Subgroups — #28374515

Order 13952.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16812724	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295664	C₂	1	1	yes	maximal, characteristic, complemented
4	#20295660	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295412	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295277	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295258	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295244	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295219	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295175	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295162	C₂	1	1	yes	maximal, characteristic, complemented
12	#20295161	C₂	1	1	yes	maximal, characteristic, complemented
13	#20295135	C₂	1	1	yes	maximal, characteristic, complemented
14	#20295100	C₂	1	1	yes	maximal, characteristic, complemented
15	#449×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
17	C₂×D₄×D₁₀₉	—	2	1	no	—
18	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
19	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
20	#16812724	—	2	4	no	—
21	C₂×#13182016	C₂²	1	1	yes	characteristic, complemented
22	C₂×#13182016	C₂²	1	1	yes	characteristic, complemented
23	C₂×D₈₇₂	C₂²	1	1	yes	characteristic
24	C₂×D₈₇₂	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13182014	C₂²	1	1	yes	characteristic
26	C₂×#13182014	C₂²	1	1	yes	characteristic, complemented
27	C₂×#13182014	C₂²	1	1	yes	characteristic, complemented
28	D₈×D₁₀₉	—	2	4	no	—
29	C₂×#13182013	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
31	#16812695	C₂²	1	1	yes	characteristic, complemented
32	#16812688	C₂²	1	1	yes	characteristic, complemented
33	#16812682	—	2	1	no	—
34	#16812675	C₂²	1	1	yes	characteristic, complemented
35	#16812674	C₂²	1	1	yes	characteristic
36	#16812673	C₂²	1	1	yes	characteristic, complemented
37	#16812672	—	2	1	no	—
38	#16812671	—	2	1	no	—
39	#16812669	—	2	1	no	—
40	#16812667	—	2	1	no	—
41	#16812667	—	2	1	no	—
42	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
43	#16812661	C₂²	1	1	yes	characteristic, complemented
44	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic
45	C₂×#13182006	—	2	1	no	—
46	#16812630	C₂²	1	1	yes	characteristic, complemented
47	#16812628	C₂²	1	1	yes	characteristic, complemented
48	#16812621	C₂²	1	1	yes	characteristic, complemented
49	#16812621	C₂²	1	1	yes	characteristic, complemented
50	#16812620	C₂²	1	1	yes	characteristic, complemented
51	#16812619	C₂²	1	1	yes	characteristic, complemented
52	#16812611	C₂²	1	1	yes	characteristic, complemented
53	#16812609	C₂²	1	1	yes	characteristic, complemented
