Subgroups — C₂×C₁₀₉×#1379 #42130547

Order 27904.

606 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×M₃₂×C₁₀₉	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₁₆×C₁₀₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#405×C₁₀₉	C₂	1	1	yes	maximal, characteristic
4	C₁₀₉×#1379	C₂	1	4	yes	maximal, direct product factor
5	C₂²×M₁₆×C₁₀₉	C₄	1	1	yes	characteristic
6	C₂³×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
7	C₂×#117×C₁₀₉	C₄	1	1	yes	characteristic
8	C₂×M₃₂×C₁₀₉	—	2	2	no	—
9	C₂×M₃₂×C₁₀₉	—	2	1	no	—
10	C₂×M₃₂×C₁₀₉	C₄	1	4	yes	complemented
11	C₂×M₃₂×C₁₀₉	C₂²	1	2	yes	—
12	C₂²×C₁₆×C₁₀₉	—	2	2	no	—
13	C₂²×C₁₆×C₁₀₉	—	2	1	no	—
14	C₂²×C₁₆×C₁₀₉	—	2	1	no	—
15	C₂²×C₁₆×C₁₀₉	—	2	1	no	—
16	C₂²×C₁₆×C₁₀₉	C₄	1	4	yes	complemented
17	C₂²×C₁₆×C₁₀₉	C₂²	1	2	yes	—
18	#405×C₁₀₉	—	2	1	no	—
19	#405×C₁₀₉	—	2	1	no	—
20	#405×C₁₀₉	C₄	1	2	yes	—
21	#405×C₁₀₉	C₂²	1	2	yes	—
22	C₂×#97×C₁₀₉	—	2	1	no	—
23	C₂×C₄×C₈×C₁₀₉	—	2	1	no	—
24	C₂³×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
25	C₂×M₁₆×C₁₀₉	—	2	1	no	—
26	C₂×M₁₆×C₁₀₉	—	2	2	no	—
27	C₂×M₁₆×C₁₀₉	C₈	1	4	yes	—
28	C₂×M₁₆×C₁₀₉	C₂×C₄	1	2	yes	—
29	C₂²×C₈×C₁₀₉	—	2	1	no	—
30	C₂²×C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₀₉	C₂×C₄	1	2	yes	—
32	C₂²×C₈×C₁₀₉	C₂×C₄	1	2	yes	—
33	C₂²×C₈×C₁₀₉	D₄	1	2	yes	—
34	C₂²×C₈×C₁₀₉	D₄	1	1	yes	characteristic
35	C₂²×C₈×C₁₀₉	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₁₀₉	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₀₉	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₀₉	Q₈	1	2	yes	—
39	C₂²×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
40	#117×C₁₀₉	—	2	1	no	—
41	#117×C₁₀₉	—	2	1	no	—
42	#117×C₁₀₉	C₈	1	2	yes	—
43	#117×C₁₀₉	C₂×C₄	1	2	yes	—
44	C₂×C₄⋊C₄×C₁₀₉	C₈	1	2	yes	—
45	C₂×C₂²⋊C₄×C₁₀₉	—	2	1	no	—
46	C₂×C₄²×C₁₀₉	—	2	1	no	—
47	M₃₂×C₁₀₉	—	2	4	no	—
48	M₃₂×C₁₀₉	—	2	2	no	—
49	M₃₂×C₁₀₉	C₂×C₄	1	4	yes	complemented
50	C₂×C₁₆×C₁₀₉	—	2	4	no	—
51	C₂×C₁₆×C₁₀₉	—	2	4	no	—
52	C₂×C₁₆×C₁₀₉	—	2	4	no	—
53	C₂×C₁₆×C₁₀₉	—	2	2	no	—
54	C₂×C₁₆×C₁₀₉	—	2	2	no	—
55	C₂×C₁₆×C₁₀₉	—	2	2	no	—
