Subgroups — #31819893

Order 17792.

1648 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14555786	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#41×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#22581622	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×C₂²⋊D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#22581615	C₂	1	1	yes	maximal, characteristic, complemented
6	#22581605	C₂	1	3	yes	maximal, complemented
7	#22581599	C₂	1	3	yes	maximal, complemented
8	#22581596	C₂	1	3	yes	maximal, complemented
9	#22581587	C₂	1	3	yes	maximal, complemented
10	#22581502	C₂	1	3	yes	maximal, complemented
11	#22581466	C₂	1	3	yes	maximal, complemented
12	#22581463	C₂	1	3	yes	maximal, complemented
13	C₄×#14555786	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×D₄×D₁₃₉	C₂	1	3	yes	maximal, complemented
15	#548×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14555786	—	2	8	no	—
17	C₂×#14555786	C₂²	1	1	yes	characteristic
18	C₂×#14555786	C₂²	1	3	yes	complemented
19	C₂×#14555786	C₂²	1	1	yes	characteristic, complemented
20	C₂×#14555786	C₂²	1	3	yes	complemented
21	C₂×#14555785	C₂²	1	3	yes	complemented
22	C₂×#14555784	C₂²	1	3	yes	complemented
23	#41×D₁₃₉	—	2	8	no	—
24	C₂×Q₈×D₁₃₉	C₂²	1	1	yes	characteristic, complemented
25	C₂²×D₅₅₆	C₂²	1	3	yes	complemented
26	C₂×D₄×D₁₃₉	C₂²	1	3	yes	—
27	C₂×D₄×D₁₃₉	C₂²	1	3	yes	complemented
28	C₂²×C₄×D₁₃₉	C₂²	1	3	yes	complemented
29	C₂²×C₄×D₁₃₉	C₂²	1	3	yes	complemented
30	#17984840	C₂²	1	3	yes	complemented
31	#17984838	C₂²	1	3	yes	complemented
32	#17984830	C₂²	1	3	yes	complemented
33	#17984827	C₂²	1	6	yes	complemented
34	#17984824	C₂²	1	6	yes	complemented
35	#17984822	C₂²	1	3	yes	complemented
36	#17984821	C₂²	1	3	yes	complemented
37	#17984818	C₂²	1	3	yes	complemented
38	#17984817	C₂²	1	3	yes	complemented
39	#17984816	C₂²	1	3	yes	complemented
40	#17984815	C₂²	1	6	yes	complemented
41	#17984815	C₂²	1	6	yes	complemented
42	#17984813	C₂²	1	3	yes	complemented
43	#17984812	C₂²	1	6	yes	complemented
44	#17984810	C₂²	1	6	yes	complemented
45	Q₈×Dic₁₃₉	C₂²	1	1	yes	characteristic, complemented
46	C₄×D₅₅₆	C₂²	1	3	yes	complemented
47	C₄×D₅₅₆	C₂²	1	3	yes	complemented
48	D₄×Dic₁₃₉	C₂²	1	3	yes	complemented
49	#17984804	C₂²	1	3	yes	complemented
50	#17984804	C₂²	1	3	yes	complemented
