Subgroups — #3475×C₂₃₉ #44482245

Order 30592.

1132 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#556×C₂₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#555×C₂₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#554×C₂₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#553×C₂₃₉	C₂	1	2	yes	maximal, complemented
5	#552×C₂₃₉	C₂	1	2	yes	maximal, complemented
6	#552×C₂₃₉	C₂	1	2	yes	maximal, complemented
7	#551×C₂₃₉	C₂	1	4	yes	maximal, complemented
8	#547×C₂₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#546×C₂₃₉	C₂	1	2	yes	maximal, complemented
10	#533×C₂₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#529×C₂₃₉	C₂	1	4	yes	maximal, complemented
12	#529×C₂₃₉	C₂	1	2	yes	maximal, complemented
13	#525×C₂₃₉	C₂	1	2	yes	maximal, complemented
14	C₄×#41×C₂₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#41×C₂₃₉	C₂	1	2	yes	maximal, complemented
16	C₂×C₄×D₄×C₂₃₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#117×C₂₃₉	C₂	1	2	yes	maximal, complemented
18	C₂×#41×C₂₃₉	C₂²	1	1	yes	characteristic
19	C₂×#41×C₂₃₉	C₂²	1	2	yes	—
20	C₂²×D₄×C₂₃₉	C₂²	1	1	yes	characteristic
21	C₂³×C₄×C₂₃₉	C₂²	1	2	yes	—
22	C₄⋊Q₈×C₂₃₉	C₂²	1	1	yes	characteristic, complemented
23	C₄⋊Q₈×C₂₃₉	C₂²	1	1	yes	characteristic, complemented
24	#126×C₂₃₉	C₂²	1	4	yes	complemented
25	#126×C₂₃₉	C₂²	1	4	yes	complemented
26	#126×C₂₃₉	C₂²	1	4	yes	complemented
27	#125×C₂₃₉	C₂²	1	4	yes	complemented
28	#125×C₂₃₉	C₂²	1	2	yes	complemented
29	#125×C₂₃₉	C₂²	1	2	yes	complemented
30	#124×C₂₃₉	C₂²	1	2	yes	—
31	#124×C₂₃₉	C₂²	1	4	yes	complemented
32	#123×C₂₃₉	C₂²	1	4	yes	—
33	#123×C₂₃₉	C₂²	1	4	yes	—
34	#123×C₂₃₉	C₂²	1	4	yes	complemented
35	#123×C₂₃₉	C₂²	1	4	yes	complemented
36	C₂²⋊Q₈×C₂₃₉	C₂²	1	2	yes	—
37	C₂²⋊Q₈×C₂₃₉	C₂²	1	2	yes	—
38	C₂²⋊Q₈×C₂₃₉	C₂²	1	2	yes	complemented
39	C₂²⋊Q₈×C₂₃₉	C₂²	1	2	yes	complemented
40	C₂²⋊Q₈×C₂₃₉	C₂²	1	2	yes	complemented
41	C₂²⋊Q₈×C₂₃₉	C₂²	1	4	yes	complemented
42	#121×C₂₃₉	C₂²	1	4	yes	—
43	#121×C₂₃₉	C₂²	1	2	yes	—
44	#121×C₂₃₉	C₂²	1	2	yes	complemented
45	#121×C₂₃₉	C₂²	1	2	yes	complemented
46	#120×C₂₃₉	C₂²	1	4	yes	—
47	C₄×Q₈×C₂₃₉	C₂²	1	2	yes	complemented
48	C₄×Q₈×C₂₃₉	C₂²	1	1	yes	characteristic, complemented
49	C₄×Q₈×C₂₃₉	C₂²	1	2	yes	complemented
50	C₄×Q₈×C₂₃₉	C₂²	1	1	yes	characteristic, complemented
51	C₄×Q₈×C₂₃₉	C₂²	1	2	yes	complemented
52	C₄×D₄×C₂₃₉	C₂²	1	1	yes	characteristic
53	C₄×D₄×C₂₃₉	C₂²	1	1	yes	characteristic
