Subgroups — #28376643

Order 13952.

1242 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295761	C₂	1	1	yes	maximal, characteristic, complemented
2	#20295737	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295729	C₂	1	2	yes	maximal, complemented
4	#20295724	C₂	1	2	yes	maximal, complemented
5	#20295703	C₂	1	4	yes	maximal, complemented
6	#20295671	C₂	1	2	yes	maximal, complemented
7	#20295667	C₂	1	2	yes	maximal, complemented
8	D₄×D₄₃₆	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295577	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295562	C₂	1	2	yes	maximal, complemented
11	#20295561	C₂	1	2	yes	maximal, complemented
12	#20295539	C₂	1	4	yes	maximal, complemented
13	C₄×#13182030	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#13182028	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#16812661	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₁₀₉	C₂	1	2	yes	maximal, complemented
17	#554×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13182030	C₂²	1	1	yes	characteristic
19	C₂×#13182030	C₂²	1	2	yes	complemented
20	C₂×#13182028	C₂²	1	1	yes	characteristic
21	C₂²×D₄₃₆	C₂²	1	2	yes	—
22	C₂×D₄×D₁₀₉	C₂²	1	2	yes	—
23	C₂²×C₄×D₁₀₉	C₂²	1	4	yes	complemented
24	#16812696	C₂²	1	1	yes	characteristic
25	#16812694	C₂²	1	4	yes	complemented
26	#16812694	C₂²	1	4	yes	complemented
27	#16812690	C₂²	1	2	yes	complemented
28	#16812688	C₂²	1	2	yes	complemented
29	#16812688	C₂²	1	2	yes	complemented
30	#16812687	C₂²	1	2	yes	complemented
31	#16812684	C₂²	1	4	yes	complemented
32	#16812684	C₂²	1	4	yes	complemented
33	#16812684	C₂²	1	4	yes	complemented
34	#16812683	C₂²	1	4	yes	complemented
35	#16812679	C₂²	1	2	yes	complemented
36	#16812675	C₂²	1	4	yes	complemented
37	#16812674	C₂²	1	2	yes	—
38	#16812674	C₂²	1	2	yes	complemented
39	#16812674	C₂²	1	4	yes	complemented
40	#16812674	C₂²	1	2	yes	complemented
41	#16812673	C₂²	1	2	yes	—
42	#16812673	C₂²	1	4	yes	complemented
43	#16812669	C₂²	1	4	yes	—
44	#16812669	C₂²	1	4	yes	complemented
45	Q₈×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
46	C₄×Dic₂₁₈	C₂²	1	1	yes	characteristic, complemented
47	#16812664	C₂²	1	1	yes	characteristic, complemented
48	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
49	C₄×D₄₃₆	C₂²	1	2	yes	complemented
50	C₄×D₄₃₆	C₂²	1	2	yes	complemented
51	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
52	#16812661	C₂²	1	2	yes	—
53	#16812661	C₂²	1	1	yes	characteristic
54	#16812661	C₂²	1	4	yes	complemented
55	#16812661	C₂²	1	2	yes	complemented
56	#16812661	C₂²	1	2	yes	complemented
57	#16812661	C₂²	1	4	yes	complemented
58	#16812661	C₂²	1	2	yes	complemented
59	#16812661	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₁₀₉	C₂²	1	4	yes	complemented
61	C₄×C₂²⋊D₁₀₉	C₂²	1	2	yes	complemented
62	#16812659	C₂²	1	4	yes	complemented
63	#16812659	C₂²	1	2	yes	complemented
64	#16812657	C₂²	1	2	yes	complemented
65	#16812657	C₂²	1	1	yes	characteristic, complemented
66	#16812657	C₂²	1	1	yes	characteristic, complemented
67	#16812657	C₂²	1	4	yes	complemented