51	C₄×C₂²⋊D₁₃₉	C₂²	1	3	yes	—
52	C₄×C₂²⋊D₁₃₉	C₂²	1	3	yes	complemented
53	(C₂²⋊D₁₃₉)⋊C₄	C₂²	1	1	yes	characteristic
54	(C₂²⋊D₁₃₉)⋊C₄	C₂²	1	3	yes	complemented
55	(C₂²⋊D₁₃₉)⋊C₄	C₂²	1	6	yes	complemented
56	#17984800	C₂²	1	3	yes	complemented
57	C₄⋊C₄×D₁₃₉	C₂²	1	3	yes	complemented
58	C₂²⋊C₄×D₁₃₉	C₂²	1	3	yes	complemented
59	C₂²⋊C₄×D₁₃₉	C₂²	1	3	yes	complemented
60	C₄²×D₁₃₉	C₂²	1	3	yes	complemented
61	C₂×#41×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
62	C₂²×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
63	#124×C₁₃₉	C₂²	1	3	yes	complemented
64	C₂²⋊Q₈×C₁₃₉	C₂²	1	3	yes	complemented
65	#121×C₁₃₉	C₂²	1	3	yes	complemented
66	C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
67	C₄×D₄×C₁₃₉	C₂²	1	3	yes	complemented
68	C₂³×D₁₃₉	C₂³	1	3	yes	—
69	C₂³×D₁₃₉	C₂³	1	3	yes	—
70	#14555786	—	2	12	no	—
71	#14555786	—	2	12	no	—
72	#14555786	—	2	4	no	—
73	#14555786	D₄	1	8	yes	complemented
74	#14555785	—	2	12	no	—
75	#14555784	—	2	12	no	—
76	C₂×Dic₂₇₈	C₂³	1	3	yes	—
77	Q₈×D₁₃₉	—	2	4	no	—
78	C₂×D₅₅₆	—	2	12	no	—
79	C₂×D₅₅₆	C₂³	1	3	yes	—
80	C₂×D₅₅₆	C₂³	1	6	yes	—
81	C₂×D₅₅₆	C₂³	1	3	yes	—
82	C₂×D₅₅₆	C₂³	1	3	yes	—
83	C₂×C₂²⋊D₁₃₉	C₂³	1	3	yes	—
84	C₂×C₂²⋊D₁₃₉	C₂³	1	6	yes	—
85	C₂×C₂²⋊D₁₃₉	C₂³	1	6	yes	—
86	C₂×C₂²⋊D₁₃₉	C₂³	1	1	yes	characteristic
87	D₄×D₁₃₉	—	2	12	no	—
88	D₄×D₁₃₉	—	2	12	no	—
89	C₂²×Dic₁₃₉	C₂³	1	1	yes	characteristic
90	C₂²×Dic₁₃₉	C₂³	1	3	yes	—
91	C₂×C₄×D₁₃₉	—	2	12	no	—
92	C₂×C₄×D₁₃₉	—	2	12	no	—
93	C₂×C₄×D₁₃₉	C₂³	1	3	yes	—
94	C₂×C₄×D₁₃₉	C₂³	1	3	yes	—
95	C₂×C₄×D₁₃₉	C₂³	1	3	yes	—
96	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
97	C₂×C₄×D₁₃₉	C₂³	1	3	yes	—
98	C₂×C₄×D₁₃₉	C₂³	1	3	yes	—
99	C₂×C₄×D₁₃₉	C₂³	1	3	yes	—
100	C₂×C₄×D₁₃₉	C₂³	1	3	yes	—
101	C₂×C₄×D₁₃₉	C₂³	1	3	yes	—
102	C₄⋊Dic₁₃₉	C₂³	1	3	yes	—
103	C₄⋊Dic₁₃₉	C₂³	1	3	yes	—
104	Dic₁₃₉⋊C₄	C₂³	1	1	yes	characteristic
105	Dic₁₃₉⋊C₄	C₂³	1	3	yes	—
106	Dic₁₃₉⋊C₄	C₂³	1	6	yes	—
107	C₂²⋊Dic₁₃₉	C₂³	1	3	yes	—
108	C₂²⋊Dic₁₃₉	C₂³	1	3	yes	—
109	(C₂×D₁₃₉)⋊C₄	C₂³	1	1	yes	characteristic
110	(C₂×D₁₃₉)⋊C₄	C₂³	1	3	yes	—
111	(C₂×D₁₃₉)⋊C₄	C₂³	1	3	yes	—
112	(C₂×D₁₃₉)⋊C₄	C₂³	1	3	yes	—
113	(C₂×D₁₃₉)⋊C₄	C₂³	1	6	yes	—
114	(C₂×D₁₃₉)⋊C₄	C₂³	1	6	yes	—
115	C₄×Dic₁₃₉	C₂³	1	1	yes	characteristic
116	C₄×Dic₁₃₉	C₂³	1	3	yes	—
117	C₄×Dic₁₃₉	C₂³	1	3	yes	—
118	#41×C₁₃₉	—	2	4	no	—
