Subgroups — C₂×C₁₀₉×#2280 #42152000

Order 27904.

7630 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#117×C₁₀₉	C₂	1	2	yes	maximal, complemented
3	C₁₀₉×#2280	C₂	1	16	yes	maximal, direct product factor
4	C₂×#381×C₁₀₉	C₂	1	2	yes	maximal, complemented
5	C₂×#380×C₁₀₉	C₂	1	4	yes	maximal, complemented
6	C₂×#379×C₁₀₉	C₂	1	2	yes	maximal
7	C₂×C₄×C₂²⋊C₄×C₁₀₉	C₂	1	4	yes	maximal, complemented
8	C₂⁶×C₁₀₉	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₁₀₉	—	2	16	no	—
10	C₂⁴×C₄×C₁₀₉	C₄	1	16	yes	complemented
11	C₂⁴×C₄×C₁₀₉	C₂²	1	2	yes	—
12	C₂⁴×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₀₉	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₁₀₉	C₂²	1	8	yes	—
15	C₂⁴×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
16	C₂×#117×C₁₀₉	—	2	16	no	—
17	C₂×#117×C₁₀₉	C₂²	1	16	yes	complemented
18	C₂²×C₄⋊C₄×C₁₀₉	C₂²	1	4	yes	complemented
19	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	8	yes	—
20	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	4	yes	—
21	C₂²×C₄²×C₁₀₉	C₂²	1	4	yes	complemented
22	#381×C₁₀₉	C₂²	1	16	yes	complemented
23	#380×C₁₀₉	C₂²	1	32	yes	complemented
24	#379×C₁₀₉	C₂²	1	16	yes	—
25	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	32	yes	complemented
26	C₂×#95×C₁₀₉	C₂²	1	8	yes	complemented
27	C₂⁵×C₁₀₉	—	2	8	no	—
28	C₂⁵×C₁₀₉	—	2	16	no	—
29	C₂⁵×C₁₀₉	C₂×C₄	1	8	yes	—
30	C₂⁵×C₁₀₉	C₂³	1	4	yes	—
31	C₂⁵×C₁₀₉	C₂³	1	1	yes	characteristic
32	C₂⁵×C₁₀₉	C₂³	1	2	yes	—
33	C₂³×C₄×C₁₀₉	—	2	8	no	—
34	C₂³×C₄×C₁₀₉	—	2	128	no	—
35	C₂³×C₄×C₁₀₉	—	2	16	no	—
36	C₂³×C₄×C₁₀₉	—	2	16	no	—
37	C₂³×C₄×C₁₀₉	—	2	64	no	—
38	C₂³×C₄×C₁₀₉	C₂×C₄	1	8	yes	—
39	C₂³×C₄×C₁₀₉	C₂×C₄	1	16	yes	—
40	C₂³×C₄×C₁₀₉	C₂×C₄	1	16	yes	—
41	C₂³×C₄×C₁₀₉	C₂×C₄	1	8	yes	—
42	C₂³×C₄×C₁₀₉	C₂×C₄	1	64	yes	complemented
43	C₂³×C₄×C₁₀₉	D₄	1	16	yes	—
44	C₂³×C₄×C₁₀₉	C₂³	1	8	yes	—
45	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₀₉	C₂³	1	8	yes	—
47	C₂³×C₄×C₁₀₉	C₂³	1	8	yes	—
48	C₂³×C₄×C₁₀₉	C₂³	1	4	yes	—
