	maximal, characteristic, complemented
7	#22581190	C₂	1	1	yes	maximal, characteristic, complemented
8	#22581168	C₂	1	1	yes	maximal, characteristic, complemented
9	#22581153	C₂	1	1	yes	maximal, characteristic, complemented
10	#22581105	C₂	1	1	yes	maximal, characteristic, complemented
11	#22581101	C₂	1	1	yes	maximal, characteristic, complemented
12	#22581093	C₂	1	1	yes	maximal, characteristic, complemented
13	#22581088	C₂	1	1	yes	maximal, characteristic, complemented
14	#22581026	C₂	1	1	yes	maximal, characteristic, complemented
15	#440×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14555786	C₂²	1	1	yes	characteristic, complemented
17	C₂×Q₈×D₁₃₉	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₅₅₆	—	2	1	no	—
19	C₂×D₄×D₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×D₄×D₁₃₉	C₂²	1	1	yes	characteristic
21	#17984869	—	2	4	no	—
22	C₂×#14555774	C₂²	1	1	yes	characteristic, complemented
23	C₂×#14555774	C₂²	1	1	yes	characteristic, complemented
24	C₂×#14555773	C₂²	1	1	yes	characteristic
25	C₂×#14555772	C₂²	1	1	yes	characteristic, complemented
26	C₂×#14555772	C₂²	1	1	yes	characteristic, complemented
27	SD₁₆×D₁₃₉	—	2	4	no	—
28	C₂×D₁₁₁₂	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₁₁₁₂	C₂²	1	1	yes	characteristic, complemented
30	C₂×#14555770	C₂²	1	1	yes	characteristic
31	C₂×#14555768	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₈×D₁₃₉	C₂²	1	1	yes	characteristic, complemented
33	#17984839	C₂²	1	1	yes	characteristic
34	#17984830	—	2	1	no	—
35	#17984830	C₂²	1	1	yes	characteristic, complemented
36	#17984822	—	2	1	no	—
37	#17984822	C₂²	1	1	yes	characteristic, complemented
38	#17984817	—	2	1	no	—
39	#17984817	C₂²	1	1	yes	characteristic
40	#17984817	C₂²	1	1	yes	characteristic
41	#17984817	C₂²	1	1	yes	characteristic, complemented
42	#17984816	—	2	1	no	—
43	#17984812	—	2	1	no	—
44	#17984812	—	2	1	no	—
45	C₄×D₅₅₆	—	2	1	no	—
46	C₄×D₅₅₆	C₂²	1	1	yes	characteristic
47	C₄⋊(C₁₃₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
48	#17984765	C₂²	1	1	yes	characteristic, complemented
49	#17984762	C₂²	1	1	yes	characteristic, complemented
50	#17984762	C₂²	1	1	yes	characteristic, complemented
51	#17984762	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
55	C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
56	C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
57	#107×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
58	#103×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