119	C₂×Q₈×C₁₃₉	—	2	4	no	—
120	C₂×Q₈×C₁₃₉	C₂³	1	3	yes	—
121	C₂×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
122	C₂×D₄×C₁₃₉	C₂³	1	3	yes	—
123	C₂×D₄×C₁₃₉	C₂³	1	3	yes	—
124	C₂²×C₄×C₁₃₉	C₂³	1	3	yes	—
125	C₂²×C₄×C₁₃₉	C₂³	1	3	yes	—
126	C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
127	C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
128	C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
130	C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
131	C₄²×C₁₃₉	C₂³	1	3	yes	—
132	C₂²×D₁₃₉	—	2	6	no	—
133	C₂²×D₁₃₉	—	2	6	no	—
134	C₂²×D₁₃₉	—	2	6	no	—
135	C₂²×D₁₃₉	—	2	6	no	—
136	C₂²×D₁₃₉	—	4	3	no	—
137	C₂²×D₁₃₉	—	4	3	no	—
138	C₂²×D₁₃₉	C₂⁴	1	3	yes	—
139	C₂²×D₁₃₉	C₂⁴	1	3	yes	—
140	C₂²×D₁₃₉	C₂⁴	1	1	yes	characteristic
141	Dic₂₇₈	—	2	6	no	—
142	D₅₅₆	—	2	12	no	—
143	D₅₅₆	—	2	6	no	—
144	D₅₅₆	—	2	6	no	—
145	D₅₅₆	C₂×D₄	1	12	yes	complemented
146	C₂²⋊D₁₃₉	—	2	12	no	—
147	C₂²⋊D₁₃₉	—	2	6	no	—
148	C₂²⋊D₁₃₉	—	4	6	no	—
149	C₂²⋊D₁₃₉	#41	1	4	yes	complemented
150	C₂×Dic₁₃₉	—	2	2	no	—
151	C₂×Dic₁₃₉	—	2	6	no	—
152	C₂×Dic₁₃₉	C₂⁴	1	3	yes	—
153	C₂×Dic₁₃₉	C₂⁴	1	3	yes	—
154	C₂×Dic₁₃₉	C₂⁴	1	1	yes	characteristic
155	C₂×Dic₁₃₉	C₂⁴	1	1	yes	characteristic
156	C₂×Dic₁₃₉	C₂⁴	1	1	yes	characteristic
157	C₄×D₁₃₉	—	2	6	no	—
158	C₄×D₁₃₉	—	2	6	no	—
159	C₄×D₁₃₉	—	2	6	no	—
160	C₄×D₁₃₉	—	2	6	no	—
161	C₄×D₁₃₉	—	2	2	no	—
162	C₄×D₁₃₉	—	2	6	no	—
163	C₄×D₁₃₉	—	2	6	no	—
164	C₄×D₁₃₉	—	4	3	no	—
165	C₄×D₁₃₉	C₂×D₄	1	12	yes	complemented
166	C₂³×C₁₃₉	C₂⁴	1	3	yes	—
167	C₂³×C₁₃₉	C₂⁴	1	1	yes	characteristic
168	Q₈×C₁₃₉	—	2	6	no	—
169	Q₈×C₁₃₉	C₂×D₄	1	4	yes	complemented
170	D₄×C₁₃₉	—	2	6	no	—
171	D₄×C₁₃₉	—	2	6	no	—
172	C₂×C₄×C₁₃₉	—	2	6	no	—
173	C₂×C₄×C₁₃₉	—	2	6	no	—
174	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₁₃₉	C₂⁴	1	3	yes	—
176	C₂×C₄×C₁₃₉	C₂⁴	1	3	yes	—
177	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₁₃₉	C₂⁴	1	3	yes	—
179	C₂²×C₁₃₉	—	2	1	no	—
180	C₂²×C₁₃₉	—	2	1	no	—
181	C₂²×C₁₃₉	—	2	3	no	—
182	C₂²×C₁₃₉	—	2	3	no	—
183	C₂²×C₁₃₉	—	2	3	no	—
184	C₂²×C₁₃₉	C₂×#41	1	2	yes	complemented
185	C₂²×C₁₃₉	C₂⁵	1	1	yes	characteristic
186	C₂×D₁₃₉	—	2	1	no	—
187	C₂×D₁₃₉	—	2	3	no	—
188	C₂×D₁₃₉	—	2	3	no	—
189	C₂×D₁₃₉	—	2	1	no	—
190	C₂×D₁₃₉	—	2	3	no	—
191	C₂×D₁₃₉	—	2	3	no	—
192	C₂×D₁₃₉	—	2	3	no	—
193	C₂×D₁₃₉	—	4	12	no	—
194	C₂×D₁₃₉	—	4	12	no	—
