Subgroups — #22624255

Order 9344.

1260 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989325	C₂	1	4	yes	maximal, complemented
2	#17989322	C₂	1	1	yes	maximal, characteristic, complemented
3	#17989257	C₂	1	1	yes	maximal, characteristic, complemented
4	#17989232	C₂	1	2	yes	maximal, complemented
5	#17989225	C₂	1	2	yes	maximal, complemented
6	D₄×D₂₉₂	C₂	1	1	yes	maximal, characteristic, complemented
7	#17989222	C₂	1	2	yes	maximal, complemented
8	#17989221	C₂	1	2	yes	maximal, complemented
9	#17989190	C₂	1	2	yes	maximal, complemented
10	#17989188	C₂	1	2	yes	maximal, complemented
11	#17989151	C₂	1	2	yes	maximal, complemented
12	#17989150	C₂	1	2	yes	maximal, complemented
13	#17989145	C₂	1	4	yes	maximal, complemented
14	#127×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#17989124	C₂	1	1	yes	maximal, characteristic, complemented
16	#17989119	C₂	1	1	yes	maximal, characteristic, complemented
17	#550×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#11924027	C₂²	1	2	yes	complemented
19	C₂²×D₂₉₂	C₂²	1	2	yes	complemented
20	C₂×D₄×D₇₃	C₂²	1	2	yes	complemented
21	C₂×D₄×D₇₃	C₂²	1	2	yes	complemented
22	C₂×D₄×D₇₃	C₂²	1	2	yes	complemented
23	C₂×D₄×D₇₃	C₂²	1	4	yes	complemented
24	C₂×D₄×D₇₃	C₂²	1	2	yes	complemented
25	#14556588	C₂²	1	1	yes	characteristic
26	#14556587	C₂²	1	2	yes	complemented
27	#14556587	C₂²	1	2	yes	complemented
28	#14556587	C₂²	1	2	yes	complemented
29	#14556587	C₂²	1	2	yes	complemented
30	#14556586	C₂²	1	2	yes	complemented
31	#14556584	C₂²	1	2	yes	complemented
32	#14556582	C₂²	1	1	yes	characteristic, complemented
33	#14556582	C₂²	1	1	yes	characteristic, complemented
34	#14556580	C₂²	1	1	yes	characteristic, complemented
35	#14556580	C₂²	1	2	yes	complemented
36	#14556579	C₂²	1	2	yes	complemented
37	#14556578	C₂²	1	1	yes	characteristic, complemented
38	#14556576	C₂²	1	2	yes	complemented
39	#14556576	C₂²	1	4	yes	complemented
40	#14556575	C₂²	1	4	yes	complemented
41	#14556574	C₂²	1	4	yes	complemented
42	#14556573	C₂²	1	2	yes	complemented
43	#14556573	C₂²	1	4	yes	complemented
44	#14556571	C₂²	1	1	yes	characteristic, complemented
45	#14556567	C₂²	1	1	yes	characteristic, complemented
46	#14556566	C₂²	1	1	yes	characteristic
47	#14556566	C₂²	1	2	yes	complemented
48	#14556565	C₂²	1	4	yes	complemented
49	#14556565	C₂²	1	4	yes	complemented
50	#14556565	C₂²	1	2	yes	complemented
51	#14556564	C₂²	1	4	yes	complemented
52	#14556563	C₂²	1	4	yes	complemented
53	#14556563	C₂²	1	4	yes	complemented
54	#14556563	C₂²	1	4	yes	complemented
55	#14556562	C₂²	1	1	yes	characteristic