59	#102×C₁₃₉	C₂²	1	1	yes	characteristic
60	#97×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₃₉	—	2	1	no	—
62	C₂³×D₁₃₉	—	2	1	no	—
63	#14555786	—	2	2	no	—
64	#14555786	—	4	1	no	—
65	C₂×Dic₂₇₈	—	2	1	no	—
66	C₂×Dic₂₇₈	C₂³	1	1	yes	characteristic
67	Q₈×D₁₃₉	—	2	2	no	—
68	Q₈×D₁₃₉	—	4	1	no	—
69	C₂×D₅₅₆	—	2	1	no	—
70	C₂×D₅₅₆	—	2	1	no	—
71	C₂×D₅₅₆	—	2	1	no	—
72	C₂×D₅₅₆	—	2	1	no	—
73	C₂×D₅₅₆	—	2	1	no	—
74	C₂×D₅₅₆	—	2	1	no	—
75	C₂×D₅₅₆	—	4	4	no	—
76	C₂×D₅₅₆	D₄	1	1	yes	characteristic
77	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
78	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
79	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
80	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
81	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
82	D₄×D₁₃₉	—	2	2	no	—
83	D₄×D₁₃₉	—	2	2	no	—
84	D₄×D₁₃₉	—	4	1	no	—
85	D₄×D₁₃₉	—	4	1	no	—
86	C₂×C₄×D₁₃₉	—	2	1	no	—
87	C₂×C₄×D₁₃₉	—	2	1	no	—
88	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
89	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
90	#14555774	—	2	2	no	—
91	#14555774	—	4	1	no	—
92	#14555773	—	2	2	no	—
93	#14555772	—	2	2	no	—
94	#14555772	—	2	2	no	—
95	D₁₁₁₂	—	2	2	no	—
96	D₁₁₁₂	—	4	1	no	—
97	#14555770	—	2	2	no	—
98	#14555768	—	2	2	no	—
99	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
100	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
101	C₈×D₁₃₉	—	2	2	no	—
102	C₄⋊Dic₁₃₉	—	2	1	no	—
103	C₄⋊Dic₁₃₉	D₄	1	1	yes	characteristic
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	—	2	1	no	—
108	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
109	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
110	(C₂×D₁₃₉)⋊C₄	D₄	1	1	yes	characteristic
111	(C₂×D₁₃₉)⋊C₄	D₄	1	1	yes	characteristic
112	C₂×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₁₃₉	—	2	1	no	—
115	SD₁₆×C₁₃₉	D₄	1	4	yes	complemented
116	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
117	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₄⋊C₄×C₁₃₉	—	2	1	no	—
119	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
120	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
121	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
122	C₄²×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	—	2	1	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	—	8	1	no	—
132	C₂²×D₁₃₉	—	8	1	no	—
133	C₂²×D₁₃₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×D₁₃₉	C₂×D₄	1	1	yes	characteristic
