Subgroups — C₂×C₁₀₉×#1813 #42138666

Order 27904.

1314 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#131×C₁₀₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#108×C₁₀₉	C₂	1	2	yes	maximal, complemented
3	C₂×#413×C₁₀₉	C₂	1	2	yes	maximal
4	C₁₀₉×#1813	C₂	1	8	yes	maximal, direct product factor
5	C₂×#338×C₁₀₉	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₁₀₉	C₂²	1	1	yes	characteristic
7	C₂×#131×C₁₀₉	—	2	4	no	—
8	C₂×#131×C₁₀₉	—	2	4	no	—
9	C₂×#131×C₁₀₉	C₄	1	4	yes	—
10	C₂×#131×C₁₀₉	C₂²	1	4	yes	—
11	C₂²×M₁₆×C₁₀₉	C₄	1	2	yes	—
12	C₂²×M₁₆×C₁₀₉	C₂²	1	4	yes	—
13	C₂²×M₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₀₉	C₄	1	2	yes	—
15	C₂³×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
16	C₂×#108×C₁₀₉	—	2	4	no	—
17	C₂×#108×C₁₀₉	—	2	4	no	—
18	C₂×#108×C₁₀₉	C₂²	1	8	yes	complemented
19	#413×C₁₀₉	—	2	4	no	—
20	#413×C₁₀₉	C₂²	1	8	yes	—
21	C₂×#101×C₁₀₉	—	2	2	no	—
22	C₂×#100×C₁₀₉	—	2	2	no	—
23	#338×C₁₀₉	C₂²	1	8	yes	complemented
24	C₂×#41×C₁₀₉	—	2	2	no	—
25	C₂×#41×C₁₀₉	—	2	2	no	—
26	C₂×#41×C₁₀₉	—	2	2	no	—
27	C₂×#41×C₁₀₉	—	2	2	no	—
28	C₂×#41×C₁₀₉	C₂×C₄	1	2	yes	—
29	C₂×#41×C₁₀₉	D₄	1	2	yes	—
30	C₂×#41×C₁₀₉	Q₈	1	2	yes	—
31	C₂×#41×C₁₀₉	C₂³	1	2	yes	—
32	C₂²×Q₈×C₁₀₉	D₄	1	1	yes	characteristic
33	C₂²×D₄×C₁₀₉	D₄	1	1	yes	characteristic
34	C₂²×D₄×C₁₀₉	Q₈	1	2	yes	—
35	C₂³×C₄×C₁₀₉	C₂×C₄	1	2	yes	—
36	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
37	#131×C₁₀₉	—	2	16	no	—
38	#131×C₁₀₉	—	2	16	no	—
39	C₂×M₁₆×C₁₀₉	—	2	2	no	—
40	C₂×M₁₆×C₁₀₉	—	2	2	no	—
41	C₂×M₁₆×C₁₀₉	—	2	4	no	—
42	C₂×M₁₆×C₁₀₉	—	2	4	no	—
43	C₂×M₁₆×C₁₀₉	—	2	4	no	—
44	C₂×M₁₆×C₁₀₉	—	2	4	no	—
45	C₂×M₁₆×C₁₀₉	—	2	4	no	—
46	C₂×M₁₆×C₁₀₉	—	2	4	no	—
47	C₂×M₁₆×C₁₀₉	—	2	4	no	—
48	C₂×M₁₆×C₁₀₉	C₂×C₄	1	8	yes	—
49	C₂×M₁₆×C₁₀₉	C₂×C₄	1	2	yes	—
50	C₂×M₁₆×C₁₀₉	C₂³	1	8	yes	—
51	C₂×M₁₆×C₁₀₉	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₀₉	—	2	4	no	—
53	C₂²×C₈×C₁₀₉	—	2	4	no	—
54	C₂²×C₈×C₁₀₉	—	2	4	no	—
55	C₂²×C₈×C₁₀₉	C₂×C₄	1	2	yes	—
56	C₂²×C₈×C₁₀₉	C₂×C₄	1	8	yes	—
57	C₂²×C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₈×C₁₀₉	C₂×C₄	1	2	yes	—
60	C₂²×C₈×C₁₀₉	D₄	1	4	yes	—
61	C₂²×C₈×C₁₀₉	D₄	1	4	yes	—
62	C₂²×C₈×C₁₀₉	C₂³	1	2	yes	—
63	#108×C₁₀₉	—	2	16	no	—
64	#101×C₁₀₉	—	2	8	no	—
65	#100×C₁₀₉	—	2	8	no	—
