Subgroups — C₂×#121×D₁₀₉ #28376250

Order 13952.

2528 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×D₁₀₉	C₂	1	2	yes	maximal, complemented
3	C₂³×C₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16812674	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16812673	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16812672	C₂	1	2	yes	maximal, complemented
7	C₂×#16812671	C₂	1	2	yes	maximal, complemented
8	C₂×#16812670	C₂	1	1	yes	maximal, characteristic, complemented
9	#121×D₁₀₉	C₂	1	16	yes	maximal, direct product factor
10	C₂×C₄⋊C₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂²⋊C₄×D₁₀₉	C₂	1	2	yes	maximal, complemented
12	C₂×#121×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×D₁₀₉	C₂²	1	2	yes	—
14	C₂⁴×D₁₀₉	C₂²	1	1	yes	characteristic
15	C₂²×D₄₃₆	C₂²	1	2	yes	complemented
16	C₂²×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₂²⋊D₁₀₉	C₂²	1	2	yes	complemented
18	C₂²×C₂²⋊D₁₀₉	C₂²	1	2	yes	complemented
19	C₂²×C₂²⋊D₁₀₉	C₂²	1	2	yes	complemented
20	C₂×D₄×D₁₀₉	—	2	16	no	—
21	C₂×D₄×D₁₀₉	—	2	8	no	—
22	C₂×D₄×D₁₀₉	C₂²	1	8	yes	complemented
23	C₂×D₄×D₁₀₉	C₂²	1	16	yes	complemented
24	C₂³×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₄×D₁₀₉	—	2	8	no	—
26	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	—
28	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₄×D₁₀₉	C₂²	1	8	yes	complemented
32	#16812674	C₂²	1	8	yes	complemented
33	#16812673	C₂²	1	8	yes	complemented
34	#16812672	C₂²	1	16	yes	complemented
35	#16812671	C₂²	1	16	yes	complemented
36	#16812670	C₂²	1	8	yes	complemented
37	C₂×C₄⋊Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
38	C₂×#13182008	C₂²	1	2	yes	complemented
39	C₄⋊C₄×D₁₀₉	C₂²	1	8	yes	complemented
40	C₂×C₂²⋊Dic₁₀₉	C₂²	1	2	yes	complemented
41	C₂×#13182006	C₂²	1	2	yes	complemented
42	C₂×#13182006	C₂²	1	2	yes	complemented
43	C₂²⋊C₄×D₁₀₉	C₂²	1	16	yes	complemented
44	C₂²×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
45	C₂²×D₄×C₁₀₉	C₂²	1	2	yes	complemented
46	C₂³×C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
47	#121×C₁₀₉	C₂²	1	8	yes	complemented
48	C₂×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
50	C₂³×D₁₀₉	—	2	4	no	—
51	C₂³×D₁₀₉	—	2	4	no	—
52	C₂³×D₁₀₉	—	2	8	no	—
53	C₂³×D₁₀₉	—	2	8	no	—
54	C₂³×D₁₀₉	—	2	8	no	—
55	C₂³×D₁₀₉	D₄	1	8	yes	complemented
56	C₂³×D₁₀₉	C₂³	1	8	yes	—