195	C₂×D₁₃₉	C₂²×D₄	1	6	yes	—
196	C₂×D₁₃₉	C₂×#41	1	2	yes	complemented
197	C₄×C₁₃₉	—	2	1	no	—
198	C₄×C₁₃₉	—	2	3	no	—
199	C₄×C₁₃₉	—	2	3	no	—
200	C₄×C₁₃₉	—	2	1	no	—
201	C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
202	Dic₁₃₉	—	2	1	no	—
203	Dic₁₃₉	—	2	3	no	—
204	Dic₁₃₉	—	2	3	no	—
205	Dic₁₃₉	C₂²×D₄	1	2	yes	—
206	Dic₁₃₉	C₂×#41	1	2	yes	complemented
207	C₂×C₁₃₉	—	2	2	no	—
208	C₂×C₁₃₉	—	4	3	no	—
209	C₂×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
210	C₂×C₁₃₉	C₂²×#41	1	1	yes	characteristic
211	C₂×C₁₃₉	#585	1	1	yes	characteristic
212	D₁₃₉	—	2	2	no	—
213	D₁₃₉	—	2	6	no	—
214	D₁₃₉	—	4	3	no	—
215	C₁₃₉	D₄×#41	1	1	yes	characteristic, complemented, Sylow
216	D₄×#41	—	139	1	no	maximal, Sylow
217	C₂²×#41	—	139	1	no	—
218	C₂²×#41	—	139	1	no	—
219	#550	—	139	1	no	—
220	D₄×Q₈	—	139	1	no	—
221	#548	—	139	1	no	—
222	#548	D₁₃₉	1	1	yes	characteristic, complemented
223	#547	—	139	3	no	—
224	#546	—	139	3	no	—
225	#546	—	139	3	no	—
226	D₄²	—	139	3	no	—
227	#532	—	139	3	no	—
228	#525	—	139	3	no	—
229	#525	—	139	3	no	—
230	C₄×#41	—	139	1	no	—
231	C₂×C₄×D₄	—	139	3	no	—
232	C₂×#41	—	278	8	no	—
233	C₂×#41	—	278	8	no	—
234	C₂×#41	—	139	3	no	—
235	C₂×#41	—	139	3	no	—
236	C₂×#41	—	139	1	no	—
237	C₂×#41	—	139	1	no	—
238	C₂×#41	—	139	3	no	—
239	C₂×#41	—	139	3	no	—
240	C₂×#41	C₂×D₁₃₉	1	1	yes	characteristic, complemented
241	C₂²×Q₈	—	139	1	no	—
242	C₂²×Q₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
243	C₂²×D₄	—	139	3	no	—
244	C₂²×D₄	—	139	3	no	—
245	C₂²×D₄	—	139	3	no	—
246	C₂³×C₄	—	139	3	no	—
247	C₂³×C₄	—	139	3	no	—
248	C₄⋊Q₈	—	139	3	no	—
249	#127	—	139	3	no	—
250	#124	—	139	3	no	—
251	#124	C₂×D₁₃₉	1	3	yes	complemented
252	#123	—	139	6	no	—
253	#123	—	139	6	no	—
254	C₂²⋊Q₈	—	139	3	no	—
255	C₂²⋊Q₈	—	139	3	no	—
256	C₂²⋊Q₈	—	139	3	no	—
257	C₂²⋊Q₈	C₂×D₁₃₉	1	3	yes	complemented
258	#121	—	139	3	no	—
259	#121	—	139	3	no	—
260	#121	—	139	3	no	—
261	#121	—	139	6	no	—
262	#121	—	139	6	no	—
263	#121	C₂×D₁₃₉	1	3	yes	complemented
264	#120	—	139	6	no	—
265	#120	—	139	6	no	—
266	C₄×Q₈	—	139	1	no	—
267	C₄×Q₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
268	C₄×D₄	—	139	3	no	—
269	C₄×D₄	—	139	3	no	—
270	C₄×D₄	—	139	3	no	—
271	C₄×D₄	—	139	3	no	—
272	C₄×D₄	—	139	3	no	—
273	C₄×D₄	—	139	1	no	—
274	C₄×D₄	—	139	3	no	—
275	C₄×D₄	—	139	6	no	—