135	Dic₂₇₈	—	2	1	no	—
136	Dic₂₇₈	—	2	1	no	—
137	Dic₂₇₈	—	4	2	no	—
138	D₅₅₆	—	2	2	no	—
139	D₅₅₆	—	2	1	no	—
140	D₅₅₆	—	2	1	no	—
141	D₅₅₆	—	2	1	no	—
142	D₅₅₆	—	2	1	no	—
143	D₅₅₆	—	2	1	no	—
144	D₅₅₆	—	2	1	no	—
145	D₅₅₆	—	4	2	no	—
146	D₅₅₆	—	4	2	no	—
147	D₅₅₆	—	4	2	no	—
148	D₅₅₆	—	4	2	no	—
149	D₅₅₆	—	4	2	no	—
150	D₅₅₆	—	8	1	no	—
151	C₂²⋊D₁₃₉	—	4	2	no	—
152	C₂²⋊D₁₃₉	—	4	2	no	—
153	C₂×Dic₁₃₉	—	2	1	no	—
154	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
155	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
156	C₄×D₁₃₉	—	2	1	no	—
157	C₄×D₁₃₉	—	2	1	no	—
158	C₄×D₁₃₉	—	2	1	no	—
159	C₄×D₁₃₉	—	2	1	no	—
160	C₄×D₁₃₉	—	4	2	no	—
161	C₄×D₁₃₉	—	4	2	no	—
162	C₁₃₉⋊C₈	—	2	1	no	—
163	C₁₃₉⋊C₈	—	2	1	no	—
164	C₂³×C₁₃₉	—	2	1	no	—
165	Q₈×C₁₃₉	—	2	1	no	—
166	Q₈×C₁₃₉	C₂×D₄	1	2	yes	complemented
167	D₄×C₁₃₉	—	2	1	no	—
168	D₄×C₁₃₉	C₂×D₄	1	2	yes	—
169	C₂×C₄×C₁₃₉	—	2	1	no	—
170	C₂×C₄×C₁₃₉	—	2	1	no	—
171	C₂×C₄×C₁₃₉	—	2	1	no	—
172	C₂×C₄×C₁₃₉	—	4	2	no	—
173	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
176	C₈×C₁₃₉	—	2	1	no	—
177	C₈×C₁₃₉	C₂×D₄	1	2	yes	complemented
178	C₂²×C₁₃₉	—	2	2	no	—
179	C₂²×C₁₃₉	—	4	1	no	—
180	C₂²×C₁₃₉	—	4	1	no	—
181	C₂²×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
182	C₂×D₁₃₉	—	2	1	no	—
183	C₂×D₁₃₉	—	2	1	no	—
184	C₂×D₁₃₉	—	2	1	no	—
185	C₂×D₁₃₉	—	2	1	no	—
186	C₂×D₁₃₉	—	2	1	no	—
187	C₂×D₁₃₉	—	4	1	no	—
188	C₂×D₁₃₉	—	4	1	no	—
189	C₂×D₁₃₉	—	4	1	no	—
190	C₂×D₁₃₉	—	4	1	no	—
191	C₂×D₁₃₉	—	4	1	no	—
192	C₂×D₁₃₉	—	4	1	no	—
193	C₂×D₁₃₉	—	4	1	no	—
194	C₂×D₁₃₉	—	4	1	no	—
195	C₂×D₁₃₉	—	4	1	no	—
196	C₂×D₁₃₉	—	8	4	no	—
197	C₂×D₁₃₉	—	8	4	no	—
198	C₂×D₁₃₉	AGL(1,ℤ/8)	1	2	yes	complemented
199	C₄×C₁₃₉	—	2	2	no	—
200	C₄×C₁₃₉	—	2	1	no	—
201	C₄×C₁₃₉	—	2	1	no	—
202	C₄×C₁₃₉	—	4	1	no	—
203	C₄×C₁₃₉	—	4	1	no	—
204	C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
205	C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
206	Dic₁₃₉	—	2	1	no	—
207	Dic₁₃₉	—	2	1	no	—
208	Dic₁₃₉	—	4	1	no	—
209	C₂×C₁₃₉	—	4	2	no	—
210	C₂×C₁₃₉	D₄²	1	1	yes	characteristic
211	C₂×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
212	C₂×C₁₃₉	#577	1	1	yes	characteristic
213	D₁₃₉	—	2	2	no	—
214	D₁₃₉	—	4	1	no	—
215	D₁₃₉	—	8	1	no	—
216	D₁₃₉	—	8	1	no	—
217	D₁₃₉	—	8	1	no	—
218	C₁₃₉	#3265	1	1	yes	characteristic, complemented, Sylow
219	#3265	—	139	1	no	maximal, Sylow
220	C₂×AGL(1,ℤ/8)	—	139	1	no	—
221	C₂²×SD₁₆	—	139	1	no	—
222	#548	—	139	1	no	—
223	D₄²	—	139	1	no	—
224	#496	—	139	1	no	—
225	#468	—	139	1	no	—
226	#466	—	139	1	no	—