54	C₄×D₄×C₂₃₉	C₂²	1	2	yes	—
55	C₄×D₄×C₂₃₉	C₂²	1	1	yes	characteristic
56	C₄×D₄×C₂₃₉	C₂²	1	2	yes	—
57	C₄×D₄×C₂₃₉	C₂²	1	1	yes	characteristic
58	C₄×D₄×C₂₃₉	C₂²	1	2	yes	—
59	C₄×D₄×C₂₃₉	C₂²	1	2	yes	—
60	C₄×D₄×C₂₃₉	C₂²	1	2	yes	—
61	C₄×D₄×C₂₃₉	C₂²	1	4	yes	complemented
62	C₄×D₄×C₂₃₉	C₂²	1	1	yes	characteristic, complemented
63	C₄×D₄×C₂₃₉	C₂²	1	4	yes	complemented
64	C₄×D₄×C₂₃₉	C₂²	1	1	yes	characteristic, complemented
65	C₄×D₄×C₂₃₉	C₂²	1	4	yes	complemented
66	#117×C₂₃₉	C₂²	1	1	yes	characteristic
67	#117×C₂₃₉	C₂²	1	2	yes	—
68	#117×C₂₃₉	C₂²	1	4	yes	—
69	#117×C₂₃₉	C₂²	1	4	yes	complemented
70	#117×C₂₃₉	C₂²	1	2	yes	complemented
71	#117×C₂₃₉	C₂²	1	2	yes	complemented
72	#117×C₂₃₉	C₂²	1	2	yes	complemented
73	#117×C₂₃₉	C₂²	1	4	yes	complemented
74	#117×C₂₃₉	C₂²	1	2	yes	complemented
75	C₂×C₄⋊C₄×C₂₃₉	C₂²	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₂₃₉	C₂²	1	2	yes	complemented
77	C₂×C₄⋊C₄×C₂₃₉	C₂²	1	2	yes	complemented
78	C₂×C₂²⋊C₄×C₂₃₉	C₂²	1	4	yes	—
79	C₂×C₂²⋊C₄×C₂₃₉	C₂²	1	2	yes	—
80	C₂×C₄²×C₂₃₉	C₂²	1	1	yes	characteristic
81	C₂×C₄²×C₂₃₉	C₂²	1	4	yes	complemented
82	C₂×C₄²×C₂₃₉	C₂²	1	2	yes	complemented
83	C₂⁴×C₂₃₉	C₂³	1	2	yes	—
84	#41×C₂₃₉	—	2	8	no	—
85	#41×C₂₃₉	—	2	4	no	—
86	C₂×Q₈×C₂₃₉	C₂³	1	2	yes	—
87	C₂×Q₈×C₂₃₉	C₂³	1	1	yes	characteristic
88	C₂×Q₈×C₂₃₉	C₂³	1	2	yes	—
89	C₂×D₄×C₂₃₉	—	2	4	no	—
90	C₂×D₄×C₂₃₉	C₂³	1	2	yes	—
91	C₂×D₄×C₂₃₉	C₂³	1	2	yes	—
92	C₂×D₄×C₂₃₉	C₂³	1	1	yes	characteristic
93	C₂×D₄×C₂₃₉	C₂³	1	4	yes	—
94	C₂×D₄×C₂₃₉	C₂³	1	1	yes	characteristic
95	C₂×D₄×C₂₃₉	C₂³	1	4	yes	—
96	C₂×D₄×C₂₃₉	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₂₃₉	—	2	8	no	—
98	C₂²×C₄×C₂₃₉	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₂₃₉	C₂³	1	4	yes	—
100	C₂²×C₄×C₂₃₉	C₂³	1	2	yes	—
101	C₂²×C₄×C₂₃₉	C₂³	1	2	yes	—
102	C₂²×C₄×C₂₃₉	C₂³	1	2	yes	—
103	C₂²×C₄×C₂₃₉	C₂³	1	2	yes	—
104	C₂²×C₄×C₂₃₉	C₂³	1	2	yes	—
105	C₂²×C₄×C₂₃₉	C₂³	1	2	yes	—
106	C₂²×C₄×C₂₃₉	C₂³	1	2	yes	—
107	C₂²×C₄×C₂₃₉	C₂³	1	1	yes	characteristic
108	C₂²×C₄×C₂₃₉	C₂³	1	4	yes	—
109	C₂²×C₄×C₂₃₉	C₂³	1	2	yes	—
110	C₂²×C₄×C₂₃₉	C₂³	1	1	yes	characteristic
111	C₄⋊C₄×C₂₃₉	C₂³	1	1	yes	characteristic
112	C₄⋊C₄×C₂₃₉	C₂³	1	1	yes	characteristic
113	C₄⋊C₄×C₂₃₉	C₂³	1	2	yes	—
114	C₄⋊C₄×C₂₃₉	C₂³	1	1	yes	characteristic
115	C₄⋊C₄×C₂₃₉	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₂₃₉	C₂³	1	2	yes	—
117	C₄⋊C₄×C₂₃₉	C₂³	1	2	yes	—
118	C₄⋊C₄×C₂₃₉	C₂³	1	4	yes	—
119	C₄⋊C₄×C₂₃₉	C₂³	1	4	yes	—
120	C₄⋊C₄×C₂₃₉	C₂³	1	2	yes	—