56	C₂×C₁₆×C₁₀₉	C₂×C₄	1	4	yes	complemented
57	#97×C₁₀₉	—	2	2	no	—
58	#97×C₁₀₉	—	2	2	no	—
59	C₄×C₈×C₁₀₉	—	2	2	no	—
60	C₄×C₈×C₁₀₉	—	2	2	no	—
61	C₂⁴×C₁₀₉	M₁₆	1	1	yes	characteristic
62	C₂²×C₄×C₁₀₉	—	2	2	no	—
63	C₂²×C₄×C₁₀₉	C₄²	1	2	yes	—
64	C₂²×C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₀₉	C₄⋊C₄	1	2	yes	—
67	C₂²×C₄×C₁₀₉	C₂×C₈	1	2	yes	—
68	C₂²×C₄×C₁₀₉	C₂×C₈	1	1	yes	characteristic
69	C₂²×C₄×C₁₀₉	C₂×C₈	1	1	yes	characteristic
70	C₂²×C₄×C₁₀₉	M₁₆	1	1	yes	characteristic
71	C₂²×C₄×C₁₀₉	M₁₆	1	2	yes	—
72	C₂²×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
73	M₁₆×C₁₀₉	—	2	4	no	—
74	M₁₆×C₁₀₉	—	2	2	no	—
75	M₁₆×C₁₀₉	C₂×C₈	1	4	yes	—
76	C₂×C₈×C₁₀₉	—	2	4	no	—
77	C₂×C₈×C₁₀₉	—	2	2	no	—
78	C₂×C₈×C₁₀₉	C₄²	1	2	yes	—
79	C₂×C₈×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₈×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₈×C₁₀₉	C₂²⋊C₄	1	2	yes	—
82	C₂×C₈×C₁₀₉	C₂²⋊C₄	1	2	yes	—
83	C₂×C₈×C₁₀₉	C₂²⋊C₄	1	2	yes	—
84	C₂×C₈×C₁₀₉	C₂²⋊C₄	1	2	yes	—
85	C₂×C₈×C₁₀₉	C₄⋊C₄	1	2	yes	—
86	C₂×C₈×C₁₀₉	C₄⋊C₄	1	2	yes	—
87	C₂×C₈×C₁₀₉	C₄⋊C₄	1	2	yes	—
88	C₂×C₈×C₁₀₉	C₄⋊C₄	1	2	yes	—
89	C₂×C₈×C₁₀₉	C₄⋊C₄	1	2	yes	—
90	C₂×C₈×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₈×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₈×C₁₀₉	C₂×D₄	1	1	yes	characteristic
93	C₂×C₈×C₁₀₉	C₂×D₄	1	1	yes	characteristic
94	C₂×C₈×C₁₀₉	C₂×D₄	1	1	yes	characteristic
95	C₂×C₈×C₁₀₉	C₂×Q₈	1	1	yes	characteristic
96	C₄⋊C₄×C₁₀₉	—	2	2	no	—
97	C₄⋊C₄×C₁₀₉	C₂×C₈	1	4	yes	—
98	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
99	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
100	C₄²×C₁₀₉	—	2	2	no	—
101	C₄²×C₁₀₉	—	2	2	no	—
102	C₁₆×C₁₀₉	—	2	4	no	—
103	C₁₆×C₁₀₉	—	2	4	no	—
104	C₂³×C₁₀₉	—	2	4	no	—
105	C₂³×C₁₀₉	#97	1	2	yes	—
106	C₂³×C₁₀₉	C₂²⋊C₈	1	1	yes	characteristic
107	C₂³×C₁₀₉	C₂²⋊C₈	1	1	yes	characteristic
108	C₂³×C₁₀₉	C₄⋊C₈	1	2	yes	—
109	C₂³×C₁₀₉	C₂×M₁₆	1	1	yes	characteristic
110	C₂×C₄×C₁₀₉	—	2	4	no	—
111	C₂×C₄×C₁₀₉	—	4	4	no	—
112	C₂×C₄×C₁₀₉	#95	1	2	yes	—
113	C₂×C₄×C₁₀₉	#95	1	2	yes	—
114	C₂×C₄×C₁₀₉	C₄×C₈	1	2	yes	—
