Subgroups — C₂×#20295702 #28376529

Order 13952.

1328 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295702	C₂	1	16	yes	maximal, direct product factor
2	C₂×#16812692	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16812692	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16812685	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16812683	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16812682	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16812681	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#16812678	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16812676	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16812668	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄×C₂²⋊D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#16812659	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#16812658	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16812655	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₂²⋊Dic₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₂²⋊C₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Dic₂₁₈	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic
21	C₂³×Dic₁₀₉	C₂²	1	1	yes	characteristic
22	C₂³×Dic₁₀₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
24	#16812692	C₂²	1	8	yes	complemented
25	#16812692	C₂²	1	8	yes	complemented
26	#16812685	C₂²	1	8	yes	complemented
27	#16812683	C₂²	1	8	yes	complemented
28	#16812682	C₂²	1	8	yes	complemented
29	#16812681	C₂²	1	8	yes	complemented
30	#16812678	C₂²	1	8	yes	complemented
31	#16812676	C₂²	1	8	yes	complemented
32	#16812668	C₂²	1	8	yes	—
33	C₄×C₂²⋊D₁₀₉	C₂²	1	8	yes	complemented
34	#16812659	C₂²	1	8	yes	complemented
35	#16812658	C₂²	1	8	yes	complemented
36	#16812655	C₂²	1	8	yes	complemented
37	C₂×C₄⋊Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄⋊Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄⋊Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×#13182008	C₂²	1	1	yes	characteristic, complemented
41	C₂×#13182008	C₂²	1	1	yes	characteristic, complemented
42	C₂×#13182008	C₂²	1	1	yes	characteristic, complemented
43	C₂×#13182008	C₂²	1	1	yes	characteristic, complemented
44	C₂×#13182008	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₂²⋊Dic₁₀₉	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊Dic₁₀₉	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊Dic₁₀₉	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊Dic₁₀₉	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊Dic₁₀₉	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊Dic₁₀₉	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊Dic₁₀₉	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊Dic₁₀₉	C₂²	1	8	yes	complemented
53	C₂×#13182006	C₂²	1	1	yes	characteristic, complemented
54	C₂×#13182006	C₂²	1	1	yes	characteristic, complemented
