Subgroups — C₁₀₉×#34265 #42152259

Order 27904.

3586 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#535×C₁₀₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#520×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₉×#2367	C₂	1	4	yes	maximal, complemented
5	C₁₀₉×#2366	C₂	1	4	yes	maximal, complemented
6	C₁₀₉×#2363	C₂	1	4	yes	maximal, complemented
7	C₁₀₉×#2361	C₂	1	4	yes	maximal, complemented
8	C₁₀₉×#2321	C₂	1	4	yes	maximal, complemented
9	C₁₀₉×#2309	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#120×C₁₀₉	C₂	1	4	yes	maximal, complemented
11	C₁₀₉×#2297	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₀₉×#2296	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₀₉×#2274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#41×C₁₀₉	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₀₉	C₂²	1	2	yes	—
17	#535×C₁₀₉	C₄	1	16	yes	complemented
18	C₂×#127×C₁₀₉	C₂²	1	2	yes	—
19	C₂×#124×C₁₀₉	C₂²	1	2	yes	—
20	C₂×#121×C₁₀₉	C₂²	1	4	yes	—
21	C₂×#120×C₁₀₉	C₂²	1	4	yes	—
22	#520×C₁₀₉	—	2	8	no	—
23	C₂×C₄×Q₈×C₁₀₉	C₂²	1	2	yes	complemented
24	C₂×C₄×D₄×C₁₀₉	—	2	8	no	—
25	C₂×C₄×D₄×C₁₀₉	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₁₀₉	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₁₀₉	C₂²	1	4	yes	—
28	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	complemented
29	C₂×C₄×D₄×C₁₀₉	C₂²	1	8	yes	complemented
30	C₂×#117×C₁₀₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₁₀₉	C₂²	1	1	yes	characteristic
32	C₂×#117×C₁₀₉	C₂²	1	1	yes	characteristic
33	C₂×#117×C₁₀₉	C₂²	1	2	yes	complemented
34	C₂²×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
36	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	—
37	C₂²×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
38	#391×C₁₀₉	C₂²	1	2	yes	complemented
39	#390×C₁₀₉	C₂²	1	2	yes	—
40	#390×C₁₀₉	C₂²	1	2	yes	—
41	#390×C₁₀₉	C₂²	1	4	yes	—
42	#390×C₁₀₉	C₂²	1	2	yes	complemented
43	#390×C₁₀₉	C₂²	1	8	yes	complemented
44	#389×C₁₀₉	C₂²	1	2	yes	complemented
45	#389×C₁₀₉	C₂²	1	2	yes	complemented
46	#388×C₁₀₉	C₂²	1	8	yes	complemented
47	#388×C₁₀₉	C₂²	1	8	yes	complemented
48	#386×C₁₀₉	C₂²	1	2	yes	—
49	#386×C₁₀₉	C₂²	1	2	yes	—
50	#386×C₁₀₉	C₂²	1	8	yes	complemented
51	#386×C₁₀₉	C₂²	1	8	yes	complemented
52	#385×C₁₀₉	C₂²	1	2	yes	—
53	#385×C₁₀₉	C₂²	1	2	yes	—
54	#385×C₁₀₉	C₂²	1	8	yes	complemented
55	#379×C₁₀₉	C₂²	1	4	yes	—
56	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	4	yes	complemented
57	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	4	yes	complemented
58	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	4	yes	complemented
59	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	4	yes	—
60	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	4	yes	complemented
61	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	8	yes	complemented
62	C₂⁵×C₁₀₉	C₂³	1	2	yes	—
63	C₂×#41×C₁₀₉	—	2	4	no	—
64	C₂×#41×C₁₀₉	—	2	4	no	—
65	C₂×#41×C₁₀₉	C₂×C₄	1	8	yes	complemented
66	C₂²×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₁₀₉	—	2	4	no	—
68	C₂²×D₄×C₁₀₉	—	2	4	no	—
69	C₂²×D₄×C₁₀₉	C₂×C₄	1	8	yes	complemented