276	C₄×D₄	—	139	3	no	—
277	C₄×D₄	—	139	3	no	—
278	C₄×D₄	C₂×D₁₃₉	1	3	yes	complemented
279	#117	—	139	3	no	—
280	C₂×C₄⋊C₄	—	139	3	no	—
281	C₂×C₂²⋊C₄	—	139	3	no	—
282	C₂×C₂²⋊C₄	—	139	3	no	—
283	C₂×C₄²	—	139	3	no	—
284	C₂⁴	—	139	3	no	—
285	C₂⁴	—	139	3	no	—
286	#41	—	2	4	no	—
287	#41	—	278	12	no	—
288	#41	—	278	4	no	—
289	#41	—	278	12	no	—
290	#41	—	278	12	no	—
291	#41	—	278	12	no	—
292	#41	—	139	8	no	—
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	—	278	4	no	—
295	C₂×Q₈	—	139	3	no	—
296	C₂×Q₈	C₂²×D₁₃₉	1	3	yes	—
297	C₂×Q₈	C₂²×D₁₃₉	1	1	yes	characteristic
298	C₂×D₄	—	278	12	no	—
299	C₂×D₄	—	278	12	no	—
300	C₂×D₄	—	278	12	no	—
301	C₂×D₄	—	139	3	no	—
302	C₂×D₄	—	139	6	no	—
303	C₂×D₄	—	139	6	no	—
304	C₂×D₄	—	139	1	no	—
305	C₂×D₄	—	139	3	no	—
306	C₂×D₄	—	139	6	no	—
307	C₂×D₄	—	139	3	no	—
308	C₂×D₄	—	139	3	no	—
309	C₂×D₄	C₂²×D₁₃₉	1	3	yes	—
310	C₂×D₄	C₂²×D₁₃₉	1	3	yes	—
311	C₂²×C₄	—	278	12	no	—
312	C₂²×C₄	—	278	12	no	—
313	C₂²×C₄	—	139	1	no	—
314	C₂²×C₄	—	139	3	no	—
315	C₂²×C₄	—	139	3	no	—
316	C₂²×C₄	—	139	3	no	—
317	C₂²×C₄	—	139	3	no	—
318	C₂²×C₄	—	139	1	no	—
319	C₂²×C₄	—	139	3	no	—
320	C₂²×C₄	—	139	3	no	—
321	C₂²×C₄	—	139	3	no	—
322	C₂²×C₄	—	139	3	no	—
323	C₂²×C₄	—	139	3	no	—
324	C₂²×C₄	C₂²×D₁₃₉	1	3	yes	—
325	C₂²×C₄	C₂²×D₁₃₉	1	3	yes	—
326	C₄⋊C₄	—	139	1	no	—
327	C₄⋊C₄	—	139	3	no	—
328	C₄⋊C₄	—	139	3	no	—
329	C₄⋊C₄	—	139	6	no	—
330	C₄⋊C₄	—	139	3	no	—
331	C₄⋊C₄	C₂²×D₁₃₉	1	3	yes	—
332	C₄⋊C₄	C₂²×D₁₃₉	1	3	yes	—
333	C₂²⋊C₄	—	139	3	no	—
334	C₂²⋊C₄	—	139	3	no	—
335	C₂²⋊C₄	—	139	1	no	—
336	C₂²⋊C₄	—	139	3	no	—
337	C₂²⋊C₄	—	139	3	no	—
338	C₂²⋊C₄	—	139	3	no	—
339	C₂²⋊C₄	—	139	6	no	—
340	C₂²⋊C₄	—	139	6	no	—
341	C₂²⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
342	C₂²⋊C₄	C₂²×D₁₃₉	1	3	yes	—
343	C₂²⋊C₄	C₂²×D₁₃₉	1	6	yes	—
344	C₄²	—	139	1	no	—
345	C₄²	—	139	3	no	—
346	C₄²	—	139	3	no	—
347	C₄²	C₂²×D₁₃₉	1	3	yes	—
348	C₂³	—	278	6	no	—
349	C₂³	—	278	6	no	—
350	C₂³	—	278	6	no	—
351	C₂³	—	278	6	no	—
352	C₂³	—	556	3	no	—
353	C₂³	—	556	3	no	—
354	C₂³	—	139	3	no	—
355	C₂³	—	139	1	no	—
356	C₂³	—	139	3	no	—
357	C₂³	C₂³×D₁₃₉	1	3	yes	—
358	C₂³	C₂³×D₁₃₉	1	1	yes	characteristic
359	Q₈	—	2	6	no	—
360	Q₈	—	278	6	no	—
361	Q₈	D₄×D₁₃₉	1	4	yes	complemented
362	D₄	—	2	6	no	—
363	D₄	—	2	6	no	—
364	D₄	—	278	12	no	—
365	D₄	—	278	6	no	—