66	C₂⁴×C₁₀₉	C₄⋊C₄	1	2	yes	—
67	C₂⁴×C₁₀₉	C₂×Q₈	1	1	yes	characteristic
68	#41×C₁₀₉	—	2	4	no	—
69	#41×C₁₀₉	—	2	4	no	—
70	#41×C₁₀₉	—	2	4	no	—
71	#41×C₁₀₉	—	2	4	no	—
72	#41×C₁₀₉	—	2	4	no	—
73	#41×C₁₀₉	—	2	4	no	—
74	#41×C₁₀₉	—	2	4	no	—
75	#41×C₁₀₉	—	2	4	no	—
76	C₂×Q₈×C₁₀₉	—	2	2	no	—
77	C₂×Q₈×C₁₀₉	—	2	2	no	—
78	C₂×Q₈×C₁₀₉	C₄⋊C₄	1	2	yes	—
79	C₂×Q₈×C₁₀₉	C₂×D₄	1	2	yes	—
80	C₂×D₄×C₁₀₉	—	2	4	no	—
81	C₂×D₄×C₁₀₉	—	2	4	no	—
82	C₂×D₄×C₁₀₉	—	2	2	no	—
83	C₂×D₄×C₁₀₉	—	2	2	no	—
84	C₂×D₄×C₁₀₉	C₄⋊C₄	1	2	yes	—
85	C₂×D₄×C₁₀₉	C₄⋊C₄	1	4	yes	—
86	C₂×D₄×C₁₀₉	C₂×D₄	1	2	yes	—
87	C₂×D₄×C₁₀₉	C₂×Q₈	1	4	yes	—
88	C₂²×C₄×C₁₀₉	—	2	2	no	—
89	C₂²×C₄×C₁₀₉	—	2	2	no	—
90	C₂²×C₄×C₁₀₉	—	2	2	no	—
91	C₂²×C₄×C₁₀₉	—	2	2	no	—
92	C₂²×C₄×C₁₀₉	C₄⋊C₄	1	2	yes	—
93	C₂²×C₄×C₁₀₉	C₄⋊C₄	1	4	yes	—
94	C₂²×C₄×C₁₀₉	C₂²×C₄	1	4	yes	—
95	C₂²×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₀₉	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₀₉	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₀₉	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₄×C₁₀₉	#41	1	2	yes	—
103	C₂²×C₄×C₁₀₉	#41	1	2	yes	—
104	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
105	M₁₆×C₁₀₉	—	2	4	no	—
106	M₁₆×C₁₀₉	—	2	4	no	—
107	M₁₆×C₁₀₉	—	2	16	no	—
108	M₁₆×C₁₀₉	—	2	8	no	—
109	M₁₆×C₁₀₉	—	2	8	no	—
110	M₁₆×C₁₀₉	—	4	4	no	—
111	M₁₆×C₁₀₉	—	4	4	no	—
112	C₂×C₈×C₁₀₉	—	2	2	no	—
113	C₂×C₈×C₁₀₉	—	2	2	no	—
114	C₂×C₈×C₁₀₉	—	2	16	no	—
115	C₂×C₈×C₁₀₉	—	2	8	no	—
116	C₂×C₈×C₁₀₉	—	4	4	no	—
117	C₂×C₈×C₁₀₉	—	4	4	no	—
118	C₂×C₈×C₁₀₉	C₂²⋊C₄	1	2	yes	—
119	C₂×C₈×C₁₀₉	C₂²⋊C₄	1	2	yes	—
120	C₂×C₈×C₁₀₉	C₂²⋊C₄	1	2	yes	—
121	C₂×C₈×C₁₀₉	C₂²⋊C₄	1	2	yes	—
122	C₂×C₈×C₁₀₉	C₂²⋊C₄	1	8	yes	—
123	C₂×C₈×C₁₀₉	C₂²×C₄	1	4	yes	—
124	C₂×C₈×C₁₀₉	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₁₀₉	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₁₀₉	C₂×D₄	1	8	yes	—
127	C₂³×C₁₀₉	—	2	2	no	—
128	C₂³×C₁₀₉	—	2	2	no	—
129	C₂³×C₁₀₉	—	4	2	no	—
130	C₂³×C₁₀₉	—	4	4	no	—
131	C₂³×C₁₀₉	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂³×C₁₀₉	C₂×C₄⋊C₄	1	4	yes	—
133	C₂³×C₁₀₉	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂³×C₁₀₉	C₂²⋊Q₈	1	2	yes	—
135	C₂³×C₁₀₉	C₂²⋊Q₈	1	2	yes	—
136	C₂³×C₁₀₉	C₂²×Q₈	1	1	yes	characteristic
137	Q₈×C₁₀₉	—	2	4	no	—
138	Q₈×C₁₀₉	—	2	4	no	—