55	C₂×#13182006	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
59	C₂⁵×C₁₀₉	C₂²	1	1	yes	characteristic
60	C₂³×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
61	C₂³×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
62	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	8	yes	complemented
67	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
68	C₂×Dic₂₁₈	—	4	2	no	—
69	C₂×Dic₂₁₈	C₂³	1	4	yes	complemented
70	C₂×C₂²⋊D₁₀₉	—	2	4	no	—
71	C₂×C₂²⋊D₁₀₉	—	2	4	no	—
72	C₂×C₂²⋊D₁₀₉	—	4	2	no	—
73	C₂×C₂²⋊D₁₀₉	C₂³	1	4	yes	—
74	C₂×C₂²⋊D₁₀₉	C₂³	1	4	yes	—
75	C₂×C₂²⋊D₁₀₉	C₂³	1	4	yes	—
76	C₂²×Dic₁₀₉	—	2	4	no	—
77	C₂²×Dic₁₀₉	—	4	2	no	—
78	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
79	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
80	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
81	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
82	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
83	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
84	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
85	C₂²×Dic₁₀₉	C₂³	1	4	yes	—
86	C₂²×Dic₁₀₉	C₂³	1	4	yes	—
87	C₂×C₄×D₁₀₉	—	4	2	no	—
88	C₂×C₄×D₁₀₉	C₂³	1	4	yes	complemented
89	C₄⋊Dic₁₀₉	C₂³	1	4	yes	complemented
90	C₄⋊Dic₁₀₉	C₂³	1	4	yes	complemented
91	C₄⋊Dic₁₀₉	C₂³	1	4	yes	complemented
92	#13182008	C₂³	1	4	yes	complemented
93	#13182008	C₂³	1	4	yes	complemented
94	#13182008	C₂³	1	4	yes	complemented
95	#13182008	C₂³	1	4	yes	complemented
96	#13182008	C₂³	1	4	yes	complemented
97	C₂²⋊Dic₁₀₉	C₂³	1	4	yes	—
98	C₂²⋊Dic₁₀₉	C₂³	1	4	yes	—
99	C₂²⋊Dic₁₀₉	C₂³	1	4	yes	—
100	C₂²⋊Dic₁₀₉	C₂³	1	4	yes	—
101	C₂²⋊Dic₁₀₉	C₂³	1	4	yes	—
102	C₂²⋊Dic₁₀₉	C₂³	1	4	yes	—
103	C₂²⋊Dic₁₀₉	C₂³	1	4	yes	—
104	#13182006	C₂³	1	4	yes	complemented
105	#13182006	C₂³	1	4	yes	complemented
106	#13182006	C₂³	1	4	yes	complemented
107	C₄×Dic₁₀₉	C₂³	1	4	yes	complemented
108	C₄×Dic₁₀₉	C₂³	1	4	yes	complemented
109	C₄×Dic₁₀₉	C₂³	1	4	yes	complemented
110	C₂⁴×C₁₀₉	—	2	4	no	—
111	C₂⁴×C₁₀₉	—	2	4	no	—
112	C₂⁴×C₁₀₉	—	4	2	no	—
113	C₂⁴×C₁₀₉	C₂³	1	1	yes	characteristic
114	C₂⁴×C₁₀₉	C₂³	1	4	yes	—
115	C₂⁴×C₁₀₉	C₂³	1	1	yes	characteristic
116	C₂⁴×C₁₀₉	C₂³	1	1	yes	characteristic
117	C₂²×C₄×C₁₀₉	—	2	4	no	—
118	C₂²×C₄×C₁₀₉	—	4	2	no	—
119	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
120	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
121	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
123	C₂²×C₄×C₁₀₉	C₂³	1	4	yes	—
124	C₂²×C₄×C₁₀₉	C₂³	1	4	yes	—
125	C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
126	C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
127	C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
128	C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
129	C₂³×C₁₀₉	—	2	2	no	—
130	C₂³×C₁₀₉	—	2	2	no	—
131	C₂³×C₁₀₉	—	2	2	no	—
132	C₂³×C₁₀₉	—	2	2	no	—
133	C₂³×C₁₀₉	—	2	8	no	—
134	C₂³×C₁₀₉	—	2	2	no	—
135	C₂³×C₁₀₉	—	2	8	no	—