366	D₄	—	278	12	no	—
367	D₄	—	278	6	no	—
368	D₄	—	278	6	no	—
369	D₄	—	556	6	no	—
370	D₄	—	139	4	no	—
371	D₄	—	139	12	no	—
372	C₂×C₄	—	2	6	no	—
373	C₂×C₄	—	2	6	no	—
374	C₂×C₄	—	278	6	no	—
375	C₂×C₄	—	278	6	no	—
376	C₂×C₄	—	278	2	no	—
377	C₂×C₄	—	278	6	no	—
378	C₂×C₄	—	278	6	no	—
379	C₂×C₄	—	278	2	no	—
380	C₂×C₄	—	278	6	no	—
381	C₂×C₄	—	278	6	no	—
382	C₂×C₄	—	278	6	no	—
383	C₂×C₄	—	556	3	no	—
384	C₂×C₄	—	139	3	no	—
385	C₂×C₄	—	139	1	no	—
386	C₂×C₄	—	139	3	no	—
387	C₂×C₄	—	139	1	no	—
388	C₂×C₄	—	139	1	no	—
389	C₂×C₄	—	139	12	no	—
390	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
391	C₂×C₄	C₂³×D₁₃₉	1	3	yes	—
392	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
393	C₂×C₄	C₂³×D₁₃₉	1	3	yes	—
394	C₂×C₄	C₂³×D₁₃₉	1	3	yes	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	3	no	—
398	C₂²	—	2	3	no	—
399	C₂²	—	2	3	no	—
400	C₂²	—	278	1	no	—
401	C₂²	—	278	3	no	—
402	C₂²	—	278	3	no	—
403	C₂²	—	278	1	no	—
404	C₂²	—	278	3	no	—
405	C₂²	—	278	3	no	—
406	C₂²	—	278	3	no	—
407	C₂²	—	556	12	no	—
408	C₂²	—	556	12	no	—
409	C₂²	—	139	6	no	—
410	C₂²	—	139	2	no	—
411	C₂²	#41×D₁₃₉	1	2	yes	complemented
412	C₂²	C₂⁴×D₁₃₉	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	3	no	—
415	C₄	—	2	3	no	—
416	C₄	—	2	1	no	—
417	C₄	—	278	1	no	—
418	C₄	—	278	3	no	—
419	C₄	—	278	3	no	—
420	C₄	—	139	2	no	—
421	C₄	—	139	2	no	—
422	C₄	C₂×D₄×D₁₃₉	1	6	yes	—
423	C₂	—	2	2	no	—
424	C₂	—	4	3	no	—
425	C₂	—	278	2	no	—
426	C₂	—	278	6	no	—
427	C₂	—	556	3	no	—
428	C₂	C₂²×D₄×D₁₃₉	1	1	yes	characteristic
429	C₂	C₂×#41×D₁₃₉	1	1	yes	characteristic
430	C₂	#22581790	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃₉
commutator, socle, cosocle	C₂²×C₁₃₉	C₂⁵
Fitting	#548×C₁₃₉	C₂
hypercenter	#548	D₁₃₉
hypocenter	C₁₃₉	D₄×#41
LCS	G ▷ C₂²×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ #548

Complements

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

N	H ≅ G/N	type
1. C₂²×#14555786	C₂	semidirect
2. C₂×#41×D₁₃₉	C₂	semidirect
3. #22581622	C₂	semidirect
4. Q₈×C₂²⋊D₁₃₉	C₂	semidirect
5. #22581615	C₂	semidirect
6. #22581605	C₂	semidirect
7. #22581599	C₂	semidirect
8. #22581596	C₂	semidirect
9. #22581587	C₂	semidirect
10. #22581502	C₂	semidirect
11. #22581466	C₂	semidirect
12. #22581463	C₂	semidirect
13. C₄×#14555786	C₂	semidirect
