Subgroups — C₁₀₉×#3521 #28360775

Order 13952.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#556×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#556×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#554×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#553×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#553×C₁₀₉	C₂	1	2	yes	maximal, complemented
6	#552×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#552×C₁₀₉	C₂	1	2	yes	maximal, complemented
8	#551×C₁₀₉	C₂	1	2	yes	maximal, complemented
9	#551×C₁₀₉	C₂	1	2	yes	maximal, complemented
10	#547×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#546×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#546×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#542×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#541×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#539×C₁₀₉	C₂	1	2	yes	maximal, complemented
16	#538×C₁₀₉	C₂	1	2	yes	maximal, complemented
17	#529×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#529×C₁₀₉	C₂	1	2	yes	maximal, complemented
19	#529×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#126×C₁₀₉	C₂	1	2	yes	maximal, complemented
21	#520×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#518×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#41×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×C₁₀₉	C₂²	1	1	yes	characteristic
25	C₂×#41×C₁₀₉	C₂²	1	1	yes	characteristic
26	C₂²×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
27	C₄⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
28	C₄⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
29	#126×C₁₀₉	C₂²	1	1	yes	characteristic
30	#126×C₁₀₉	C₂²	1	2	yes	—
31	#126×C₁₀₉	C₂²	1	2	yes	—
32	#126×C₁₀₉	C₂²	1	2	yes	—
33	#126×C₁₀₉	C₂²	1	2	yes	—
34	#126×C₁₀₉	C₂²	1	2	yes	complemented
35	#126×C₁₀₉	C₂²	1	2	yes	complemented
36	#126×C₁₀₉	C₂²	1	2	yes	complemented
37	#126×C₁₀₉	C₂²	1	2	yes	complemented
38	#126×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
39	#126×C₁₀₉	C₂²	1	2	yes	complemented
40	#126×C₁₀₉	C₂²	1	2	yes	complemented
41	#125×C₁₀₉	C₂²	1	2	yes	complemented
42	#125×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
43	#125×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
44	#125×C₁₀₉	C₂²	1	2	yes	complemented
45	#125×C₁₀₉	C₂²	1	2	yes	complemented
46	#125×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
47	#124×C₁₀₉	C₂²	1	1	yes	characteristic
48	#124×C₁₀₉	C₂²	1	1	yes	characteristic
49	#124×C₁₀₉	C₂²	1	2	yes	—
50	#124×C₁₀₉	C₂²	1	1	yes	characteristic
51	#124×C₁₀₉	C₂²	1	2	yes	complemented
52	#123×C₁₀₉	C₂²	1	2	yes	—
53	#123×C₁₀₉	C₂²	1	1	yes	characteristic
54	#123×C₁₀₉	C₂²	1	2	yes	—
55	#123×C₁₀₉	C₂²	1	2	yes	—
56	#123×C₁₀₉	C₂²	1	2	yes	complemented
57	#123×C₁₀₉	C₂²	1	2	yes	complemented
58	#123×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
59	#123×C₁₀₉	C₂²	1	2	yes	complemented
60	#123×C₁₀₉	C₂²	1	2	yes	complemented
61	#123×C₁₀₉	C₂²	1	2	yes	complemented
62	C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
63	C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
64	C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
65	C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
66	C₂²⋊Q₈×C₁₀₉	C₂²	1	2	yes	complemented
67	C₂²⋊Q₈×C₁₀₉	C₂²	1	2	yes	complemented
68	C₂²⋊Q₈×C₁₀₉	C₂²	1	2	yes	complemented
69	C₂²⋊Q₈×C₁₀₉	C₂²	1	2	yes	complemented
70	C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
71	C₂²⋊Q₈×C₁₀₉	C₂²	1	2	yes	complemented
72	#121×C₁₀₉	C₂²	1	1	yes	characteristic
73	#121×C₁₀₉	C₂²	1	1	yes	characteristic
74	#121×C₁₀₉	C₂²	1	2	yes	—
75	#121×C₁₀₉	C₂²	1	2	yes	—
76	#121×C₁₀₉	C₂²	1	1	yes	characteristic
77	#121×C₁₀₉	C₂²	1	2	yes	complemented
78	#121×C₁₀₉	C₂²	1	2	yes	complemented
79	#120×C₁₀₉	C₂²	1	2	yes	—
80	#120×C₁₀₉	C₂²	1	2	yes	—
81	C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
82	C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
83	C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
84	C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
85	C₄×Q₈×C₁₀₉	C₂²	1	2	yes	complemented
86	C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