139	D₄×C₁₀₉	—	2	8	no	—
140	D₄×C₁₀₉	—	2	8	no	—
141	D₄×C₁₀₉	—	2	4	no	—
142	D₄×C₁₀₉	—	2	4	no	—
143	C₂×C₄×C₁₀₉	—	2	2	no	—
144	C₂×C₄×C₁₀₉	—	2	2	no	—
145	C₂×C₄×C₁₀₉	—	2	4	no	—
146	C₂×C₄×C₁₀₉	—	2	4	no	—
147	C₂×C₄×C₁₀₉	—	2	4	no	—
148	C₂×C₄×C₁₀₉	—	2	4	no	—
149	C₂×C₄×C₁₀₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₀₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₀₉	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂×C₄×C₁₀₉	C₂×C₄⋊C₄	1	4	yes	—
153	C₂×C₄×C₁₀₉	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₀₉	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₀₉	#117	1	1	yes	characteristic
156	C₂×C₄×C₁₀₉	#117	1	2	yes	—
157	C₂×C₄×C₁₀₉	#117	1	1	yes	characteristic
158	C₂×C₄×C₁₀₉	#121	1	2	yes	—
159	C₂×C₄×C₁₀₉	#121	1	2	yes	—
160	C₂×C₄×C₁₀₉	#121	1	2	yes	—
161	C₂×C₄×C₁₀₉	#121	1	2	yes	—
162	C₂×C₄×C₁₀₉	C₂²⋊Q₈	1	2	yes	—
163	C₂×C₄×C₁₀₉	C₂²⋊Q₈	1	2	yes	—
164	C₂×C₄×C₁₀₉	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
166	C₂×C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
168	C₈×C₁₀₉	—	2	4	no	—
169	C₈×C₁₀₉	—	4	8	no	—
170	C₈×C₁₀₉	C₂×C₂²⋊C₄	1	4	yes	—
171	C₈×C₁₀₉	C₂×C₂²⋊C₄	1	4	yes	—
172	C₂²×C₁₀₉	—	2	2	no	—
173	C₂²×C₁₀₉	—	2	4	no	—
174	C₂²×C₁₀₉	—	2	4	no	—
175	C₂²×C₁₀₉	—	4	1	no	—
176	C₂²×C₁₀₉	—	4	2	no	—
177	C₂²×C₁₀₉	—	4	1	no	—
178	C₂²×C₁₀₉	—	4	4	no	—
179	C₂²×C₁₀₉	—	4	4	no	—
180	C₂²×C₁₀₉	—	4	4	no	—
181	C₂²×C₁₀₉	#380	1	1	yes	characteristic
182	C₂²×C₁₀₉	#380	1	2	yes	—
183	C₂²×C₁₀₉	#380	1	1	yes	characteristic
184	C₂²×C₁₀₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
185	C₂²×C₁₀₉	C₂×C₂²⋊Q₈	1	2	yes	—
186	C₄×C₁₀₉	—	2	4	no	—
187	C₄×C₁₀₉	#380	1	1	yes	characteristic
188	C₄×C₁₀₉	#380	1	1	yes	characteristic
189	C₄×C₁₀₉	#380	1	2	yes	—
190	C₄×C₁₀₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
191	C₄×C₁₀₉	C₂×#117	1	1	yes	characteristic
192	C₄×C₁₀₉	C₂×#121	1	2	yes	—
193	C₂×#1813	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂×C₁₀₉	—	2	1	no	—
195	C₂×C₁₀₉	—	2	1	no	—
196	C₂×C₁₀₉	—	2	2	no	—
197	C₂×C₁₀₉	—	2	2	no	—
198	C₂×C₁₀₉	—	4	4	no	—
199	C₂×C₁₀₉	#1813	1	2	yes	direct product factor
200	C₂×C₁₀₉	C₂×#380	1	1	yes	characteristic
201	C₂²×#131	C₂×C₁₀₉	1	1	yes	characteristic
202	C₂²×#108	C₂×C₁₀₉	1	2	yes	complemented
203	C₂×#413	C₂×C₁₀₉	1	2	yes	—