57	C₂³×D₁₀₉	C₂³	1	2	yes	—
58	C₂³×D₁₀₉	C₂³	1	4	yes	—
59	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
60	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
61	C₂×D₄₃₆	—	2	8	no	—
62	C₂×D₄₃₆	—	2	4	no	—
63	C₂×D₄₃₆	C₂³	1	8	yes	complemented
64	C₂×D₄₃₆	C₂³	1	4	yes	complemented
65	C₂×C₂²⋊D₁₀₉	—	2	8	no	—
66	C₂×C₂²⋊D₁₀₉	—	2	8	no	—
67	C₂×C₂²⋊D₁₀₉	—	2	8	no	—
68	C₂×C₂²⋊D₁₀₉	C₂³	1	8	yes	complemented
69	C₂×C₂²⋊D₁₀₉	C₂³	1	8	yes	complemented
70	C₂×C₂²⋊D₁₀₉	C₂³	1	8	yes	complemented
71	D₄×D₁₀₉	—	2	64	no	—
72	D₄×D₁₀₉	—	2	32	no	—
73	C₂²×Dic₁₀₉	—	2	4	no	—
74	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
75	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
76	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
77	C₂²×Dic₁₀₉	C₂³	1	4	yes	complemented
78	C₂×C₄×D₁₀₉	—	2	4	no	—
79	C₂×C₄×D₁₀₉	—	2	8	no	—
80	C₂×C₄×D₁₀₉	—	2	4	no	—
81	C₂×C₄×D₁₀₉	—	2	4	no	—
82	C₂×C₄×D₁₀₉	—	2	32	no	—
83	C₂×C₄×D₁₀₉	D₄	1	8	yes	complemented
84	C₂×C₄×D₁₀₉	C₂³	1	4	yes	—
85	C₂×C₄×D₁₀₉	C₂³	1	8	yes	—
86	C₂×C₄×D₁₀₉	C₂³	1	4	yes	—
87	C₂×C₄×D₁₀₉	C₂³	1	4	yes	complemented
88	C₂×C₄×D₁₀₉	C₂³	1	4	yes	complemented
89	C₄⋊Dic₁₀₉	C₂³	1	4	yes	complemented
90	#13182008	C₂³	1	8	yes	complemented
91	C₂²⋊Dic₁₀₉	C₂³	1	8	yes	complemented
92	#13182006	C₂³	1	8	yes	complemented
93	#13182006	C₂³	1	8	yes	complemented
94	C₂⁴×C₁₀₉	C₂³	1	2	yes	—
95	C₂⁴×C₁₀₉	C₂³	1	1	yes	characteristic
96	C₂×D₄×C₁₀₉	—	2	8	no	—
97	C₂×D₄×C₁₀₉	—	2	4	no	—
98	C₂×D₄×C₁₀₉	C₂³	1	4	yes	complemented
99	C₂×D₄×C₁₀₉	C₂³	1	8	yes	complemented
100	C₂²×C₄×C₁₀₉	—	2	4	no	—
101	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
103	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₁₀₉	C₂³	1	4	yes	complemented
105	C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	complemented
106	C₂²⋊C₄×C₁₀₉	C₂³	1	8	yes	complemented
107	C₂³×C₁₀₉	—	2	2	no	—
108	C₂³×C₁₀₉	—	2	2	no	—
109	C₂³×C₁₀₉	—	2	4	no	—
110	C₂³×C₁₀₉	—	2	4	no	—
111	C₂³×C₁₀₉	—	2	4	no	—
112	C₂³×C₁₀₉	C₂×D₄	1	4	yes	complemented
113	C₂³×C₁₀₉	C₂⁴	1	4	yes	—
114	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
115	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
116	C₂²×D₁₀₉	—	2	2	no	—
117	C₂²×D₁₀₉	—	2	2	no	—
118	C₂²×D₁₀₉	—	2	32	no	—
119	C₂²×D₁₀₉	—	2	8	no	—
120	C₂²×D₁₀₉	—	2	8	no	—
121	C₂²×D₁₀₉	—	2	4	no	—
122	C₂²×D₁₀₉	—	2	4	no	—
123	C₂²×D₁₀₉	—	2	4	no	—
124	C₂²×D₁₀₉	—	2	16	no	—