121	C₄⋊C₄×C₂₃₉	C₂³	1	2	yes	—
122	C₄⋊C₄×C₂₃₉	C₂³	1	2	yes	—
123	C₄⋊C₄×C₂₃₉	C₂³	1	4	yes	—
124	C₄⋊C₄×C₂₃₉	C₂³	1	4	yes	—
125	C₄⋊C₄×C₂₃₉	C₂³	1	4	yes	—
126	C₄⋊C₄×C₂₃₉	C₂³	1	4	yes	—
127	C₄⋊C₄×C₂₃₉	C₂³	1	2	yes	—
128	C₂²⋊C₄×C₂₃₉	C₂³	1	2	yes	—
129	C₂²⋊C₄×C₂₃₉	C₂³	1	4	yes	—
130	C₂²⋊C₄×C₂₃₉	C₂³	1	2	yes	—
131	C₂²⋊C₄×C₂₃₉	C₂³	1	4	yes	—
132	C₂²⋊C₄×C₂₃₉	C₂³	1	4	yes	—
133	C₂²⋊C₄×C₂₃₉	C₂³	1	2	yes	—
134	C₂²⋊C₄×C₂₃₉	C₂³	1	2	yes	—
135	C₂²⋊C₄×C₂₃₉	C₂³	1	2	yes	—
136	C₂²⋊C₄×C₂₃₉	C₂³	1	4	yes	—
137	C₂²⋊C₄×C₂₃₉	C₂³	1	2	yes	—
138	C₂²⋊C₄×C₂₃₉	C₂³	1	2	yes	—
139	C₂²⋊C₄×C₂₃₉	C₂³	1	4	yes	—
140	C₂²⋊C₄×C₂₃₉	C₂³	1	4	yes	—
141	C₂²⋊C₄×C₂₃₉	C₂³	1	4	yes	—
142	C₄²×C₂₃₉	C₂³	1	1	yes	characteristic
143	C₄²×C₂₃₉	C₂³	1	1	yes	characteristic
144	C₄²×C₂₃₉	C₂³	1	4	yes	—
145	C₄²×C₂₃₉	C₂³	1	4	yes	—
146	C₄²×C₂₃₉	C₂³	1	2	yes	—
147	C₄²×C₂₃₉	C₂³	1	2	yes	—
148	C₄²×C₂₃₉	C₂³	1	1	yes	characteristic
149	C₄²×C₂₃₉	C₂³	1	1	yes	characteristic
150	C₄²×C₂₃₉	C₂³	1	2	yes	—
151	C₄²×C₂₃₉	C₂³	1	4	yes	—
152	C₂³×C₂₃₉	—	2	4	no	—
153	C₂³×C₂₃₉	—	2	4	no	—
154	C₂³×C₂₃₉	—	4	2	no	—
155	C₂³×C₂₃₉	C₂⁴	1	2	yes	—
156	C₂³×C₂₃₉	C₂⁴	1	2	yes	—
157	C₂³×C₂₃₉	C₂⁴	1	1	yes	characteristic
158	C₂³×C₂₃₉	C₂⁴	1	2	yes	—
159	Q₈×C₂₃₉	—	2	2	no	—
160	Q₈×C₂₃₉	—	2	4	no	—
161	Q₈×C₂₃₉	—	4	2	no	—
162	D₄×C₂₃₉	—	2	4	no	—
163	D₄×C₂₃₉	—	2	4	no	—
164	D₄×C₂₃₉	—	2	8	no	—
165	D₄×C₂₃₉	—	2	2	no	—
166	D₄×C₂₃₉	—	2	2	no	—
167	D₄×C₂₃₉	—	4	4	no	—
168	D₄×C₂₃₉	#41	1	4	yes	complemented
169	C₂×C₄×C₂₃₉	—	2	4	no	—
170	C₂×C₄×C₂₃₉	—	2	8	no	—
171	C₂×C₄×C₂₃₉	—	2	4	no	—
172	C₂×C₄×C₂₃₉	—	2	4	no	—
173	C₂×C₄×C₂₃₉	—	2	4	no	—
174	C₂×C₄×C₂₃₉	—	2	4	no	—
175	C₂×C₄×C₂₃₉	—	2	2	no	—
176	C₂×C₄×C₂₃₉	—	2	4	no	—
177	C₂×C₄×C₂₃₉	—	2	4	no	—
178	C₂×C₄×C₂₃₉	—	4	2	no	—
179	C₂×C₄×C₂₃₉	—	4	4	no	—
180	C₂×C₄×C₂₃₉	—	4	1	no	—
181	C₂×C₄×C₂₃₉	#41	1	4	yes	complemented
182	C₂×C₄×C₂₃₉	C₂⁴	1	2	yes	—
183	C₂×C₄×C₂₃₉	C₂⁴	1	2	yes	—
184	C₂×C₄×C₂₃₉	C₂⁴	1	1	yes	characteristic
185	C₂×C₄×C₂₃₉	C₂⁴	1	2	yes	—
186	C₂×C₄×C₂₃₉	C₂⁴	1	1	yes	characteristic
187	C₂×C₄×C₂₃₉	C₂⁴	1	4	yes	—
188	C₂×C₄×C₂₃₉	C₂⁴	1	2	yes	—
189	C₂×C₄×C₂₃₉	C₂⁴	1	4	yes	—
190	C₂×C₄×C₂₃₉	C₂⁴	1	1	yes	characteristic
191	C₂×C₄×C₂₃₉	C₂⁴	1	2	yes	—
192	C₂×C₄×C₂₃₉	C₂⁴	1	1	yes	characteristic
193	C₂×C₄×C₂₃₉	C₂⁴	1	1	yes	characteristic
194	C₂×C₄×C₂₃₉	C₂⁴	1	1	yes	characteristic
195	C₂²×C₂₃₉	—	2	2	no	—
196	C₂²×C₂₃₉	—	2	1	no	—
197	C₂²×C₂₃₉	—	2	2	no	—
198	C₂²×C₂₃₉	—	2	1	no	—
199	C₂²×C₂₃₉	—	2	2	no	—
200	C₂²×C₂₃₉	—	2	2	no	—
201	C₂²×C₂₃₉	—	2	2	no	—