204	#1813	C₂×C₁₀₉	1	8	yes	direct product factor
205	C₂×#338	C₂×C₁₀₉	1	2	yes	complemented
206	C₁₀₉	C₂×#1813	1	1	yes	characteristic, direct product factor, Sylow
207	C₂²×#41	C₂²×C₁₀₉	1	1	yes	characteristic
208	C₂×#131	—	2	4	no	—
209	C₂×#131	—	2	4	no	—
210	C₂×#131	C₄×C₁₀₉	1	4	yes	—
211	C₂×#131	C₂²×C₁₀₉	1	4	yes	—
212	C₂²×M₁₆	C₄×C₁₀₉	1	2	yes	—
213	C₂²×M₁₆	C₂²×C₁₀₉	1	4	yes	—
214	C₂²×M₁₆	C₂²×C₁₀₉	1	1	yes	characteristic
215	C₂³×C₈	C₄×C₁₀₉	1	2	yes	—
216	C₂³×C₈	C₂²×C₁₀₉	1	1	yes	characteristic
217	C₂×#108	—	2	4	no	—
218	C₂×#108	—	2	4	no	—
219	C₂×#108	C₂²×C₁₀₉	1	8	yes	complemented
220	#413	—	2	4	no	—
221	#413	C₂²×C₁₀₉	1	8	yes	—
222	C₂×#101	—	2	2	no	—
223	C₂×#100	—	2	2	no	—
224	#338	C₂²×C₁₀₉	1	8	yes	complemented
225	C₂×#41	—	2	2	no	—
226	C₂×#41	—	2	2	no	—
227	C₂×#41	—	2	2	no	—
228	C₂×#41	—	2	2	no	—
229	C₂×#41	C₂×C₄×C₁₀₉	1	2	yes	—
230	C₂×#41	D₄×C₁₀₉	1	2	yes	—
231	C₂×#41	Q₈×C₁₀₉	1	2	yes	—
232	C₂×#41	C₂³×C₁₀₉	1	2	yes	—
233	C₂²×Q₈	D₄×C₁₀₉	1	1	yes	characteristic
234	C₂²×D₄	D₄×C₁₀₉	1	1	yes	characteristic
235	C₂²×D₄	Q₈×C₁₀₉	1	2	yes	—
236	C₂³×C₄	C₂×C₄×C₁₀₉	1	2	yes	—
237	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
238	#131	—	2	16	no	—
239	#131	—	2	16	no	—
240	C₂×M₁₆	—	2	2	no	—
241	C₂×M₁₆	—	2	2	no	—
242	C₂×M₁₆	—	2	4	no	—
243	C₂×M₁₆	—	2	4	no	—
244	C₂×M₁₆	—	2	4	no	—
245	C₂×M₁₆	—	2	4	no	—
246	C₂×M₁₆	—	2	4	no	—
247	C₂×M₁₆	—	2	4	no	—
248	C₂×M₁₆	—	2	4	no	—
249	C₂×M₁₆	C₂×C₄×C₁₀₉	1	8	yes	—
250	C₂×M₁₆	C₂×C₄×C₁₀₉	1	2	yes	—
251	C₂×M₁₆	C₂³×C₁₀₉	1	8	yes	—
252	C₂×M₁₆	C₂³×C₁₀₉	1	2	yes	—
253	C₂²×C₈	—	2	4	no	—
254	C₂²×C₈	—	2	4	no	—
255	C₂²×C₈	—	2	4	no	—
256	C₂²×C₈	C₂×C₄×C₁₀₉	1	2	yes	—
257	C₂²×C₈	C₂×C₄×C₁₀₉	1	8	yes	—
258	C₂²×C₈	C₂×C₄×C₁₀₉	1	1	yes	characteristic
259	C₂²×C₈	C₂×C₄×C₁₀₉	1	1	yes	characteristic
260	C₂²×C₈	C₂×C₄×C₁₀₉	1	2	yes	—
261	C₂²×C₈	D₄×C₁₀₉	1	4	yes	—
262	C₂²×C₈	D₄×C₁₀₉	1	4	yes	—
263	C₂²×C₈	C₂³×C₁₀₉	1	2	yes	—
264	#108	—	2	16	no	—
265	#101	—	2	8	no	—
266	#100	—	2	8	no	—
267	C₂⁴	C₄⋊C₄×C₁₀₉	1	2	yes	—
268	C₂⁴	C₂×Q₈×C₁₀₉	1	1	yes	characteristic
269	#41	—	2	4	no	—
270	#41	—	2	4	no	—
271	#41	—	2	4	no	—
272	#41	—	2	4	no	—
273	#41	—	2	4	no	—
274	#41	—	2	4	no	—
275	#41	—	2	4	no	—
276	#41	—	2	4	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	C₄⋊C₄×C₁₀₉	1	2	yes	—