56	#14556562	C₂²	1	2	yes	complemented
57	#14556562	C₂²	1	4	yes	complemented
58	#14556561	C₂²	1	4	yes	complemented
59	#14556561	C₂²	1	4	yes	complemented
60	#14556559	C₂²	1	4	yes	complemented
61	#14556559	C₂²	1	4	yes	complemented
62	#14556559	C₂²	1	4	yes	complemented
63	#14556559	C₂²	1	4	yes	complemented
64	C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
65	C₄×D₂₉₂	C₂²	1	2	yes	complemented
66	C₄×D₂₉₂	C₂²	1	1	yes	characteristic, complemented
67	C₄×D₂₉₂	C₂²	1	2	yes	complemented
68	D₄×Dic₇₃	C₂²	1	2	yes	complemented
69	#14556553	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
71	#14556550	C₂²	1	2	yes	complemented
72	#14556548	C₂²	1	2	yes	complemented
73	C₂×#11924005	C₂²	1	4	yes	complemented
74	C₄²×D₇₃	C₂²	1	1	yes	characteristic, complemented
75	C₂×#41×C₇₃	C₂²	1	2	yes	complemented
76	#127×C₇₃	C₂²	1	1	yes	characteristic, complemented
77	#127×C₇₃	C₂²	1	2	yes	complemented
78	#121×C₇₃	C₂²	1	4	yes	complemented
79	#121×C₇₃	C₂²	1	2	yes	complemented
80	C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₄×C₇₃	C₂²	1	2	yes	complemented
82	C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₇₃	C₂³	1	4	yes	—
84	C₂³×D₇₃	C₂³	1	4	yes	—
85	#11924027	—	4	4	no	—
86	C₂×Dic₁₄₆	C₂³	1	1	yes	characteristic
87	C₂×D₂₉₂	—	4	4	no	—
88	C₂×D₂₉₂	C₂³	1	2	yes	—
89	C₂×D₂₉₂	C₂³	1	2	yes	—
90	C₂×D₂₉₂	C₂³	1	1	yes	characteristic
91	C₂×D₂₉₂	C₂³	1	2	yes	—
92	C₂×D₂₉₂	C₂³	1	4	yes	—
93	C₂×D₂₉₂	C₂³	1	2	yes	—
94	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
95	C₂×C₂²⋊D₇₃	C₂³	1	4	yes	—
96	C₂×C₂²⋊D₇₃	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₇₃	C₂³	1	4	yes	—
98	C₂×C₂²⋊D₇₃	C₂³	1	4	yes	—
99	C₂×C₂²⋊D₇₃	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₇₃	C₂³	1	4	yes	—
101	D₄×D₇₃	—	4	4	no	—
102	D₄×D₇₃	—	4	4	no	—
103	D₄×D₇₃	—	4	4	no	—
104	D₄×D₇₃	—	4	4	no	—
105	D₄×D₇₃	—	4	8	no	—
106	C₂²×Dic₇₃	C₂³	1	4	yes	—
107	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
109	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
110	C₂×C₄×D₇₃	C₂³	1	2	yes	—
111	C₂×C₄×D₇₃	C₂³	1	4	yes	—
112	C₄⋊Dic₇₃	C₂³	1	2	yes	—
113	C₄⋊Dic₇₃	C₂³	1	2	yes	—
114	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
115	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
116	C₄⋊Dic₇₃	C₂³	1	2	yes	—
117	#11924007	C₂³	1	2	yes	—
118	#11924007	C₂³	1	2	yes	—
119	#11924007	C₂³	1	2	yes	—
120	#11924007	C₂³	1	2	yes	—
121	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
122	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
123	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
124	C₂²⋊Dic₇₃	C₂³	1	4	yes	—
125	#11924005	C₂³	1	2	yes	—