202	C₂²×C₂₃₉	—	2	2	no	—
203	C₂²×C₂₃₉	—	2	2	no	—
204	C₂²×C₂₃₉	—	2	2	no	—
205	C₂²×C₂₃₉	—	4	8	no	—
206	C₂²×C₂₃₉	C₂×#41	1	2	yes	—
207	C₂²×C₂₃₉	C₂×#41	1	4	yes	—
208	C₂²×C₂₃₉	C₂⁵	1	1	yes	characteristic
209	C₄×C₂₃₉	—	2	2	no	—
210	C₄×C₂₃₉	—	2	2	no	—
211	C₄×C₂₃₉	—	2	2	no	—
212	C₄×C₂₃₉	—	2	1	no	—
213	C₄×C₂₃₉	—	2	4	no	—
214	C₄×C₂₃₉	—	2	2	no	—
215	C₄×C₂₃₉	—	2	1	no	—
216	C₄×C₂₃₉	—	2	2	no	—
217	C₄×C₂₃₉	—	2	4	no	—
218	C₄×C₂₃₉	—	2	1	no	—
219	C₄×C₂₃₉	C₂×#41	1	2	yes	—
220	C₄×C₂₃₉	C₂×#41	1	2	yes	—
221	C₄×C₂₃₉	C₂×#41	1	2	yes	—
222	C₂×C₂₃₉	—	2	2	no	—
223	C₂×C₂₃₉	—	2	4	no	—
224	C₂×C₂₃₉	—	4	2	no	—
225	C₂×C₂₃₉	—	4	2	no	—
226	C₂×C₂₃₉	C₂²×#41	1	1	yes	characteristic
227	C₂×C₂₃₉	C₂²×#41	1	1	yes	characteristic
228	C₂×C₂₃₉	#585	1	1	yes	characteristic
229	C₂₃₉	#3475	1	1	yes	characteristic, direct product factor, Sylow
230	#3475	C₂₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	#556	C₂×C₂₃₉	1	1	yes	characteristic, complemented
232	#555	C₂×C₂₃₉	1	1	yes	characteristic, complemented
233	#554	C₂×C₂₃₉	1	1	yes	characteristic, complemented
234	#553	C₂×C₂₃₉	1	2	yes	complemented
235	#552	C₂×C₂₃₉	1	2	yes	complemented
236	#552	C₂×C₂₃₉	1	2	yes	complemented
237	#551	C₂×C₂₃₉	1	4	yes	complemented
238	#547	C₂×C₂₃₉	1	1	yes	characteristic, complemented
239	#546	C₂×C₂₃₉	1	2	yes	complemented
240	#533	C₂×C₂₃₉	1	1	yes	characteristic, complemented
241	#529	C₂×C₂₃₉	1	4	yes	complemented
242	#529	C₂×C₂₃₉	1	2	yes	complemented
243	#525	C₂×C₂₃₉	1	2	yes	complemented
244	C₄×#41	C₂×C₂₃₉	1	1	yes	characteristic, complemented
245	C₄×#41	C₂×C₂₃₉	1	2	yes	complemented
246	C₂×C₄×D₄	C₂×C₂₃₉	1	1	yes	characteristic, complemented
247	C₂×#117	C₂×C₂₃₉	1	2	yes	complemented
248	C₂×#41	C₂²×C₂₃₉	1	1	yes	characteristic
249	C₂×#41	C₂²×C₂₃₉	1	2	yes	—
250	C₂²×D₄	C₂²×C₂₃₉	1	1	yes	characteristic
251	C₂³×C₄	C₂²×C₂₃₉	1	2	yes	—
252	C₄⋊Q₈	C₂²×C₂₃₉	1	1	yes	characteristic, complemented
253	C₄⋊Q₈	C₂²×C₂₃₉	1	1	yes	characteristic, complemented
254	#126	C₂²×C₂₃₉	1	4	yes	complemented
255	#126	C₂²×C₂₃₉	1	4	yes	complemented
256	#126	C₂²×C₂₃₉	1	4	yes	complemented
257	#125	C₂²×C₂₃₉	1	4	yes	complemented
258	#125	C₂²×C₂₃₉	1	2	yes	complemented
259	#125	C₂²×C₂₃₉	1	2	yes	complemented
260	#124	C₂²×C₂₃₉	1	2	yes	—
261	#124	C₂²×C₂₃₉	1	4	yes	complemented
262	#123	C₂²×C₂₃₉	1	4	yes	—
263	#123	C₂²×C₂₃₉	1	4	yes	—
264	#123	C₂²×C₂₃₉	1	4	yes	complemented
265	#123	C₂²×C₂₃₉	1	4	yes	complemented
266	C₂²⋊Q₈	C₂²×C₂₃₉	1	2	yes	—
