Subgroups — C₁₀₉×#2443 #28359697

Order 13952.

674 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#123×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#121×C₁₀₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×D₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄⋊C₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#399×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#398×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#397×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#394×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#388×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#387×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#386×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#386×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#386×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#385×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#385×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
18	C₂²×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
20	C₂³×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
21	C₂³×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
22	C₂³×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
23	#123×C₁₀₉	—	2	4	no	—
24	#121×C₁₀₉	—	2	4	no	—
25	C₄×D₄×C₁₀₉	—	2	4	no	—
26	C₂×C₄⋊C₄×C₁₀₉	—	2	4	no	—
27	C₂×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
46	C₂×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
47	#95×C₁₀₉	C₂²	1	1	yes	characteristic
48	#95×C₁₀₉	C₂²	1	1	yes	characteristic
49	#95×C₁₀₉	C₂²	1	1	yes	characteristic
50	#95×C₁₀₉	C₂²	1	1	yes	characteristic
51	#95×C₁₀₉	C₂²	1	1	yes	characteristic
52	#95×C₁₀₉	C₂²	1	1	yes	characteristic
53	#95×C₁₀₉	C₂²	1	1	yes	characteristic
54	#95×C₁₀₉	C₂²	1	1	yes	characteristic
55	C₂⁴×C₁₀₉	C₂³	1	1	yes	characteristic
56	C₂⁴×C₁₀₉	C₂³	1	1	yes	characteristic
57	C₂⁴×C₁₀₉	C₂³	1	1	yes	characteristic
58	C₂×D₄×C₁₀₉	—	2	2	no	—
59	C₂×D₄×C₁₀₉	—	2	2	no	—
60	C₂×D₄×C₁₀₉	—	2	2	no	—
61	C₂×D₄×C₁₀₉	—	2	2	no	—
62	C₂×D₄×C₁₀₉	—	2	2	no	—
63	C₂×D₄×C₁₀₉	—	2	2	no	—
64	C₂×D₄×C₁₀₉	—	2	2	no	—
65	C₂×D₄×C₁₀₉	—	4	1	no	—
66	C₂×D₄×C₁₀₉	D₄	1	4	yes	—
67	C₂²×C₄×C₁₀₉	—	2	2	no	—
68	C₂²×C₄×C₁₀₉	—	2	2	no	—
69	C₂²×C₄×C₁₀₉	—	2	2	no	—
70	C₂²×C₄×C₁₀₉	—	2	2	no	—
71	C₂²×C₄×C₁₀₉	—	2	2	no	—
72	C₂²×C₄×C₁₀₉	—	2	2	no	—
73	C₂²×C₄×C₁₀₉	—	2	2	no	—
74	C₂²×C₄×C₁₀₉	—	2	2	no	—
75	C₂²×C₄×C₁₀₉	—	2	2	no	—
76	C₂²×C₄×C₁₀₉	—	4	1	no	—
77	C₂²×C₄×C₁₀₉	—	4	1	no	—
78	C₂²×C₄×C₁₀₉	—	4	1	no	—
79	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
91	C₄⋊C₄×C₁₀₉	—	2	2	no	—