227	#463	—	139	1	no	—
228	#460	—	139	1	no	—
229	#450	—	139	1	no	—
230	#449	—	139	1	no	—
231	#448	—	139	1	no	—
232	#447	—	139	1	no	—
233	#440	D₁₃₉	1	1	yes	characteristic, complemented
234	#435	—	139	1	no	—
235	C₂×#41	—	139	1	no	—
236	C₂²×Q₈	—	139	1	no	—
237	C₂²×D₄	—	278	1	no	—
238	C₂²×D₄	—	139	1	no	—
239	C₂²×D₄	—	139	1	no	—
240	AGL(1,ℤ/8)	—	278	4	no	—
241	C₂×SD₁₆	—	278	4	no	—
242	C₂×SD₁₆	—	139	1	no	—
243	C₂×SD₁₆	—	139	1	no	—
244	C₂×SD₁₆	—	139	1	no	—
245	C₂×SD₁₆	—	139	1	no	—
246	C₂×SD₁₆	—	139	1	no	—
247	C₂×SD₁₆	C₂×D₁₃₉	1	1	yes	characteristic
248	C₂×D₈	—	139	1	no	—
249	C₂×D₈	—	139	1	no	—
250	C₂×D₈	—	139	1	no	—
251	C₂×M₁₆	—	139	1	no	—
252	C₂²×C₈	—	139	1	no	—
253	#127	—	139	1	no	—
254	#124	—	278	1	no	—
255	#124	—	139	1	no	—
256	C₂²⋊Q₈	—	278	1	no	—
257	C₂²⋊Q₈	—	139	1	no	—
258	#121	—	278	1	no	—
259	#121	—	278	1	no	—
260	#121	—	139	1	no	—
261	#121	—	139	1	no	—
262	#121	—	139	1	no	—
263	#120	—	278	1	no	—
264	#120	—	278	1	no	—
265	C₄×Q₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
266	C₄×D₄	—	278	1	no	—
267	C₄×D₄	—	139	1	no	—
268	C₄×D₄	C₂×D₁₃₉	1	1	yes	characteristic
269	#107	C₂×D₁₃₉	1	1	yes	characteristic, complemented
270	C₄⋊C₈	—	139	1	no	—
271	#103	—	139	1	no	—
272	#103	C₂×D₁₃₉	1	1	yes	characteristic, complemented
273	#102	—	139	1	no	—
274	#102	—	139	1	no	—
275	#102	—	139	1	no	—
276	#102	C₂×D₁₃₉	1	1	yes	characteristic
277	C₂²⋊C₈	—	139	1	no	—
278	C₂²⋊C₈	—	139	1	no	—
279	#97	C₂×D₁₃₉	1	1	yes	characteristic, complemented
280	C₂⁴	—	278	1	no	—
281	C₂⁴	—	278	1	no	—
282	#41	—	278	2	no	—
283	#41	—	556	1	no	—
284	C₂×Q₈	—	278	1	no	—
285	C₂×Q₈	—	278	2	no	—
286	C₂×Q₈	—	556	1	no	—
287	C₂×Q₈	—	139	1	no	—
288	C₂×Q₈	C₂²×D₁₃₉	1	1	yes	characteristic
289	C₂×D₄	—	278	1	no	—
290	C₂×D₄	—	278	1	no	—
291	C₂×D₄	—	278	1	no	—
292	C₂×D₄	—	278	1	no	—
293	C₂×D₄	—	278	2	no	—
294	C₂×D₄	—	278	2	no	—
295	C₂×D₄	—	278	1	no	—
296	C₂×D₄	—	278	1	no	—
297	C₂×D₄	—	278	1	no	—
298	C₂×D₄	—	278	1	no	—
299	C₂×D₄	—	556	4	no	—
300	C₂×D₄	—	556	1	no	—
301	C₂×D₄	—	556	1	no	—
302	C₂×D₄	—	139	1	no	—
303	C₂×D₄	—	139	1	no	—
304	C₂×D₄	—	139	1	no	—
305	C₂×D₄	—	139	1	no	—
306	C₂×D₄	C₂²×D₁₃₉	1	1	yes	characteristic
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	278	1	no	—
309	C₂²×C₄	—	278	1	no	—
310	C₂²×C₄	—	139	1	no	—
311	C₂²×C₄	—	139	1	no	—
312	SD₁₆	—	278	2	no	—
313	SD₁₆	—	278	2	no	—
314	SD₁₆	—	278	2	no	—
315	SD₁₆	—	278	2	no	—
316	SD₁₆	—	556	1	no	—
317	SD₁₆	D₅₅₆	1	4	yes	complemented
318	D₈	—	278	2	no	—
319	D₈	—	278	2	no	—