125	C₂²×D₁₀₉	—	2	16	no	—
126	C₂²×D₁₀₉	—	2	16	no	—
127	C₂²×D₁₀₉	—	4	32	no	—
128	C₂²×D₁₀₉	C₂×D₄	1	4	yes	—
129	C₂²×D₁₀₉	C₂×D₄	1	4	yes	—
130	C₂²×D₁₀₉	C₂×D₄	1	16	yes	complemented
131	C₂²×D₁₀₉	C₂×D₄	1	4	yes	complemented
132	C₂²×D₁₀₉	#41	1	4	yes	—
133	C₂²×D₁₀₉	C₂⁴	1	4	yes	—
134	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
135	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
136	D₄×C₁₀₉	—	2	16	no	—
137	D₄×C₁₀₉	—	2	8	no	—
138	C₂×C₄×C₁₀₉	—	2	2	no	—
139	C₂×C₄×C₁₀₉	—	2	4	no	—
140	C₂×C₄×C₁₀₉	—	2	8	no	—
141	C₂×C₄×C₁₀₉	C₂×D₄	1	4	yes	complemented
142	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
143	C₂×C₄×C₁₀₉	C₂⁴	1	4	yes	—
144	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
145	C₂²⋊D₁₀₉	—	2	16	no	—
146	C₂²⋊D₁₀₉	—	2	16	no	—
147	C₂²⋊D₁₀₉	—	2	16	no	—
148	C₂×Dic₁₀₉	—	2	2	no	—
149	C₂×Dic₁₀₉	—	2	4	no	—
150	C₂×Dic₁₀₉	—	2	8	no	—
151	C₂×Dic₁₀₉	C₂×D₄	1	4	yes	complemented
152	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
153	C₂×Dic₁₀₉	C₂⁴	1	4	yes	—
154	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
155	D₄₃₆	—	2	16	no	—
156	D₄₃₆	—	2	8	no	—
157	C₄×D₁₀₉	—	2	8	no	—
158	C₄×D₁₀₉	—	2	16	no	—
159	C₄×D₁₀₉	—	2	8	no	—
160	C₄×D₁₀₉	—	2	8	no	—
161	C₄×D₁₀₉	C₂×D₄	1	16	yes	complemented
162	C₂²×C₁₀₉	—	2	8	no	—
163	C₂²×C₁₀₉	—	2	2	no	—
164	C₂²×C₁₀₉	—	2	2	no	—
165	C₂²×C₁₀₉	—	2	4	no	—
166	C₂²×C₁₀₉	—	2	4	no	—
167	C₂²×C₁₀₉	—	2	4	no	—
168	C₂²×C₁₀₉	—	4	8	no	—
169	C₂²×C₁₀₉	C₂²×D₄	1	2	yes	—
170	C₂²×C₁₀₉	C₂²×D₄	1	2	yes	—
171	C₂²×C₁₀₉	C₂²×D₄	1	4	yes	complemented
172	C₂²×C₁₀₉	C₂×#41	1	2	yes	—
173	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
174	C₂×D₁₀₉	—	2	8	no	—
175	C₂×D₁₀₉	—	2	2	no	—
176	C₂×D₁₀₉	—	2	2	no	—
177	C₂×D₁₀₉	—	2	32	no	—
178	C₂×D₁₀₉	—	2	4	no	—
179	C₂×D₁₀₉	—	2	4	no	—
180	C₂×D₁₀₉	—	2	4	no	—
181	C₂×D₁₀₉	—	4	8	no	—
182	C₂×D₁₀₉	—	4	32	no	—
183	C₂×D₁₀₉	#121	1	16	yes	direct product factor
184	C₂×D₁₀₉	C₂²×D₄	1	4	yes	—
185	C₂×D₁₀₉	C₂²×D₄	1	4	yes	—
186	C₂×D₁₀₉	C₂²×D₄	1	4	yes	complemented
187	C₂×D₁₀₉	C₂×#41	1	4	yes	—
188	C₄×C₁₀₉	—	2	2	no	—
189	C₄×C₁₀₉	—	2	4	no	—
190	C₄×C₁₀₉	C₂²×D₄	1	4	yes	complemented
191	Dic₁₀₉	—	2	2	no	—
192	Dic₁₀₉	—	2	4	no	—
193	Dic₁₀₉	C₂²×D₄	1	4	yes	complemented
194	C₂×C₁₀₉	—	2	4	no	—
195	C₂×C₁₀₉	—	4	4	no	—
196	C₂×C₁₀₉	C₂×#121	1	4	yes	complemented
197	C₂×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