54	C₂×#41×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×SD₁₆×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
56	C₂×D₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
57	#121×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
58	#103×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
59	#102×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
60	C₂²⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₀₉	—	2	1	no	—
62	C₂³×D₁₀₉	—	2	1	no	—
63	C₂³×D₁₀₉	—	2	1	no	—
64	C₂×D₄₃₆	—	2	2	no	—
65	C₂×D₄₃₆	—	2	1	no	—
66	C₂×D₄₃₆	—	2	1	no	—
67	C₂×D₄₃₆	—	4	1	no	—
68	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
69	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
70	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
72	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
73	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
74	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
75	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
76	C₂×C₂²⋊D₁₀₉	D₄	1	1	yes	characteristic
77	D₄×D₁₀₉	—	2	2	no	—
78	D₄×D₁₀₉	—	2	2	no	—
79	D₄×D₁₀₉	—	4	1	no	—
80	D₄×D₁₀₉	—	4	1	no	—
81	D₄×D₁₀₉	—	4	4	no	—
82	C₂²×Dic₁₀₉	—	2	1	no	—
83	C₂×C₄×D₁₀₉	—	2	1	no	—
84	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
85	#13182016	—	2	2	no	—
86	#13182016	—	2	2	no	—
87	D₈₇₂	—	2	2	no	—
88	D₈₇₂	—	4	1	no	—
89	#13182014	—	2	2	no	—
90	#13182014	—	2	2	no	—
91	#13182014	D₄	1	4	yes	complemented
92	#13182013	—	2	2	no	—
93	C₂×#11724784	C₂³	1	1	yes	characteristic
94	C₂×#11724784	C₂³	1	1	yes	characteristic
95	C₈×D₁₀₉	—	2	2	no	—
96	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
97	#13182008	—	2	1	no	—
98	#13182008	D₄	1	1	yes	characteristic
99	C₂²⋊Dic₁₀₉	—	2	1	no	—
100	C₂²⋊Dic₁₀₉	D₄	1	1	yes	characteristic
101	#13182006	—	2	1	no	—
102	#13182006	—	2	1	no	—
103	#13182006	—	2	1	no	—
104	#13182006	—	2	1	no	—
105	#13182006	—	2	1	no	—
106	#13182006	—	2	1	no	—
107	#13182006	D₄	1	1	yes	characteristic
108	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
109	#41×C₁₀₉	—	2	2	no	—
110	#41×C₁₀₉	—	4	1	no	—
111	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
112	C₂×D₄×C₁₀₉	—	2	1	no	—
113	C₂×D₄×C₁₀₉	—	2	1	no	—
114	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
115	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₁₀₉	—	2	1	no	—
117	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
118	SD₁₆×C₁₀₉	—	4	1	no	—
119	D₈×C₁₀₉	—	2	2	no	—
120	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
121	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
122	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
123	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
124	C₂³×C₁₀₉	—	2	1	no	—