87	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
88	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
89	C₄×D₄×C₁₀₉	C₂²	1	2	yes	—
90	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
91	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
92	C₄×D₄×C₁₀₉	C₂²	1	2	yes	—
93	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
94	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
95	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
96	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
97	C₄×D₄×C₁₀₉	C₂²	1	2	yes	complemented
98	C₄×D₄×C₁₀₉	C₂²	1	2	yes	complemented
99	C₄×D₄×C₁₀₉	C₂²	1	2	yes	complemented
100	C₄×D₄×C₁₀₉	C₂²	1	2	yes	complemented
101	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
102	C₄×D₄×C₁₀₉	C₂²	1	2	yes	complemented
103	C₄×D₄×C₁₀₉	C₂²	1	2	yes	complemented
104	#117×C₁₀₉	C₂²	1	1	yes	characteristic
105	#117×C₁₀₉	C₂²	1	1	yes	characteristic
106	#117×C₁₀₉	C₂²	1	2	yes	complemented
107	#117×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
108	#117×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
109	#117×C₁₀₉	C₂²	1	2	yes	complemented
110	#117×C₁₀₉	C₂²	1	2	yes	complemented
111	#117×C₁₀₉	C₂²	1	2	yes	complemented
112	#117×C₁₀₉	C₂²	1	2	yes	complemented
113	C₂×C₄⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
114	C₂×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₄⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
116	C₂×C₄⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
117	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	—
118	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	—
119	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	—
120	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	—
121	C₂×C₄²×C₁₀₉	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
123	C₂⁴×C₁₀₉	C₂³	1	2	yes	—
124	#41×C₁₀₉	—	2	4	no	—
125	#41×C₁₀₉	—	2	4	no	—
126	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
127	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
128	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
129	C₂×Q₈×C₁₀₉	C₂³	1	2	yes	—
130	C₂×D₄×C₁₀₉	—	2	4	no	—
131	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
132	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
133	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
134	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
135	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
136	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
137	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
138	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
139	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
140	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
142	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
143	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
144	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
145	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
146	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
147	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
148	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
149	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
150	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
151	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
152	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
153	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
154	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
155	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
156	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
157	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
158	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
159	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
160	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
161	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
162	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
163	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
164	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
165	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