198	C₂×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
199	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
200	D₁₀₉	—	2	4	no	—
201	D₁₀₉	—	4	4	no	—
202	D₁₀₉	C₂×#121	1	8	yes	direct product factor
203	C₂²×#121	—	109	1	no	maximal, Sylow
204	C₁₀₉	C₂²×#121	1	1	yes	characteristic, complemented, Sylow
205	C₂³×D₄	—	109	1	no	—
206	C₂³×D₄	—	109	2	no	—
207	C₂⁴×C₄	—	109	1	no	—
208	C₂×#121	—	109	1	no	—
209	C₂×#121	—	109	2	no	—
210	C₂×#121	—	109	1	no	—
211	C₂×#121	—	109	16	no	—
212	C₂×#121	—	109	1	no	—
213	C₂×#121	—	109	2	no	—
214	C₂×#121	D₁₀₉	1	1	yes	characteristic, direct product factor
215	C₂²×C₄⋊C₄	—	109	1	no	—
216	C₂²×C₂²⋊C₄	—	109	2	no	—
217	C₂⁵	—	109	1	no	—
218	C₂⁵	—	109	2	no	—
219	C₂²×D₄	—	109	2	no	—
220	C₂²×D₄	—	109	2	no	—
221	C₂²×D₄	—	109	2	no	—
222	C₂²×D₄	—	109	8	no	—
223	C₂²×D₄	—	109	16	no	—
224	C₂²×D₄	—	109	2	no	—
225	C₂²×D₄	—	109	1	no	—
226	C₂²×D₄	—	218	8	no	—
227	C₂²×D₄	—	218	16	no	—
228	C₂²×D₄	C₂×D₁₀₉	1	2	yes	complemented
229	C₂²×D₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
230	C₂³×C₄	—	109	1	no	—
231	C₂³×C₄	—	109	1	no	—
232	C₂³×C₄	—	109	1	no	—
233	C₂³×C₄	—	109	2	no	—
234	C₂³×C₄	—	109	1	no	—
235	C₂³×C₄	—	109	1	no	—
236	C₂³×C₄	—	109	8	no	—
237	C₂³×C₄	—	218	8	no	—
238	C₂³×C₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
239	#121	—	109	8	no	—
240	#121	—	109	16	no	—
241	#121	—	109	8	no	—
242	#121	—	109	8	no	—
243	#121	—	109	16	no	—
244	#121	C₂×D₁₀₉	1	8	yes	direct product factor
245	C₂×C₄⋊C₄	—	109	2	no	—
246	C₂×C₄⋊C₄	—	109	1	no	—
247	C₂×C₄⋊C₄	—	109	8	no	—
248	C₂×C₄⋊C₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
249	C₂×C₂²⋊C₄	—	109	2	no	—
250	C₂×C₂²⋊C₄	—	109	2	no	—
251	C₂×C₂²⋊C₄	—	109	2	no	—
252	C₂×C₂²⋊C₄	—	109	16	no	—
253	C₂×C₂²⋊C₄	C₂×D₁₀₉	1	2	yes	complemented
254	C₂⁴	—	109	1	no	—
255	C₂⁴	—	109	8	no	—
256	C₂⁴	—	109	4	no	—
257	C₂⁴	—	109	1	no	—
258	C₂⁴	—	109	8	no	—
259	C₂⁴	—	109	2	no	—
260	C₂⁴	—	218	8	no	—
261	C₂⁴	—	218	8	no	—
262	C₂⁴	—	218	8	no	—
263	C₂⁴	—	218	4	no	—
264	C₂⁴	—	218	4	no	—
265	C₂⁴	C₂²×D₁₀₉	1	2	yes	—
266	C₂⁴	C₂²×D₁₀₉	1	1	yes	characteristic
267	C₂×D₄	—	2	8	no	—
268	C₂×D₄	—	2	4	no	—
269	C₂×D₄	—	109	8	no	—
270	C₂×D₄	—	109	8	no	—
271	C₂×D₄	—	109	8	no	—
272	C₂×D₄	—	109	8	no	—
273	C₂×D₄	—	109	4	no	—
274	C₂×D₄	—	218	8	no	—
275	C₂×D₄	—	218	32	no	—
276	C₂×D₄	—	218	8	no	—
277	C₂×D₄	—	218	64	no	—