92	C₄⋊C₄×C₁₀₉	—	2	2	no	—
93	C₄⋊C₄×C₁₀₉	—	2	2	no	—
94	C₄⋊C₄×C₁₀₉	—	2	2	no	—
95	C₄⋊C₄×C₁₀₉	—	2	2	no	—
96	C₄⋊C₄×C₁₀₉	—	2	2	no	—
97	C₄⋊C₄×C₁₀₉	—	4	1	no	—
98	C₄⋊C₄×C₁₀₉	D₄	1	4	yes	complemented
99	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
100	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
101	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
102	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
103	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
104	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
105	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
106	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
107	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
108	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
109	C₂²⋊C₄×C₁₀₉	—	4	1	no	—
110	C₄²×C₁₀₉	—	2	2	no	—
111	C₂³×C₁₀₉	—	2	1	no	—
112	C₂³×C₁₀₉	—	2	1	no	—
113	C₂³×C₁₀₉	—	2	1	no	—
114	C₂³×C₁₀₉	—	2	1	no	—
115	C₂³×C₁₀₉	—	2	1	no	—
116	C₂³×C₁₀₉	—	2	1	no	—
117	C₂³×C₁₀₉	—	2	1	no	—
118	C₂³×C₁₀₉	—	2	1	no	—
119	C₂³×C₁₀₉	—	2	1	no	—
120	C₂³×C₁₀₉	—	2	1	no	—
121	C₂³×C₁₀₉	—	2	1	no	—
122	C₂³×C₁₀₉	—	2	1	no	—
123	C₂³×C₁₀₉	—	2	1	no	—
124	C₂³×C₁₀₉	—	2	1	no	—
125	C₂³×C₁₀₉	—	2	1	no	—
126	C₂³×C₁₀₉	—	2	1	no	—
127	C₂³×C₁₀₉	—	2	1	no	—
128	C₂³×C₁₀₉	C₂×D₄	1	2	yes	—
129	C₂³×C₁₀₉	C₂×D₄	1	2	yes	—
130	C₂³×C₁₀₉	#41	1	2	yes	—
131	C₂³×C₁₀₉	#41	1	2	yes	—
132	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
133	D₄×C₁₀₉	—	2	8	no	—
134	D₄×C₁₀₉	—	4	4	no	—
135	D₄×C₁₀₉	—	4	4	no	—
136	C₂×C₄×C₁₀₉	—	2	8	no	—
137	C₂×C₄×C₁₀₉	—	2	1	no	—
138	C₂×C₄×C₁₀₉	—	2	1	no	—
139	C₂×C₄×C₁₀₉	—	2	1	no	—
140	C₂×C₄×C₁₀₉	—	2	1	no	—
141	C₂×C₄×C₁₀₉	—	2	1	no	—
142	C₂×C₄×C₁₀₉	—	2	1	no	—
143	C₂×C₄×C₁₀₉	—	2	1	no	—
144	C₂×C₄×C₁₀₉	—	2	1	no	—
145	C₂×C₄×C₁₀₉	—	2	1	no	—
146	C₂×C₄×C₁₀₉	—	2	1	no	—
147	C₂×C₄×C₁₀₉	—	2	1	no	—
148	C₂×C₄×C₁₀₉	—	2	1	no	—
149	C₂×C₄×C₁₀₉	—	2	1	no	—
150	C₂×C₄×C₁₀₉	—	2	1	no	—
151	C₂×C₄×C₁₀₉	—	2	1	no	—
152	C₂×C₄×C₁₀₉	—	2	1	no	—
153	C₂×C₄×C₁₀₉	—	2	1	no	—
154	C₂×C₄×C₁₀₉	—	2	1	no	—
155	C₂×C₄×C₁₀₉	—	2	1	no	—
156	C₂×C₄×C₁₀₉	—	2	1	no	—
157	C₂×C₄×C₁₀₉	—	2	1	no	—
158	C₂×C₄×C₁₀₉	—	2	1	no	—
159	C₂×C₄×C₁₀₉	—	2	1	no	—
160	C₂×C₄×C₁₀₉	—	2	1	no	—
161	C₂×C₄×C₁₀₉	—	2	1	no	—
162	C₂×C₄×C₁₀₉	—	2	1	no	—
163	C₂×C₄×C₁₀₉	—	2	1	no	—
164	C₂×C₄×C₁₀₉	—	2	1	no	—
165	C₂×C₄×C₁₀₉	—	2	1	no	—
166	C₂×C₄×C₁₀₉	—	2	1	no	—
167	C₂×C₄×C₁₀₉	—	2	1	no	—
168	C₂×C₄×C₁₀₉	—	4	4	no	—
169	C₂×C₄×C₁₀₉	—	4	4	no	—
170	C₂×C₄×C₁₀₉	—	4	4	no	—
171	C₂×C₄×C₁₀₉	C₂×D₄	1	2	yes	—
172	C₂×C₄×C₁₀₉	C₂×D₄	1	2	yes	—
173	C₂×C₄×C₁₀₉	C₂×D₄	1	2	yes	—
174	C₂×C₄×C₁₀₉	C₂×D₄	1	2	yes	—