70	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
71	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
72	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
73	C₂²×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₁₀₉	C₂³	1	8	yes	—
75	C₂³×C₄×C₁₀₉	—	2	8	no	—
76	C₂³×C₄×C₁₀₉	—	4	8	no	—
77	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₀₉	C₂³	1	8	yes	—
79	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
80	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₀₉	C₂³	1	4	yes	—
82	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
84	#127×C₁₀₉	C₂×C₄	1	16	yes	complemented
85	#124×C₁₀₉	C₂×C₄	1	16	yes	complemented
86	#121×C₁₀₉	C₂×C₄	1	32	yes	complemented
87	#120×C₁₀₉	C₂×C₄	1	32	yes	complemented
88	C₄×Q₈×C₁₀₉	—	2	8	no	—
89	C₄×D₄×C₁₀₉	—	2	16	no	—
90	C₄×D₄×C₁₀₉	—	2	16	no	—
91	C₄×D₄×C₁₀₉	—	2	16	no	—
92	C₄×D₄×C₁₀₉	—	2	8	no	—
93	C₄×D₄×C₁₀₉	—	4	16	no	—
94	#117×C₁₀₉	—	2	4	no	—
95	#117×C₁₀₉	—	2	4	no	—
96	#117×C₁₀₉	—	2	8	no	—
97	#117×C₁₀₉	C₂×C₄	1	8	yes	complemented
98	C₂×C₄⋊C₄×C₁₀₉	—	2	8	no	—
99	C₂×C₄⋊C₄×C₁₀₉	D₄	1	8	yes	complemented
100	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
105	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
106	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
109	C₂×C₂²⋊C₄×C₁₀₉	—	2	8	no	—
110	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	8	yes	—
111	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
112	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
113	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
115	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	8	yes	—
116	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	8	yes	—
117	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	8	yes	—
120	C₂×C₄²×C₁₀₉	—	2	4	no	—
121	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
122	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
123	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
125	C₂×C₄²×C₁₀₉	C₂³	1	4	yes	—
126	C₂×C₄²×C₁₀₉	C₂³	1	8	yes	—
127	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
128	#95×C₁₀₉	C₂³	1	8	yes	—
129	#95×C₁₀₉	C₂³	1	4	yes	—
130	#95×C₁₀₉	C₂³	1	4	yes	—
131	#95×C₁₀₉	C₂³	1	4	yes	—
132	#95×C₁₀₉	C₂³	1	4	yes	—
133	C₂⁴×C₁₀₉	—	2	4	no	—
134	C₂⁴×C₁₀₉	—	2	4	no	—
135	C₂⁴×C₁₀₉	—	4	4	no	—
136	C₂⁴×C₁₀₉	—	4	4	no	—
137	C₂⁴×C₁₀₉	C₂²×C₄	1	8	yes	—
138	C₂⁴×C₁₀₉	C₂⁴	1	4	yes	—
139	C₂⁴×C₁₀₉	C₂⁴	1	2	yes	—
140	C₂⁴×C₁₀₉	C₂⁴	1	1	yes	characteristic
141	#41×C₁₀₉	—	2	32	no	—
142	C₂×Q₈×C₁₀₉	—	2	2	no	—
143	C₂×Q₈×C₁₀₉	—	2	2	no	—
144	C₂×Q₈×C₁₀₉	C₂²×C₄	1	4	yes	complemented
145	C₂×D₄×C₁₀₉	—	2	4	no	—
146	C₂×D₄×C₁₀₉	—	2	4	no	—
147	C₂×D₄×C₁₀₉	—	2	32	no	—
148	C₂×D₄×C₁₀₉	—	2	4	no	—
149	C₂×D₄×C₁₀₉	—	2	4	no	—
150	C₂×D₄×C₁₀₉	—	2	2	no	—
151	C₂×D₄×C₁₀₉	—	2	4	no	—
152	C₂×D₄×C₁₀₉	—	2	4	no	—
153	C₂×D₄×C₁₀₉	—	2	2	no	—
154	C₂×D₄×C₁₀₉	—	4	8	no	—
155	C₂×D₄×C₁₀₉	—	4	8	no	—
156	C₂×D₄×C₁₀₉	C₂²×C₄	1	8	yes	—
157	C₂×D₄×C₁₀₉	C₂²×C₄	1	8	yes	—
158	C₂×D₄×C₁₀₉	C₂²×C₄	1	8	yes	—
159	C₂×D₄×C₁₀₉	C₂²×C₄	1	4	yes	complemented
160	C₂×D₄×C₁₀₉	C₂²×C₄	1	32	yes	complemented
161	C₂²×C₄×C₁₀₉	—	2	2	no	—
162	C₂²×C₄×C₁₀₉	—	2	4	no	—