267	C₂²⋊Q₈	C₂²×C₂₃₉	1	2	yes	—
268	C₂²⋊Q₈	C₂²×C₂₃₉	1	2	yes	complemented
269	C₂²⋊Q₈	C₂²×C₂₃₉	1	2	yes	complemented
270	C₂²⋊Q₈	C₂²×C₂₃₉	1	2	yes	complemented
271	C₂²⋊Q₈	C₂²×C₂₃₉	1	4	yes	complemented
272	#121	C₂²×C₂₃₉	1	4	yes	—
273	#121	C₂²×C₂₃₉	1	2	yes	—
274	#121	C₂²×C₂₃₉	1	2	yes	complemented
275	#121	C₂²×C₂₃₉	1	2	yes	complemented
276	#120	C₂²×C₂₃₉	1	4	yes	—
277	C₄×Q₈	C₂²×C₂₃₉	1	2	yes	complemented
278	C₄×Q₈	C₂²×C₂₃₉	1	1	yes	characteristic, complemented
279	C₄×Q₈	C₂²×C₂₃₉	1	2	yes	complemented
280	C₄×Q₈	C₂²×C₂₃₉	1	1	yes	characteristic, complemented
281	C₄×Q₈	C₂²×C₂₃₉	1	2	yes	complemented
282	C₄×D₄	C₂²×C₂₃₉	1	1	yes	characteristic
283	C₄×D₄	C₂²×C₂₃₉	1	1	yes	characteristic
284	C₄×D₄	C₂²×C₂₃₉	1	2	yes	—
285	C₄×D₄	C₂²×C₂₃₉	1	1	yes	characteristic
286	C₄×D₄	C₂²×C₂₃₉	1	2	yes	—
287	C₄×D₄	C₂²×C₂₃₉	1	1	yes	characteristic
288	C₄×D₄	C₂²×C₂₃₉	1	2	yes	—
289	C₄×D₄	C₂²×C₂₃₉	1	2	yes	—
290	C₄×D₄	C₂²×C₂₃₉	1	2	yes	—
291	C₄×D₄	C₂²×C₂₃₉	1	4	yes	complemented
292	C₄×D₄	C₂²×C₂₃₉	1	1	yes	characteristic, complemented
293	C₄×D₄	C₂²×C₂₃₉	1	4	yes	complemented
294	C₄×D₄	C₂²×C₂₃₉	1	1	yes	characteristic, complemented
295	C₄×D₄	C₂²×C₂₃₉	1	4	yes	complemented
296	#117	C₂²×C₂₃₉	1	1	yes	characteristic
297	#117	C₂²×C₂₃₉	1	2	yes	—
298	#117	C₂²×C₂₃₉	1	4	yes	—
299	#117	C₂²×C₂₃₉	1	4	yes	complemented
300	#117	C₂²×C₂₃₉	1	2	yes	complemented
301	#117	C₂²×C₂₃₉	1	2	yes	complemented
302	#117	C₂²×C₂₃₉	1	2	yes	complemented
303	#117	C₂²×C₂₃₉	1	4	yes	complemented
304	#117	C₂²×C₂₃₉	1	2	yes	complemented
305	C₂×C₄⋊C₄	C₂²×C₂₃₉	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂²×C₂₃₉	1	2	yes	complemented
307	C₂×C₄⋊C₄	C₂²×C₂₃₉	1	2	yes	complemented
308	C₂×C₂²⋊C₄	C₂²×C₂₃₉	1	4	yes	—
309	C₂×C₂²⋊C₄	C₂²×C₂₃₉	1	2	yes	—
310	C₂×C₄²	C₂²×C₂₃₉	1	1	yes	characteristic
311	C₂×C₄²	C₂²×C₂₃₉	1	4	yes	complemented
312	C₂×C₄²	C₂²×C₂₃₉	1	2	yes	complemented
313	C₂⁴	C₂³×C₂₃₉	1	2	yes	—
314	#41	—	2	8	no	—
315	#41	—	2	4	no	—
316	C₂×Q₈	C₂³×C₂₃₉	1	2	yes	—
317	C₂×Q₈	C₂³×C₂₃₉	1	1	yes	characteristic
318	C₂×Q₈	C₂³×C₂₃₉	1	2	yes	—
319	C₂×D₄	—	2	4	no	—
320	C₂×D₄	C₂³×C₂₃₉	1	2	yes	—
321	C₂×D₄	C₂³×C₂₃₉	1	2	yes	—
322	C₂×D₄	C₂³×C₂₃₉	1	1	yes	characteristic
323	C₂×D₄	C₂³×C₂₃₉	1	4	yes	—
324	C₂×D₄	C₂³×C₂₃₉	1	1	yes	characteristic
325	C₂×D₄	C₂³×C₂₃₉	1	4	yes	—
326	C₂×D₄	C₂³×C₂₃₉	1	1	yes	characteristic
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	C₂³×C₂₃₉	1	1	yes	characteristic
329	C₂²×C₄	C₂³×C₂₃₉	1	2	yes	—
330	C₂²×C₄	C₂³×C₂₃₉	1	4	yes	—