175	C₂×C₄×C₁₀₉	#41	1	2	yes	—
176	C₂²×C₁₀₉	—	2	2	no	—
177	C₂²×C₁₀₉	—	2	2	no	—
178	C₂²×C₁₀₉	—	2	2	no	—
179	C₂²×C₁₀₉	—	2	2	no	—
180	C₂²×C₁₀₉	—	2	2	no	—
181	C₂²×C₁₀₉	—	2	2	no	—
182	C₂²×C₁₀₉	—	2	2	no	—
183	C₂²×C₁₀₉	—	2	2	no	—
184	C₂²×C₁₀₉	—	2	2	no	—
185	C₂²×C₁₀₉	—	4	1	no	—
186	C₂²×C₁₀₉	—	4	1	no	—
187	C₂²×C₁₀₉	—	4	1	no	—
188	C₂²×C₁₀₉	—	4	1	no	—
189	C₂²×C₁₀₉	—	4	1	no	—
190	C₂²×C₁₀₉	—	4	1	no	—
191	C₂²×C₁₀₉	—	4	1	no	—
192	C₂²×C₁₀₉	—	4	1	no	—
193	C₂²×C₁₀₉	—	4	1	no	—
194	C₂²×C₁₀₉	—	4	1	no	—
195	C₂²×C₁₀₉	—	4	1	no	—
196	C₂²×C₁₀₉	#123	1	4	yes	complemented
197	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
198	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
199	C₂²×C₁₀₉	C₂×#41	1	1	yes	characteristic
200	C₂²×C₁₀₉	C₂×#41	1	1	yes	characteristic
201	C₂²×C₁₀₉	C₂×#41	1	1	yes	characteristic
202	C₂²×C₁₀₉	H(5,𝔽₂)	1	1	yes	characteristic
203	C₂²×C₁₀₉	2₋¹⁺⁴	1	1	yes	characteristic
204	C₄×C₁₀₉	—	2	2	no	—
205	C₄×C₁₀₉	—	2	2	no	—
206	C₄×C₁₀₉	—	2	2	no	—
207	C₄×C₁₀₉	—	2	2	no	—
208	C₄×C₁₀₉	—	2	2	no	—
209	C₄×C₁₀₉	—	4	1	no	—
210	C₄×C₁₀₉	—	4	1	no	—
211	C₄×C₁₀₉	—	4	1	no	—
212	C₄×C₁₀₉	—	4	1	no	—
213	C₄×C₁₀₉	—	4	1	no	—
214	C₄×C₁₀₉	—	4	1	no	—
215	C₄×C₁₀₉	—	4	1	no	—
216	C₂×C₁₀₉	—	2	4	no	—
217	C₂×C₁₀₉	—	4	2	no	—
218	C₂×C₁₀₉	—	8	1	no	—
219	C₂×C₁₀₉	C₂×#123	1	1	yes	characteristic
220	C₂×C₁₀₉	#525	1	1	yes	characteristic
221	C₂×C₁₀₉	#539	1	1	yes	characteristic
222	C₂×C₁₀₉	D₄²	1	1	yes	characteristic
223	C₂×C₁₀₉	#547	1	1	yes	characteristic
224	C₂×C₁₀₉	#548	1	1	yes	characteristic
225	C₂×C₁₀₉	#553	1	1	yes	characteristic
226	#2443	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₁₀₉	#2443	1	1	yes	characteristic, direct product factor, Sylow
228	C₂×#123	C₂×C₁₀₉	1	1	yes	characteristic, complemented
229	C₂×#121	C₂×C₁₀₉	1	1	yes	characteristic
230	C₂×C₄×D₄	C₂×C₁₀₉	1	1	yes	characteristic, complemented
231	C₂²×C₄⋊C₄	C₂×C₁₀₉	1	1	yes	characteristic, complemented
232	#399	C₂×C₁₀₉	1	1	yes	characteristic, complemented
233	#398	C₂×C₁₀₉	1	1	yes	characteristic, complemented
234	#397	C₂×C₁₀₉	1	1	yes	characteristic, complemented
235	#394	C₂×C₁₀₉	1	1	yes	characteristic, complemented
236	#388	C₂×C₁₀₉	1	1	yes	characteristic, complemented
237	#387	C₂×C₁₀₉	1	1	yes	characteristic, complemented
238	#386	C₂×C₁₀₉	1	1	yes	characteristic, complemented
239	#386	C₂×C₁₀₉	1	1	yes	characteristic, complemented
240	#386	C₂×C₁₀₉	1	1	yes	characteristic, complemented
241	#385	C₂×C₁₀₉	1	1	yes	characteristic, complemented
242	#385	C₂×C₁₀₉	1	1	yes	characteristic, complemented
243	C₂²×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