115	C₂×C₄×C₁₀₉	C₄×C₈	1	2	yes	—
116	C₂×C₄×C₁₀₉	#97	1	2	yes	—
117	C₂×C₄×C₁₀₉	C₂²⋊C₈	1	1	yes	characteristic
118	C₂×C₄×C₁₀₉	C₂²⋊C₈	1	1	yes	characteristic
119	C₂×C₄×C₁₀₉	C₂²⋊C₈	1	2	yes	—
120	C₂×C₄×C₁₀₉	C₂²⋊C₈	1	2	yes	—
121	C₂×C₄×C₁₀₉	C₄⋊C₈	1	2	yes	—
122	C₂×C₄×C₁₀₉	C₄⋊C₈	1	2	yes	—
123	C₂×C₄×C₁₀₉	C₄⋊C₈	1	2	yes	—
124	C₂×C₄×C₁₀₉	C₂×C₄²	1	1	yes	characteristic
125	C₂×C₄×C₁₀₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	C₂×C₄×C₁₀₉	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₄×C₁₀₉	C₂²×C₈	1	1	yes	characteristic
128	C₂×C₄×C₁₀₉	C₂²×C₈	1	1	yes	characteristic
129	C₂×C₄×C₁₀₉	C₂×M₁₆	1	1	yes	characteristic
130	C₈×C₁₀₉	—	2	4	no	—
131	C₈×C₁₀₉	#95	1	2	yes	—
132	C₈×C₁₀₉	#95	1	2	yes	—
133	C₈×C₁₀₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₈×C₁₀₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₈×C₁₀₉	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₈×C₁₀₉	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂²×C₁₀₉	—	2	2	no	—
138	C₂²×C₁₀₉	—	2	2	no	—
139	C₂²×C₁₀₉	—	2	4	no	—
140	C₂²×C₁₀₉	—	2	4	no	—
141	C₂²×C₁₀₉	#336	1	2	yes	—
142	C₂²×C₁₀₉	#336	1	2	yes	—
143	C₂²×C₁₀₉	#350	1	4	yes	—
144	C₂²×C₁₀₉	C₂×#97	1	1	yes	characteristic
145	C₂²×C₁₀₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
146	C₂²×C₁₀₉	C₂×C₄⋊C₈	1	1	yes	characteristic
147	C₄×C₁₀₉	—	4	4	no	—
148	C₄×C₁₀₉	#336	1	2	yes	—
149	C₄×C₁₀₉	#336	1	2	yes	—
150	C₄×C₁₀₉	C₂×#95	1	1	yes	characteristic
151	C₄×C₁₀₉	C₂×C₄×C₈	1	1	yes	characteristic
152	C₄×C₁₀₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
153	C₄×C₁₀₉	C₂×C₄⋊C₈	1	1	yes	characteristic
154	C₂×#1379	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂×C₁₀₉	—	2	2	no	—
156	C₂×C₁₀₉	—	2	1	no	—
157	C₂×C₁₀₉	—	2	1	no	—
158	C₂×C₁₀₉	#1379	1	4	yes	direct product factor
159	C₂×C₁₀₉	C₂×#336	1	1	yes	characteristic
160	C₂×C₁₀₉	C₂×#350	1	2	yes	—
161	C₂²×M₃₂	C₂×C₁₀₉	1	1	yes	characteristic
162	C₂³×C₁₆	C₂×C₁₀₉	1	1	yes	characteristic
163	C₂×#405	C₂×C₁₀₉	1	1	yes	characteristic
164	#1379	C₂×C₁₀₉	1	4	yes	direct product factor