125	C₂³×C₁₀₉	—	2	1	no	—
126	C₂³×C₁₀₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×D₁₀₉	—	2	1	no	—
128	C₂²×D₁₀₉	—	2	1	no	—
129	C₂²×D₁₀₉	—	2	1	no	—
130	C₂²×D₁₀₉	—	4	2	no	—
131	C₂²×D₁₀₉	—	4	2	no	—
132	C₂²×D₁₀₉	—	4	2	no	—
133	C₂²×D₁₀₉	—	4	2	no	—
134	C₂²×D₁₀₉	—	4	2	no	—
135	C₂²×D₁₀₉	—	4	2	no	—
136	C₂²×D₁₀₉	—	8	1	no	—
137	C₂²×D₁₀₉	—	8	1	no	—
138	C₂²×D₁₀₉	—	8	1	no	—
139	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
140	Q₈×C₁₀₉	—	2	1	no	—
141	Q₈×C₁₀₉	—	2	1	no	—
142	D₄×C₁₀₉	—	2	1	no	—
143	D₄×C₁₀₉	—	2	1	no	—
144	D₄×C₁₀₉	—	2	1	no	—
145	D₄×C₁₀₉	—	4	2	no	—
146	D₄×C₁₀₉	—	4	2	no	—
147	D₄×C₁₀₉	C₂×D₄	1	2	yes	complemented
148	C₂×C₄×C₁₀₉	—	2	1	no	—
149	C₂×C₄×C₁₀₉	—	2	1	no	—
150	C₂×C₄×C₁₀₉	—	2	1	no	—
151	C₂×C₄×C₁₀₉	—	2	1	no	—
152	C₂×C₄×C₁₀₉	—	4	2	no	—
153	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
155	C₂²⋊D₁₀₉	—	2	2	no	—
156	C₂²⋊D₁₀₉	—	4	2	no	—
157	C₂²⋊D₁₀₉	—	4	2	no	—
158	C₂²⋊D₁₀₉	—	4	2	no	—
159	C₂²⋊D₁₀₉	—	8	1	no	—
160	C₂²⋊D₁₀₉	—	8	1	no	—
161	C₂×Dic₁₀₉	—	2	1	no	—
162	C₂×Dic₁₀₉	—	8	1	no	—
163	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
164	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
165	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
166	D₄₃₆	—	2	1	no	—
167	D₄₃₆	—	2	1	no	—
168	D₄₃₆	—	2	1	no	—
169	D₄₃₆	—	2	1	no	—
170	D₄₃₆	—	2	1	no	—
171	D₄₃₆	—	4	2	no	—
172	D₄₃₆	—	4	2	no	—
173	D₄₃₆	C₂×D₄	1	2	yes	—
174	C₄×D₁₀₉	—	2	1	no	—
175	C₄×D₁₀₉	—	2	1	no	—
176	C₄×D₁₀₉	—	4	2	no	—
177	C₈×C₁₀₉	—	2	1	no	—
178	C₈×C₁₀₉	—	2	1	no	—
179	#11724784	—	2	1	no	—
180	#11724784	C₂×D₄	1	2	yes	complemented
181	C₂²×C₁₀₉	—	2	2	no	—
182	C₂²×C₁₀₉	—	2	1	no	—
183	C₂²×C₁₀₉	—	2	1	no	—
184	C₂²×C₁₀₉	—	2	1	no	—
185	C₂²×C₁₀₉	—	4	1	no	—
186	C₂²×C₁₀₉	—	4	1	no	—
187	C₂²×C₁₀₉	—	4	1	no	—
188	C₂²×C₁₀₉	—	4	1	no	—
189	C₂²×C₁₀₉	—	4	1	no	—
190	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
191	C₂×D₁₀₉	—	2	1	no	—
192	C₂×D₁₀₉	—	2	1	no	—
193	C₂×D₁₀₉	—	2	2	no	—
194	C₂×D₁₀₉	—	4	1	no	—
195	C₂×D₁₀₉	—	4	1	no	—
196	C₂×D₁₀₉	—	4	1	no	—
197	C₂×D₁₀₉	—	4	1	no	—
198	C₂×D₁₀₉	—	4	1	no	—
199	C₂×D₁₀₉	—	4	1	no	—
200	C₂×D₁₀₉	—	4	1	no	—
201	C₂×D₁₀₉	—	4	1	no	—
202	C₂×D₁₀₉	—	8	4	no	—
203	C₂×D₁₀₉	—	8	4	no	—
204	C₂×D₁₀₉	—	8	4	no	—
205	C₂×D₁₀₉	AGL(1,ℤ/8)	1	2	yes	complemented
206	C₄×C₁₀₉	—	2	1	no	—
207	C₄×C₁₀₉	—	4	1	no	—
208	C₄×C₁₀₉	—	4	1	no	—
209	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
210	C₄×C₁₀₉	H(5,𝔽₂)	1	1	yes	characteristic
211	Dic₁₀₉	—	2	1	no	—
212	Dic₁₀₉	—	2	1	no	—
213	Dic₁₀₉	—	2	1	no	—
214	Dic₁₀₉	—	4	1	no	—
215	C₂×C₁₀₉	—	4	1	no	—
216	C₂×C₁₀₉	—	4	2	no	—
217	C₂×C₁₀₉	—	8	1	no	—
218	C₂×C₁₀₉	D₄²	1	1	yes	characteristic
219	C₂×C₁₀₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