68	#16812655	C₂²	1	2	yes	complemented
69	C₄⋊C₄×D₁₀₉	C₂²	1	2	yes	complemented
70	C₂×#13182006	C₂²	1	4	yes	complemented
71	C₂²⋊C₄×D₁₀₉	C₂²	1	4	yes	complemented
72	C₂×C₄×Dic₁₀₉	C₂²	1	2	yes	complemented
73	C₄²×D₁₀₉	C₂²	1	2	yes	complemented
74	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
75	C₄⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
76	#125×C₁₀₉	C₂²	1	2	yes	complemented
77	C₂²⋊Q₈×C₁₀₉	C₂²	1	4	yes	complemented
78	C₂²⋊Q₈×C₁₀₉	C₂²	1	2	yes	complemented
79	C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
80	C₄×D₄×C₁₀₉	C₂²	1	2	yes	—
81	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
83	C₂³×D₁₀₉	C₂³	1	4	yes	—
84	#13182030	—	2	4	no	—
85	#13182030	—	4	4	no	—
86	#13182028	—	2	4	no	—
87	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
88	C₂×D₄₃₆	—	2	8	no	—
89	C₂×D₄₃₆	C₂³	1	4	yes	—
90	C₂×D₄₃₆	C₂³	1	2	yes	—
91	C₂×D₄₃₆	C₂³	1	2	yes	—
92	C₂×D₄₃₆	C₂³	1	2	yes	—
93	C₂×D₄₃₆	C₂³	1	2	yes	—
94	C₂×D₄₃₆	C₂³	1	4	yes	—
95	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊D₁₀₉	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
98	D₄×D₁₀₉	—	2	8	no	—
99	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
100	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
101	C₂×C₄×D₁₀₉	—	4	8	no	—
102	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
103	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
104	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
108	C₂×C₄×D₁₀₉	C₂³	1	4	yes	—
109	C₂×C₄×D₁₀₉	C₂³	1	4	yes	—
110	C₂×C₄×D₁₀₉	C₂³	1	4	yes	—
111	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
112	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
113	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
114	C₄⋊Dic₁₀₉	C₂³	1	4	yes	—
115	#13182008	C₂³	1	4	yes	—
116	#13182008	C₂³	1	2	yes	—
117	#13182008	C₂³	1	2	yes	—
118	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
119	#13182006	C₂³	1	4	yes	—
120	#13182006	C₂³	1	4	yes	—
121	#13182006	C₂³	1	2	yes	—
122	#13182006	C₂³	1	4	yes	—
123	#13182006	C₂³	1	4	yes	—
124	#13182006	C₂³	1	4	yes	—
125	#13182006	C₂³	1	2	yes	—
126	#13182006	C₂³	1	2	yes	—
127	#13182006	C₂³	1	2	yes	—
128	#13182006	C₂³	1	4	yes	—
129	#13182006	C₂³	1	4	yes	—
130	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
131	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
132	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
133	C₄×Dic₁₀₉	C₂³	1	2	yes	—
134	C₄×Dic₁₀₉	C₂³	1	2	yes	—
135	C₄×Dic₁₀₉	C₂³	1	2	yes	—
136	C₄×Dic₁₀₉	C₂³	1	2	yes	—
137	C₄×Dic₁₀₉	C₂³	1	2	yes	—
138	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
139	C₂×Q₈×C₁₀₉	C₂³	1	2	yes	—
140	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
142	C₂²×C₄×C₁₀₉	C₂³	1	4	yes	—
143	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
145	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
146	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
147	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
148	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