166	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
167	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
168	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
169	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
170	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
171	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
172	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
173	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
174	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
175	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
176	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
177	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
178	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
179	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
180	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
181	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
182	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
183	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
184	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
185	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
186	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
187	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
188	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
189	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
190	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
191	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
199	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
200	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
201	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
202	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
203	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
204	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
205	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
206	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
207	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
208	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
209	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
210	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
211	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
212	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
213	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
214	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
215	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
216	C₄²×C₁₀₉	C₂³	1	2	yes	—
217	C₄²×C₁₀₉	C₂³	1	2	yes	—
218	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
219	C₄²×C₁₀₉	C₂³	1	2	yes	—
220	C₄²×C₁₀₉	C₂³	1	2	yes	—
221	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
222	C₄²×C₁₀₉	C₂³	1	2	yes	—
223	C₄²×C₁₀₉	C₂³	1	2	yes	—
224	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
225	C₂³×C₁₀₉	—	2	4	no	—
226	C₂³×C₁₀₉	—	4	2	no	—
227	C₂³×C₁₀₉	—	4	2	no	—
228	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
229	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
230	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
231	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
232	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
233	Q₈×C₁₀₉	—	2	2	no	—
234	Q₈×C₁₀₉	—	2	2	no	—
235	Q₈×C₁₀₉	—	4	1	no	—
236	Q₈×C₁₀₉	—	4	2	no	—
237	D₄×C₁₀₉	—	2	4	no	—
238	D₄×C₁₀₉	—	2	4	no	—
239	D₄×C₁₀₉	—	2	4	no	—
240	D₄×C₁₀₉	—	2	2	no	—
241	D₄×C₁₀₉	—	4	2	no	—
242	D₄×C₁₀₉	—	4	1	no	—
243	D₄×C₁₀₉	—	4	1	no	—
244	D₄×C₁₀₉	—	4	2	no	—
245	D₄×C₁₀₉	—	4	1	no	—
246	D₄×C₁₀₉	#41	1	4	yes	—
247	C₂×C₄×C₁₀₉	—	2	4	no	—
248	C₂×C₄×C₁₀₉	—	2	4	no	—
249	C₂×C₄×C₁₀₉	—	2	2	no	—
250	C₂×C₄×C₁₀₉	—	2	2	no	—
251	C₂×C₄×C₁₀₉	—	2	2	no	—
252	C₂×C₄×C₁₀₉	—	4	2	no	—
253	C₂×C₄×C₁₀₉	—	4	1	no	—
254	C₂×C₄×C₁₀₉	—	4	2	no	—
255	C₂×C₄×C₁₀₉	—	4	2	no	—
256	C₂×C₄×C₁₀₉	—	4	2	no	—
257	C₂×C₄×C₁₀₉	—	4	2	no	—
258	C₂×C₄×C₁₀₉	—	4	1	no	—
259	C₂×C₄×C₁₀₉	—	4	2	no	—
260	C₂×C₄×C₁₀₉	—	4	2	no	—
261	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
265	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