163	C₂²×C₄×C₁₀₉	—	2	4	no	—
164	C₂²×C₄×C₁₀₉	—	2	4	no	—
165	C₂²×C₄×C₁₀₉	—	2	2	no	—
166	C₂²×C₄×C₁₀₉	—	2	16	no	—
167	C₂²×C₄×C₁₀₉	—	2	16	no	—
168	C₂²×C₄×C₁₀₉	—	2	8	no	—
169	C₂²×C₄×C₁₀₉	—	4	4	no	—
170	C₂²×C₄×C₁₀₉	—	4	8	no	—
171	C₂²×C₄×C₁₀₉	—	4	2	no	—
172	C₂²×C₄×C₁₀₉	—	4	8	no	—
173	C₂²×C₄×C₁₀₉	—	4	32	no	—
174	C₂²×C₄×C₁₀₉	C₂²×C₄	1	4	yes	—
175	C₂²×C₄×C₁₀₉	C₂²×C₄	1	8	yes	complemented
176	C₂²×C₄×C₁₀₉	C₂×D₄	1	8	yes	—
177	C₂²×C₄×C₁₀₉	C₂×D₄	1	4	yes	—
178	C₂²×C₄×C₁₀₉	#41	1	4	yes	—
179	C₂²×C₄×C₁₀₉	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₀₉	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₁₀₉	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
189	C₄⋊C₄×C₁₀₉	—	2	2	no	—
190	C₄⋊C₄×C₁₀₉	—	2	8	no	—
191	C₄⋊C₄×C₁₀₉	—	2	2	no	—
192	C₄⋊C₄×C₁₀₉	—	2	4	no	—
193	C₄⋊C₄×C₁₀₉	—	2	8	no	—
194	C₄⋊C₄×C₁₀₉	—	4	4	no	—
195	C₄⋊C₄×C₁₀₉	C₂²×C₄	1	8	yes	complemented
196	C₄⋊C₄×C₁₀₉	C₂×D₄	1	8	yes	—
197	C₄⋊C₄×C₁₀₉	C₂×D₄	1	8	yes	—
198	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
199	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
200	C₂²⋊C₄×C₁₀₉	—	2	16	no	—
201	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
202	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
203	C₂²⋊C₄×C₁₀₉	—	4	8	no	—
204	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
205	C₂²⋊C₄×C₁₀₉	—	4	8	no	—
206	C₂²⋊C₄×C₁₀₉	C₂²×C₄	1	8	yes	—
207	C₂²⋊C₄×C₁₀₉	C₂²×C₄	1	32	yes	complemented
208	C₄²×C₁₀₉	—	2	4	no	—
209	C₄²×C₁₀₉	—	2	4	no	—
210	C₄²×C₁₀₉	—	2	8	no	—
211	C₄²×C₁₀₉	—	2	4	no	—
212	C₄²×C₁₀₉	—	2	4	no	—
213	C₄²×C₁₀₉	—	4	8	no	—
214	C₄²×C₁₀₉	C₂²×C₄	1	8	yes	complemented
215	C₂³×C₁₀₉	—	2	2	no	—
216	C₂³×C₁₀₉	—	2	2	no	—
217	C₂³×C₁₀₉	—	2	16	no	—
218	C₂³×C₁₀₉	—	2	2	no	—
219	C₂³×C₁₀₉	—	2	4	no	—
220	C₂³×C₁₀₉	—	2	2	no	—
221	C₂³×C₁₀₉	—	2	4	no	—
222	C₂³×C₁₀₉	—	2	4	no	—
223	C₂³×C₁₀₉	—	2	8	no	—
224	C₂³×C₁₀₉	—	2	4	no	—
225	C₂³×C₁₀₉	—	2	8	no	—
226	C₂³×C₁₀₉	—	4	16	no	—
227	C₂³×C₁₀₉	—	4	8	no	—
228	C₂³×C₁₀₉	—	4	8	no	—
229	C₂³×C₁₀₉	—	4	16	no	—
230	C₂³×C₁₀₉	C₂³×C₄	1	8	yes	—
231	C₂³×C₁₀₉	C₂³×C₄	1	4	yes	—
232	C₂³×C₁₀₉	C₂³×C₄	1	2	yes	—
233	C₂³×C₁₀₉	C₂²×D₄	1	2	yes	—
234	C₂³×C₁₀₉	C₂×#41	1	2	yes	—
235	C₂³×C₁₀₉	C₂⁵	1	1	yes	characteristic
236	Q₈×C₁₀₉	—	2	8	no	—
237	D₄×C₁₀₉	—	2	16	no	—
238	D₄×C₁₀₉	—	2	16	no	—
239	D₄×C₁₀₉	—	2	16	no	—
240	D₄×C₁₀₉	—	2	8	no	—
241	D₄×C₁₀₉	—	4	32	no	—
242	C₂×C₄×C₁₀₉	—	2	8	no	—
243	C₂×C₄×C₁₀₉	—	2	2	no	—
244	C₂×C₄×C₁₀₉	—	2	2	no	—
245	C₂×C₄×C₁₀₉	—	2	2	no	—
246	C₂×C₄×C₁₀₉	—	2	4	no	—
247	C₂×C₄×C₁₀₉	—	2	8	no	—
248	C₂×C₄×C₁₀₉	—	2	2	no	—
249	C₂×C₄×C₁₀₉	—	2	4	no	—
250	C₂×C₄×C₁₀₉	—	2	16	no	—
251	C₂×C₄×C₁₀₉	—	2	2	no	—
252	C₂×C₄×C₁₀₉	—	2	2	no	—
253	C₂×C₄×C₁₀₉	—	2	2	no	—
254	C₂×C₄×C₁₀₉	—	2	4	no	—
255	C₂×C₄×C₁₀₉	—	2	4	no	—
256	C₂×C₄×C₁₀₉	—	2	4	no	—
257	C₂×C₄×C₁₀₉	—	2	4	no	—
258	C₂×C₄×C₁₀₉	—	2	4	no	—
259	C₂×C₄×C₁₀₉	—	2	2	no	—
260	C₂×C₄×C₁₀₉	—	2	2	no	—
261	C₂×C₄×C₁₀₉	—	4	8	no	—
262	C₂×C₄×C₁₀₉	—	4	32	no	—
263	C₂×C₄×C₁₀₉	—	4	4	no	—
264	C₂×C₄×C₁₀₉	—	8	8	no	—
265	C₂×C₄×C₁₀₉	C₄×D₄	1	16	yes	complemented
266	C₂×C₄×C₁₀₉	C₂³×C₄	1	8	yes	—
267	C₂×C₄×C₁₀₉	C₂³×C₄	1	4	yes	—
268	C₂×C₄×C₁₀₉	C₂³×C₄	1	2	yes	—
269	C₂×C₄×C₁₀₉	C₂³×C₄	1	2	yes	—