149	C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
150	C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
151	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
152	C₄²×C₁₀₉	C₂³	1	2	yes	—
153	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
154	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
155	C₂²×D₁₀₉	—	2	8	no	—
156	C₂²×D₁₀₉	—	2	8	no	—
157	C₂²×D₁₀₉	—	4	4	no	—
158	C₂²×D₁₀₉	C₂⁴	1	4	yes	—
159	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
160	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
161	Q₈×C₁₀₉	—	2	2	no	—
162	Q₈×C₁₀₉	—	4	2	no	—
163	D₄×C₁₀₉	#41	1	4	yes	complemented
164	C₂×C₄×C₁₀₉	—	2	4	no	—
165	C₂×C₄×C₁₀₉	—	4	4	no	—
166	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
167	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
168	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
169	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
170	C₂×C₄×C₁₀₉	C₂⁴	1	4	yes	—
171	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
173	C₂²⋊D₁₀₉	—	2	8	no	—
174	C₂²⋊D₁₀₉	—	2	4	no	—
175	C₂×Dic₁₀₉	—	2	4	no	—
176	C₂×Dic₁₀₉	—	2	4	no	—
177	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
178	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
179	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
180	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
181	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
182	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
183	D₄₃₆	—	2	8	no	—
184	D₄₃₆	—	2	4	no	—
185	D₄₃₆	—	2	4	no	—
186	D₄₃₆	—	2	4	no	—
187	D₄₃₆	—	4	4	no	—
188	D₄₃₆	—	4	2	no	—
189	D₄₃₆	#41	1	4	yes	complemented
190	C₄×D₁₀₉	—	2	4	no	—
191	C₄×D₁₀₉	—	2	4	no	—
192	C₄×D₁₀₉	—	2	2	no	—
193	C₄×D₁₀₉	—	2	2	no	—
194	C₄×D₁₀₉	—	2	4	no	—
195	C₄×D₁₀₉	—	2	8	no	—
196	C₄×D₁₀₉	—	2	2	no	—
197	C₄×D₁₀₉	—	4	4	no	—
198	C₄×D₁₀₉	—	4	4	no	—
199	Dic₂₁₈	—	2	2	no	—
200	C₂²×C₁₀₉	—	2	2	no	—
201	C₂²×C₁₀₉	—	2	2	no	—
202	C₂²×C₁₀₉	C₂×#41	1	4	yes	—
203	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
204	C₂×D₁₀₉	—	2	2	no	—
205	C₂×D₁₀₉	—	2	2	no	—
206	C₂×D₁₀₉	—	2	1	no	—
207	C₂×D₁₀₉	—	2	1	no	—
208	C₂×D₁₀₉	—	2	4	no	—
209	C₂×D₁₀₉	—	2	4	no	—
210	C₂×D₁₀₉	—	2	4	no	—
211	C₂×D₁₀₉	—	2	1	no	—
212	C₂×D₁₀₉	—	4	16	no	—
213	C₂×D₁₀₉	C₂×#41	1	4	yes	—
214	C₄×C₁₀₉	—	2	2	no	—
215	C₄×C₁₀₉	—	2	2	no	—
216	C₄×C₁₀₉	—	2	2	no	—
217	C₄×C₁₀₉	—	2	4	no	—
218	C₄×C₁₀₉	—	2	1	no	—
219	C₄×C₁₀₉	C₂×#41	1	2	yes	—
220	C₄×C₁₀₉	C₂×#41	1	2	yes	—
221	Dic₁₀₉	—	2	2	no	—
222	Dic₁₀₉	—	2	1	no	—
223	Dic₁₀₉	—	2	1	no	—
224	Dic₁₀₉	—	2	2	no	—
225	Dic₁₀₉	—	2	2	no	—
226	Dic₁₀₉	H(5,𝔽₂)	1	2	yes	—
227	C₂×C₁₀₉	—	2	4	no	—
228	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
229	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
230	C₂×C₁₀₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
231	D₁₀₉	—	2	4	no	—
232	D₁₀₉	—	4	1	no	—
233	D₁₀₉	—	4	4	no	—
234	#3481	—	109	1	no	maximal, Sylow
235	C₁₀₉	#3481	1	1	yes	characteristic, complemented, Sylow
236	#559	—	109	1	no	—
237	#554	—	109	1	no	—
238	#554	D₁₀₉	1	1	yes	characteristic, complemented
239	#553	—	109	2	no	—