266	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
268	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
269	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
271	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
273	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
275	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
277	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
279	C₂²×C₁₀₉	—	2	2	no	—
280	C₂²×C₁₀₉	—	2	2	no	—
281	C₂²×C₁₀₉	—	2	1	no	—
282	C₂²×C₁₀₉	—	2	1	no	—
283	C₂²×C₁₀₉	—	2	1	no	—
284	C₂²×C₁₀₉	—	2	2	no	—
285	C₂²×C₁₀₉	—	2	1	no	—
286	C₂²×C₁₀₉	—	2	1	no	—
287	C₂²×C₁₀₉	—	2	1	no	—
288	C₂²×C₁₀₉	—	2	2	no	—
289	C₂²×C₁₀₉	—	2	2	no	—
290	C₂²×C₁₀₉	—	2	1	no	—
291	C₂²×C₁₀₉	—	2	1	no	—
292	C₂²×C₁₀₉	—	2	1	no	—
293	C₂²×C₁₀₉	—	8	4	no	—
294	C₂²×C₁₀₉	C₂×#41	1	4	yes	—
295	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
296	C₄×C₁₀₉	—	2	1	no	—
297	C₄×C₁₀₉	—	2	1	no	—
298	C₄×C₁₀₉	—	2	1	no	—
299	C₄×C₁₀₉	—	2	2	no	—
300	C₄×C₁₀₉	—	2	2	no	—
301	C₄×C₁₀₉	—	2	1	no	—
302	C₄×C₁₀₉	—	2	2	no	—
303	C₄×C₁₀₉	—	2	1	no	—
304	C₄×C₁₀₉	—	2	1	no	—
305	C₄×C₁₀₉	—	2	2	no	—
306	C₄×C₁₀₉	—	2	1	no	—
307	C₄×C₁₀₉	—	2	1	no	—
308	C₄×C₁₀₉	—	2	1	no	—
309	C₄×C₁₀₉	—	2	2	no	—
310	C₄×C₁₀₉	—	2	1	no	—
311	C₄×C₁₀₉	—	2	2	no	—
312	C₄×C₁₀₉	—	2	1	no	—
313	C₄×C₁₀₉	C₂×#41	1	2	yes	—
314	C₂×C₁₀₉	—	2	4	no	—
315	C₂×C₁₀₉	—	4	1	no	—
316	C₂×C₁₀₉	—	4	1	no	—
317	C₂×C₁₀₉	—	4	2	no	—
318	C₂×C₁₀₉	—	4	1	no	—
319	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
320	C₂×C₁₀₉	#585	1	1	yes	characteristic
321	C₂×C₁₀₉	#585	1	1	yes	characteristic
322	#3521	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
323	C₁₀₉	#3521	1	1	yes	characteristic, direct product factor, Sylow
324	#556	C₂×C₁₀₉	1	1	yes	characteristic, complemented
325	#556	C₂×C₁₀₉	1	1	yes	characteristic, complemented
326	#554	C₂×C₁₀₉	1	1	yes	characteristic, complemented
327	#553	C₂×C₁₀₉	1	1	yes	characteristic, complemented
328	#553	C₂×C₁₀₉	1	2	yes	complemented
329	#552	C₂×C₁₀₉	1	1	yes	characteristic, complemented
330	#552	C₂×C₁₀₉	1	2	yes	complemented
331	#551	C₂×C₁₀₉	1	2	yes	complemented
332	#551	C₂×C₁₀₉	1	2	yes	complemented
333	#547	C₂×C₁₀₉	1	1	yes	characteristic, complemented
334	#546	C₂×C₁₀₉	1	1	yes	characteristic, complemented
335	#546	C₂×C₁₀₉	1	1	yes	characteristic, complemented
336	#542	C₂×C₁₀₉	1	1	yes	characteristic, complemented
337	#541	C₂×C₁₀₉	1	1	yes	characteristic, complemented
338	#539	C₂×C₁₀₉	1	2	yes	complemented
339	#538	C₂×C₁₀₉	1	2	yes	complemented
340	#529	C₂×C₁₀₉	1	1	yes	characteristic, complemented
341	#529	C₂×C₁₀₉	1	2	yes	complemented
342	#529	C₂×C₁₀₉	1	1	yes	characteristic, complemented
343	C₂×#126	C₂×C₁₀₉	1	2	yes	complemented
344	#520	C₂×C₁₀₉	1	1	yes	characteristic, complemented
345	#518	C₂×C₁₀₉	1	1	yes	characteristic, complemented
346	C₄×#41	C₂×C₁₀₉	1	1	yes	characteristic, complemented
347	C₂×#41	C₂²×C₁₀₉	1	1	yes	characteristic
348	C₂×#41	C₂²×C₁₀₉	1	1	yes	characteristic
349	C₂²×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
350	C₄⋊Q₈	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
351	C₄⋊Q₈	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
352	#126	C₂²×C₁₀₉	1	1	yes	characteristic
353	#126	C₂²×C₁₀₉	1	2	yes	—
354	#126	C₂²×C₁₀₉	1	2	yes	—
355	#126	C₂²×C₁₀₉	1	2	yes	—
356	#126	C₂²×C₁₀₉	1	2	yes	—
357	#126	C₂²×C₁₀₉	1	2	yes	complemented
358	#126	C₂²×C₁₀₉	1	2	yes	complemented
359	#126	C₂²×C₁₀₉	1	2	yes	complemented
360	#126	C₂²×C₁₀₉	1	2	yes	complemented
361	#126	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
362	#126	C₂²×C₁₀₉	1	2	yes	complemented
363	#126	C₂²×C₁₀₉	1	2	yes	complemented
364	#125	C₂²×C₁₀₉	1	2	yes	complemented
365	#125	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
366	#125	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
367	#125	C₂²×C₁₀₉	1	2	yes	complemented
368	#125	C₂²×C₁₀₉	1	2	yes	complemented
369	#125	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
370	#124	C₂²×C₁₀₉	1	1	yes	characteristic
371	#124	C₂²×C₁₀₉	1	1	yes	characteristic
372	#124	C₂²×C₁₀₉	1	2	yes	—
373	#124	C₂²×C₁₀₉	1	1	yes	characteristic
374	#124	C₂²×C₁₀₉	1	2	yes	complemented