270	C₂×C₄×C₁₀₉	C₂²×D₄	1	8	yes	—
271	C₂×C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
272	C₂×C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
273	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
274	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
275	C₂×C₄×C₁₀₉	H(5,𝔽₂)	1	4	yes	—
276	C₂²×C₁₀₉	—	2	4	no	—
277	C₂²×C₁₀₉	—	2	2	no	—
278	C₂²×C₁₀₉	—	2	2	no	—
279	C₂²×C₁₀₉	—	2	4	no	—
280	C₂²×C₁₀₉	—	2	4	no	—
281	C₂²×C₁₀₉	—	2	8	no	—
282	C₂²×C₁₀₉	—	2	8	no	—
283	C₂²×C₁₀₉	—	2	16	no	—
284	C₂²×C₁₀₉	—	4	32	no	—
285	C₂²×C₁₀₉	—	4	4	no	—
286	C₂²×C₁₀₉	—	4	2	no	—
287	C₂²×C₁₀₉	—	4	2	no	—
288	C₂²×C₁₀₉	—	4	4	no	—
289	C₂²×C₁₀₉	—	4	4	no	—
290	C₂²×C₁₀₉	—	4	8	no	—
291	C₂²×C₁₀₉	C₂×C₄×D₄	1	4	yes	—
292	C₂²×C₁₀₉	C₂⁴×C₄	1	1	yes	characteristic
293	C₂²×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
294	C₂²×C₁₀₉	C₂²×#41	1	1	yes	characteristic
295	C₂²×C₁₀₉	C₂×H(5,𝔽₂)	1	2	yes	—
296	C₂²×C₁₀₉	#585	1	2	yes	—
297	C₄×C₁₀₉	—	2	4	no	—
298	C₄×C₁₀₉	—	2	8	no	—
299	C₄×C₁₀₉	—	2	4	no	—
300	C₄×C₁₀₉	—	2	8	no	—
301	C₄×C₁₀₉	—	4	2	no	—
302	C₄×C₁₀₉	—	4	2	no	—
303	C₄×C₁₀₉	—	4	2	no	—
304	C₄×C₁₀₉	—	4	4	no	—
305	C₄×C₁₀₉	C₂×C₄×D₄	1	4	yes	—
306	C₄×C₁₀₉	C₂×C₄×D₄	1	4	yes	—
307	#34265	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
308	C₂×C₁₀₉	—	2	4	no	—
309	C₂×C₁₀₉	—	4	4	no	—
310	C₂×C₁₀₉	—	4	8	no	—
311	C₂×C₁₀₉	C₂²×C₄×D₄	1	1	yes	characteristic
312	C₂×C₁₀₉	C₄×H(5,𝔽₂)	1	2	yes	—
313	C₂×C₁₀₉	#3484	1	1	yes	characteristic
314	C₂×C₁₀₉	#3487	1	1	yes	characteristic
315	C₂×C₁₀₉	#3506	1	2	yes	—
316	C₂×#535	C₂×C₁₀₉	1	1	yes	characteristic
317	C₂×#520	C₂×C₁₀₉	1	1	yes	characteristic, complemented
318	C₂²×C₄×D₄	C₂×C₁₀₉	1	1	yes	characteristic, complemented
319	#2367	C₂×C₁₀₉	1	4	yes	complemented
320	#2366	C₂×C₁₀₉	1	4	yes	complemented
321	#2363	C₂×C₁₀₉	1	4	yes	complemented
322	#2361	C₂×C₁₀₉	1	4	yes	complemented
323	#2321	C₂×C₁₀₉	1	4	yes	complemented
324	#2309	C₂×C₁₀₉	1	1	yes	characteristic, complemented
325	C₄×#120	C₂×C₁₀₉	1	4	yes	complemented
326	#2297	C₂×C₁₀₉	1	1	yes	characteristic, complemented
327	#2296	C₂×C₁₀₉	1	1	yes	characteristic, complemented
328	#2274	C₂×C₁₀₉	1	1	yes	characteristic, complemented
329	C₁₀₉	#34265	1	1	yes	characteristic, direct product factor, Sylow
330	C₂²×#41	C₂²×C₁₀₉	1	1	yes	characteristic
331	C₂³×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
332	C₂⁴×C₄	C₂²×C₁₀₉	1	2	yes	—
333	#535	C₄×C₁₀₉	1	16	yes	complemented
334	C₂×#127	C₂²×C₁₀₉	1	2	yes	—
335	C₂×#124	C₂²×C₁₀₉	1	2	yes	—
336	C₂×#121	C₂²×C₁₀₉	1	4	yes	—
337	C₂×#120	C₂²×C₁₀₉	1	4	yes	—
338	#520	—	2	8	no	—
339	C₂×C₄×Q₈	C₂²×C₁₀₉	1	2	yes	complemented
340	C₂×C₄×D₄	—	2	8	no	—
341	C₂×C₄×D₄	C₂²×C₁₀₉	1	4	yes	—
342	C₂×C₄×D₄	C₂²×C₁₀₉	1	4	yes	—
343	C₂×C₄×D₄	C₂²×C₁₀₉	1	4	yes	—
344	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	complemented
345	C₂×C₄×D₄	C₂²×C₁₀₉	1	8	yes	complemented
346	C₂×#117	C₂²×C₁₀₉	1	1	yes	characteristic
347	C₂×#117	C₂²×C₁₀₉	1	1	yes	characteristic
348	C₂×#117	C₂²×C₁₀₉	1	1	yes	characteristic
349	C₂×#117	C₂²×C₁₀₉	1	2	yes	complemented
350	C₂²×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