278	C₂×D₄	—	218	8	no	—
279	C₂×D₄	—	218	8	no	—
280	C₂×D₄	—	218	4	no	—
281	C₂×D₄	C₂²×D₁₀₉	1	8	yes	complemented
282	C₂×D₄	C₂²×D₁₀₉	1	4	yes	complemented
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	109	1	no	—
285	C₂²×C₄	—	109	8	no	—
286	C₂²×C₄	—	109	4	no	—
287	C₂²×C₄	—	109	4	no	—
288	C₂²×C₄	—	109	1	no	—
289	C₂²×C₄	—	109	2	no	—
290	C₂²×C₄	—	109	4	no	—
291	C₂²×C₄	—	109	8	no	—
292	C₂²×C₄	—	109	4	no	—
293	C₂²×C₄	—	109	4	no	—
294	C₂²×C₄	—	218	4	no	—
295	C₂²×C₄	—	218	32	no	—
296	C₂²×C₄	—	218	4	no	—
297	C₂²×C₄	—	218	8	no	—
298	C₂²×C₄	—	218	4	no	—
299	C₂²×C₄	—	218	4	no	—
300	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
301	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
302	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
303	C₂²×C₄	C₂²×D₁₀₉	1	4	yes	complemented
304	C₄⋊C₄	—	109	8	no	—
305	C₄⋊C₄	—	109	4	no	—
306	C₄⋊C₄	C₂²×D₁₀₉	1	4	yes	complemented
307	C₂²⋊C₄	—	109	8	no	—
308	C₂²⋊C₄	—	109	8	no	—
309	C₂²⋊C₄	—	109	8	no	—
310	C₂²⋊C₄	C₂²×D₁₀₉	1	8	yes	complemented
311	C₂³	—	2	2	no	—
312	C₂³	—	2	2	no	—
313	C₂³	—	2	4	no	—
314	C₂³	—	2	4	no	—
315	C₂³	—	2	4	no	—
316	C₂³	—	109	4	no	—
317	C₂³	—	109	4	no	—
318	C₂³	—	109	4	no	—
319	C₂³	—	109	2	no	—
320	C₂³	—	109	4	no	—
321	C₂³	—	109	16	no	—
322	C₂³	—	109	2	no	—
323	C₂³	—	109	4	no	—
324	C₂³	—	436	32	no	—
325	C₂³	—	218	16	no	—
326	C₂³	—	218	16	no	—
327	C₂³	—	218	16	no	—
328	C₂³	—	218	8	no	—
329	C₂³	—	218	32	no	—
330	C₂³	—	218	8	no	—
331	C₂³	—	218	4	no	—
332	C₂³	—	218	4	no	—
333	C₂³	—	218	4	no	—
334	C₂³	—	218	2	no	—
335	C₂³	—	218	2	no	—
336	C₂³	D₄×D₁₀₉	1	4	yes	complemented
337	C₂³	C₂³×D₁₀₉	1	4	yes	—
338	C₂³	C₂³×D₁₀₉	1	2	yes	—
339	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
340	D₄	—	2	16	no	—
341	D₄	—	2	8	no	—
342	D₄	—	218	16	no	—
343	D₄	—	218	16	no	—
344	D₄	—	218	16	no	—
345	D₄	—	218	16	no	—
346	D₄	—	218	8	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	109	4	no	—
351	C₂×C₄	—	109	2	no	—
352	C₂×C₄	—	109	16	no	—
353	C₂×C₄	—	109	2	no	—
354	C₂×C₄	—	109	4	no	—
355	C₂×C₄	—	218	8	no	—
356	C₂×C₄	—	218	8	no	—
357	C₂×C₄	—	218	16	no	—
358	C₂×C₄	—	218	8	no	—
359	C₂×C₄	—	218	2	no	—
360	C₂×C₄	—	218	4	no	—
361	C₂×C₄	—	218	8	no	—
362	C₂×C₄	D₄×D₁₀₉	1	4	yes	complemented
363	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
364	C₂×C₄	C₂³×D₁₀₉	1	4	yes	—