375	#123	C₂²×C₁₀₉	1	2	yes	—
376	#123	C₂²×C₁₀₉	1	1	yes	characteristic
377	#123	C₂²×C₁₀₉	1	2	yes	—
378	#123	C₂²×C₁₀₉	1	2	yes	—
379	#123	C₂²×C₁₀₉	1	2	yes	complemented
380	#123	C₂²×C₁₀₉	1	2	yes	complemented
381	#123	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
382	#123	C₂²×C₁₀₉	1	2	yes	complemented
383	#123	C₂²×C₁₀₉	1	2	yes	complemented
384	#123	C₂²×C₁₀₉	1	2	yes	complemented
385	C₂²⋊Q₈	C₂²×C₁₀₉	1	1	yes	characteristic
386	C₂²⋊Q₈	C₂²×C₁₀₉	1	1	yes	characteristic
387	C₂²⋊Q₈	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
388	C₂²⋊Q₈	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
389	C₂²⋊Q₈	C₂²×C₁₀₉	1	2	yes	complemented
390	C₂²⋊Q₈	C₂²×C₁₀₉	1	2	yes	complemented
391	C₂²⋊Q₈	C₂²×C₁₀₉	1	2	yes	complemented
392	C₂²⋊Q₈	C₂²×C₁₀₉	1	2	yes	complemented
393	C₂²⋊Q₈	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
394	C₂²⋊Q₈	C₂²×C₁₀₉	1	2	yes	complemented
395	#121	C₂²×C₁₀₉	1	1	yes	characteristic
396	#121	C₂²×C₁₀₉	1	1	yes	characteristic
397	#121	C₂²×C₁₀₉	1	2	yes	—
398	#121	C₂²×C₁₀₉	1	2	yes	—
399	#121	C₂²×C₁₀₉	1	1	yes	characteristic
400	#121	C₂²×C₁₀₉	1	2	yes	complemented
401	#121	C₂²×C₁₀₉	1	2	yes	complemented
402	#120	C₂²×C₁₀₉	1	2	yes	—
403	#120	C₂²×C₁₀₉	1	2	yes	—
404	C₄×Q₈	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
405	C₄×Q₈	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
406	C₄×Q₈	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
407	C₄×Q₈	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
408	C₄×Q₈	C₂²×C₁₀₉	1	2	yes	complemented
409	C₄×Q₈	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
410	C₄×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
411	C₄×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
412	C₄×D₄	C₂²×C₁₀₉	1	2	yes	—
413	C₄×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
414	C₄×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
415	C₄×D₄	C₂²×C₁₀₉	1	2	yes	—
416	C₄×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
417	C₄×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
418	C₄×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
419	C₄×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
420	C₄×D₄	C₂²×C₁₀₉	1	2	yes	complemented
421	C₄×D₄	C₂²×C₁₀₉	1	2	yes	complemented
422	C₄×D₄	C₂²×C₁₀₉	1	2	yes	complemented
423	C₄×D₄	C₂²×C₁₀₉	1	2	yes	complemented
424	C₄×D₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
425	C₄×D₄	C₂²×C₁₀₉	1	2	yes	complemented
426	C₄×D₄	C₂²×C₁₀₉	1	2	yes	complemented
427	#117	C₂²×C₁₀₉	1	1	yes	characteristic
428	#117	C₂²×C₁₀₉	1	1	yes	characteristic
429	#117	C₂²×C₁₀₉	1	2	yes	complemented
430	#117	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
431	#117	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
432	#117	C₂²×C₁₀₉	1	2	yes	complemented
433	#117	C₂²×C₁₀₉	1	2	yes	complemented
434	#117	C₂²×C₁₀₉	1	2	yes	complemented
435	#117	C₂²×C₁₀₉	1	2	yes	complemented
436	C₂×C₄⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
437	C₂×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
438	C₂×C₄⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
439	C₂×C₄⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
440	C₂×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	—
441	C₂×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	—
442	C₂×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	—
443	C₂×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	—
444	C₂×C₄²	C₂²×C₁₀₉	1	2	yes	complemented
445	C₂×C₄²	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
446	C₂⁴	C₂³×C₁₀₉	1	2	yes	—
447	#41	—	2	4	no	—
448	#41	—	2	4	no	—
449	C₂×Q₈	C₂³×C₁₀₉	1	1	yes	characteristic
450	C₂×Q₈	C₂³×C₁₀₉	1	1	yes	characteristic
451	C₂×Q₈	C₂³×C₁₀₉	1	1	yes	characteristic
452	C₂×Q₈	C₂³×C₁₀₉	1	2	yes	—
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	C₂³×C₁₀₉	1	2	yes	—
455	C₂×D₄	C₂³×C₁₀₉	1	1	yes	characteristic
456	C₂×D₄	C₂³×C₁₀₉	1	2	yes	—
457	C₂×D₄	C₂³×C₁₀₉	1	2	yes	—
458	C₂×D₄	C₂³×C₁₀₉	1	1	yes	characteristic
459	C₂×D₄	C₂³×C₁₀₉	1	1	yes	characteristic
460	C₂×D₄	C₂³×C₁₀₉	1	2	yes	—
461	C₂×D₄	C₂³×C₁₀₉	1	2	yes	—
462	C₂×D₄	C₂³×C₁₀₉	1	1	yes	characteristic
463	C₂×D₄	C₂³×C₁₀₉	1	1	yes	characteristic