351	C₂²×C₄⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
352	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	—
353	C₂²×C₄²	C₂²×C₁₀₉	1	1	yes	characteristic
354	#391	C₂²×C₁₀₉	1	2	yes	complemented
355	#390	C₂²×C₁₀₉	1	2	yes	—
356	#390	C₂²×C₁₀₉	1	2	yes	—
357	#390	C₂²×C₁₀₉	1	4	yes	—
358	#390	C₂²×C₁₀₉	1	8	yes	complemented
359	#390	C₂²×C₁₀₉	1	2	yes	complemented
360	#389	C₂²×C₁₀₉	1	2	yes	complemented
361	#389	C₂²×C₁₀₉	1	2	yes	complemented
362	#388	C₂²×C₁₀₉	1	8	yes	complemented
363	#388	C₂²×C₁₀₉	1	8	yes	complemented
364	#386	C₂²×C₁₀₉	1	2	yes	—
365	#386	C₂²×C₁₀₉	1	2	yes	—
366	#386	C₂²×C₁₀₉	1	8	yes	complemented
367	#386	C₂²×C₁₀₉	1	8	yes	complemented
368	#385	C₂²×C₁₀₉	1	2	yes	—
369	#385	C₂²×C₁₀₉	1	2	yes	—
370	#385	C₂²×C₁₀₉	1	8	yes	complemented
371	#379	C₂²×C₁₀₉	1	4	yes	—
372	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	4	yes	complemented
373	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	4	yes	complemented
374	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	4	yes	complemented
375	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	4	yes	—
376	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	4	yes	complemented
377	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	8	yes	complemented
378	C₂⁵	C₂³×C₁₀₉	1	2	yes	—
379	C₂×#41	—	2	4	no	—
380	C₂×#41	—	2	4	no	—
381	C₂×#41	C₂×C₄×C₁₀₉	1	8	yes	complemented
382	C₂²×Q₈	C₂³×C₁₀₉	1	1	yes	characteristic
383	C₂²×D₄	—	2	4	no	—
384	C₂²×D₄	—	2	4	no	—
385	C₂²×D₄	C₂×C₄×C₁₀₉	1	8	yes	complemented
386	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
387	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
388	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
389	C₂²×D₄	C₂³×C₁₀₉	1	1	yes	characteristic
390	C₂²×D₄	C₂³×C₁₀₉	1	8	yes	—
391	C₂³×C₄	—	2	8	no	—
392	C₂³×C₄	—	4	8	no	—
393	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
394	C₂³×C₄	C₂³×C₁₀₉	1	8	yes	—
395	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
396	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
397	C₂³×C₄	C₂³×C₁₀₉	1	4	yes	—
398	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
399	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
400	#127	C₂×C₄×C₁₀₉	1	16	yes	complemented
401	#124	C₂×C₄×C₁₀₉	1	16	yes	complemented
402	#121	C₂×C₄×C₁₀₉	1	32	yes	complemented
403	#120	C₂×C₄×C₁₀₉	1	32	yes	complemented
404	C₄×Q₈	—	2	8	no	—
405	C₄×D₄	—	2	16	no	—
406	C₄×D₄	—	2	16	no	—
407	C₄×D₄	—	2	16	no	—
408	C₄×D₄	—	2	8	no	—
409	C₄×D₄	—	4	16	no	—
410	#117	—	2	4	no	—
411	#117	—	2	4	no	—
412	#117	—	2	8	no	—
413	#117	C₂×C₄×C₁₀₉	1	8	yes	complemented
414	C₂×C₄⋊C₄	—	2	8	no	—
415	C₂×C₄⋊C₄	D₄×C₁₀₉	1	8	yes	complemented
416	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	4	yes	—
418	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
420	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	4	yes	—
421	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	4	yes	—
422	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
423	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
424	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
425	C₂×C₂²⋊C₄	—	2	8	no	—