49	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₀₉	C₂³	1	4	yes	—
51	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
52	#117×C₁₀₉	—	2	64	no	—
53	C₂×C₄⋊C₄×C₁₀₉	—	2	16	no	—
54	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	16	yes	complemented
55	C₂×C₂²⋊C₄×C₁₀₉	—	2	16	no	—
56	C₂×C₂²⋊C₄×C₁₀₉	—	2	32	no	—
57	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	16	yes	—
58	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	32	yes	—
59	C₂×C₄²×C₁₀₉	—	2	16	no	—
60	C₂×C₄²×C₁₀₉	C₂³	1	16	yes	complemented
61	#95×C₁₀₉	C₂³	1	32	yes	complemented
62	C₂⁴×C₁₀₉	—	2	128	no	—
63	C₂⁴×C₁₀₉	—	2	32	no	—
64	C₂⁴×C₁₀₉	—	2	64	no	—
65	C₂⁴×C₁₀₉	—	2	16	no	—
66	C₂⁴×C₁₀₉	—	2	8	no	—
67	C₂⁴×C₁₀₉	—	2	32	no	—
68	C₂⁴×C₁₀₉	—	2	8	no	—
69	C₂⁴×C₁₀₉	—	2	8	no	—
70	C₂⁴×C₁₀₉	C₂²×C₄	1	16	yes	—
71	C₂⁴×C₁₀₉	C₂²×C₄	1	4	yes	—
72	C₂⁴×C₁₀₉	C₂²×C₄	1	8	yes	—
73	C₂⁴×C₁₀₉	C₂×D₄	1	8	yes	—
74	C₂⁴×C₁₀₉	#41	1	16	yes	—
75	C₂⁴×C₁₀₉	C₂⁴	1	2	yes	—
76	C₂⁴×C₁₀₉	C₂⁴	1	4	yes	—
77	C₂⁴×C₁₀₉	C₂⁴	1	1	yes	characteristic
78	C₂²×C₄×C₁₀₉	—	2	32	no	—
79	C₂²×C₄×C₁₀₉	—	2	16	no	—
80	C₂²×C₄×C₁₀₉	—	2	8	no	—
81	C₂²×C₄×C₁₀₉	—	2	64	no	—
82	C₂²×C₄×C₁₀₉	—	2	64	no	—
83	C₂²×C₄×C₁₀₉	—	2	256	no	—
84	C₂²×C₄×C₁₀₉	—	2	32	no	—
85	C₂²×C₄×C₁₀₉	—	2	32	no	—
86	C₂²×C₄×C₁₀₉	—	2	16	no	—
87	C₂²×C₄×C₁₀₉	—	2	32	no	—
88	C₂²×C₄×C₁₀₉	C₂²⋊C₄	1	64	yes	complemented
89	C₂²×C₄×C₁₀₉	C₂²×C₄	1	8	yes	—
90	C₂²×C₄×C₁₀₉	C₂²×C₄	1	16	yes	—
91	C₂²×C₄×C₁₀₉	C₂²×C₄	1	32	yes	—
92	C₂²×C₄×C₁₀₉	C₂²×C₄	1	32	yes	—
93	C₂²×C₄×C₁₀₉	C₂²×C₄	1	4	yes	—
94	C₂²×C₄×C₁₀₉	C₂²×C₄	1	4	yes	—
95	C₂²×C₄×C₁₀₉	C₂²×C₄	1	16	yes	—
96	C₂²×C₄×C₁₀₉	C₂×D₄	1	8	yes	—
97	C₂²×C₄×C₁₀₉	C₂×D₄	1	8	yes	—
98	C₂²×C₄×C₁₀₉	C₂×D₄	1	32	yes	—
99	C₂²×C₄×C₁₀₉	C₂⁴	1	16	yes	—
100	C₂²×C₄×C₁₀₉	C₂⁴	1	4	yes	—
101	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
102	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
103	C₄⋊C₄×C₁₀₉	—	2	32	no	—
104	C₂²⋊C₄×C₁₀₉	—	2	32	no	—
105	C₂²⋊C₄×C₁₀₉	—	2	64	no	—
106	C₄²×C₁₀₉	—	2	32	no	—