464	C₂²×C₄	C₂³×C₁₀₉	1	2	yes	—
465	C₂²×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
466	C₂²×C₄	C₂³×C₁₀₉	1	2	yes	—
467	C₂²×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
468	C₂²×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
469	C₂²×C₄	C₂³×C₁₀₉	1	2	yes	—
470	C₂²×C₄	C₂³×C₁₀₉	1	2	yes	—
471	C₂²×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
472	C₂²×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
473	C₂²×C₄	C₂³×C₁₀₉	1	2	yes	—
474	C₂²×C₄	C₂³×C₁₀₉	1	2	yes	—
475	C₂²×C₄	C₂³×C₁₀₉	1	2	yes	—
476	C₂²×C₄	C₂³×C₁₀₉	1	2	yes	—
477	C₂²×C₄	C₂³×C₁₀₉	1	2	yes	—
478	C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
479	C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
480	C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
481	C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
482	C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
483	C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
484	C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
485	C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
486	C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
487	C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
488	C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
489	C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
490	C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
491	C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
492	C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
493	C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
494	C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
495	C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
496	C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
497	C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
498	C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
499	C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
500	C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
501	C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
502	C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
503	C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
504	C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
505	C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
506	C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
507	C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
508	C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
509	C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
510	C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
511	C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
512	C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
513	C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
514	C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
515	C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
516	C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
517	C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
518	C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
519	C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
520	C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
521	C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
522	C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
523	C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
524	C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
525	C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
526	C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
527	C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
528	C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
529	C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
530	C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
531	C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
532	C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
533	C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
534	C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
535	C₂²⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