126	#11924005	C₂³	1	2	yes	—
127	#11924005	C₂³	1	4	yes	—
128	#11924005	C₂³	1	4	yes	—
129	#11924005	C₂³	1	2	yes	—
130	#11924005	C₂³	1	2	yes	—
131	#11924005	C₂³	1	4	yes	—
132	#11924005	C₂³	1	2	yes	—
133	#11924005	C₂³	1	4	yes	—
134	#11924005	C₂³	1	2	yes	—
135	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
136	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
137	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
138	C₄×Dic₇₃	C₂³	1	2	yes	—
139	#41×C₇₃	—	4	4	no	—
140	C₂×Q₈×C₇₃	C₂³	1	1	yes	characteristic
141	C₂×D₄×C₇₃	C₂³	1	1	yes	characteristic
142	C₂×D₄×C₇₃	C₂³	1	2	yes	—
143	C₂×D₄×C₇₃	C₂³	1	2	yes	—
144	C₂×D₄×C₇₃	C₂³	1	4	yes	—
145	C₂×D₄×C₇₃	C₂³	1	2	yes	—
146	C₂×D₄×C₇₃	C₂³	1	4	yes	—
147	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
148	C₂²×C₄×C₇₃	C₂³	1	4	yes	—
149	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
150	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
151	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
152	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
153	C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
154	C₄²×C₇₃	C₂³	1	1	yes	characteristic
155	C₄²×C₇₃	C₂³	1	2	yes	—
156	C₂³×C₇₃	C₂⁴	1	2	yes	—
157	C₂³×C₇₃	C₂⁴	1	4	yes	—
158	C₂²×D₇₃	—	2	8	no	—
159	C₂²×D₇₃	—	4	4	no	—
160	C₂²×D₇₃	—	4	4	no	—
161	C₂²×D₇₃	—	4	4	no	—
162	C₂²×D₇₃	—	4	4	no	—
163	C₂²×D₇₃	—	4	4	no	—
164	C₂²×D₇₃	C₂⁴	1	2	yes	—
165	C₂²×D₇₃	C₂⁴	1	4	yes	—
166	C₂²×D₇₃	C₂⁴	1	1	yes	characteristic
167	Q₈×C₇₃	—	2	2	no	—
168	D₄×C₇₃	—	2	4	no	—
169	D₄×C₇₃	—	2	2	no	—
170	D₄×C₇₃	—	2	4	no	—
171	D₄×C₇₃	—	4	4	no	—
172	D₄×C₇₃	—	4	2	no	—
173	D₄×C₇₃	—	4	4	no	—
174	C₂×C₄×C₇₃	—	2	4	no	—
175	C₂×C₄×C₇₃	—	4	4	no	—
176	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
178	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
179	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
180	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
181	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
182	C₂²⋊D₇₃	—	2	4	no	—
183	C₂²⋊D₇₃	—	4	4	no	—
184	C₂²⋊D₇₃	—	4	4	no	—
185	C₂²⋊D₇₃	—	4	4	no	—
186	C₂²⋊D₇₃	—	4	4	no	—
187	C₂²⋊D₇₃	—	4	4	no	—
188	C₂²⋊D₇₃	—	4	4	no	—
189	C₂×Dic₇₃	—	4	4	no	—
190	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
191	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
192	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
193	C₂×Dic₇₃	C₂⁴	1	2	yes	—
194	C₂×Dic₇₃	C₂⁴	1	2	yes	—
195	C₂×Dic₇₃	C₂⁴	1	2	yes	—
196	D₂₉₂	—	2	4	no	—
197	D₂₉₂	—	2	4	no	—
198	D₂₉₂	—	2	4	no	—
199	D₂₉₂	—	2	2	no	—
200	D₂₉₂	—	4	2	no	—
201	D₂₉₂	—	4	4	no	—
202	C₄×D₇₃	—	2	2	no	—
203	C₄×D₇₃	—	2	2	no	—