331	C₂²×C₄	C₂³×C₂₃₉	1	2	yes	—
332	C₂²×C₄	C₂³×C₂₃₉	1	2	yes	—
333	C₂²×C₄	C₂³×C₂₃₉	1	2	yes	—
334	C₂²×C₄	C₂³×C₂₃₉	1	2	yes	—
335	C₂²×C₄	C₂³×C₂₃₉	1	2	yes	—
336	C₂²×C₄	C₂³×C₂₃₉	1	2	yes	—
337	C₂²×C₄	C₂³×C₂₃₉	1	1	yes	characteristic
338	C₂²×C₄	C₂³×C₂₃₉	1	4	yes	—
339	C₂²×C₄	C₂³×C₂₃₉	1	2	yes	—
340	C₂²×C₄	C₂³×C₂₃₉	1	1	yes	characteristic
341	C₄⋊C₄	C₂³×C₂₃₉	1	1	yes	characteristic
342	C₄⋊C₄	C₂³×C₂₃₉	1	1	yes	characteristic
343	C₄⋊C₄	C₂³×C₂₃₉	1	2	yes	—
344	C₄⋊C₄	C₂³×C₂₃₉	1	1	yes	characteristic
345	C₄⋊C₄	C₂³×C₂₃₉	1	1	yes	characteristic
346	C₄⋊C₄	C₂³×C₂₃₉	1	2	yes	—
347	C₄⋊C₄	C₂³×C₂₃₉	1	2	yes	—
348	C₄⋊C₄	C₂³×C₂₃₉	1	4	yes	—
349	C₄⋊C₄	C₂³×C₂₃₉	1	4	yes	—
350	C₄⋊C₄	C₂³×C₂₃₉	1	2	yes	—
351	C₄⋊C₄	C₂³×C₂₃₉	1	2	yes	—
352	C₄⋊C₄	C₂³×C₂₃₉	1	2	yes	—
353	C₄⋊C₄	C₂³×C₂₃₉	1	4	yes	—
354	C₄⋊C₄	C₂³×C₂₃₉	1	4	yes	—
355	C₄⋊C₄	C₂³×C₂₃₉	1	4	yes	—
356	C₄⋊C₄	C₂³×C₂₃₉	1	4	yes	—
357	C₄⋊C₄	C₂³×C₂₃₉	1	2	yes	—
358	C₂²⋊C₄	C₂³×C₂₃₉	1	2	yes	—
359	C₂²⋊C₄	C₂³×C₂₃₉	1	4	yes	—
360	C₂²⋊C₄	C₂³×C₂₃₉	1	2	yes	—
361	C₂²⋊C₄	C₂³×C₂₃₉	1	4	yes	—
362	C₂²⋊C₄	C₂³×C₂₃₉	1	4	yes	—
363	C₂²⋊C₄	C₂³×C₂₃₉	1	2	yes	—
364	C₂²⋊C₄	C₂³×C₂₃₉	1	2	yes	—
365	C₂²⋊C₄	C₂³×C₂₃₉	1	2	yes	—
366	C₂²⋊C₄	C₂³×C₂₃₉	1	4	yes	—
367	C₂²⋊C₄	C₂³×C₂₃₉	1	2	yes	—
368	C₂²⋊C₄	C₂³×C₂₃₉	1	2	yes	—
369	C₂²⋊C₄	C₂³×C₂₃₉	1	4	yes	—
370	C₂²⋊C₄	C₂³×C₂₃₉	1	4	yes	—
371	C₂²⋊C₄	C₂³×C₂₃₉	1	4	yes	—
372	C₄²	C₂³×C₂₃₉	1	1	yes	characteristic
373	C₄²	C₂³×C₂₃₉	1	1	yes	characteristic
374	C₄²	C₂³×C₂₃₉	1	1	yes	characteristic
375	C₄²	C₂³×C₂₃₉	1	1	yes	characteristic
376	C₄²	C₂³×C₂₃₉	1	2	yes	—
377	C₄²	C₂³×C₂₃₉	1	4	yes	—
378	C₄²	C₂³×C₂₃₉	1	4	yes	—
379	C₄²	C₂³×C₂₃₉	1	4	yes	—
380	C₄²	C₂³×C₂₃₉	1	2	yes	—
381	C₄²	C₂³×C₂₃₉	1	2	yes	—
382	C₂³	—	2	4	no	—
383	C₂³	—	2	4	no	—
384	C₂³	—	4	2	no	—
385	C₂³	C₂⁴×C₂₃₉	1	2	yes	—
386	C₂³	C₂⁴×C₂₃₉	1	2	yes	—
387	C₂³	C₂⁴×C₂₃₉	1	1	yes	characteristic
388	C₂³	C₂⁴×C₂₃₉	1	2	yes	—
389	Q₈	—	2	2	no	—
390	Q₈	—	2	4	no	—
391	Q₈	—	4	2	no	—
392	D₄	—	2	4	no	—
393	D₄	—	2	4	no	—
394	D₄	—	2	8	no	—
395	D₄	—	2	2	no	—
396	D₄	—	2	2	no	—
397	D₄	—	4	4	no	—
398	D₄	#41×C₂₃₉	1	4	yes	complemented
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	#41×C₂₃₉	1	4	yes	complemented
412	C₂×C₄	C₂⁴×C₂₃₉	1	2	yes	—
413	C₂×C₄	C₂⁴×C₂₃₉	1	2	yes	—
414	C₂×C₄	C₂⁴×C₂₃₉	1	1	yes	characteristic
415	C₂×C₄	C₂⁴×C₂₃₉	1	2	yes	—
416	C₂×C₄	C₂⁴×C₂₃₉	1	1	yes	characteristic
417	C₂×C₄	C₂⁴×C₂₃₉	1	4	yes	—
418	C₂×C₄	C₂⁴×C₂₃₉	1	2	yes	—
419	C₂×C₄	C₂⁴×C₂₃₉	1	4	yes	—