426	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	8	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	8	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	8	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	8	yes	—
436	C₂×C₄²	—	2	4	no	—
437	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
438	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
439	C₂×C₄²	C₂³×C₁₀₉	1	4	yes	—
440	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
441	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
442	C₂×C₄²	C₂³×C₁₀₉	1	8	yes	—
443	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
444	#95	C₂³×C₁₀₉	1	8	yes	—
445	#95	C₂³×C₁₀₉	1	4	yes	—
446	#95	C₂³×C₁₀₉	1	4	yes	—
447	#95	C₂³×C₁₀₉	1	4	yes	—
448	#95	C₂³×C₁₀₉	1	4	yes	—
449	C₂⁴	—	2	4	no	—
450	C₂⁴	—	2	4	no	—
451	C₂⁴	—	4	4	no	—
452	C₂⁴	—	4	4	no	—
453	C₂⁴	C₂²×C₄×C₁₀₉	1	8	yes	—
454	C₂⁴	C₂⁴×C₁₀₉	1	4	yes	—
455	C₂⁴	C₂⁴×C₁₀₉	1	2	yes	—
456	C₂⁴	C₂⁴×C₁₀₉	1	1	yes	characteristic
457	#41	—	2	32	no	—
458	C₂×Q₈	—	2	2	no	—
459	C₂×Q₈	—	2	2	no	—
460	C₂×Q₈	C₂²×C₄×C₁₀₉	1	4	yes	complemented
461	C₂×D₄	—	2	4	no	—
462	C₂×D₄	—	2	4	no	—
463	C₂×D₄	—	2	32	no	—
464	C₂×D₄	—	2	4	no	—
465	C₂×D₄	—	2	4	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	4	no	—
468	C₂×D₄	—	2	4	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	4	8	no	—
471	C₂×D₄	—	4	8	no	—
472	C₂×D₄	C₂²×C₄×C₁₀₉	1	8	yes	—
473	C₂×D₄	C₂²×C₄×C₁₀₉	1	8	yes	—
474	C₂×D₄	C₂²×C₄×C₁₀₉	1	8	yes	—
475	C₂×D₄	C₂²×C₄×C₁₀₉	1	4	yes	complemented
476	C₂×D₄	C₂²×C₄×C₁₀₉	1	32	yes	complemented
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	16	no	—
483	C₂²×C₄	—	2	16	no	—
484	C₂²×C₄	—	2	8	no	—
485	C₂²×C₄	—	4	4	no	—
486	C₂²×C₄	—	4	8	no	—
487	C₂²×C₄	—	4	2	no	—
488	C₂²×C₄	—	4	8	no	—
489	C₂²×C₄	—	4	32	no	—
490	C₂²×C₄	C₂²×C₄×C₁₀₉	1	4	yes	—
491	C₂²×C₄	C₂²×C₄×C₁₀₉	1	8	yes	complemented
492	C₂²×C₄	C₂×D₄×C₁₀₉	1	8	yes	—
493	C₂²×C₄	C₂×D₄×C₁₀₉	1	4	yes	—
494	C₂²×C₄	#41×C₁₀₉	1	4	yes	—
495	C₂²×C₄	C₂⁴×C₁₀₉	1	4	yes	—
496	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
497	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
498	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
499	C₂²×C₄	C₂⁴×C₁₀₉	1	4	yes	—
500	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
501	C₂²×C₄	C₂⁴×C₁₀₉	1	4	yes	—
502	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
503	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
504	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	8	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	4	no	—
509	C₄⋊C₄	—	2	8	no	—
510	C₄⋊C₄	—	4	4	no	—
511	C₄⋊C₄	C₂²×C₄×C₁₀₉	1	8	yes	complemented
512	C₄⋊C₄	C₂×D₄×C₁₀₉	1	8	yes	—
513	C₄⋊C₄	C₂×D₄×C₁₀₉	1	8	yes	—
514	C₂²⋊C₄	—	2	4	no	—
515	C₂²⋊C₄	—	2	4	no	—
516	C₂²⋊C₄	—	2	16	no	—
517	C₂²⋊C₄	—	2	8	no	—
518	C₂²⋊C₄	—	2	8	no	—
519	C₂²⋊C₄	—	4	8	no	—
520	C₂²⋊C₄	—	4	4	no	—
521	C₂²⋊C₄	—	4	8	no	—
522	C₂²⋊C₄	C₂²×C₄×C₁₀₉	1	8	yes	—
523	C₂²⋊C₄	C₂²×C₄×C₁₀₉	1	32	yes	complemented
524	C₄²	—	2	4	no	—
525	C₄²	—	2	4	no	—
526	C₄²	—	2	8	no	—
527	C₄²	—	2	4	no	—
528	C₄²	—	2	4	no	—
529	C₄²	—	4	8	no	—
530	C₄²	C₂²×C₄×C₁₀₉	1	8	yes	complemented