107	C₂³×C₁₀₉	—	2	128	no	—
108	C₂³×C₁₀₉	—	2	256	no	—
109	C₂³×C₁₀₉	—	2	32	no	—
110	C₂³×C₁₀₉	—	2	16	no	—
111	C₂³×C₁₀₉	—	2	16	no	—
112	C₂³×C₁₀₉	—	2	16	no	—
113	C₂³×C₁₀₉	—	2	64	no	—
114	C₂³×C₁₀₉	—	2	32	no	—
115	C₂³×C₁₀₉	—	2	64	no	—
116	C₂³×C₁₀₉	—	2	8	no	—
117	C₂³×C₁₀₉	—	2	8	no	—
118	C₂³×C₁₀₉	—	2	8	no	—
119	C₂³×C₁₀₉	C₂×C₂²⋊C₄	1	16	yes	—
120	C₂³×C₁₀₉	#117	1	32	yes	complemented
121	C₂³×C₁₀₉	C₂³×C₄	1	4	yes	—
122	C₂³×C₁₀₉	C₂³×C₄	1	8	yes	—
123	C₂³×C₁₀₉	C₂³×C₄	1	2	yes	—
124	C₂³×C₁₀₉	C₂²×D₄	1	8	yes	—
125	C₂³×C₁₀₉	C₂²×D₄	1	4	yes	—
126	C₂³×C₁₀₉	C₂×#41	1	16	yes	—
127	C₂³×C₁₀₉	C₂×#41	1	8	yes	—
128	C₂³×C₁₀₉	C₂⁵	1	1	yes	characteristic
129	C₂×C₄×C₁₀₉	—	2	32	no	—
130	C₂×C₄×C₁₀₉	—	2	16	no	—
131	C₂×C₄×C₁₀₉	—	2	8	no	—
132	C₂×C₄×C₁₀₉	—	2	64	no	—
133	C₂×C₄×C₁₀₉	—	2	64	no	—
134	C₂×C₄×C₁₀₉	—	2	16	no	—
135	C₂×C₄×C₁₀₉	—	2	32	no	—
136	C₂×C₄×C₁₀₉	—	4	32	no	—
137	C₂×C₄×C₁₀₉	C₂×C₂²⋊C₄	1	16	yes	—
138	C₂×C₄×C₁₀₉	C₂×C₂²⋊C₄	1	16	yes	—
139	C₂×C₄×C₁₀₉	C₂×C₂²⋊C₄	1	64	yes	complemented
140	C₂×C₄×C₁₀₉	C₂³×C₄	1	8	yes	—
141	C₂×C₄×C₁₀₉	C₂³×C₄	1	4	yes	—
142	C₂×C₄×C₁₀₉	C₂³×C₄	1	4	yes	—
143	C₂×C₄×C₁₀₉	C₂²×D₄	1	8	yes	—
144	C₂×C₄×C₁₀₉	C₂²×D₄	1	8	yes	—
145	C₂²×C₁₀₉	—	2	128	no	—
146	C₂²×C₁₀₉	—	2	8	no	—
147	C₂²×C₁₀₉	—	2	8	no	—
148	C₂²×C₁₀₉	—	2	8	no	—
149	C₂²×C₁₀₉	—	2	16	no	—
150	C₂²×C₁₀₉	—	2	32	no	—
151	C₂²×C₁₀₉	—	2	32	no	—
152	C₂²×C₁₀₉	—	2	64	no	—
153	C₂²×C₁₀₉	C₂²×C₂²⋊C₄	1	8	yes	—
154	C₂²×C₁₀₉	C₂²×C₂²⋊C₄	1	4	yes	—
155	C₂²×C₁₀₉	C₂×#117	1	8	yes	—
156	C₂²×C₁₀₉	C₂×#117	1	16	yes	complemented
157	C₂²×C₁₀₉	#525	1	16	yes	—
158	C₂²×C₁₀₉	C₂⁴×C₄	1	1	yes	characteristic
159	C₂²×C₁₀₉	C₂³×D₄	1	2	yes	—
160	C₂²×C₁₀₉	C₂²×#41	1	4	yes	—
161	C₄×C₁₀₉	—	2	8	no	—
162	C₄×C₁₀₉	—	4	16	no	—
163	C₄×C₁₀₉	C₂²×C₂²⋊C₄	1	8	yes	—
164	C₄×C₁₀₉	C₂²×C₂²⋊C₄	1	8	yes	—
165	C₂×#2280	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂×C₁₀₉	—	2	8	no	—
167	C₂×C₁₀₉	—	2	16	no	—
168	C₂×C₁₀₉	#2280	1	8	yes	direct product factor
169	C₂×C₁₀₉	C₂³×C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₁₀₉	C₂²×#117	1	2	yes	—