420	C₂×C₄	C₂⁴×C₂₃₉	1	1	yes	characteristic
421	C₂×C₄	C₂⁴×C₂₃₉	1	2	yes	—
422	C₂×C₄	C₂⁴×C₂₃₉	1	1	yes	characteristic
423	C₂×C₄	C₂⁴×C₂₃₉	1	1	yes	characteristic
424	C₂×C₄	C₂⁴×C₂₃₉	1	1	yes	characteristic
425	C₂²	—	2	2	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	4	8	no	—
436	C₂²	C₂×#41×C₂₃₉	1	2	yes	—
437	C₂²	C₂×#41×C₂₃₉	1	4	yes	—
438	C₂²	C₂⁵×C₂₃₉	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	4	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	2	no	—
447	C₄	—	2	4	no	—
448	C₄	—	2	1	no	—
449	C₄	C₂×#41×C₂₃₉	1	2	yes	—
450	C₄	C₂×#41×C₂₃₉	1	2	yes	—
451	C₄	C₂×#41×C₂₃₉	1	2	yes	—
452	C₂	—	2	2	no	—
453	C₂	—	2	4	no	—
454	C₂	—	4	2	no	—
455	C₂	—	4	2	no	—
456	C₂	C₂²×#41×C₂₃₉	1	1	yes	characteristic
457	C₂	C₂²×#41×C₂₃₉	1	1	yes	characteristic
458	C₂	#585×C₂₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃₉	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₃₉
socle	C₂²×C₂₃₉	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #556×C₂₃₉	C₂	semidirect
2. #555×C₂₃₉	C₂	semidirect
3. #554×C₂₃₉	C₂	semidirect
4. #553×C₂₃₉	C₂	semidirect
5. #552×C₂₃₉	C₂	semidirect
6. #552×C₂₃₉	C₂	semidirect
7. #551×C₂₃₉	C₂	semidirect
8. #547×C₂₃₉	C₂	semidirect
9. #546×C₂₃₉	C₂	semidirect
10. #533×C₂₃₉	C₂	semidirect
11. #529×C₂₃₉	C₂	semidirect
12. #529×C₂₃₉	C₂	semidirect
13. #525×C₂₃₉	C₂	semidirect
14. C₄×#41×C₂₃₉	C₂	semidirect
15. C₄×#41×C₂₃₉	C₂	semidirect
16. C₂×C₄×D₄×C₂₃₉	C₂	semidirect
17. C₂×#117×C₂₃₉	C₂	semidirect
22. C₄⋊Q₈×C₂₃₉	C₂²	semidirect
23. C₄⋊Q₈×C₂₃₉	C₂²	semidirect
24. #126×C₂₃₉	C₂²	semidirect
25. #126×C₂₃₉	C₂²	semidirect
26. #126×C₂₃₉	C₂²	semidirect
27. #125×C₂₃₉	C₂²	semidirect
28. #125×C₂₃₉	C₂²	semidirect
29. #125×C₂₃₉	C₂²	semidirect
31. #124×C₂₃₉	C₂²	semidirect
34. #123×C₂₃₉	C₂²	semidirect
35. #123×C₂₃₉	C₂²	semidirect
38. C₂²⋊Q₈×C₂₃₉	C₂²	semidirect
39. C₂²⋊Q₈×C₂₃₉	C₂²	semidirect
40. C₂²⋊Q₈×C₂₃₉	C₂²	semidirect
41. C₂²⋊Q₈×C₂₃₉	C₂²	semidirect
44. #121×C₂₃₉	C₂²	semidirect
45. #121×C₂₃₉	C₂²	semidirect
47. C₄×Q₈×C₂₃₉	C₂²	semidirect
48. C₄×Q₈×C₂₃₉	C₂²	semidirect
49. C₄×Q₈×C₂₃₉	C₂²	semidirect
50. C₄×Q₈×C₂₃₉	C₂²	semidirect
51. C₄×Q₈×C₂₃₉	C₂²	semidirect
61. C₄×D₄×C₂₃₉	C₂²	semidirect
62. C₄×D₄×C₂₃₉	C₂²	semidirect
63. C₄×D₄×C₂₃₉	C₂²	semidirect
64. C₄×D₄×C₂₃₉	C₂²	semidirect
65. C₄×D₄×C₂₃₉	C₂²	semidirect
69. #117×C₂₃₉	C₂²	semidirect
70. #117×C₂₃₉	C₂²	semidirect
71. #117×C₂₃₉	C₂²	semidirect
72. #117×C₂₃₉	C₂²	semidirect
73. #117×C₂₃₉	C₂²	semidirect