204	C₄×D₇₃	—	2	2	no	—
205	C₄×D₇₃	—	2	4	no	—
206	C₄×D₇₃	—	4	4	no	—
207	Dic₁₄₆	—	2	2	no	—
208	C₂²×C₇₃	—	2	4	no	—
209	C₂²×C₇₃	—	2	2	no	—
210	C₂²×C₇₃	—	2	2	no	—
211	C₂²×C₇₃	—	2	4	no	—
212	C₂²×C₇₃	—	2	4	no	—
213	C₂²×C₇₃	—	2	2	no	—
214	C₂²×C₇₃	C₂⁵	1	1	yes	characteristic
215	C₂×D₇₃	—	2	1	no	—
216	C₂×D₇₃	—	2	1	no	—
217	C₂×D₇₃	—	2	2	no	—
218	C₂×D₇₃	—	2	4	no	—
219	C₂×D₇₃	—	2	2	no	—
220	C₂×D₇₃	—	2	4	no	—
221	C₂×D₇₃	—	2	2	no	—
222	C₂×D₇₃	—	2	4	no	—
223	C₂×D₇₃	—	8	8	no	—
224	C₂×D₇₃	—	8	8	no	—
225	C₂×D₇₃	H(5,𝔽₂)	1	2	yes	—
226	C₄×C₇₃	—	2	1	no	—
227	C₄×C₇₃	—	2	2	no	—
228	C₄×C₇₃	—	2	2	no	—
229	C₄×C₇₃	—	2	2	no	—
230	C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
231	C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
232	Dic₇₃	—	2	2	no	—
233	Dic₇₃	—	2	2	no	—
234	Dic₇₃	—	2	1	no	—
235	Dic₇₃	—	2	1	no	—
236	Dic₇₃	—	2	1	no	—
237	Dic₇₃	—	2	2	no	—
238	C₂×C₇₃	—	4	2	no	—
239	C₂×C₇₃	—	4	4	no	—
240	C₂×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
241	C₂×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
242	C₂×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
243	D₇₃	—	2	2	no	—
244	D₇₃	—	4	2	no	—
245	D₇₃	—	4	4	no	—
246	#3543	—	73	1	no	maximal, Sylow
247	C₇₃	#3543	1	1	yes	characteristic, complemented, Sylow
248	#560	—	73	4	no	—
249	#559	—	73	1	no	—
250	#550	—	73	1	no	—
251	#550	D₇₃	1	1	yes	characteristic, complemented
252	#546	—	73	2	no	—
253	#546	—	73	2	no	—
254	D₄²	—	73	2	no	—
255	D₄²	—	73	2	no	—
256	D₄²	—	73	1	no	—
257	#540	—	73	2	no	—
258	#540	—	73	2	no	—
259	#535	—	73	2	no	—
260	#535	—	73	2	no	—
261	#534	—	73	4	no	—
262	C₂×#127	—	73	1	no	—
263	#529	—	73	1	no	—
264	#529	—	73	1	no	—
265	C₂×#41	—	73	2	no	—
266	C₂×#41	C₂×D₇₃	1	2	yes	complemented
267	C₂²×D₄	—	73	2	no	—
268	C₂²×D₄	—	73	2	no	—
269	C₂²×D₄	—	73	2	no	—
270	C₂²×D₄	—	73	4	no	—
271	C₂²×D₄	—	73	2	no	—
272	C₂²×D₄	—	73	2	no	—
273	#127	—	73	2	no	—
274	#127	—	73	2	no	—
275	#127	—	73	2	no	—
276	#127	—	73	2	no	—
277	#127	—	73	1	no	—
278	#127	C₂×D₇₃	1	1	yes	characteristic, complemented
279	#127	C₂×D₇₃	1	2	yes	complemented
280	#126	—	73	2	no	—
281	#126	—	73	2	no	—
282	#125	—	73	1	no	—
283	#125	—	73	1	no	—
284	#124	—	73	1	no	—
285	#124	—	73	2	no	—
286	#124	—	73	1	no	—
287	#124	—	73	2	no	—
288	#123	—	73	4	no	—
289	#123	—	73	2	no	—
290	#123	—	73	4	no	—
291	#123	—	73	2	no	—
292	#123	—	73	4	no	—
293	#123	—	73	4	no	—
294	C₂²⋊Q₈	—	73	1	no	—
295	C₂²⋊Q₈	—	73	1	no	—
296	#121	—	73	1	no	—
297	#121	—	73	4	no	—
298	#121	—	73	4	no	—
299	#121	—	73	4	no	—
300	#121	—	73	2	no	—
301	#121	—	73	4	no	—
302	#121	—	73	4	no	—
303	#121	—	73	4	no	—