171	C₂×C₁₀₉	C₂×#525	1	4	yes	—
172	C₂⁵×C₄	C₂×C₁₀₉	1	1	yes	characteristic
173	C₂²×#117	C₂×C₁₀₉	1	2	yes	complemented
174	#2280	C₂×C₁₀₉	1	16	yes	direct product factor
175	C₂×#381	C₂×C₁₀₉	1	2	yes	complemented
176	C₂×#380	C₂×C₁₀₉	1	4	yes	complemented
177	C₂×#379	C₂×C₁₀₉	1	2	yes	—
178	C₂×C₄×C₂²⋊C₄	C₂×C₁₀₉	1	4	yes	complemented
179	C₁₀₉	C₂×#2280	1	1	yes	characteristic, direct product factor, Sylow
180	C₂⁶	C₂²×C₁₀₉	1	1	yes	characteristic
181	C₂⁴×C₄	—	2	16	no	—
182	C₂⁴×C₄	C₄×C₁₀₉	1	16	yes	complemented
183	C₂⁴×C₄	C₂²×C₁₀₉	1	2	yes	—
184	C₂⁴×C₄	C₂²×C₁₀₉	1	2	yes	—
185	C₂⁴×C₄	C₂²×C₁₀₉	1	1	yes	characteristic
186	C₂⁴×C₄	C₂²×C₁₀₉	1	8	yes	—
187	C₂⁴×C₄	C₂²×C₁₀₉	1	1	yes	characteristic
188	C₂×#117	—	2	16	no	—
189	C₂×#117	C₂²×C₁₀₉	1	16	yes	complemented
190	C₂²×C₄⋊C₄	C₂²×C₁₀₉	1	4	yes	complemented
191	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	4	yes	—
192	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	8	yes	—
193	C₂²×C₄²	C₂²×C₁₀₉	1	4	yes	complemented
194	#381	C₂²×C₁₀₉	1	16	yes	complemented
195	#380	C₂²×C₁₀₉	1	32	yes	complemented
196	#379	C₂²×C₁₀₉	1	16	yes	—
197	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	32	yes	complemented
198	C₂×#95	C₂²×C₁₀₉	1	8	yes	complemented
199	C₂⁵	—	2	8	no	—
200	C₂⁵	—	2	16	no	—
201	C₂⁵	C₂×C₄×C₁₀₉	1	8	yes	—
202	C₂⁵	C₂³×C₁₀₉	1	4	yes	—
203	C₂⁵	C₂³×C₁₀₉	1	1	yes	characteristic
204	C₂⁵	C₂³×C₁₀₉	1	2	yes	—
205	C₂³×C₄	—	2	8	no	—
206	C₂³×C₄	—	2	128	no	—
207	C₂³×C₄	—	2	16	no	—
208	C₂³×C₄	—	2	16	no	—
209	C₂³×C₄	—	2	64	no	—
210	C₂³×C₄	C₂×C₄×C₁₀₉	1	8	yes	—
211	C₂³×C₄	C₂×C₄×C₁₀₉	1	16	yes	—
212	C₂³×C₄	C₂×C₄×C₁₀₉	1	16	yes	—
213	C₂³×C₄	C₂×C₄×C₁₀₉	1	8	yes	—
214	C₂³×C₄	C₂×C₄×C₁₀₉	1	64	yes	complemented
215	C₂³×C₄	D₄×C₁₀₉	1	16	yes	—
216	C₂³×C₄	C₂³×C₁₀₉	1	8	yes	—
217	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
218	C₂³×C₄	C₂³×C₁₀₉	1	8	yes	—
219	C₂³×C₄	C₂³×C₁₀₉	1	8	yes	—
220	C₂³×C₄	C₂³×C₁₀₉	1	4	yes	—