165	C₁₀₉	C₂×#1379	1	1	yes	characteristic, direct product factor, Sylow
166	C₂²×M₁₆	C₄×C₁₀₉	1	1	yes	characteristic
167	C₂³×C₈	C₂²×C₁₀₉	1	1	yes	characteristic
168	C₂×#117	C₄×C₁₀₉	1	1	yes	characteristic
169	C₂×M₃₂	—	2	2	no	—
170	C₂×M₃₂	—	2	1	no	—
171	C₂×M₃₂	C₄×C₁₀₉	1	4	yes	complemented
172	C₂×M₃₂	C₂²×C₁₀₉	1	2	yes	—
173	C₂²×C₁₆	—	2	2	no	—
174	C₂²×C₁₆	—	2	1	no	—
175	C₂²×C₁₆	—	2	1	no	—
176	C₂²×C₁₆	—	2	1	no	—
177	C₂²×C₁₆	C₄×C₁₀₉	1	4	yes	complemented
178	C₂²×C₁₆	C₂²×C₁₀₉	1	2	yes	—
179	#405	—	2	1	no	—
180	#405	—	2	1	no	—
181	#405	C₄×C₁₀₉	1	2	yes	—
182	#405	C₂²×C₁₀₉	1	2	yes	—
183	C₂×#97	—	2	1	no	—
184	C₂×C₄×C₈	—	2	1	no	—
185	C₂³×C₄	C₂×C₄×C₁₀₉	1	1	yes	characteristic
186	C₂×M₁₆	—	2	1	no	—
187	C₂×M₁₆	—	2	2	no	—
188	C₂×M₁₆	C₈×C₁₀₉	1	4	yes	—
189	C₂×M₁₆	C₂×C₄×C₁₀₉	1	2	yes	—
190	C₂²×C₈	—	2	1	no	—
191	C₂²×C₈	C₂×C₄×C₁₀₉	1	1	yes	characteristic
192	C₂²×C₈	C₂×C₄×C₁₀₉	1	2	yes	—
193	C₂²×C₈	C₂×C₄×C₁₀₉	1	2	yes	—
194	C₂²×C₈	D₄×C₁₀₉	1	2	yes	—
195	C₂²×C₈	D₄×C₁₀₉	1	1	yes	characteristic
196	C₂²×C₈	D₄×C₁₀₉	1	1	yes	characteristic
197	C₂²×C₈	D₄×C₁₀₉	1	1	yes	characteristic
198	C₂²×C₈	D₄×C₁₀₉	1	1	yes	characteristic
199	C₂²×C₈	Q₈×C₁₀₉	1	2	yes	—
200	C₂²×C₈	C₂³×C₁₀₉	1	1	yes	characteristic
201	#117	—	2	1	no	—
202	#117	—	2	1	no	—
203	#117	C₈×C₁₀₉	1	2	yes	—
204	#117	C₂×C₄×C₁₀₉	1	2	yes	—
205	C₂×C₄⋊C₄	C₈×C₁₀₉	1	2	yes	—
206	C₂×C₂²⋊C₄	—	2	1	no	—
207	C₂×C₄²	—	2	1	no	—
208	M₃₂	—	2	4	no	—
209	M₃₂	—	2	2	no	—
210	M₃₂	C₂×C₄×C₁₀₉	1	4	yes	complemented
211	C₂×C₁₆	—	2	4	no	—
212	C₂×C₁₆	—	2	4	no	—
213	C₂×C₁₆	—	2	4	no	—
214	C₂×C₁₆	—	2	2	no	—
215	C₂×C₁₆	—	2	2	no	—
216	C₂×C₁₆	—	2	2	no	—
217	C₂×C₁₆	C₂×C₄×C₁₀₉	1	4	yes	complemented
218	#97	—	2	2	no	—
219	#97	—	2	2	no	—
220	C₄×C₈	—	2	2	no	—
221	C₄×C₈	—	2	2	no	—
222	C₂⁴	M₁₆×C₁₀₉	1	1	yes	characteristic
223	C₂²×C₄	—	2	2	no	—
224	C₂²×C₄	C₄²×C₁₀₉	1	2	yes	—
225	C₂²×C₄	C₂²⋊C₄×C₁₀₉	1	1	yes	characteristic
226	C₂²×C₄	C₂²⋊C₄×C₁₀₉	1	1	yes	characteristic
227	C₂²×C₄	C₄⋊C₄×C₁₀₉	1	2	yes	—
228	C₂²×C₄	C₂×C₈×C₁₀₉	1	2	yes	—
229	C₂²×C₄	C₂×C₈×C₁₀₉	1	1	yes	characteristic
230	C₂²×C₄	C₂×C₈×C₁₀₉	1	1	yes	characteristic