14. C₄×D₄×D₁₃₉	C₂	semidirect
15. #548×C₁₃₉	C₂	semidirect
18. C₂×#14555786	C₂²	semidirect
19. C₂×#14555786	C₂²	semidirect
20. C₂×#14555786	C₂²	semidirect
21. C₂×#14555785	C₂²	semidirect
22. C₂×#14555784	C₂²	semidirect
24. C₂×Q₈×D₁₃₉	C₂²	semidirect
25. C₂²×D₅₅₆	C₂²	semidirect
27. C₂×D₄×D₁₃₉	C₂²	semidirect
28. C₂²×C₄×D₁₃₉	C₂²	semidirect
29. C₂²×C₄×D₁₃₉	C₂²	semidirect
30. #17984840	C₂²	semidirect
31. #17984838	C₂²	semidirect
32. #17984830	C₂²	semidirect
33. #17984827	C₂²	semidirect
34. #17984824	C₂²	semidirect
35. #17984822	C₂²	semidirect
36. #17984821	C₂²	semidirect
37. #17984818	C₂²	semidirect
38. #17984817	C₂²	semidirect
39. #17984816	C₂²	semidirect
40. #17984815	C₂²	semidirect
41. #17984815	C₂²	semidirect
42. #17984813	C₂²	semidirect
43. #17984812	C₂²	semidirect
44. #17984810	C₂²	semidirect
45. Q₈×Dic₁₃₉	C₂²	semidirect
46. C₄×D₅₅₆	C₂²	semidirect
47. C₄×D₅₅₆	C₂²	semidirect
48. D₄×Dic₁₃₉	C₂²	semidirect
49. #17984804	C₂²	semidirect
50. #17984804	C₂²	semidirect
52. C₄×C₂²⋊D₁₃₉	C₂²	semidirect
54. (C₂²⋊D₁₃₉)⋊C₄	C₂²	semidirect
55. (C₂²⋊D₁₃₉)⋊C₄	C₂²	semidirect
56. #17984800	C₂²	semidirect
57. C₄⋊C₄×D₁₃₉	C₂²	semidirect
58. C₂²⋊C₄×D₁₃₉	C₂²	semidirect
59. C₂²⋊C₄×D₁₃₉	C₂²	semidirect
60. C₄²×D₁₃₉	C₂²	semidirect
61. C₂×#41×C₁₃₉	C₂²	semidirect
62. C₂²×Q₈×C₁₃₉	C₂²	semidirect
63. #124×C₁₃₉	C₂²	semidirect
64. C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
65. #121×C₁₃₉	C₂²	semidirect
66. C₄×Q₈×C₁₃₉	C₂²	semidirect
67. C₄×D₄×C₁₃₉	C₂²	semidirect
73. #14555786	D₄	semidirect
145. D₅₅₆	C₂×D₄	semidirect
149. C₂²⋊D₁₃₉	#41	semidirect
165. C₄×D₁₃₉	C₂×D₄	semidirect
169. Q₈×C₁₃₉	C₂×D₄	semidirect
184. C₂²×C₁₃₉	C₂×#41	semidirect
196. C₂×D₁₃₉	C₂×#41	semidirect
206. Dic₁₃₉	C₂×#41	semidirect
215. C₁₃₉	D₄×#41	semidirect
222. #548	D₁₃₉	semidirect
240. C₂×#41	C₂×D₁₃₉	semidirect
242. C₂²×Q₈	C₂×D₁₃₉	semidirect
251. #124	C₂×D₁₃₉	semidirect
257. C₂²⋊Q₈	C₂×D₁₃₉	semidirect
263. #121	C₂×D₁₃₉	semidirect
267. C₄×Q₈	C₂×D₁₃₉	semidirect
278. C₄×D₄	C₂×D₁₃₉	semidirect
361. Q₈	D₄×D₁₃₉	semidirect
411. C₂²	#41×D₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14555786	2
C₂×#41×D₁₃₉	2
#22581622	2
Q₈×C₂²⋊D₁₃₉	2
#22581615	2
#22581605	2
#22581599	2
#22581596	2
#22581587	2
#22581502	2
#22581466	2
#22581463	2
C₄×#14555786	2
C₄×D₄×D₁₃₉	2
#548×C₁₃₉	2
D₄×#41	139