320	D₈	—	556	1	no	—
321	M₁₆	—	278	2	no	—
322	C₂×C₈	—	278	2	no	—
323	C₂×C₈	—	139	1	no	—
324	C₂×C₈	—	139	1	no	—
325	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
326	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	278	1	no	—
329	C₄⋊C₄	—	139	1	no	—
330	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
331	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	278	1	no	—
334	C₂²⋊C₄	—	278	1	no	—
335	C₂²⋊C₄	—	278	1	no	—
336	C₂²⋊C₄	—	278	1	no	—
337	C₂²⋊C₄	—	278	1	no	—
338	C₂²⋊C₄	—	278	1	no	—
339	C₂²⋊C₄	—	139	1	no	—
340	C₂²⋊C₄	—	139	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	C₂²×D₁₃₉	1	1	yes	characteristic
343	C₂³	—	2	1	no	—
344	C₂³	—	278	1	no	—
345	C₂³	—	278	1	no	—
346	C₂³	—	278	1	no	—
347	C₂³	—	556	2	no	—
348	C₂³	—	556	2	no	—
349	C₂³	—	556	2	no	—
350	C₂³	—	556	2	no	—
351	C₂³	—	1112	1	no	—
352	C₂³	—	1112	1	no	—
353	C₂³	—	139	1	no	—
354	C₂³	—	139	1	no	—
355	Q₈	—	2	1	no	—
356	Q₈	—	278	1	no	—
357	Q₈	—	278	1	no	—
358	Q₈	—	556	2	no	—
359	Q₈	C₂×D₅₅₆	1	2	yes	complemented
360	D₄	—	2	1	no	—
361	D₄	—	278	2	no	—
362	D₄	—	278	1	no	—
363	D₄	—	278	1	no	—
364	D₄	—	278	1	no	—
365	D₄	—	278	1	no	—
366	D₄	—	278	1	no	—
367	D₄	—	278	1	no	—
368	D₄	—	556	2	no	—
369	D₄	—	556	2	no	—
370	D₄	—	556	2	no	—
371	D₄	—	556	2	no	—
372	D₄	—	556	2	no	—
373	D₄	—	556	2	no	—
374	D₄	—	556	2	no	—
375	D₄	—	1112	1	no	—
376	D₄	C₂×D₅₅₆	1	2	yes	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	278	1	no	—
382	C₂×C₄	—	278	1	no	—
383	C₂×C₄	—	278	1	no	—
384	C₂×C₄	—	278	1	no	—
385	C₂×C₄	—	278	1	no	—
386	C₂×C₄	—	556	2	no	—
387	C₂×C₄	—	556	2	no	—
388	C₂×C₄	—	139	1	no	—
389	C₂×C₄	—	139	1	no	—
390	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
391	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	278	1	no	—
395	C₈	—	278	1	no	—
396	C₈	C₂×D₅₅₆	1	2	yes	complemented
397	C₂²	—	2	2	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	278	1	no	—
401	C₂²	—	278	1	no	—
402	C₂²	—	278	1	no	—
403	C₂²	—	278	1	no	—
404	C₂²	—	278	1	no	—
405	C₂²	—	556	1	no	—
406	C₂²	—	556	1	no	—
407	C₂²	—	556	1	no	—
408	C₂²	—	556	1	no	—
409	C₂²	—	556	1	no	—
410	C₂²	—	556	1	no	—
411	C₂²	—	556	1	no	—
412	C₂²	—	556	1	no	—
413	C₂²	—	556	1	no	—
414	C₂²	—	1112	4	no	—
415	C₂²	—	1112	4	no	—
416	C₂²	—	139	2	no	—
417	C₂²	C₂×D₄×D₁₃₉	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	1	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	1	no	—
423	C₄	—	278	1	no	—
424	C₄	—	278	1	no	—
425	C₄	—	556	1	no	—