231	C₂²×C₄	M₁₆×C₁₀₉	1	1	yes	characteristic
232	C₂²×C₄	M₁₆×C₁₀₉	1	2	yes	—
233	C₂²×C₄	C₂²×C₄×C₁₀₉	1	1	yes	characteristic
234	M₁₆	—	2	4	no	—
235	M₁₆	—	2	2	no	—
236	M₁₆	C₂×C₈×C₁₀₉	1	4	yes	—
237	C₂×C₈	—	2	4	no	—
238	C₂×C₈	—	2	2	no	—
239	C₂×C₈	C₄²×C₁₀₉	1	2	yes	—
240	C₂×C₈	C₂²⋊C₄×C₁₀₉	1	1	yes	characteristic
241	C₂×C₈	C₂²⋊C₄×C₁₀₉	1	1	yes	characteristic
242	C₂×C₈	C₂²⋊C₄×C₁₀₉	1	2	yes	—
243	C₂×C₈	C₂²⋊C₄×C₁₀₉	1	2	yes	—
244	C₂×C₈	C₂²⋊C₄×C₁₀₉	1	2	yes	—
245	C₂×C₈	C₂²⋊C₄×C₁₀₉	1	2	yes	—
246	C₂×C₈	C₄⋊C₄×C₁₀₉	1	2	yes	—
247	C₂×C₈	C₄⋊C₄×C₁₀₉	1	2	yes	—
248	C₂×C₈	C₄⋊C₄×C₁₀₉	1	2	yes	—
249	C₂×C₈	C₄⋊C₄×C₁₀₉	1	2	yes	—
250	C₂×C₈	C₄⋊C₄×C₁₀₉	1	2	yes	—
251	C₂×C₈	C₂²×C₄×C₁₀₉	1	1	yes	characteristic
252	C₂×C₈	C₂²×C₄×C₁₀₉	1	1	yes	characteristic
253	C₂×C₈	C₂×D₄×C₁₀₉	1	1	yes	characteristic
254	C₂×C₈	C₂×D₄×C₁₀₉	1	1	yes	characteristic
255	C₂×C₈	C₂×D₄×C₁₀₉	1	1	yes	characteristic
256	C₂×C₈	C₂×Q₈×C₁₀₉	1	1	yes	characteristic
257	C₄⋊C₄	—	2	2	no	—
258	C₄⋊C₄	C₂×C₈×C₁₀₉	1	4	yes	—
259	C₂²⋊C₄	—	2	2	no	—
260	C₂²⋊C₄	—	2	2	no	—
261	C₄²	—	2	2	no	—
262	C₄²	—	2	2	no	—
263	C₁₆	—	2	4	no	—
264	C₁₆	—	2	4	no	—
265	C₂³	—	2	4	no	—
266	C₂³	#97×C₁₀₉	1	2	yes	—
267	C₂³	C₂²⋊C₈×C₁₀₉	1	1	yes	characteristic
268	C₂³	C₂²⋊C₈×C₁₀₉	1	1	yes	characteristic
269	C₂³	C₄⋊C₈×C₁₀₉	1	2	yes	—
270	C₂³	C₂×M₁₆×C₁₀₉	1	1	yes	characteristic
271	C₂×C₄	—	2	4	no	—
272	C₂×C₄	—	4	4	no	—
273	C₂×C₄	#95×C₁₀₉	1	2	yes	—
274	C₂×C₄	#95×C₁₀₉	1	2	yes	—
275	C₂×C₄	C₄×C₈×C₁₀₉	1	2	yes	—
276	C₂×C₄	C₄×C₈×C₁₀₉	1	2	yes	—
277	C₂×C₄	#97×C₁₀₉	1	2	yes	—
278	C₂×C₄	C₂²⋊C₈×C₁₀₉	1	1	yes	characteristic
279	C₂×C₄	C₂²⋊C₈×C₁₀₉	1	1	yes	characteristic
280	C₂×C₄	C₂²⋊C₈×C₁₀₉	1	2	yes	—
281	C₂×C₄	C₂²⋊C₈×C₁₀₉	1	2	yes	—
282	C₂×C₄	C₄⋊C₈×C₁₀₉	1	2	yes	—
283	C₂×C₄	C₄⋊C₈×C₁₀₉	1	2	yes	—
284	C₂×C₄	C₄⋊C₈×C₁₀₉	1	2	yes	—
285	C₂×C₄	C₂×C₄²×C₁₀₉	1	1	yes	characteristic
286	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₉	1	1	yes	characteristic
287	C₂×C₄	C₂×C₄⋊C₄×C₁₀₉	1	1	yes	characteristic
288	C₂×C₄	C₂²×C₈×C₁₀₉	1	1	yes	characteristic
289	C₂×C₄	C₂²×C₈×C₁₀₉	1	1	yes	characteristic