280	C₂×Q₈	C₂×D₄×C₁₀₉	1	2	yes	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	C₄⋊C₄×C₁₀₉	1	2	yes	—
286	C₂×D₄	C₄⋊C₄×C₁₀₉	1	4	yes	—
287	C₂×D₄	C₂×D₄×C₁₀₉	1	2	yes	—
288	C₂×D₄	C₂×Q₈×C₁₀₉	1	4	yes	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	C₄⋊C₄×C₁₀₉	1	2	yes	—
294	C₂²×C₄	C₄⋊C₄×C₁₀₉	1	4	yes	—
295	C₂²×C₄	C₂²×C₄×C₁₀₉	1	4	yes	—
296	C₂²×C₄	C₂²×C₄×C₁₀₉	1	1	yes	characteristic
297	C₂²×C₄	C₂²×C₄×C₁₀₉	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₁₀₉	1	2	yes	—
299	C₂²×C₄	C₂×D₄×C₁₀₉	1	2	yes	—
300	C₂²×C₄	C₂×D₄×C₁₀₉	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₁₀₉	1	1	yes	characteristic
302	C₂²×C₄	C₂×Q₈×C₁₀₉	1	1	yes	characteristic
303	C₂²×C₄	#41×C₁₀₉	1	2	yes	—
304	C₂²×C₄	#41×C₁₀₉	1	2	yes	—
305	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
306	M₁₆	—	2	4	no	—
307	M₁₆	—	2	4	no	—
308	M₁₆	—	2	16	no	—
309	M₁₆	—	2	8	no	—
310	M₁₆	—	2	8	no	—
311	M₁₆	—	4	4	no	—
312	M₁₆	—	4	4	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	16	no	—
316	C₂×C₈	—	2	8	no	—
317	C₂×C₈	—	4	4	no	—
318	C₂×C₈	—	4	4	no	—
319	C₂×C₈	C₂²⋊C₄×C₁₀₉	1	2	yes	—
320	C₂×C₈	C₂²⋊C₄×C₁₀₉	1	2	yes	—
321	C₂×C₈	C₂²⋊C₄×C₁₀₉	1	2	yes	—
322	C₂×C₈	C₂²⋊C₄×C₁₀₉	1	2	yes	—
323	C₂×C₈	C₂²⋊C₄×C₁₀₉	1	8	yes	—
324	C₂×C₈	C₂²×C₄×C₁₀₉	1	4	yes	—
325	C₂×C₈	C₂²×C₄×C₁₀₉	1	2	yes	—
326	C₂×C₈	C₂²×C₄×C₁₀₉	1	2	yes	—
327	C₂×C₈	C₂×D₄×C₁₀₉	1	8	yes	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	4	no	—
332	C₂³	C₂×C₄⋊C₄×C₁₀₉	1	1	yes	characteristic
333	C₂³	C₂×C₄⋊C₄×C₁₀₉	1	4	yes	—
334	C₂³	C₂×C₄⋊C₄×C₁₀₉	1	1	yes	characteristic
335	C₂³	C₂²⋊Q₈×C₁₀₉	1	2	yes	—
336	C₂³	C₂²⋊Q₈×C₁₀₉	1	2	yes	—
337	C₂³	C₂²×Q₈×C₁₀₉	1	1	yes	characteristic
338	Q₈	—	2	4	no	—
339	Q₈	—	2	4	no	—
340	D₄	—	2	8	no	—
341	D₄	—	2	8	no	—
342	D₄	—	2	4	no	—
343	D₄	—	2	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₉	1	1	yes	characteristic
351	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₉	1	1	yes	characteristic
352	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₉	1	2	yes	—
353	C₂×C₄	C₂×C₄⋊C₄×C₁₀₉	1	4	yes	—
354	C₂×C₄	C₂×C₄⋊C₄×C₁₀₉	1	1	yes	characteristic
355	C₂×C₄	C₂×C₄⋊C₄×C₁₀₉	1	1	yes	characteristic
356	C₂×C₄	#117×C₁₀₉	1	1	yes	characteristic
357	C₂×C₄	#117×C₁₀₉	1	1	yes	characteristic
358	C₂×C₄	#117×C₁₀₉	1	2	yes	—
359	C₂×C₄	#121×C₁₀₉	1	2	yes	—