221	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
222	C₂³×C₄	C₂³×C₁₀₉	1	4	yes	—
223	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
224	#117	—	2	64	no	—
225	C₂×C₄⋊C₄	—	2	16	no	—
226	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	16	yes	complemented
227	C₂×C₂²⋊C₄	—	2	16	no	—
228	C₂×C₂²⋊C₄	—	2	32	no	—
229	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	16	yes	—
230	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	32	yes	—
231	C₂×C₄²	—	2	16	no	—
232	C₂×C₄²	C₂³×C₁₀₉	1	16	yes	complemented
233	#95	C₂³×C₁₀₉	1	32	yes	complemented
234	C₂⁴	—	2	128	no	—
235	C₂⁴	—	2	32	no	—
236	C₂⁴	—	2	64	no	—
237	C₂⁴	—	2	16	no	—
238	C₂⁴	—	2	8	no	—
239	C₂⁴	—	2	32	no	—
240	C₂⁴	—	2	8	no	—
241	C₂⁴	—	2	8	no	—
242	C₂⁴	C₂²×C₄×C₁₀₉	1	16	yes	—
243	C₂⁴	C₂²×C₄×C₁₀₉	1	4	yes	—
244	C₂⁴	C₂²×C₄×C₁₀₉	1	8	yes	—
245	C₂⁴	C₂×D₄×C₁₀₉	1	8	yes	—
246	C₂⁴	#41×C₁₀₉	1	16	yes	—
247	C₂⁴	C₂⁴×C₁₀₉	1	2	yes	—
248	C₂⁴	C₂⁴×C₁₀₉	1	4	yes	—
249	C₂⁴	C₂⁴×C₁₀₉	1	1	yes	characteristic
250	C₂²×C₄	—	2	32	no	—
251	C₂²×C₄	—	2	16	no	—
252	C₂²×C₄	—	2	8	no	—
253	C₂²×C₄	—	2	64	no	—
254	C₂²×C₄	—	2	64	no	—
255	C₂²×C₄	—	2	256	no	—
256	C₂²×C₄	—	2	32	no	—
257	C₂²×C₄	—	2	32	no	—
258	C₂²×C₄	—	2	16	no	—
259	C₂²×C₄	—	2	32	no	—
260	C₂²×C₄	C₂²⋊C₄×C₁₀₉	1	64	yes	complemented
261	C₂²×C₄	C₂²×C₄×C₁₀₉	1	8	yes	—
262	C₂²×C₄	C₂²×C₄×C₁₀₉	1	16	yes	—
263	C₂²×C₄	C₂²×C₄×C₁₀₉	1	32	yes	—
264	C₂²×C₄	C₂²×C₄×C₁₀₉	1	32	yes	—
265	C₂²×C₄	C₂²×C₄×C₁₀₉	1	4	yes	—
266	C₂²×C₄	C₂²×C₄×C₁₀₉	1	4	yes	—
267	C₂²×C₄	C₂²×C₄×C₁₀₉	1	16	yes	—
268	C₂²×C₄	C₂×D₄×C₁₀₉	1	8	yes	—
269	C₂²×C₄	C₂×D₄×C₁₀₉	1	8	yes	—
270	C₂²×C₄	C₂×D₄×C₁₀₉	1	32	yes	—
271	C₂²×C₄	C₂⁴×C₁₀₉	1	16	yes	—
272	C₂²×C₄	C₂⁴×C₁₀₉	1	4	yes	—
273	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
274	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
275	C₄⋊C₄	—	2	32	no	—
276	C₂²⋊C₄	—	2	32	no	—
277	C₂²⋊C₄	—	2	64	no	—
278	C₄²	—	2	32	no	—
279	C₂³	—	2	256	no	—
280	C₂³	—	2	128	no	—
281	C₂³	—	2	32	no	—
282	C₂³	—	2	16	no	—
283	C₂³	—	2	16	no	—