536	C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
537	C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
538	C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
539	C₄²	C₂³×C₁₀₉	1	2	yes	—
540	C₄²	C₂³×C₁₀₉	1	2	yes	—
541	C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
542	C₄²	C₂³×C₁₀₉	1	2	yes	—
543	C₄²	C₂³×C₁₀₉	1	2	yes	—
544	C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
545	C₄²	C₂³×C₁₀₉	1	2	yes	—
546	C₄²	C₂³×C₁₀₉	1	2	yes	—
547	C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
548	C₂³	—	2	4	no	—
549	C₂³	—	4	2	no	—
550	C₂³	—	4	2	no	—
551	C₂³	C₂⁴×C₁₀₉	1	1	yes	characteristic
552	C₂³	C₂⁴×C₁₀₉	1	2	yes	—
553	C₂³	C₂⁴×C₁₀₉	1	1	yes	characteristic
554	C₂³	C₂⁴×C₁₀₉	1	1	yes	characteristic
555	C₂³	C₂⁴×C₁₀₉	1	2	yes	—
556	Q₈	—	2	2	no	—
557	Q₈	—	2	2	no	—
558	Q₈	—	4	1	no	—
559	Q₈	—	4	2	no	—
560	D₄	—	2	4	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	4	no	—
563	D₄	—	2	2	no	—
564	D₄	—	4	2	no	—
565	D₄	—	4	1	no	—
566	D₄	—	4	1	no	—
567	D₄	—	4	2	no	—
568	D₄	—	4	1	no	—
569	D₄	#41×C₁₀₉	1	4	yes	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	2	no	—
578	C₂×C₄	—	4	2	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
585	C₂×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
586	C₂×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
587	C₂×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
588	C₂×C₄	C₂⁴×C₁₀₉	1	2	yes	—
589	C₂×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
590	C₂×C₄	C₂⁴×C₁₀₉	1	2	yes	—
591	C₂×C₄	C₂⁴×C₁₀₉	1	2	yes	—
592	C₂×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
593	C₂×C₄	C₂⁴×C₁₀₉	1	2	yes	—
594	C₂×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
595	C₂×C₄	C₂⁴×C₁₀₉	1	2	yes	—
596	C₂×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
597	C₂×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
598	C₂×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
599	C₂×C₄	C₂⁴×C₁₀₉	1	2	yes	—
600	C₂×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
601	C₂×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	1	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	8	4	no	—
617	C₂²	C₂×#41×C₁₀₉	1	4	yes	—
618	C₂²	C₂⁵×C₁₀₉	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	2	2	no	—
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	C₂×#41×C₁₀₉	1	2	yes	—
637	C₂	—	2	4	no	—
638	C₂	—	4	1	no	—
639	C₂	—	4	2	no	—
640	C₂	—	4	1	no	—
641	C₂	—	4	1	no	—
642	C₂	C₂²×#41×C₁₀₉	1	1	yes	characteristic
643	C₂	#585×C₁₀₉	1	1	yes	characteristic
644	C₂	#585×C₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₀₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #556×C₁₀₉	C₂	semidirect
2. #556×C₁₀₉	C₂	semidirect
3. #554×C₁₀₉	C₂	semidirect
4. #553×C₁₀₉	C₂	semidirect
5. #553×C₁₀₉	C₂	semidirect
6. #552×C₁₀₉	C₂	semidirect
7. #552×C₁₀₉	C₂	semidirect
8. #551×C₁₀₉	C₂	semidirect
9. #551×C₁₀₉	C₂	semidirect
10. #547×C₁₀₉	C₂	semidirect
11. #546×C₁₀₉	C₂	semidirect
12. #546×C₁₀₉	C₂	semidirect
13. #542×C₁₀₉	C₂	semidirect
14. #541×C₁₀₉	C₂	semidirect
15. #539×C₁₀₉	C₂	semidirect
16. #538×C₁₀₉	C₂	semidirect
17. #529×C₁₀₉	C₂	semidirect
18. #529×C₁₀₉	C₂	semidirect
19. #529×C₁₀₉	C₂	semidirect
20. C₂×#126×C₁₀₉	C₂	semidirect
21. #520×C₁₀₉	C₂	semidirect
22. #518×C₁₀₉	C₂	semidirect
23. C₄×#41×C₁₀₉	C₂	semidirect
27. C₄⋊Q₈×C₁₀₉	C₂²	semidirect
28. C₄⋊Q₈×C₁₀₉	C₂²	semidirect
34. #126×C₁₀₉	C₂²	semidirect
35. #126×C₁₀₉	C₂²	semidirect
36. #126×C₁₀₉	C₂²	semidirect
37. #126×C₁₀₉	C₂²	semidirect
38. #126×C₁₀₉	C₂²	semidirect
39. #126×C₁₀₉	C₂²	semidirect
40. #126×C₁₀₉	C₂²	semidirect
41. #125×C₁₀₉	C₂²	semidirect
42. #125×C₁₀₉	C₂²	semidirect
43. #125×C₁₀₉	C₂²	semidirect
44. #125×C₁₀₉	C₂²	semidirect
45. #125×C₁₀₉	C₂²	semidirect
46. #125×C₁₀₉	C₂²	semidirect
51. #124×C₁₀₉	C₂²	semidirect
56. #123×C₁₀₉	C₂²	semidirect
57. #123×C₁₀₉	C₂²	semidirect
58. #123×C₁₀₉	C₂²	semidirect
59. #123×C₁₀₉	C₂²	semidirect
60. #123×C₁₀₉	C₂²	semidirect
61. #123×C₁₀₉	C₂²	semidirect
64. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
65. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
66. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
67. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
68. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
69. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
70. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
71. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
77. #121×C₁₀₉	C₂²	semidirect
78. #121×C₁₀₉	C₂²	semidirect
81. C₄×Q₈×C₁₀₉	C₂²	semidirect
82. C₄×Q₈×C₁₀₉	C₂²	semidirect
83. C₄×Q₈×C₁₀₉	C₂²	semidirect
84. C₄×Q₈×C₁₀₉	C₂²	semidirect
85. C₄×Q₈×C₁₀₉	C₂²	semidirect
86. C₄×Q₈×C₁₀₉	C₂²	semidirect
97. C₄×D₄×C₁₀₉	C₂²	semidirect
98. C₄×D₄×C₁₀₉	C₂²	semidirect
99. C₄×D₄×C₁₀₉	C₂²	semidirect
100. C₄×D₄×C₁₀₉	C₂²	semidirect
101. C₄×D₄×C₁₀₉	C₂²	semidirect
102. C₄×D₄×C₁₀₉	C₂²	semidirect
103. C₄×D₄×C₁₀₉	C₂²	semidirect
106. #117×C₁₀₉	C₂²	semidirect
107. #117×C₁₀₉	C₂²	semidirect
108. #117×C₁₀₉	C₂²	semidirect
109. #117×C₁₀₉	C₂²	semidirect
110. #117×C₁₀₉	C₂²	semidirect
111. #117×C₁₀₉	C₂²	semidirect
112. #117×C₁₀₉	C₂²	semidirect
113. C₂×C₄⋊C₄×C₁₀₉	C₂²	semidirect
114. C₂×C₄⋊C₄×C₁₀₉	C₂²	semidirect
115. C₂×C₄⋊C₄×C₁₀₉	C₂²	semidirect
116. C₂×C₄⋊C₄×C₁₀₉	C₂²	semidirect
121. C₂×C₄²×C₁₀₉	C₂²	semidirect
122. C₂×C₄²×C₁₀₉	C₂²	semidirect
322. #3521	C₁₀₉	direct (N × H)
323. C₁₀₉	#3521	direct (N × H)
324. #556	C₂×C₁₀₉	semidirect
325. #556	C₂×C₁₀₉	semidirect
326. #554	C₂×C₁₀₉	semidirect
327. #553	C₂×C₁₀₉	semidirect
328. #553	C₂×C₁₀₉	semidirect
329. #552	C₂×C₁₀₉	semidirect
330. #552	C₂×C₁₀₉	semidirect
331. #551	C₂×C₁₀₉	semidirect
332. #551	C₂×C₁₀₉	semidirect
333. #547	C₂×C₁₀₉	semidirect
334. #546	C₂×C₁₀₉	semidirect
335. #546	C₂×C₁₀₉	semidirect
336. #542	C₂×C₁₀₉	semidirect
337. #541	C₂×C₁₀₉	semidirect
338. #539	C₂×C₁₀₉	semidirect
339. #538	C₂×C₁₀₉	semidirect
340. #529	C₂×C₁₀₉	semidirect
341. #529	C₂×C₁₀₉	semidirect
342. #529	C₂×C₁₀₉	semidirect
343. C₂×#126	C₂×C₁₀₉	semidirect
344. #520	C₂×C₁₀₉	semidirect
345. #518	C₂×C₁₀₉	semidirect
346. C₄×#41	C₂×C₁₀₉	semidirect
350. C₄⋊Q₈	C₂²×C₁₀₉	semidirect
351. C₄⋊Q₈	C₂²×C₁₀₉	semidirect
357. #126	C₂²×C₁₀₉	semidirect
358. #126	C₂²×C₁₀₉	semidirect
359. #126	C₂²×C₁₀₉	semidirect
360. #126	C₂²×C₁₀₉	semidirect
361. #126	C₂²×C₁₀₉	semidirect
362. #126	C₂²×C₁₀₉	semidirect
363. #126	C₂²×C₁₀₉	semidirect
364. #125	C₂²×C₁₀₉	semidirect
365. #125	C₂²×C₁₀₉	semidirect
366. #125	C₂²×C₁₀₉	semidirect
367. #125	C₂²×C₁₀₉	semidirect
368. #125	C₂²×C₁₀₉	semidirect
369. #125	C₂²×C₁₀₉	semidirect
374. #124	C₂²×C₁₀₉	semidirect
379. #123	C₂²×C₁₀₉	semidirect
380. #123	C₂²×C₁₀₉	semidirect
381. #123	C₂²×C₁₀₉	semidirect
382. #123	C₂²×C₁₀₉	semidirect
383. #123	C₂²×C₁₀₉	semidirect
384. #123	C₂²×C₁₀₉	semidirect
387. C₂²⋊Q₈	C₂²×C₁₀₉	semidirect
388. C₂²⋊Q₈	C₂²×C₁₀₉	semidirect
389. C₂²⋊Q₈	C₂²×C₁₀₉	semidirect
390. C₂²⋊Q₈	C₂²×C₁₀₉	semidirect
391. C₂²⋊Q₈	C₂²×C₁₀₉	semidirect
392. C₂²⋊Q₈	C₂²×C₁₀₉	semidirect
393. C₂²⋊Q₈	C₂²×C₁₀₉	semidirect
394. C₂²⋊Q₈	C₂²×C₁₀₉	semidirect
400. #121	C₂²×C₁₀₉	semidirect
401. #121	C₂²×C₁₀₉	semidirect
404. C₄×Q₈	C₂²×C₁₀₉	semidirect
405. C₄×Q₈	C₂²×C₁₀₉	semidirect
406. C₄×Q₈	C₂²×C₁₀₉	semidirect
407. C₄×Q₈	C₂²×C₁₀₉	semidirect
408. C₄×Q₈	C₂²×C₁₀₉	semidirect
409. C₄×Q₈	C₂²×C₁₀₉	semidirect
420. C₄×D₄	C₂²×C₁₀₉	semidirect
421. C₄×D₄	C₂²×C₁₀₉	semidirect
422. C₄×D₄	C₂²×C₁₀₉	semidirect
423. C₄×D₄	C₂²×C₁₀₉	semidirect
424. C₄×D₄	C₂²×C₁₀₉	semidirect
425. C₄×D₄	C₂²×C₁₀₉	semidirect
426. C₄×D₄	C₂²×C₁₀₉	semidirect
429. #117	C₂²×C₁₀₉	semidirect
430. #117	C₂²×C₁₀₉	semidirect
431. #117	C₂²×C₁₀₉	semidirect
432. #117	C₂²×C₁₀₉	semidirect
433. #117	C₂²×C₁₀₉	semidirect
434. #117	C₂²×C₁₀₉	semidirect
435. #117	C₂²×C₁₀₉	semidirect
436. C₂×C₄⋊C₄	C₂²×C₁₀₉	semidirect
437. C₂×C₄⋊C₄	C₂²×C₁₀₉	semidirect
438. C₂×C₄⋊C₄	C₂²×C₁₀₉	semidirect
439. C₂×C₄⋊C₄	C₂²×C₁₀₉	semidirect
444. C₂×C₄²	C₂²×C₁₀₉	semidirect
445. C₂×C₄²	C₂²×C₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
#556×C₁₀₉	2
#554×C₁₀₉	2
#553×C₁₀₉	2
#552×C₁₀₉	2
#551×C₁₀₉	2
#547×C₁₀₉	2
#546×C₁₀₉	2
#542×C₁₀₉	2
#541×C₁₀₉	2
#539×C₁₀₉	2
#538×C₁₀₉	2
#529×C₁₀₉	2
C₂×#126×C₁₀₉	2
#520×C₁₀₉	2
#518×C₁₀₉	2
C₄×#41×C₁₀₉	2
#3521	109

Subgroups — C109×#3521 #28360775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₉×#3521 #28360775