426	C₄	C₂²×D₅₅₆	1	1	yes	characteristic
427	C₄	#17984888	1	1	yes	characteristic
428	C₂	—	4	2	no	—
429	C₂	—	278	2	no	—
430	C₂	—	556	1	no	—
431	C₂	—	1112	1	no	—
432	C₂	—	1112	1	no	—
433	C₂	—	1112	1	no	—
434	C₂	D₄×D₅₅₆	1	1	yes	characteristic
435	C₂	AGL(1,ℤ/8)×D₁₃₉	1	1	yes	characteristic
436	C₂	#22581762	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₃₉
commutator, cosocle	C₂×C₄×C₁₃₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₃₉
Fitting	#440×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂²×D₄
hypercenter	#440	D₁₃₉
hypocenter	C₁₃₉	#3265
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #440

Complements

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

N	H ≅ G/N	type
1. C₂×#17984869	C₂	semidirect
2. C₂×SD₁₆×D₁₃₉	C₂	semidirect
3. #22581615	C₂	semidirect
4. D₄×D₅₅₆	C₂	semidirect
5. #22581342	C₂	semidirect
6. #22581200	C₂	semidirect
7. #22581190	C₂	semidirect
8. #22581168	C₂	semidirect
9. #22581153	C₂	semidirect
10. #22581105	C₂	semidirect
11. #22581101	C₂	semidirect
12. #22581093	C₂	semidirect
13. #22581088	C₂	semidirect
14. #22581026	C₂	semidirect
15. #440×C₁₃₉	C₂	semidirect
16. C₂×#14555786	C₂²	semidirect
17. C₂×Q₈×D₁₃₉	C₂²	semidirect
22. C₂×#14555774	C₂²	semidirect
23. C₂×#14555774	C₂²	semidirect
25. C₂×#14555772	C₂²	semidirect
26. C₂×#14555772	C₂²	semidirect
28. C₂×D₁₁₁₂	C₂²	semidirect
29. C₂×D₁₁₁₂	C₂²	semidirect
31. C₂×#14555768	C₂²	semidirect
32. C₂×C₈×D₁₃₉	C₂²	semidirect
35. #17984830	C₂²	semidirect
37. #17984822	C₂²	semidirect
41. #17984817	C₂²	semidirect
47. C₄⋊(C₁₃₉⋊C₈)	C₂²	semidirect
48. #17984765	C₂²	semidirect
49. #17984762	C₂²	semidirect
50. #17984762	C₂²	semidirect
51. #17984762	C₂²	semidirect
52. (C₂×D₁₃₉)⋊C₈	C₂²	semidirect
53. (C₂×D₁₃₉)⋊C₈	C₂²	semidirect
55. C₄×Q₈×C₁₃₉	C₂²	semidirect
57. #107×C₁₃₉	C₂²	semidirect
58. #103×C₁₃₉	C₂²	semidirect
60. #97×C₁₃₉	C₂²	semidirect
115. SD₁₆×C₁₃₉	D₄	semidirect
166. Q₈×C₁₃₉	C₂×D₄	semidirect
177. C₈×C₁₃₉	C₂×D₄	semidirect
198. C₂×D₁₃₉	AGL(1,ℤ/8)	semidirect
218. C₁₃₉	#3265	semidirect
233. #440	D₁₃₉	semidirect
265. C₄×Q₈	C₂×D₁₃₉	semidirect
269. #107	C₂×D₁₃₉	semidirect
272. #103	C₂×D₁₃₉	semidirect
279. #97	C₂×D₁₃₉	semidirect
317. SD₁₆	D₅₅₆	semidirect
359. Q₈	C₂×D₅₅₆	semidirect
396. C₈	C₂×D₅₅₆	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×SD₁₆×D₁₃₉	2
#22581615	2
D₄×D₅₅₆	2
#22581342	2
#22581200	2
#22581190	2
#22581168	2
#22581153	2
#22581105	2
#22581101	2
#22581093	2
#22581088	2
#22581026	2
#440×C₁₃₉	2
#3265	139