136	C₂³×C₁₀₉	—	2	2	no	—
137	C₂³×C₁₀₉	—	2	2	no	—
138	C₂³×C₁₀₉	—	4	4	no	—
139	C₂³×C₁₀₉	—	4	16	no	—
140	C₂³×C₁₀₉	#41	1	4	yes	—
141	C₂³×C₁₀₉	#41	1	4	yes	—
142	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
143	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
144	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
145	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
146	C₂²×D₁₀₉	—	2	2	no	—
147	C₂²×D₁₀₉	—	2	2	no	—
148	C₂²×D₁₀₉	—	2	2	no	—
149	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
150	C₂×C₄×C₁₀₉	—	2	8	no	—
151	C₂×C₄×C₁₀₉	—	2	2	no	—
152	C₂×C₄×C₁₀₉	—	2	2	no	—
153	C₂×C₄×C₁₀₉	—	2	2	no	—
154	C₂×C₄×C₁₀₉	—	2	2	no	—
155	C₂×C₄×C₁₀₉	—	4	4	no	—
156	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
157	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
158	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
159	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
160	C₂²⋊D₁₀₉	—	2	8	no	—
161	C₂²⋊D₁₀₉	—	2	8	no	—
162	C₂²⋊D₁₀₉	—	4	4	no	—
163	C₂×Dic₁₀₉	—	2	8	no	—
164	C₂×Dic₁₀₉	—	2	2	no	—
165	C₂×Dic₁₀₉	—	2	2	no	—
166	C₂×Dic₁₀₉	—	2	2	no	—
167	C₂×Dic₁₀₉	—	2	2	no	—
168	C₂×Dic₁₀₉	—	2	2	no	—
169	C₂×Dic₁₀₉	—	2	2	no	—
170	C₂×Dic₁₀₉	—	2	2	no	—
171	C₂×Dic₁₀₉	—	4	4	no	—
172	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
173	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
174	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
175	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
176	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
177	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
178	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
179	C₄×D₁₀₉	—	4	4	no	—
180	Dic₂₁₈	—	4	4	no	—
181	C₂²×C₁₀₉	—	2	8	no	—
182	C₂²×C₁₀₉	—	2	8	no	—
183	C₂²×C₁₀₉	—	2	2	no	—
184	C₂²×C₁₀₉	—	2	2	no	—
185	C₂²×C₁₀₉	—	2	2	no	—
186	C₂²×C₁₀₉	—	2	2	no	—
187	C₂²×C₁₀₉	—	2	2	no	—
188	C₂²×C₁₀₉	—	2	2	no	—
189	C₂²×C₁₀₉	—	2	2	no	—
190	C₂²×C₁₀₉	—	4	16	no	—
191	C₂²×C₁₀₉	—	4	4	no	—
192	C₂²×C₁₀₉	C₂×#41	1	4	yes	—
193	C₂²×C₁₀₉	C₂×#41	1	2	yes	—
194	C₂²×C₁₀₉	C₂×#41	1	4	yes	—
195	C₂²×C₁₀₉	C₂×#41	1	2	yes	—
196	C₂²×C₁₀₉	H(5,𝔽₂)	1	2	yes	—
197	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
198	C₂×D₁₀₉	—	2	2	no	—
199	C₂×D₁₀₉	—	2	2	no	—
200	C₂×D₁₀₉	—	2	2	no	—
201	C₂×D₁₀₉	—	4	4	no	—
202	C₄×C₁₀₉	—	2	2	no	—
203	C₄×C₁₀₉	—	2	2	no	—
204	C₄×C₁₀₉	—	2	2	no	—
205	C₄×C₁₀₉	—	2	2	no	—
206	Dic₁₀₉	—	2	2	no	—
207	Dic₁₀₉	—	2	2	no	—
208	Dic₁₀₉	—	2	2	no	—
209	Dic₁₀₉	—	2	2	no	—
210	Dic₁₀₉	—	2	2	no	—
211	Dic₁₀₉	—	2	2	no	—
212	Dic₁₀₉	—	2	2	no	—
213	C₂×C₁₀₉	—	2	4	no	—
214	C₂×C₁₀₉	—	2	4	no	—
215	C₂×C₁₀₉	—	4	2	no	—
216	C₂×C₁₀₉	#551	1	4	yes	complemented
217	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
218	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
219	C₂×C₁₀₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
220	D₁₀₉	—	4	2	no	—
221	C₂×#551	—	109	1	no	maximal, Sylow