365	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
366	C₂²	—	2	8	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	4	no	—
370	C₂²	—	2	4	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	4	8	no	—
373	C₂²	—	109	16	no	—
374	C₂²	—	109	4	no	—
375	C₂²	—	109	4	no	—
376	C₂²	—	109	4	no	—
377	C₂²	—	109	4	no	—
378	C₂²	—	436	32	no	—
379	C₂²	—	436	8	no	—
380	C₂²	—	218	32	no	—
381	C₂²	—	218	4	no	—
382	C₂²	—	218	4	no	—
383	C₂²	—	218	4	no	—
384	C₂²	—	218	8	no	—
385	C₂²	—	218	2	no	—
386	C₂²	—	218	2	no	—
387	C₂²	C₂×D₄×D₁₀₉	1	2	yes	—
388	C₂²	C₂×D₄×D₁₀₉	1	2	yes	—
389	C₂²	C₂×D₄×D₁₀₉	1	4	yes	complemented
390	C₂²	#41×D₁₀₉	1	2	yes	—
391	C₂²	C₂⁴×D₁₀₉	1	1	yes	characteristic
392	C₄	—	2	2	no	—
393	C₄	—	2	4	no	—
394	C₄	—	109	4	no	—
395	C₄	—	218	2	no	—
396	C₄	—	218	4	no	—
397	C₄	C₂×D₄×D₁₀₉	1	4	yes	complemented
398	C₂	—	2	4	no	—
399	C₂	—	4	4	no	—
400	C₂	—	109	8	no	—
401	C₂	—	436	4	no	—
402	C₂	—	218	4	no	—
403	C₂	#121×D₁₀₉	1	4	yes	direct product factor
404	C₂	C₂²×D₄×D₁₀₉	1	1	yes	characteristic
405	C₂	C₂²×D₄×D₁₀₉	1	1	yes	characteristic
406	C₂	C₂×#41×D₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₁₀₉
commutator, cosocle	C₂²×C₁₀₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₀₉
Fitting	C₂×#121×C₁₀₉	C₂
socle	C₂³×C₁₀₉	C₂⁴
hypercenter	C₂×#121	D₁₀₉
hypocenter	C₁₀₉	C₂²×#121
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂³ ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. C₂²×D₄×D₁₀₉	C₂	semidirect
2. C₂²×D₄×D₁₀₉	C₂	semidirect
3. C₂³×C₄×D₁₀₉	C₂	semidirect
4. C₂×#16812674	C₂	semidirect
5. C₂×#16812673	C₂	semidirect
6. C₂×#16812672	C₂	semidirect
7. C₂×#16812671	C₂	semidirect
8. C₂×#16812670	C₂	semidirect
9. #121×D₁₀₉	C₂	direct (N × H)
10. C₂×C₄⋊C₄×D₁₀₉	C₂	semidirect
11. C₂×C₂²⋊C₄×D₁₀₉	C₂	semidirect
12. C₂×#121×C₁₀₉	C₂	semidirect
15. C₂²×D₄₃₆	C₂²	semidirect
16. C₂²×D₄₃₆	C₂²	semidirect
17. C₂²×C₂²⋊D₁₀₉	C₂²	semidirect
18. C₂²×C₂²⋊D₁₀₉	C₂²	semidirect
19. C₂²×C₂²⋊D₁₀₉	C₂²	semidirect
22. C₂×D₄×D₁₀₉	C₂²	semidirect
23. C₂×D₄×D₁₀₉	C₂²	semidirect
24. C₂³×Dic₁₀₉	C₂²	semidirect
29. C₂²×C₄×D₁₀₉	C₂²	semidirect
30. C₂²×C₄×D₁₀₉	C₂²	semidirect
31. C₂²×C₄×D₁₀₉	C₂²	semidirect
32. #16812674	C₂²	semidirect
33. #16812673	C₂²	semidirect
34. #16812672	C₂²	semidirect
35. #16812671	C₂²	semidirect
36. #16812670	C₂²	semidirect
37. C₂×C₄⋊Dic₁₀₉	C₂²	semidirect
38. C₂×#13182008	C₂²	semidirect