220	C₂×C₁₀₉	#576	1	1	yes	characteristic
221	D₁₀₉	—	2	2	no	—
222	D₁₀₉	—	4	2	no	—
223	D₁₀₉	—	8	1	no	—
224	D₁₀₉	—	8	1	no	—
225	#3264	—	109	1	no	maximal, Sylow
226	C₁₀₉	#3264	1	1	yes	characteristic, complemented, Sylow
227	C₂×AGL(1,ℤ/8)	—	109	1	no	—
228	C₂²×D₈	—	109	1	no	—
229	#546	—	109	1	no	—
230	D₄²	—	109	1	no	—
231	#496	—	109	1	no	—
232	#469	—	109	1	no	—
233	#465	—	109	1	no	—
234	#463	—	109	1	no	—
235	#459	—	109	1	no	—
236	#450	—	109	1	no	—
237	#449	D₁₀₉	1	1	yes	characteristic, complemented
238	#447	—	109	1	no	—
239	#447	—	109	1	no	—
240	#442	—	109	1	no	—
241	#435	—	109	1	no	—
242	C₂×#41	C₂×D₁₀₉	1	1	yes	characteristic, complemented
243	C₂²×D₄	—	109	1	no	—
244	C₂²×D₄	—	109	1	no	—
245	C₂²×D₄	—	109	1	no	—
246	C₂²×D₄	—	218	1	no	—
247	AGL(1,ℤ/8)	—	218	4	no	—
248	C₂×SD₁₆	—	109	1	no	—
249	C₂×SD₁₆	—	109	1	no	—
250	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
251	C₂×D₈	—	109	1	no	—
252	C₂×D₈	—	109	1	no	—
253	C₂×D₈	—	109	1	no	—
254	C₂×D₈	—	109	1	no	—
255	C₂×D₈	—	109	1	no	—
256	C₂×D₈	—	218	4	no	—
257	C₂×D₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
258	C₂×M₁₆	—	109	1	no	—
259	C₂²×C₈	—	109	1	no	—
260	#127	—	109	1	no	—
261	#124	—	109	1	no	—
262	#123	—	218	1	no	—
263	C₂²⋊Q₈	—	109	1	no	—
264	#121	—	109	1	no	—
265	#121	—	109	1	no	—
266	#121	—	218	1	no	—
267	#121	—	218	1	no	—
268	#121	C₂×D₁₀₉	1	1	yes	characteristic, complemented
269	#120	—	218	1	no	—
270	#120	—	218	1	no	—
271	#120	—	218	1	no	—
272	C₄×D₄	—	109	1	no	—
273	C₄×D₄	—	109	1	no	—
274	C₄×D₄	—	109	1	no	—
275	C₂×C₂²⋊C₄	—	218	1	no	—
276	#106	—	109	1	no	—
277	C₄⋊C₈	—	109	1	no	—
278	#103	C₂×D₁₀₉	1	1	yes	characteristic, complemented
279	#102	—	109	1	no	—
280	#102	—	109	1	no	—
281	#102	—	109	1	no	—
282	#102	—	109	1	no	—
283	#102	C₂×D₁₀₉	1	1	yes	characteristic, complemented
284	C₂²⋊C₈	—	109	1	no	—
285	C₂²⋊C₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
286	#97	—	109	1	no	—
287	C₂⁴	—	218	1	no	—
288	C₂⁴	—	218	1	no	—
289	C₂⁴	—	218	1	no	—
290	#41	—	2	2	no	—
291	#41	—	4	1	no	—
292	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	109	1	no	—
296	C₂×D₄	—	109	1	no	—
297	C₂×D₄	—	109	1	no	—
298	C₂×D₄	—	109	1	no	—
299	C₂×D₄	—	436	1	no	—
300	C₂×D₄	—	436	4	no	—
301	C₂×D₄	—	436	1	no	—
302	C₂×D₄	—	436	1	no	—
303	C₂×D₄	—	218	2	no	—
304	C₂×D₄	—	218	1	no	—
305	C₂×D₄	—	218	1	no	—
306	C₂×D₄	—	218	1	no	—
307	C₂×D₄	—	218	1	no	—
308	C₂×D₄	—	218	1	no	—
309	C₂×D₄	—	218	2	no	—
310	C₂×D₄	—	218	1	no	—
311	C₂×D₄	—	218	2	no	—
312	C₂×D₄	—	218	1	no	—
313	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
314	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	109	1	no	—
317	C₂²×C₄	—	218	1	no	—
318	C₂²×C₄	—	218	1	no	—