290	C₂×C₄	C₂×M₁₆×C₁₀₉	1	1	yes	characteristic
291	C₈	—	2	4	no	—
292	C₈	#95×C₁₀₉	1	2	yes	—
293	C₈	#95×C₁₀₉	1	2	yes	—
294	C₈	C₂×C₂²⋊C₄×C₁₀₉	1	1	yes	characteristic
295	C₈	C₂×C₂²⋊C₄×C₁₀₉	1	1	yes	characteristic
296	C₈	C₂×C₄⋊C₄×C₁₀₉	1	1	yes	characteristic
297	C₈	C₂×C₄⋊C₄×C₁₀₉	1	1	yes	characteristic
298	C₂²	—	2	2	no	—
299	C₂²	—	2	2	no	—
300	C₂²	—	2	4	no	—
301	C₂²	—	2	4	no	—
302	C₂²	#336×C₁₀₉	1	2	yes	—
303	C₂²	#336×C₁₀₉	1	2	yes	—
304	C₂²	#350×C₁₀₉	1	4	yes	—
305	C₂²	C₂×#97×C₁₀₉	1	1	yes	characteristic
306	C₂²	C₂×C₂²⋊C₈×C₁₀₉	1	1	yes	characteristic
307	C₂²	C₂×C₄⋊C₈×C₁₀₉	1	1	yes	characteristic
308	C₄	—	4	4	no	—
309	C₄	#336×C₁₀₉	1	2	yes	—
310	C₄	#336×C₁₀₉	1	2	yes	—
311	C₄	C₂×#95×C₁₀₉	1	1	yes	characteristic
312	C₄	C₂×C₄×C₈×C₁₀₉	1	1	yes	characteristic
313	C₄	C₂×C₂²⋊C₈×C₁₀₉	1	1	yes	characteristic
314	C₄	C₂×C₄⋊C₈×C₁₀₉	1	1	yes	characteristic
315	C₂	—	2	2	no	—
316	C₂	—	2	1	no	—
317	C₂	—	2	1	no	—
318	C₂	C₁₀₉×#1379	1	4	yes	direct product factor
319	C₂	C₂×#336×C₁₀₉	1	1	yes	characteristic
320	C₂	C₂×#350×C₁₀₉	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈×C₁₀₉	D₄
commutator	C₄	C₂×C₄×C₈×C₁₀₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₀₉
socle	C₂³×C₁₀₉	C₂²⋊C₈
prime radical	C₂⁴×C₁₀₉	M₁₆
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₀₉ ◁ C₂³×C₈×C₁₀₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₀₉×#1379	C₂	direct (N × H)
10. C₂×M₃₂×C₁₀₉	C₄	semidirect
16. C₂²×C₁₆×C₁₀₉	C₄	semidirect
49. M₃₂×C₁₀₉	C₂×C₄	semidirect
56. C₂×C₁₆×C₁₀₉	C₂×C₄	semidirect
154. C₂×#1379	C₁₀₉	direct (N × H)
158. C₂×C₁₀₉	#1379	direct (N × H)
164. #1379	C₂×C₁₀₉	direct (N × H)
165. C₁₀₉	C₂×#1379	direct (N × H)
171. C₂×M₃₂	C₄×C₁₀₉	semidirect
177. C₂²×C₁₆	C₄×C₁₀₉	semidirect
210. M₃₂	C₂×C₄×C₁₀₉	semidirect
217. C₂×C₁₆	C₂×C₄×C₁₀₉	semidirect
318. C₂	C₁₀₉×#1379	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×M₃₂×C₁₀₉	2
C₂³×C₁₆×C₁₀₉	2
C₂×#405×C₁₀₉	2
C₁₀₉×#1379	2
C₂×#1379	109

Subgroups — C2×C109×#1379 #42130547

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₉×#1379 #42130547