531	C₂³	—	2	2	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	2	16	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	4	no	—
539	C₂³	—	2	8	no	—
540	C₂³	—	2	4	no	—
541	C₂³	—	2	8	no	—
542	C₂³	—	4	16	no	—
543	C₂³	—	4	8	no	—
544	C₂³	—	4	8	no	—
545	C₂³	—	4	16	no	—
546	C₂³	C₂³×C₄×C₁₀₉	1	8	yes	—
547	C₂³	C₂³×C₄×C₁₀₉	1	4	yes	—
548	C₂³	C₂³×C₄×C₁₀₉	1	2	yes	—
549	C₂³	C₂²×D₄×C₁₀₉	1	2	yes	—
550	C₂³	C₂×#41×C₁₀₉	1	2	yes	—
551	C₂³	C₂⁵×C₁₀₉	1	1	yes	characteristic
552	Q₈	—	2	8	no	—
553	D₄	—	2	16	no	—
554	D₄	—	2	16	no	—
555	D₄	—	2	16	no	—
556	D₄	—	2	8	no	—
557	D₄	—	4	32	no	—
558	C₂×C₄	—	2	8	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	8	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	16	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	4	8	no	—
578	C₂×C₄	—	4	32	no	—
579	C₂×C₄	—	4	4	no	—
580	C₂×C₄	—	8	8	no	—
581	C₂×C₄	C₄×D₄×C₁₀₉	1	16	yes	complemented
582	C₂×C₄	C₂³×C₄×C₁₀₉	1	8	yes	—
583	C₂×C₄	C₂³×C₄×C₁₀₉	1	4	yes	—
584	C₂×C₄	C₂³×C₄×C₁₀₉	1	2	yes	—
585	C₂×C₄	C₂³×C₄×C₁₀₉	1	2	yes	—
586	C₂×C₄	C₂²×D₄×C₁₀₉	1	8	yes	—
587	C₂×C₄	C₂²×D₄×C₁₀₉	1	2	yes	—
588	C₂×C₄	C₂²×D₄×C₁₀₉	1	2	yes	—
589	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
590	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
591	C₂×C₄	H(5,𝔽₂)×C₁₀₉	1	4	yes	—
592	C₂²	—	2	2	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	2	4	no	—
595	C₂²	—	2	4	no	—
596	C₂²	—	2	4	no	—
597	C₂²	—	2	8	no	—
598	C₂²	—	2	8	no	—
599	C₂²	—	2	16	no	—
600	C₂²	—	4	32	no	—
601	C₂²	—	4	4	no	—
602	C₂²	—	4	2	no	—
603	C₂²	—	4	4	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	8	no	—
606	C₂²	—	4	4	no	—
607	C₂²	C₂×C₄×D₄×C₁₀₉	1	4	yes	—
608	C₂²	C₂⁴×C₄×C₁₀₉	1	1	yes	characteristic
609	C₂²	C₂³×D₄×C₁₀₉	1	1	yes	characteristic
610	C₂²	C₂²×#41×C₁₀₉	1	1	yes	characteristic
611	C₂²	C₂×H(5,𝔽₂)×C₁₀₉	1	2	yes	—
612	C₂²	#585×C₁₀₉	1	2	yes	—
613	C₄	—	2	4	no	—
614	C₄	—	2	8	no	—
615	C₄	—	2	4	no	—
616	C₄	—	2	8	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	2	no	—
619	C₄	—	4	2	no	—
620	C₄	—	4	4	no	—
621	C₄	C₂×C₄×D₄×C₁₀₉	1	4	yes	—
622	C₄	C₂×C₄×D₄×C₁₀₉	1	4	yes	—
623	C₂	—	2	4	no	—
624	C₂	—	4	8	no	—
625	C₂	—	4	4	no	—
626	C₂	C₂²×C₄×D₄×C₁₀₉	1	1	yes	characteristic
627	C₂	C₄×H(5,𝔽₂)×C₁₀₉	1	2	yes	—
628	C₂	C₁₀₉×#3484	1	1	yes	characteristic
629	C₂	C₁₀₉×#3487	1	1	yes	characteristic
630	C₂	C₁₀₉×#3506	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₀₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₀₉
Frattini, cosocle	C₂³	C₂⁵×C₁₀₉
prime radical	C₂×#535×C₁₀₉	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#520×C₁₀₉	C₂	semidirect
3. C₂²×C₄×D₄×C₁₀₉	C₂	semidirect
4. C₁₀₉×#2367	C₂	semidirect
5. C₁₀₉×#2366	C₂	semidirect
6. C₁₀₉×#2363	C₂	semidirect
7. C₁₀₉×#2361	C₂	semidirect
8. C₁₀₉×#2321	C₂	semidirect
9. C₁₀₉×#2309	C₂	semidirect
10. C₄×#120×C₁₀₉	C₂	semidirect
11. C₁₀₉×#2297	C₂	semidirect
12. C₁₀₉×#2296	C₂	semidirect
13. C₁₀₉×#2274	C₂	semidirect
17. #535×C₁₀₉	C₄	semidirect
23. C₂×C₄×Q₈×C₁₀₉	C₂²	semidirect
28. C₂×C₄×D₄×C₁₀₉	C₂²	semidirect
29. C₂×C₄×D₄×C₁₀₉	C₂²	semidirect
33. C₂×#117×C₁₀₉	C₂²	semidirect
35. C₂²×C₄⋊C₄×C₁₀₉	C₂²	semidirect
38. #391×C₁₀₉	C₂²	semidirect