222	C₁₀₉	C₂×#551	1	1	yes	characteristic, complemented, Sylow
223	#551	—	109	16	no	—
224	C₂×#126	—	109	1	no	—
225	C₂×#126	—	109	1	no	—
226	C₂×#124	—	109	1	no	—
227	C₂×#123	—	109	1	no	—
228	C₂×#123	—	109	1	no	—
229	C₂×#123	—	109	1	no	—
230	C₂×C₂²⋊Q₈	—	109	1	no	—
231	C₂×C₂²⋊Q₈	—	109	1	no	—
232	C₂×#120	—	109	1	no	—
233	C₂×C₄×D₄	—	109	1	no	—
234	C₂×C₄×D₄	—	109	1	no	—
235	C₂×#117	—	109	1	no	—
236	C₂×#117	—	109	1	no	—
237	C₂²×C₂²⋊C₄	—	109	1	no	—
238	C₂²×C₂²⋊C₄	D₁₀₉	1	1	yes	characteristic, complemented
239	C₂⁵	C₂×D₁₀₉	1	1	yes	characteristic
240	C₂²×Q₈	—	109	1	no	—
241	C₂²×D₄	—	109	1	no	—
242	C₂²×D₄	—	109	1	no	—
243	C₂²×D₄	—	109	1	no	—
244	C₂³×C₄	—	109	1	no	—
245	C₂³×C₄	—	109	1	no	—
246	C₂³×C₄	—	109	1	no	—
247	C₂³×C₄	C₂×D₁₀₉	1	1	yes	characteristic
248	C₂³×C₄	C₂×D₁₀₉	1	1	yes	characteristic
249	#126	—	109	8	no	—
250	#126	—	109	8	no	—
251	#124	—	109	8	no	—
252	#123	—	109	8	no	—
253	#123	—	109	8	no	—
254	#123	—	109	8	no	—
255	C₂²⋊Q₈	—	109	8	no	—
256	C₂²⋊Q₈	—	109	8	no	—
257	#120	—	109	8	no	—
258	C₄×D₄	—	109	8	no	—
259	C₄×D₄	—	109	8	no	—
260	#117	—	109	8	no	—
261	#117	—	109	8	no	—
262	C₂×C₄⋊C₄	—	109	1	no	—
263	C₂×C₄⋊C₄	—	109	1	no	—
264	C₂×C₄⋊C₄	—	109	1	no	—
265	C₂×C₄⋊C₄	—	109	1	no	—
266	C₂×C₄⋊C₄	—	109	1	no	—
267	C₂×C₄⋊C₄	—	109	1	no	—
268	C₂×C₄⋊C₄	—	109	1	no	—
269	C₂×C₄⋊C₄	—	109	1	no	—
270	C₂×C₂²⋊C₄	—	109	1	no	—
271	C₂×C₂²⋊C₄	—	109	1	no	—
272	C₂×C₂²⋊C₄	—	109	1	no	—
273	C₂×C₂²⋊C₄	—	109	1	no	—
274	C₂×C₂²⋊C₄	—	109	8	no	—
275	C₂×C₂²⋊C₄	—	109	1	no	—
276	C₂×C₂²⋊C₄	—	109	1	no	—
277	C₂×C₂²⋊C₄	—	109	1	no	—
278	C₂×C₂²⋊C₄	—	109	1	no	—
279	C₂×C₂²⋊C₄	—	109	1	no	—
280	C₂×C₂²⋊C₄	—	109	1	no	—
281	C₂×C₂²⋊C₄	C₂×D₁₀₉	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	C₂×D₁₀₉	1	1	yes	characteristic
283	C₂×C₂²⋊C₄	C₂×D₁₀₉	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	C₂×D₁₀₉	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	C₂×D₁₀₉	1	8	yes	complemented
286	C₂×C₄²	—	109	1	no	—
287	C₂×C₄²	—	109	1	no	—
288	C₂×C₄²	—	109	1	no	—
289	C₂⁴	—	2	4	no	—
290	C₂⁴	—	2	4	no	—
291	C₂⁴	—	4	2	no	—
292	C₂⁴	—	109	1	no	—
293	C₂⁴	C₂²×D₁₀₉	1	1	yes	characteristic
294	C₂⁴	C₂²×D₁₀₉	1	4	yes	—
295	C₂⁴	C₂²×D₁₀₉	1	1	yes	characteristic
296	C₂⁴	C₂²×D₁₀₉	1	1	yes	characteristic
297	C₂×Q₈	—	109	4	no	—
298	C₂×Q₈	—	436	2	no	—
299	C₂×D₄	—	109	4	no	—
300	C₂×D₄	—	109	4	no	—
301	C₂×D₄	—	109	4	no	—
302	C₂×D₄	—	436	2	no	—
303	C₂×D₄	—	218	4	no	—
304	C₂×D₄	—	218	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	109	4	no	—
308	C₂²×C₄	—	109	4	no	—
309	C₂²×C₄	—	109	1	no	—
310	C₂²×C₄	—	109	1	no	—
311	C₂²×C₄	—	109	1	no	—
312	C₂²×C₄	—	109	1	no	—
313	C₂²×C₄	—	109	1	no	—
314	C₂²×C₄	—	109	1	no	—
315	C₂²×C₄	—	109	1	no	—
316	C₂²×C₄	—	109	4	no	—
317	C₂²×C₄	—	436	2	no	—
318	C₂²×C₄	—	436	2	no	—
319	C₂²×C₄	—	218	4	no	—
320	C₂²×C₄	C₂²×D₁₀₉	1	4	yes	—
321	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
322	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