39. C₄⋊C₄×D₁₀₉	C₂²	semidirect
40. C₂×C₂²⋊Dic₁₀₉	C₂²	semidirect
41. C₂×#13182006	C₂²	semidirect
42. C₂×#13182006	C₂²	semidirect
43. C₂²⋊C₄×D₁₀₉	C₂²	semidirect
44. C₂²×D₄×C₁₀₉	C₂²	semidirect
45. C₂²×D₄×C₁₀₉	C₂²	semidirect
46. C₂³×C₄×C₁₀₉	C₂²	semidirect
47. #121×C₁₀₉	C₂²	semidirect
48. C₂×C₄⋊C₄×C₁₀₉	C₂²	semidirect
49. C₂×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
55. C₂³×D₁₀₉	D₄	semidirect
63. C₂×D₄₃₆	C₂³	semidirect
64. C₂×D₄₃₆	C₂³	semidirect
68. C₂×C₂²⋊D₁₀₉	C₂³	semidirect
69. C₂×C₂²⋊D₁₀₉	C₂³	semidirect
70. C₂×C₂²⋊D₁₀₉	C₂³	semidirect
77. C₂²×Dic₁₀₉	C₂³	semidirect
83. C₂×C₄×D₁₀₉	D₄	semidirect
87. C₂×C₄×D₁₀₉	C₂³	semidirect
88. C₂×C₄×D₁₀₉	C₂³	semidirect
89. C₄⋊Dic₁₀₉	C₂³	semidirect
90. #13182008	C₂³	semidirect
91. C₂²⋊Dic₁₀₉	C₂³	semidirect
92. #13182006	C₂³	semidirect
93. #13182006	C₂³	semidirect
98. C₂×D₄×C₁₀₉	C₂³	semidirect
99. C₂×D₄×C₁₀₉	C₂³	semidirect
104. C₂²×C₄×C₁₀₉	C₂³	semidirect
105. C₄⋊C₄×C₁₀₉	C₂³	semidirect
106. C₂²⋊C₄×C₁₀₉	C₂³	semidirect
112. C₂³×C₁₀₉	C₂×D₄	semidirect
130. C₂²×D₁₀₉	C₂×D₄	semidirect
131. C₂²×D₁₀₉	C₂×D₄	semidirect
141. C₂×C₄×C₁₀₉	C₂×D₄	semidirect
151. C₂×Dic₁₀₉	C₂×D₄	semidirect
161. C₄×D₁₀₉	C₂×D₄	semidirect
171. C₂²×C₁₀₉	C₂²×D₄	semidirect
183. C₂×D₁₀₉	#121	direct (N × H)
186. C₂×D₁₀₉	C₂²×D₄	semidirect
190. C₄×C₁₀₉	C₂²×D₄	semidirect
193. Dic₁₀₉	C₂²×D₄	semidirect
196. C₂×C₁₀₉	C₂×#121	semidirect
202. D₁₀₉	C₂×#121	direct (N × H)
204. C₁₀₉	C₂²×#121	semidirect
214. C₂×#121	D₁₀₉	direct (N × H)
228. C₂²×D₄	C₂×D₁₀₉	semidirect
229. C₂²×D₄	C₂×D₁₀₉	semidirect
238. C₂³×C₄	C₂×D₁₀₉	semidirect
244. #121	C₂×D₁₀₉	direct (N × H)
248. C₂×C₄⋊C₄	C₂×D₁₀₉	semidirect
253. C₂×C₂²⋊C₄	C₂×D₁₀₉	semidirect
281. C₂×D₄	C₂²×D₁₀₉	semidirect
282. C₂×D₄	C₂²×D₁₀₉	semidirect
303. C₂²×C₄	C₂²×D₁₀₉	semidirect
306. C₄⋊C₄	C₂²×D₁₀₉	semidirect
310. C₂²⋊C₄	C₂²×D₁₀₉	semidirect
336. C₂³	D₄×D₁₀₉	semidirect
362. C₂×C₄	D₄×D₁₀₉	semidirect
389. C₂²	C₂×D₄×D₁₀₉	semidirect
397. C₄	C₂×D₄×D₁₀₉	semidirect
403. C₂	#121×D₁₀₉	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×D₄×D₁₀₉	2
C₂³×C₄×D₁₀₉	2
C₂×#16812674	2
C₂×#16812673	2
C₂×#16812672	2
C₂×#16812671	2
C₂×#16812670	2
#121×D₁₀₉	2
C₂×C₄⋊C₄×D₁₀₉	2
C₂×C₂²⋊C₄×D₁₀₉	2
C₂×#121×C₁₀₉	2
C₂²×#121	109

Subgroups — C2×#121×D109 #28376250

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#121×D₁₀₉ #28376250