319	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
320	SD₁₆	—	4	1	no	—
321	SD₁₆	—	218	2	no	—
322	SD₁₆	—	218	2	no	—
323	D₈	—	2	2	no	—
324	D₈	—	109	4	no	—
325	D₈	—	436	1	no	—
326	D₈	—	218	2	no	—
327	D₈	—	218	2	no	—
328	D₈	—	218	2	no	—
329	M₁₆	—	218	2	no	—
330	C₂×C₈	—	109	1	no	—
331	C₂×C₈	—	109	1	no	—
332	C₂×C₈	—	218	2	no	—
333	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
334	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
335	C₄⋊C₄	—	109	1	no	—
336	C₄⋊C₄	—	109	1	no	—
337	C₄⋊C₄	—	218	1	no	—
338	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
339	C₂²⋊C₄	—	2	1	no	—
340	C₂²⋊C₄	—	109	1	no	—
341	C₂²⋊C₄	—	109	1	no	—
342	C₂²⋊C₄	—	218	1	no	—
343	C₂²⋊C₄	—	218	1	no	—
344	C₂²⋊C₄	—	218	1	no	—
345	C₂²⋊C₄	—	218	1	no	—
346	C₂²⋊C₄	—	218	1	no	—
347	C₂²⋊C₄	—	218	1	no	—
348	C₂²⋊C₄	—	218	1	no	—
349	C₄²	—	109	1	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	872	1	no	—
353	C₂³	—	872	1	no	—
354	C₂³	—	872	1	no	—
355	C₂³	—	109	1	no	—
356	C₂³	—	436	2	no	—
357	C₂³	—	436	2	no	—
358	C₂³	—	436	2	no	—
359	C₂³	—	436	2	no	—
360	C₂³	—	436	2	no	—
361	C₂³	—	436	2	no	—
362	C₂³	—	218	1	no	—
363	C₂³	—	218	1	no	—
364	C₂³	—	218	1	no	—
365	C₂³	D₄×D₁₀₉	1	1	yes	characteristic
366	Q₈	—	2	1	no	—
367	Q₈	—	2	1	no	—
368	D₄	—	2	1	no	—
369	D₄	—	2	1	no	—
370	D₄	—	2	1	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	872	1	no	—
374	D₄	—	872	1	no	—
375	D₄	—	109	2	no	—
376	D₄	—	436	2	no	—
377	D₄	—	436	2	no	—
378	D₄	—	436	2	no	—
379	D₄	—	436	2	no	—
380	D₄	—	436	2	no	—
381	D₄	—	218	2	no	—
382	D₄	—	218	1	no	—
383	D₄	—	218	1	no	—
384	D₄	—	218	1	no	—
385	D₄	—	218	1	no	—
386	D₄	—	218	1	no	—
387	D₄	D₄×D₁₀₉	1	2	yes	complemented
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	872	1	no	—
394	C₂×C₄	—	109	1	no	—
395	C₂×C₄	—	109	1	no	—
396	C₂×C₄	—	109	1	no	—
397	C₂×C₄	—	436	2	no	—
398	C₂×C₄	—	218	1	no	—
399	C₂×C₄	—	218	1	no	—
400	C₂×C₄	—	218	1	no	—
401	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
402	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	109	2	no	—
406	C₈	—	218	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	872	4	no	—
417	C₂²	—	872	4	no	—
418	C₂²	—	872	4	no	—
419	C₂²	—	109	2	no	—
420	C₂²	—	436	1	no	—
421	C₂²	—	436	1	no	—
422	C₂²	—	436	1	no	—
423	C₂²	—	436	1	no	—
424	C₂²	—	436	1	no	—
425	C₂²	—	436	1	no	—
426	C₂²	—	436	1	no	—
427	C₂²	—	436	1	no	—
428	C₂²	—	218	2	no	—
429	C₂²	—	218	1	no	—
430	C₂²	—	218	1	no	—
431	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	4	1	no	—
434	C₄	—	4	1	no	—
435	C₄	—	436	1	no	—
436	C₄	—	218	1	no	—
437	C₄	—	218	1	no	—
438	C₄	—	218	1	no	—
439	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
440	C₄	#16812744	1	1	yes	characteristic