323	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
324	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
325	C₂²×C₄	C₂²×D₁₀₉	1	4	yes	—
326	C₄⋊C₄	—	109	4	no	—
327	C₄⋊C₄	—	109	4	no	—
328	C₄⋊C₄	—	109	4	no	—
329	C₄⋊C₄	—	109	4	no	—
330	C₄⋊C₄	—	109	4	no	—
331	C₄⋊C₄	—	109	4	no	—
332	C₄⋊C₄	—	109	4	no	—
333	C₄⋊C₄	—	109	4	no	—
334	C₂²⋊C₄	—	109	4	no	—
335	C₂²⋊C₄	—	109	4	no	—
336	C₂²⋊C₄	—	109	4	no	—
337	C₂²⋊C₄	—	109	4	no	—
338	C₂²⋊C₄	—	109	4	no	—
339	C₂²⋊C₄	—	109	4	no	—
340	C₂²⋊C₄	—	109	4	no	—
341	C₂²⋊C₄	—	109	4	no	—
342	C₂²⋊C₄	—	109	4	no	—
343	C₂²⋊C₄	—	109	4	no	—
344	C₂²⋊C₄	C₂²×D₁₀₉	1	4	yes	—
345	C₂²⋊C₄	C₂²×D₁₀₉	1	4	yes	—
346	C₂²⋊C₄	C₂²×D₁₀₉	1	4	yes	—
347	C₂²⋊C₄	C₂²×D₁₀₉	1	4	yes	—
348	C₄²	—	109	4	no	—
349	C₄²	—	109	4	no	—
350	C₄²	—	109	4	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	8	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	8	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	4	4	no	—
361	C₂³	—	4	16	no	—
362	C₂³	—	109	2	no	—
363	C₂³	—	218	2	no	—
364	C₂³	—	218	2	no	—
365	C₂³	—	218	2	no	—
366	C₂³	#13182028	1	4	yes	—
367	C₂³	#13182029	1	4	yes	—
368	C₂³	C₂³×D₁₀₉	1	2	yes	—
369	C₂³	C₂³×D₁₀₉	1	2	yes	—
370	C₂³	C₂³×D₁₀₉	1	2	yes	—
371	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
372	Q₈	—	436	4	no	—
373	D₄	—	436	4	no	—
374	D₄	—	218	8	no	—
375	D₄	—	218	8	no	—
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	109	2	no	—
383	C₂×C₄	—	109	2	no	—
384	C₂×C₄	—	109	2	no	—
385	C₂×C₄	—	109	2	no	—
386	C₂×C₄	—	109	2	no	—
387	C₂×C₄	—	109	2	no	—
388	C₂×C₄	—	109	2	no	—
389	C₂×C₄	—	436	4	no	—
390	C₂×C₄	—	436	4	no	—
391	C₂×C₄	—	218	2	no	—
392	C₂×C₄	—	218	8	no	—
393	C₂×C₄	—	218	2	no	—
394	C₂×C₄	—	218	2	no	—
395	C₂×C₄	—	218	2	no	—
396	C₂×C₄	—	218	2	no	—
397	C₂×C₄	—	218	2	no	—
398	C₂×C₄	—	218	2	no	—
399	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
400	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
401	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
402	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
403	C₂²	—	2	8	no	—
404	C₂²	—	2	8	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	16	no	—
413	C₂²	—	4	4	no	—
414	C₂²	—	436	4	no	—
415	C₂²	—	218	2	no	—
416	C₂²	—	218	2	no	—
417	C₂²	—	218	2	no	—
418	C₂²	C₂×#13182028	1	4	yes	—
419	C₂²	C₂×#13182028	1	2	yes	—
420	C₂²	C₂×#13182029	1	4	yes	—
421	C₂²	C₂×#13182029	1	2	yes	—
422	C₂²	#16812744	1	2	yes	—
423	C₂²	C₂⁴×D₁₀₉	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	218	2	no	—
429	C₄	—	218	2	no	—
430	C₄	—	218	2	no	—
431	C₄	—	218	2	no	—
432	C₄	—	218	2	no	—
433	C₄	—	218	2	no	—
434	C₄	—	218	2	no	—
435	C₂	—	2	4	no	—
436	C₂	—	2	4	no	—
437	C₂	—	4	2	no	—
438	C₂	—	436	2	no	—
439	C₂	#20295702	1	4	yes	direct product factor
440	C₂	C₂²×#13182028	1	1	yes	characteristic
441	C₂	C₂²×#13182029	1	1	yes	characteristic
442	C₂	C₂×#16812744	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₁₀₉