240	#553	—	109	2	no	—
241	#551	—	109	4	no	—
242	#546	—	109	2	no	—
243	#546	—	109	2	no	—
244	D₄²	—	109	1	no	—
245	#532	—	109	1	no	—
246	#529	—	109	2	no	—
247	#529	—	109	2	no	—
248	#525	—	109	4	no	—
249	C₄×#41	—	109	1	no	—
250	C₄×#41	—	109	1	no	—
251	C₂×C₄×D₄	—	109	2	no	—
252	C₂×C₄×D₄	—	109	2	no	—
253	C₂×#41	—	109	2	no	—
254	C₂×#41	—	109	1	no	—
255	C₂×#41	—	109	1	no	—
256	C₂²×D₄	—	109	2	no	—
257	C₂²×D₄	—	109	2	no	—
258	C₂³×C₄	—	109	4	no	—
259	C₄⋊Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
260	#127	—	109	1	no	—
261	#126	—	109	4	no	—
262	#126	—	109	4	no	—
263	#125	—	109	2	no	—
264	#125	C₂×D₁₀₉	1	2	yes	complemented
265	#124	—	109	2	no	—
266	#124	—	109	2	no	—
267	#124	—	109	2	no	—
268	#123	—	109	4	no	—
269	#123	—	109	4	no	—
270	#123	—	109	4	no	—
271	#123	—	109	4	no	—
272	C₂²⋊Q₈	—	109	4	no	—
273	C₂²⋊Q₈	—	109	2	no	—
274	C₂²⋊Q₈	C₂×D₁₀₉	1	4	yes	complemented
275	C₂²⋊Q₈	C₂×D₁₀₉	1	2	yes	complemented
276	#121	—	109	4	no	—
277	#121	—	109	2	no	—
278	#121	—	109	4	no	—
279	#121	—	109	2	no	—
280	#121	—	109	2	no	—
281	#121	—	109	2	no	—
282	#120	—	109	4	no	—
283	#120	—	109	4	no	—
284	C₄×Q₈	—	109	1	no	—
285	C₄×Q₈	—	109	1	no	—
286	C₄×Q₈	—	109	1	no	—
287	C₄×Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
288	C₄×D₄	—	109	1	no	—
289	C₄×D₄	—	109	4	no	—
290	C₄×D₄	—	109	2	no	—
291	C₄×D₄	—	109	1	no	—
292	C₄×D₄	—	109	4	no	—
293	C₄×D₄	—	109	2	no	—
294	C₄×D₄	—	109	2	no	—
295	C₄×D₄	—	109	2	no	—
296	C₄×D₄	—	109	4	no	—
297	C₄×D₄	—	109	2	no	—
298	C₄×D₄	—	109	2	no	—
299	C₄×D₄	—	109	4	no	—
300	C₄×D₄	—	109	2	no	—
301	C₄×D₄	—	109	2	no	—
302	C₄×D₄	—	109	1	no	—
303	C₄×D₄	—	109	2	no	—
304	C₄×D₄	C₂×D₁₀₉	1	2	yes	—
305	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic
306	#117	—	109	2	no	—
307	#117	—	109	1	no	—
308	#117	—	109	1	no	—
309	#117	—	109	4	no	—
310	#117	—	109	2	no	—
311	C₂×C₄⋊C₄	—	109	2	no	—
312	C₂×C₄⋊C₄	C₂×D₁₀₉	1	2	yes	complemented
313	C₂×C₂²⋊C₄	—	109	4	no	—
314	C₂×C₂²⋊C₄	—	109	4	no	—
315	C₂×C₄²	—	109	2	no	—
316	C₂×C₄²	—	109	2	no	—
317	C₂×C₄²	—	109	1	no	—
318	C₂⁴	—	109	4	no	—
319	#41	—	436	4	no	—
320	#41	—	218	4	no	—
321	#41	—	218	4	no	—
322	C₂×Q₈	—	109	1	no	—
323	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
324	C₂×Q₈	C₂²×D₁₀₉	1	2	yes	—
325	C₂×D₄	—	109	2	no	—
326	C₂×D₄	—	109	4	no	—
327	C₂×D₄	—	109	1	no	—
328	C₂×D₄	—	109	2	no	—
329	C₂×D₄	—	109	4	no	—
330	C₂×D₄	—	109	2	no	—
331	C₂×D₄	—	109	4	no	—
332	C₂×D₄	—	109	2	no	—
333	C₂×D₄	—	109	2	no	—
334	C₂×D₄	—	218	8	no	—
335	C₂×D₄	—	218	8	no	—
336	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
337	C₂²×C₄	—	109	2	no	—
338	C₂²×C₄	—	109	2	no	—
339	C₂²×C₄	—	109	4	no	—
340	C₂²×C₄	—	109	4	no	—
341	C₂²×C₄	—	109	2	no	—
342	C₂²×C₄	—	109	2	no	—
343	C₂²×C₄	—	109	1	no	—
344	C₂²×C₄	—	109	1	no	—
345	C₂²×C₄	—	109	2	no	—
346	C₂²×C₄	—	109	1	no	—
347	C₂²×C₄	—	109	4	no	—
348	C₂²×C₄	—	436	8	no	—
349	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
350	C₂²×C₄	C₂²×D₁₀₉	1	4	yes	—
351	C₄⋊C₄	—	109	4	no	—
352	C₄⋊C₄	—	109	2	no	—
353	C₄⋊C₄	—	109	2	no	—
354	C₄⋊C₄	—	109	1	no	—