441	C₂	—	4	1	no	—
442	C₂	—	4	2	no	—
443	C₂	—	8	1	no	—
444	C₂	—	872	1	no	—
445	C₂	—	872	1	no	—
446	C₂	—	436	2	no	—
447	C₂	—	218	2	no	—
448	C₂	#20295658	1	1	yes	characteristic
449	C₂	AGL(1,ℤ/8)×D₁₀₉	1	1	yes	characteristic
450	C₂	#20295828	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₀₉
commutator, cosocle	C₂×C₄×C₁₀₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₀₉
Fitting	#449×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²×D₄
hypercenter	#449	D₁₀₉
hypocenter	C₁₀₉	#3264
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #449

Complements

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

N	H ≅ G/N	type
1. C₂×#16812724	C₂	semidirect
2. C₂×D₈×D₁₀₉	C₂	semidirect
3. #20295664	C₂	semidirect
4. #20295660	C₂	semidirect
5. #20295412	C₂	semidirect
6. #20295277	C₂	semidirect
7. #20295258	C₂	semidirect
8. #20295244	C₂	semidirect
9. #20295219	C₂	semidirect
10. #20295175	C₂	semidirect
11. #20295162	C₂	semidirect
12. #20295161	C₂	semidirect
13. #20295135	C₂	semidirect
14. #20295100	C₂	semidirect
15. #449×C₁₀₉	C₂	semidirect
16. C₂²×D₄₃₆	C₂²	semidirect
19. C₂×D₄×D₁₀₉	C₂²	semidirect
21. C₂×#13182016	C₂²	semidirect
22. C₂×#13182016	C₂²	semidirect
24. C₂×D₈₇₂	C₂²	semidirect
26. C₂×#13182014	C₂²	semidirect
27. C₂×#13182014	C₂²	semidirect
29. C₂×#13182013	C₂²	semidirect
30. C₂×C₈×D₁₀₉	C₂²	semidirect
31. #16812695	C₂²	semidirect
32. #16812688	C₂²	semidirect
34. #16812675	C₂²	semidirect
36. #16812673	C₂²	semidirect
42. D₄×Dic₁₀₉	C₂²	semidirect
43. #16812661	C₂²	semidirect
46. #16812630	C₂²	semidirect
47. #16812628	C₂²	semidirect
48. #16812621	C₂²	semidirect
49. #16812621	C₂²	semidirect
50. #16812620	C₂²	semidirect
51. #16812619	C₂²	semidirect
52. #16812611	C₂²	semidirect
53. #16812609	C₂²	semidirect
54. C₂×#41×C₁₀₉	C₂²	semidirect
55. C₂×SD₁₆×C₁₀₉	C₂²	semidirect
56. C₂×D₈×C₁₀₉	C₂²	semidirect
57. #121×C₁₀₉	C₂²	semidirect
58. #103×C₁₀₉	C₂²	semidirect
59. #102×C₁₀₉	C₂²	semidirect
60. C₂²⋊C₈×C₁₀₉	C₂²	semidirect
91. #13182014	D₄	semidirect
147. D₄×C₁₀₉	C₂×D₄	semidirect
180. #11724784	C₂×D₄	semidirect
205. C₂×D₁₀₉	AGL(1,ℤ/8)	semidirect
226. C₁₀₉	#3264	semidirect
237. #449	D₁₀₉	semidirect
242. C₂×#41	C₂×D₁₀₉	semidirect
250. C₂×SD₁₆	C₂×D₁₀₉	semidirect
257. C₂×D₈	C₂×D₁₀₉	semidirect
268. #121	C₂×D₁₀₉	semidirect
278. #103	C₂×D₁₀₉	semidirect
283. #102	C₂×D₁₀₉	semidirect
285. C₂²⋊C₈	C₂×D₁₀₉	semidirect
387. D₄	D₄×D₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16812724	2
C₂×D₈×D₁₀₉	2
#20295664	2
#20295660	2
#20295412	2
#20295277	2
#20295258	2
#20295244	2
#20295219	2
#20295175	2
#20295162	2
#20295161	2
#20295135	2
#20295100	2
#449×C₁₀₉	2
#3264	109