284	C₂³	—	2	16	no	—
285	C₂³	—	2	64	no	—
286	C₂³	—	2	32	no	—
287	C₂³	—	2	64	no	—
288	C₂³	—	2	8	no	—
289	C₂³	—	2	8	no	—
290	C₂³	—	2	8	no	—
291	C₂³	C₂×C₂²⋊C₄×C₁₀₉	1	16	yes	—
292	C₂³	#117×C₁₀₉	1	32	yes	complemented
293	C₂³	C₂³×C₄×C₁₀₉	1	4	yes	—
294	C₂³	C₂³×C₄×C₁₀₉	1	8	yes	—
295	C₂³	C₂³×C₄×C₁₀₉	1	2	yes	—
296	C₂³	C₂²×D₄×C₁₀₉	1	8	yes	—
297	C₂³	C₂²×D₄×C₁₀₉	1	4	yes	—
298	C₂³	C₂×#41×C₁₀₉	1	16	yes	—
299	C₂³	C₂×#41×C₁₀₉	1	8	yes	—
300	C₂³	C₂⁵×C₁₀₉	1	1	yes	characteristic
301	C₂×C₄	—	2	32	no	—
302	C₂×C₄	—	2	16	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	2	64	no	—
305	C₂×C₄	—	2	64	no	—
306	C₂×C₄	—	2	16	no	—
307	C₂×C₄	—	2	32	no	—
308	C₂×C₄	—	4	32	no	—
309	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₉	1	16	yes	—
310	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₉	1	16	yes	—
311	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₉	1	64	yes	complemented
312	C₂×C₄	C₂³×C₄×C₁₀₉	1	8	yes	—
313	C₂×C₄	C₂³×C₄×C₁₀₉	1	4	yes	—
314	C₂×C₄	C₂³×C₄×C₁₀₉	1	4	yes	—
315	C₂×C₄	C₂²×D₄×C₁₀₉	1	8	yes	—
316	C₂×C₄	C₂²×D₄×C₁₀₉	1	8	yes	—
317	C₂²	—	2	128	no	—
318	C₂²	—	2	32	no	—
319	C₂²	—	2	64	no	—
320	C₂²	—	2	8	no	—
321	C₂²	—	2	8	no	—
322	C₂²	—	2	8	no	—
323	C₂²	—	2	16	no	—
324	C₂²	—	2	32	no	—
325	C₂²	C₂²×C₂²⋊C₄×C₁₀₉	1	8	yes	—
326	C₂²	C₂²×C₂²⋊C₄×C₁₀₉	1	4	yes	—
327	C₂²	C₂×#117×C₁₀₉	1	8	yes	—
328	C₂²	C₂×#117×C₁₀₉	1	16	yes	complemented
329	C₂²	#525×C₁₀₉	1	16	yes	—
330	C₂²	C₂⁴×C₄×C₁₀₉	1	1	yes	characteristic
331	C₂²	C₂³×D₄×C₁₀₉	1	2	yes	—
332	C₂²	C₂²×#41×C₁₀₉	1	4	yes	—
333	C₄	—	2	8	no	—
334	C₄	—	4	16	no	—
335	C₄	C₂²×C₂²⋊C₄×C₁₀₉	1	8	yes	—
336	C₄	C₂²×C₂²⋊C₄×C₁₀₉	1	8	yes	—
337	C₂	—	2	8	no	—
338	C₂	—	2	16	no	—
339	C₂	C₁₀₉×#2280	1	8	yes	direct product factor
340	C₂	C₂³×C₂²⋊C₄×C₁₀₉	1	1	yes	characteristic
341	C₂	C₂²×#117×C₁₀₉	1	2	yes	—
342	C₂	C₂×#525×C₁₀₉	1	4	yes	—

	subgroup	G/H
center	C₂³×C₄×C₁₀₉	C₂³
commutator	C₂²	C₂⁴×C₄×C₁₀₉
Frattini, cosocle	C₂³	C₂⁵×C₁₀₉
socle	C₂⁴×C₁₀₉	C₂⁴