42. #390×C₁₀₉	C₂²	semidirect
43. #390×C₁₀₉	C₂²	semidirect
44. #389×C₁₀₉	C₂²	semidirect
45. #389×C₁₀₉	C₂²	semidirect
46. #388×C₁₀₉	C₂²	semidirect
47. #388×C₁₀₉	C₂²	semidirect
50. #386×C₁₀₉	C₂²	semidirect
51. #386×C₁₀₉	C₂²	semidirect
54. #385×C₁₀₉	C₂²	semidirect
56. C₄×C₄⋊C₄×C₁₀₉	C₂²	semidirect
57. C₄×C₄⋊C₄×C₁₀₉	C₂²	semidirect
58. C₄×C₄⋊C₄×C₁₀₉	C₂²	semidirect
60. C₄×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
61. C₄×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
65. C₂×#41×C₁₀₉	C₂×C₄	semidirect
69. C₂²×D₄×C₁₀₉	C₂×C₄	semidirect
84. #127×C₁₀₉	C₂×C₄	semidirect
85. #124×C₁₀₉	C₂×C₄	semidirect
86. #121×C₁₀₉	C₂×C₄	semidirect
87. #120×C₁₀₉	C₂×C₄	semidirect
97. #117×C₁₀₉	C₂×C₄	semidirect
99. C₂×C₄⋊C₄×C₁₀₉	D₄	semidirect
144. C₂×Q₈×C₁₀₉	C₂²×C₄	semidirect
159. C₂×D₄×C₁₀₉	C₂²×C₄	semidirect
160. C₂×D₄×C₁₀₉	C₂²×C₄	semidirect
175. C₂²×C₄×C₁₀₉	C₂²×C₄	semidirect
195. C₄⋊C₄×C₁₀₉	C₂²×C₄	semidirect
207. C₂²⋊C₄×C₁₀₉	C₂²×C₄	semidirect
214. C₄²×C₁₀₉	C₂²×C₄	semidirect
265. C₂×C₄×C₁₀₉	C₄×D₄	semidirect
307. #34265	C₁₀₉	direct (N × H)
317. C₂×#520	C₂×C₁₀₉	semidirect
318. C₂²×C₄×D₄	C₂×C₁₀₉	semidirect
319. #2367	C₂×C₁₀₉	semidirect
320. #2366	C₂×C₁₀₉	semidirect
321. #2363	C₂×C₁₀₉	semidirect
322. #2361	C₂×C₁₀₉	semidirect
323. #2321	C₂×C₁₀₉	semidirect
324. #2309	C₂×C₁₀₉	semidirect
325. C₄×#120	C₂×C₁₀₉	semidirect
326. #2297	C₂×C₁₀₉	semidirect
327. #2296	C₂×C₁₀₉	semidirect
328. #2274	C₂×C₁₀₉	semidirect
329. C₁₀₉	#34265	direct (N × H)
333. #535	C₄×C₁₀₉	semidirect
339. C₂×C₄×Q₈	C₂²×C₁₀₉	semidirect
344. C₂×C₄×D₄	C₂²×C₁₀₉	semidirect
345. C₂×C₄×D₄	C₂²×C₁₀₉	semidirect
349. C₂×#117	C₂²×C₁₀₉	semidirect
351. C₂²×C₄⋊C₄	C₂²×C₁₀₉	semidirect
354. #391	C₂²×C₁₀₉	semidirect
358. #390	C₂²×C₁₀₉	semidirect
359. #390	C₂²×C₁₀₉	semidirect
360. #389	C₂²×C₁₀₉	semidirect
361. #389	C₂²×C₁₀₉	semidirect
362. #388	C₂²×C₁₀₉	semidirect
363. #388	C₂²×C₁₀₉	semidirect
366. #386	C₂²×C₁₀₉	semidirect
367. #386	C₂²×C₁₀₉	semidirect
370. #385	C₂²×C₁₀₉	semidirect
372. C₄×C₄⋊C₄	C₂²×C₁₀₉	semidirect
373. C₄×C₄⋊C₄	C₂²×C₁₀₉	semidirect
374. C₄×C₄⋊C₄	C₂²×C₁₀₉	semidirect
376. C₄×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
377. C₄×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
381. C₂×#41	C₂×C₄×C₁₀₉	semidirect
385. C₂²×D₄	C₂×C₄×C₁₀₉	semidirect
400. #127	C₂×C₄×C₁₀₉	semidirect
401. #124	C₂×C₄×C₁₀₉	semidirect
402. #121	C₂×C₄×C₁₀₉	semidirect
403. #120	C₂×C₄×C₁₀₉	semidirect
413. #117	C₂×C₄×C₁₀₉	semidirect
415. C₂×C₄⋊C₄	D₄×C₁₀₉	semidirect
460. C₂×Q₈	C₂²×C₄×C₁₀₉	semidirect
475. C₂×D₄	C₂²×C₄×C₁₀₉	semidirect
476. C₂×D₄	C₂²×C₄×C₁₀₉	semidirect
491. C₂²×C₄	C₂²×C₄×C₁₀₉	semidirect
511. C₄⋊C₄	C₂²×C₄×C₁₀₉	semidirect
523. C₂²⋊C₄	C₂²×C₄×C₁₀₉	semidirect
530. C₄²	C₂²×C₄×C₁₀₉	semidirect
581. C₂×C₄	C₄×D₄×C₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#535×C₁₀₉	2
C₂×#520×C₁₀₉	2
C₂²×C₄×D₄×C₁₀₉	2
C₁₀₉×#2367	2
C₁₀₉×#2366	2
C₁₀₉×#2363	2
C₁₀₉×#2361	2
C₁₀₉×#2321	2
C₁₀₉×#2309	2
C₄×#120×C₁₀₉	2
C₁₀₉×#2297	2
C₁₀₉×#2296	2
C₁₀₉×#2274	2
#34265	109

Subgroups — C109×#34265 #42152259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₉×#34265 #42152259