244	C₂²×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
245	C₂²×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
246	C₂³×C₄	C₂²×C₁₀₉	1	1	yes	characteristic
247	C₂³×C₄	C₂²×C₁₀₉	1	1	yes	characteristic
248	C₂³×C₄	C₂²×C₁₀₉	1	1	yes	characteristic
249	C₂³×C₄	C₂²×C₁₀₉	1	1	yes	characteristic
250	#123	—	2	4	no	—
251	#121	—	2	4	no	—
252	C₄×D₄	—	2	4	no	—
253	C₂×C₄⋊C₄	—	2	4	no	—
254	C₂×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
255	C₂×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
268	C₂×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
271	C₂×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
272	C₂×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
273	C₂×C₄²	C₂²×C₁₀₉	1	1	yes	characteristic
274	#95	C₂²×C₁₀₉	1	1	yes	characteristic
275	#95	C₂²×C₁₀₉	1	1	yes	characteristic
276	#95	C₂²×C₁₀₉	1	1	yes	characteristic
277	#95	C₂²×C₁₀₉	1	1	yes	characteristic
278	#95	C₂²×C₁₀₉	1	1	yes	characteristic
279	#95	C₂²×C₁₀₉	1	1	yes	characteristic
280	#95	C₂²×C₁₀₉	1	1	yes	characteristic
281	#95	C₂²×C₁₀₉	1	1	yes	characteristic
282	C₂⁴	C₂³×C₁₀₉	1	1	yes	characteristic
283	C₂⁴	C₂³×C₁₀₉	1	1	yes	characteristic
284	C₂⁴	C₂³×C₁₀₉	1	1	yes	characteristic
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	D₄×C₁₀₉	1	4	yes	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
307	C₂²×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
308	C₂²×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
309	C₂²×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
310	C₂²×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
311	C₂²×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
312	C₂²×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
313	C₂²×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
314	C₂²×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
315	C₂²×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
316	C₂²×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
317	C₂²×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	D₄×C₁₀₉	1	4	yes	complemented
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	2	2	no	—
333	C₂²⋊C₄	—	2	2	no	—
334	C₂²⋊C₄	—	2	2	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	4	1	no	—
337	C₄²	—	2	2	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	2	1	no	—
347	C₂³	—	2	1	no	—
348	C₂³	—	2	1	no	—
349	C₂³	—	2	1	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	C₂×D₄×C₁₀₉	1	2	yes	—
356	C₂³	C₂×D₄×C₁₀₉	1	2	yes	—
357	C₂³	#41×C₁₀₉	1	2	yes	—
358	C₂³	#41×C₁₀₉	1	2	yes	—