355	C₄⋊C₄	—	109	1	no	—
356	C₄⋊C₄	—	109	2	no	—
357	C₄⋊C₄	—	109	4	no	—
358	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
359	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
360	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
361	C₄⋊C₄	C₂²×D₁₀₉	1	4	yes	—
362	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
363	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
364	C₄⋊C₄	C₂²×D₁₀₉	1	4	yes	—
365	C₂²⋊C₄	—	109	2	no	—
366	C₂²⋊C₄	—	109	2	no	—
367	C₂²⋊C₄	—	109	4	no	—
368	C₂²⋊C₄	—	109	4	no	—
369	C₂²⋊C₄	—	109	4	no	—
370	C₂²⋊C₄	—	109	4	no	—
371	C₂²⋊C₄	—	109	4	no	—
372	C₂²⋊C₄	—	109	2	no	—
373	C₂²⋊C₄	—	109	2	no	—
374	C₂²⋊C₄	—	109	2	no	—
375	C₂²⋊C₄	—	109	4	no	—
376	C₂²⋊C₄	—	109	4	no	—
377	C₂²⋊C₄	C₂²×D₁₀₉	1	4	yes	—
378	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
379	C₄²	—	109	1	no	—
380	C₄²	—	109	1	no	—
381	C₄²	—	109	1	no	—
382	C₄²	—	109	2	no	—
383	C₄²	—	109	2	no	—
384	C₄²	—	109	2	no	—
385	C₄²	—	109	2	no	—
386	C₄²	—	109	2	no	—
387	C₄²	C₂²×D₁₀₉	1	2	yes	—
388	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
389	C₂³	—	109	2	no	—
390	C₂³	—	109	4	no	—
391	C₂³	—	109	1	no	—
392	C₂³	—	436	4	no	—
393	C₂³	—	218	8	no	—
394	C₂³	—	218	8	no	—
395	C₂³	C₂³×D₁₀₉	1	2	yes	—
396	Q₈	—	2	2	no	—
397	Q₈	—	4	2	no	—
398	Q₈	—	218	2	no	—
399	D₄	—	109	4	no	—
400	D₄	—	436	4	no	—
401	D₄	—	436	2	no	—
402	D₄	—	218	8	no	—
403	D₄	—	218	4	no	—
404	D₄	—	218	8	no	—
405	D₄	—	218	4	no	—
406	D₄	—	218	4	no	—
407	D₄	—	218	4	no	—
408	D₄	#13182030	1	4	yes	complemented
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	109	1	no	—
412	C₂×C₄	—	109	1	no	—
413	C₂×C₄	—	109	1	no	—
414	C₂×C₄	—	109	2	no	—
415	C₂×C₄	—	109	2	no	—
416	C₂×C₄	—	109	2	no	—
417	C₂×C₄	—	436	4	no	—
418	C₂×C₄	—	436	4	no	—
419	C₂×C₄	—	218	4	no	—
420	C₂×C₄	—	218	8	no	—
421	C₂×C₄	—	218	2	no	—
422	C₂×C₄	—	218	4	no	—
423	C₂×C₄	—	218	4	no	—
424	C₂×C₄	—	218	4	no	—
425	C₂×C₄	—	218	2	no	—
426	C₂×C₄	—	218	4	no	—
427	C₂×C₄	—	218	2	no	—
428	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
429	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
430	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
431	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
432	C₂×C₄	C₂³×D₁₀₉	1	4	yes	—
433	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
434	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	109	4	no	—
438	C₂²	—	436	16	no	—
439	C₂²	—	218	1	no	—
440	C₂²	—	218	4	no	—
441	C₂²	—	218	1	no	—
442	C₂²	—	218	4	no	—
443	C₂²	—	218	4	no	—
444	C₂²	—	218	1	no	—
445	C₂²	—	218	2	no	—
446	C₂²	—	218	2	no	—
447	C₂²	C₂×#13182030	1	4	yes	—
448	C₂²	C₂⁴×D₁₀₉	1	1	yes	characteristic
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	2	4	no	—
453	C₄	—	2	1	no	—
454	C₄	—	109	2	no	—
455	C₄	—	218	1	no	—
456	C₄	—	218	1	no	—
457	C₄	—	218	2	no	—
458	C₄	—	218	2	no	—
459	C₄	—	218	2	no	—
460	C₄	#41×D₁₀₉	1	2	yes	—
461	C₄	C₂×#13182030	1	2	yes	—
462	C₂	—	2	4	no	—
463	C₂	—	436	4	no	—
464	C₂	—	436	1	no	—
465	C₂	—	218	4	no	—
466	C₂	C₂×#41×D₁₀₉	1	1	yes	characteristic
467	C₂	C₂²×#13182030	1	1	yes	characteristic