360	C₂×C₄	#121×C₁₀₉	1	2	yes	—
361	C₂×C₄	#121×C₁₀₉	1	2	yes	—
362	C₂×C₄	#121×C₁₀₉	1	2	yes	—
363	C₂×C₄	C₂²⋊Q₈×C₁₀₉	1	2	yes	—
364	C₂×C₄	C₂²⋊Q₈×C₁₀₉	1	2	yes	—
365	C₂×C₄	C₂³×C₄×C₁₀₉	1	1	yes	characteristic
366	C₂×C₄	C₂²×D₄×C₁₀₉	1	2	yes	—
367	C₂×C₄	C₂²×D₄×C₁₀₉	1	1	yes	characteristic
368	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
369	C₈	—	2	4	no	—
370	C₈	—	4	8	no	—
371	C₈	C₂×C₂²⋊C₄×C₁₀₉	1	4	yes	—
372	C₈	C₂×C₂²⋊C₄×C₁₀₉	1	4	yes	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	4	no	—
375	C₂²	—	2	4	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	4	4	no	—
381	C₂²	—	4	4	no	—
382	C₂²	#380×C₁₀₉	1	1	yes	characteristic
383	C₂²	#380×C₁₀₉	1	2	yes	—
384	C₂²	#380×C₁₀₉	1	1	yes	characteristic
385	C₂²	C₂²×C₄⋊C₄×C₁₀₉	1	1	yes	characteristic
386	C₂²	C₂×C₂²⋊Q₈×C₁₀₉	1	2	yes	—
387	C₄	—	2	4	no	—
388	C₄	#380×C₁₀₉	1	1	yes	characteristic
389	C₄	#380×C₁₀₉	1	1	yes	characteristic
390	C₄	#380×C₁₀₉	1	2	yes	—
391	C₄	C₂²×C₂²⋊C₄×C₁₀₉	1	1	yes	characteristic
392	C₄	C₂×#117×C₁₀₉	1	1	yes	characteristic
393	C₄	C₂×#121×C₁₀₉	1	2	yes	—
394	C₂	—	2	1	no	—
395	C₂	—	2	1	no	—
396	C₂	—	2	2	no	—
397	C₂	—	2	2	no	—
398	C₂	—	4	4	no	—
399	C₂	C₁₀₉×#1813	1	2	yes	direct product factor
400	C₂	C₂×#380×C₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₀₉	#117
commutator	C₂×C₄	C₂³×C₄×C₁₀₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₉
socle	C₂²×C₁₀₉	#380
prime radical	C₂²×#41×C₁₀₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₀₉ ◁ C₂²×M₁₆×C₁₀₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#108×C₁₀₉	C₂	semidirect
4. C₁₀₉×#1813	C₂	direct (N × H)
5. C₂×#338×C₁₀₉	C₂	semidirect
18. C₂×#108×C₁₀₉	C₂²	semidirect
23. #338×C₁₀₉	C₂²	semidirect
193. C₂×#1813	C₁₀₉	direct (N × H)
199. C₂×C₁₀₉	#1813	direct (N × H)
202. C₂²×#108	C₂×C₁₀₉	semidirect
204. #1813	C₂×C₁₀₉	direct (N × H)
205. C₂×#338	C₂×C₁₀₉	semidirect
206. C₁₀₉	C₂×#1813	direct (N × H)
219. C₂×#108	C₂²×C₁₀₉	semidirect
224. #338	C₂²×C₁₀₉	semidirect
399. C₂	C₁₀₉×#1813	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×#131×C₁₀₉	2
C₂²×#108×C₁₀₉	2
C₂×#413×C₁₀₉	2
C₁₀₉×#1813	2
C₂×#338×C₁₀₉	2
C₂×#1813	109

Subgroups — C2×C109×#1813 #42138666

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₉×#1813 #42138666