359	C₂³	C₂⁴×C₁₀₉	1	1	yes	characteristic
360	D₄	—	2	8	no	—
361	D₄	—	4	4	no	—
362	D₄	—	4	4	no	—
363	C₂×C₄	—	2	8	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	C₂×D₄×C₁₀₉	1	2	yes	—
399	C₂×C₄	C₂×D₄×C₁₀₉	1	2	yes	—
400	C₂×C₄	C₂×D₄×C₁₀₉	1	2	yes	—
401	C₂×C₄	C₂×D₄×C₁₀₉	1	2	yes	—
402	C₂×C₄	#41×C₁₀₉	1	2	yes	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	#123×C₁₀₉	1	4	yes	complemented
424	C₂²	C₂²×D₄×C₁₀₉	1	1	yes	characteristic
425	C₂²	C₂²×D₄×C₁₀₉	1	1	yes	characteristic
426	C₂²	C₂×#41×C₁₀₉	1	1	yes	characteristic
427	C₂²	C₂×#41×C₁₀₉	1	1	yes	characteristic
428	C₂²	C₂×#41×C₁₀₉	1	1	yes	characteristic
429	C₂²	H(5,𝔽₂)×C₁₀₉	1	1	yes	characteristic
430	C₂²	2₋¹⁺⁴×C₁₀₉	1	1	yes	characteristic
431	C₄	—	2	2	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	—	4	1	no	—
443	C₂	—	2	4	no	—
444	C₂	—	4	2	no	—
445	C₂	—	8	1	no	—
446	C₂	C₂×#123×C₁₀₉	1	1	yes	characteristic
447	C₂	#525×C₁₀₉	1	1	yes	characteristic
448	C₂	#539×C₁₀₉	1	1	yes	characteristic
449	C₂	D₄²×C₁₀₉	1	1	yes	characteristic
450	C₂	#547×C₁₀₉	1	1	yes	characteristic
451	C₂	#548×C₁₀₉	1	1	yes	characteristic
452	C₂	#553×C₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₀₉
prime radical	C₂×#121×C₁₀₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#123×C₁₀₉	C₂	semidirect
3. C₂×C₄×D₄×C₁₀₉	C₂	semidirect
4. C₂²×C₄⋊C₄×C₁₀₉	C₂	semidirect
5. #399×C₁₀₉	C₂	semidirect
6. #398×C₁₀₉	C₂	semidirect
7. #397×C₁₀₉	C₂	semidirect
8. #394×C₁₀₉	C₂	semidirect
9. #388×C₁₀₉	C₂	semidirect
10. #387×C₁₀₉	C₂	semidirect
11. #386×C₁₀₉	C₂	semidirect
12. #386×C₁₀₉	C₂	semidirect
13. #386×C₁₀₉	C₂	semidirect
14. #385×C₁₀₉	C₂	semidirect
15. #385×C₁₀₉	C₂	semidirect
98. C₄⋊C₄×C₁₀₉	D₄	semidirect
196. C₂²×C₁₀₉	#123	semidirect
226. #2443	C₁₀₉	direct (N × H)
227. C₁₀₉	#2443	direct (N × H)
228. C₂×#123	C₂×C₁₀₉	semidirect
230. C₂×C₄×D₄	C₂×C₁₀₉	semidirect
231. C₂²×C₄⋊C₄	C₂×C₁₀₉	semidirect
232. #399	C₂×C₁₀₉	semidirect
233. #398	C₂×C₁₀₉	semidirect
234. #397	C₂×C₁₀₉	semidirect
235. #394	C₂×C₁₀₉	semidirect
236. #388	C₂×C₁₀₉	semidirect
237. #387	C₂×C₁₀₉	semidirect
238. #386	C₂×C₁₀₉	semidirect
239. #386	C₂×C₁₀₉	semidirect
240. #386	C₂×C₁₀₉	semidirect
241. #385	C₂×C₁₀₉	semidirect
242. #385	C₂×C₁₀₉	semidirect
325. C₄⋊C₄	D₄×C₁₀₉	semidirect
423. C₂²	#123×C₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#123×C₁₀₉	2
C₂×#121×C₁₀₉	2
C₂×C₄×D₄×C₁₀₉	2
C₂²×C₄⋊C₄×C₁₀₉	2
#399×C₁₀₉	2
#398×C₁₀₉	2
#397×C₁₀₉	2
#394×C₁₀₉	2
#388×C₁₀₉	2
#387×C₁₀₉	2
#386×C₁₀₉	2
#385×C₁₀₉	2
#2443	109

Subgroups — C109×#2443 #28359697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₉×#2443 #28359697