468	C₂	H(5,𝔽₂)×D₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₉
commutator, socle, cosocle	C₂²×C₁₀₉	C₂⁵
Fitting	#554×C₁₀₉	C₂
hypercenter	#554	D₁₀₉
hypocenter	C₁₀₉	#3481
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #20295761	C₂	semidirect
2. #20295737	C₂	semidirect
3. #20295729	C₂	semidirect
4. #20295724	C₂	semidirect
5. #20295703	C₂	semidirect
6. #20295671	C₂	semidirect
7. #20295667	C₂	semidirect
8. D₄×D₄₃₆	C₂	semidirect
9. #20295577	C₂	semidirect
10. #20295562	C₂	semidirect
11. #20295561	C₂	semidirect
12. #20295539	C₂	semidirect
13. C₄×#13182030	C₂	semidirect
14. C₄×#13182028	C₂	semidirect
15. C₂×#16812661	C₂	semidirect
16. C₄×D₄×D₁₀₉	C₂	semidirect
17. #554×C₁₀₉	C₂	semidirect
19. C₂×#13182030	C₂²	semidirect
23. C₂²×C₄×D₁₀₉	C₂²	semidirect
25. #16812694	C₂²	semidirect
26. #16812694	C₂²	semidirect
27. #16812690	C₂²	semidirect
28. #16812688	C₂²	semidirect
29. #16812688	C₂²	semidirect
30. #16812687	C₂²	semidirect
31. #16812684	C₂²	semidirect
32. #16812684	C₂²	semidirect
33. #16812684	C₂²	semidirect
34. #16812683	C₂²	semidirect
35. #16812679	C₂²	semidirect
36. #16812675	C₂²	semidirect
38. #16812674	C₂²	semidirect
39. #16812674	C₂²	semidirect
40. #16812674	C₂²	semidirect
42. #16812673	C₂²	semidirect
44. #16812669	C₂²	semidirect
45. Q₈×Dic₁₀₉	C₂²	semidirect
46. C₄×Dic₂₁₈	C₂²	semidirect
47. #16812664	C₂²	semidirect
49. C₄×D₄₃₆	C₂²	semidirect
50. C₄×D₄₃₆	C₂²	semidirect
54. #16812661	C₂²	semidirect
55. #16812661	C₂²	semidirect
56. #16812661	C₂²	semidirect
57. #16812661	C₂²	semidirect
58. #16812661	C₂²	semidirect
59. #16812661	C₂²	semidirect
60. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
61. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
62. #16812659	C₂²	semidirect
63. #16812659	C₂²	semidirect
64. #16812657	C₂²	semidirect
65. #16812657	C₂²	semidirect
66. #16812657	C₂²	semidirect
67. #16812657	C₂²	semidirect
68. #16812655	C₂²	semidirect
69. C₄⋊C₄×D₁₀₉	C₂²	semidirect
70. C₂×#13182006	C₂²	semidirect
71. C₂²⋊C₄×D₁₀₉	C₂²	semidirect
72. C₂×C₄×Dic₁₀₉	C₂²	semidirect
73. C₄²×D₁₀₉	C₂²	semidirect
74. C₄²×D₁₀₉	C₂²	semidirect
75. C₄⋊Q₈×C₁₀₉	C₂²	semidirect
76. #125×C₁₀₉	C₂²	semidirect
77. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
78. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
79. C₄×Q₈×C₁₀₉	C₂²	semidirect
82. C₂×C₄⋊C₄×C₁₀₉	C₂²	semidirect
163. D₄×C₁₀₉	#41	semidirect
189. D₄₃₆	#41	semidirect
235. C₁₀₉	#3481	semidirect
238. #554	D₁₀₉	semidirect
259. C₄⋊Q₈	C₂×D₁₀₉	semidirect
264. #125	C₂×D₁₀₉	semidirect
274. C₂²⋊Q₈	C₂×D₁₀₉	semidirect
275. C₂²⋊Q₈	C₂×D₁₀₉	semidirect
287. C₄×Q₈	C₂×D₁₀₉	semidirect
312. C₂×C₄⋊C₄	C₂×D₁₀₉	semidirect
408. D₄	#13182030	semidirect

Maximal subgroups

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

subgroup	index
#20295761	2
#20295737	2
#20295729	2
#20295724	2
#20295703	2
#20295671	2
#20295667	2
D₄×D₄₃₆	2
#20295577	2
#20295562	2
#20295561	2
#20295539	2
C₄×#13182030	2
C₄×#13182028	2
C₂×#16812661	2
C₄×D₄×D₁₀₉	2
#554×C₁₀₉	2
#3481	109