74. #117×C₂₃₉	C₂²	semidirect
76. C₂×C₄⋊C₄×C₂₃₉	C₂²	semidirect
77. C₂×C₄⋊C₄×C₂₃₉	C₂²	semidirect
81. C₂×C₄²×C₂₃₉	C₂²	semidirect
82. C₂×C₄²×C₂₃₉	C₂²	semidirect
168. D₄×C₂₃₉	#41	semidirect
181. C₂×C₄×C₂₃₉	#41	semidirect
229. C₂₃₉	#3475	direct (N × H)
230. #3475	C₂₃₉	direct (N × H)
231. #556	C₂×C₂₃₉	semidirect
232. #555	C₂×C₂₃₉	semidirect
233. #554	C₂×C₂₃₉	semidirect
234. #553	C₂×C₂₃₉	semidirect
235. #552	C₂×C₂₃₉	semidirect
236. #552	C₂×C₂₃₉	semidirect
237. #551	C₂×C₂₃₉	semidirect
238. #547	C₂×C₂₃₉	semidirect
239. #546	C₂×C₂₃₉	semidirect
240. #533	C₂×C₂₃₉	semidirect
241. #529	C₂×C₂₃₉	semidirect
242. #529	C₂×C₂₃₉	semidirect
243. #525	C₂×C₂₃₉	semidirect
244. C₄×#41	C₂×C₂₃₉	semidirect
245. C₄×#41	C₂×C₂₃₉	semidirect
246. C₂×C₄×D₄	C₂×C₂₃₉	semidirect
247. C₂×#117	C₂×C₂₃₉	semidirect
252. C₄⋊Q₈	C₂²×C₂₃₉	semidirect
253. C₄⋊Q₈	C₂²×C₂₃₉	semidirect
254. #126	C₂²×C₂₃₉	semidirect
255. #126	C₂²×C₂₃₉	semidirect
256. #126	C₂²×C₂₃₉	semidirect
257. #125	C₂²×C₂₃₉	semidirect
258. #125	C₂²×C₂₃₉	semidirect
259. #125	C₂²×C₂₃₉	semidirect
261. #124	C₂²×C₂₃₉	semidirect
264. #123	C₂²×C₂₃₉	semidirect
265. #123	C₂²×C₂₃₉	semidirect
268. C₂²⋊Q₈	C₂²×C₂₃₉	semidirect
269. C₂²⋊Q₈	C₂²×C₂₃₉	semidirect
270. C₂²⋊Q₈	C₂²×C₂₃₉	semidirect
271. C₂²⋊Q₈	C₂²×C₂₃₉	semidirect
274. #121	C₂²×C₂₃₉	semidirect
275. #121	C₂²×C₂₃₉	semidirect
277. C₄×Q₈	C₂²×C₂₃₉	semidirect
278. C₄×Q₈	C₂²×C₂₃₉	semidirect
279. C₄×Q₈	C₂²×C₂₃₉	semidirect
280. C₄×Q₈	C₂²×C₂₃₉	semidirect
281. C₄×Q₈	C₂²×C₂₃₉	semidirect
291. C₄×D₄	C₂²×C₂₃₉	semidirect
292. C₄×D₄	C₂²×C₂₃₉	semidirect
293. C₄×D₄	C₂²×C₂₃₉	semidirect
294. C₄×D₄	C₂²×C₂₃₉	semidirect
295. C₄×D₄	C₂²×C₂₃₉	semidirect
299. #117	C₂²×C₂₃₉	semidirect
300. #117	C₂²×C₂₃₉	semidirect
301. #117	C₂²×C₂₃₉	semidirect
302. #117	C₂²×C₂₃₉	semidirect
303. #117	C₂²×C₂₃₉	semidirect
304. #117	C₂²×C₂₃₉	semidirect
306. C₂×C₄⋊C₄	C₂²×C₂₃₉	semidirect
307. C₂×C₄⋊C₄	C₂²×C₂₃₉	semidirect
311. C₂×C₄²	C₂²×C₂₃₉	semidirect
312. C₂×C₄²	C₂²×C₂₃₉	semidirect
398. D₄	#41×C₂₃₉	semidirect
411. C₂×C₄	#41×C₂₃₉	semidirect

Maximal subgroups

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

subgroup	index
#556×C₂₃₉	2
#555×C₂₃₉	2
#554×C₂₃₉	2
#553×C₂₃₉	2
#552×C₂₃₉	2
#551×C₂₃₉	2
#547×C₂₃₉	2
#546×C₂₃₉	2
#533×C₂₃₉	2
#529×C₂₃₉	2
#525×C₂₃₉	2
C₄×#41×C₂₃₉	2
C₂×C₄×D₄×C₂₃₉	2
C₂×#117×C₂₃₉	2
#3475	239

Subgroups — #3475×C239 #44482245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3475×C₂₃₉ #44482245