commutator, cosocle	C₂²×C₁₀₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₀₉
Fitting	C₂²×C₂²⋊C₄×C₁₀₉	C₂
socle	C₂³×C₁₀₉	C₂⁴
prime radical	C₂×#16812668	C₂
hypercenter	C₂²×C₂²⋊C₄	D₁₀₉
hypocenter	C₁₀₉	C₂×#551
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. #20295702	C₂	direct (N × H)
2. C₂×#16812692	C₂	semidirect
3. C₂×#16812692	C₂	semidirect
4. C₂×#16812685	C₂	semidirect
5. C₂×#16812683	C₂	semidirect
6. C₂×#16812682	C₂	semidirect
7. C₂×#16812681	C₂	semidirect
8. C₂×#16812678	C₂	semidirect
9. C₂×#16812676	C₂	semidirect
11. C₂×C₄×C₂²⋊D₁₀₉	C₂	semidirect
12. C₂×#16812659	C₂	semidirect
13. C₂×#16812658	C₂	semidirect
14. C₂×#16812655	C₂	semidirect
15. C₂²×C₂²⋊Dic₁₀₉	C₂	semidirect
16. C₂²×C₂²⋊C₄×C₁₀₉	C₂	semidirect
17. C₂²×Dic₂₁₈	C₂²	semidirect
23. C₂²×C₄×D₁₀₉	C₂²	semidirect
24. #16812692	C₂²	semidirect
25. #16812692	C₂²	semidirect
26. #16812685	C₂²	semidirect
27. #16812683	C₂²	semidirect
28. #16812682	C₂²	semidirect
29. #16812681	C₂²	semidirect
30. #16812678	C₂²	semidirect
31. #16812676	C₂²	semidirect
33. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
34. #16812659	C₂²	semidirect
35. #16812658	C₂²	semidirect
36. #16812655	C₂²	semidirect
37. C₂×C₄⋊Dic₁₀₉	C₂²	semidirect
38. C₂×C₄⋊Dic₁₀₉	C₂²	semidirect
39. C₂×C₄⋊Dic₁₀₉	C₂²	semidirect
40. C₂×#13182008	C₂²	semidirect
41. C₂×#13182008	C₂²	semidirect
42. C₂×#13182008	C₂²	semidirect
43. C₂×#13182008	C₂²	semidirect
44. C₂×#13182008	C₂²	semidirect
52. C₂×C₂²⋊Dic₁₀₉	C₂²	semidirect
53. C₂×#13182006	C₂²	semidirect
54. C₂×#13182006	C₂²	semidirect
55. C₂×#13182006	C₂²	semidirect
56. C₂×C₄×Dic₁₀₉	C₂²	semidirect
57. C₂×C₄×Dic₁₀₉	C₂²	semidirect
58. C₂×C₄×Dic₁₀₉	C₂²	semidirect
66. C₂×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
69. C₂×Dic₂₁₈	C₂³	semidirect
88. C₂×C₄×D₁₀₉	C₂³	semidirect
89. C₄⋊Dic₁₀₉	C₂³	semidirect
90. C₄⋊Dic₁₀₉	C₂³	semidirect
91. C₄⋊Dic₁₀₉	C₂³	semidirect
92. #13182008	C₂³	semidirect
93. #13182008	C₂³	semidirect
94. #13182008	C₂³	semidirect
95. #13182008	C₂³	semidirect
96. #13182008	C₂³	semidirect
104. #13182006	C₂³	semidirect
105. #13182006	C₂³	semidirect
106. #13182006	C₂³	semidirect
107. C₄×Dic₁₀₉	C₂³	semidirect
108. C₄×Dic₁₀₉	C₂³	semidirect
109. C₄×Dic₁₀₉	C₂³	semidirect
216. C₂×C₁₀₉	#551	semidirect
222. C₁₀₉	C₂×#551	semidirect
238. C₂²×C₂²⋊C₄	D₁₀₉	semidirect
285. C₂×C₂²⋊C₄	C₂×D₁₀₉	semidirect
439. C₂	#20295702	direct (N × H)

Maximal subgroups

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

subgroup	index
#20295702	2
C₂×#16812692	2
C₂×#16812685	2
C₂×#16812683	2
C₂×#16812682	2
C₂×#16812681	2
C₂×#16812678	2
C₂×#16812676	2
C₂×#16812668	2
C₂×C₄×C₂²⋊D₁₀₉	2
C₂×#16812659	2
C₂×#16812658	2
C₂×#16812655	2
C₂²×C₂²⋊Dic₁₀₉	2
C₂²×C₂²⋊C₄×C₁₀₉	2
C₂×#551	109

Subgroups — C2×#20295702 #28376529

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20295702 #28376529