prime radical	C₂⁶×C₁₀₉	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₀₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#117×C₁₀₉	C₂	semidirect
3. C₁₀₉×#2280	C₂	direct (N × H)
4. C₂×#381×C₁₀₉	C₂	semidirect
5. C₂×#380×C₁₀₉	C₂	semidirect
7. C₂×C₄×C₂²⋊C₄×C₁₀₉	C₂	semidirect
10. C₂⁴×C₄×C₁₀₉	C₄	semidirect
17. C₂×#117×C₁₀₉	C₂²	semidirect
18. C₂²×C₄⋊C₄×C₁₀₉	C₂²	semidirect
21. C₂²×C₄²×C₁₀₉	C₂²	semidirect
22. #381×C₁₀₉	C₂²	semidirect
23. #380×C₁₀₉	C₂²	semidirect
25. C₄×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
26. C₂×#95×C₁₀₉	C₂²	semidirect
42. C₂³×C₄×C₁₀₉	C₂×C₄	semidirect
54. C₂×C₄⋊C₄×C₁₀₉	C₂³	semidirect
60. C₂×C₄²×C₁₀₉	C₂³	semidirect
61. #95×C₁₀₉	C₂³	semidirect
88. C₂²×C₄×C₁₀₉	C₂²⋊C₄	semidirect
120. C₂³×C₁₀₉	#117	semidirect
139. C₂×C₄×C₁₀₉	C₂×C₂²⋊C₄	semidirect
156. C₂²×C₁₀₉	C₂×#117	semidirect
165. C₂×#2280	C₁₀₉	direct (N × H)
168. C₂×C₁₀₉	#2280	direct (N × H)
173. C₂²×#117	C₂×C₁₀₉	semidirect
174. #2280	C₂×C₁₀₉	direct (N × H)
175. C₂×#381	C₂×C₁₀₉	semidirect
176. C₂×#380	C₂×C₁₀₉	semidirect
178. C₂×C₄×C₂²⋊C₄	C₂×C₁₀₉	semidirect
179. C₁₀₉	C₂×#2280	direct (N × H)
182. C₂⁴×C₄	C₄×C₁₀₉	semidirect
189. C₂×#117	C₂²×C₁₀₉	semidirect
190. C₂²×C₄⋊C₄	C₂²×C₁₀₉	semidirect
193. C₂²×C₄²	C₂²×C₁₀₉	semidirect
194. #381	C₂²×C₁₀₉	semidirect
195. #380	C₂²×C₁₀₉	semidirect
197. C₄×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
198. C₂×#95	C₂²×C₁₀₉	semidirect
214. C₂³×C₄	C₂×C₄×C₁₀₉	semidirect
226. C₂×C₄⋊C₄	C₂³×C₁₀₉	semidirect
232. C₂×C₄²	C₂³×C₁₀₉	semidirect
233. #95	C₂³×C₁₀₉	semidirect
260. C₂²×C₄	C₂²⋊C₄×C₁₀₉	semidirect
292. C₂³	#117×C₁₀₉	semidirect
311. C₂×C₄	C₂×C₂²⋊C₄×C₁₀₉	semidirect
328. C₂²	C₂×#117×C₁₀₉	semidirect
339. C₂	C₁₀₉×#2280	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₄×C₁₀₉	2
C₂²×#117×C₁₀₉	2
C₁₀₉×#2280	2
C₂×#381×C₁₀₉	2
C₂×#380×C₁₀₉	2
C₂×#379×C₁₀₉	2
C₂×C₄×C₂²⋊C₄×C₁₀₉	2
C₂×#2280	109

Subgroups — C2×C109×#2280 #42152000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₉×#2280 #42152000