304	#121	—	73	2	no	—
305	#121	—	73	1	no	—
306	#121	—	73	2	no	—
307	#121	—	73	4	no	—
308	#121	C₂×D₇₃	1	4	yes	complemented
309	#121	C₂×D₇₃	1	2	yes	complemented
310	#120	—	73	4	no	—
311	#120	—	73	4	no	—
312	#120	—	73	4	no	—
313	#120	—	73	4	no	—
314	#120	—	73	4	no	—
315	#120	—	73	4	no	—
316	C₄×Q₈	—	73	1	no	—
317	C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
318	C₄×D₄	—	73	2	no	—
319	C₄×D₄	—	73	2	no	—
320	C₄×D₄	—	73	2	no	—
321	C₄×D₄	—	73	2	no	—
322	C₄×D₄	—	73	1	no	—
323	C₄×D₄	—	73	2	no	—
324	C₄×D₄	C₂×D₇₃	1	1	yes	characteristic, complemented
325	C₄×D₄	C₂×D₇₃	1	2	yes	complemented
326	#117	—	73	2	no	—
327	#117	—	73	2	no	—
328	C₂×C₂²⋊C₄	—	73	4	no	—
329	C₂×C₄²	—	73	1	no	—
330	C₂⁴	—	73	4	no	—
331	C₂⁴	—	73	4	no	—
332	#41	—	4	4	no	—
333	#41	—	292	4	no	—
334	C₂×Q₈	—	73	1	no	—
335	C₂×Q₈	C₂²×D₇₃	1	1	yes	characteristic
336	C₂×D₄	—	292	4	no	—
337	C₂×D₄	—	292	8	no	—
338	C₂×D₄	—	292	4	no	—
339	C₂×D₄	—	292	4	no	—
340	C₂×D₄	—	292	4	no	—
341	C₂×D₄	—	292	4	no	—
342	C₂×D₄	—	73	4	no	—
343	C₂×D₄	—	73	4	no	—
344	C₂×D₄	—	73	4	no	—
345	C₂×D₄	—	73	4	no	—
346	C₂×D₄	—	73	4	no	—
347	C₂×D₄	—	73	4	no	—
348	C₂×D₄	—	73	2	no	—
349	C₂×D₄	—	73	4	no	—
350	C₂×D₄	—	73	2	no	—
351	C₂×D₄	—	73	2	no	—
352	C₂×D₄	—	73	2	no	—
353	C₂×D₄	—	73	1	no	—
354	C₂×D₄	—	73	2	no	—
355	C₂×D₄	C₂²×D₇₃	1	2	yes	—
356	C₂×D₄	C₂²×D₇₃	1	1	yes	characteristic
357	C₂×D₄	C₂²×D₇₃	1	2	yes	—
358	C₂×D₄	C₂²×D₇₃	1	4	yes	—
359	C₂×D₄	C₂²×D₇₃	1	4	yes	—
360	C₂×D₄	C₂²×D₇₃	1	2	yes	—
361	C₂²×C₄	—	73	4	no	—
362	C₂²×C₄	—	73	4	no	—
363	C₂²×C₄	—	73	1	no	—
364	C₂²×C₄	—	73	1	no	—
365	C₂²×C₄	—	73	1	no	—
366	C₂²×C₄	—	73	2	no	—
367	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
368	C₂²×C₄	C₂²×D₇₃	1	4	yes	—
369	C₄⋊C₄	—	73	2	no	—
370	C₄⋊C₄	—	73	2	no	—
371	C₄⋊C₄	—	73	2	no	—
372	C₄⋊C₄	—	73	2	no	—
373	C₄⋊C₄	—	73	2	no	—
374	C₄⋊C₄	—	73	2	no	—
375	C₄⋊C₄	—	73	1	no	—
376	C₄⋊C₄	—	73	1	no	—
377	C₄⋊C₄	—	73	2	no	—
378	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
379	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
380	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
381	C₂²⋊C₄	—	73	2	no	—
382	C₂²⋊C₄	—	73	2	no	—
383	C₂²⋊C₄	—	73	2	no	—
384	C₂²⋊C₄	—	73	4	no	—
385	C₂²⋊C₄	—	73	2	no	—
386	C₂²⋊C₄	—	73	2	no	—
387	C₂²⋊C₄	—	73	4	no	—
388	C₂²⋊C₄	—	73	4	no	—
389	C₂²⋊C₄	—	73	2	no	—
390	C₂²⋊C₄	—	73	2	no	—
391	C₂²⋊C₄	—	73	2	no	—
392	C₂²⋊C₄	—	73	2	no	—
393	C₂²⋊C₄	—	73	4	no	—
394	C₂²⋊C₄	—	73	4	no	—
395	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
396	C₂²⋊C₄	C₂²×D₇₃	1	4	yes	—
397	C₄²	—	73	1	no	—
398	C₄²	—	73	1	no	—
399	C₄²	—	73	1	no	—
400	C₄²	—	73	2	no	—
401	C₄²	C₂²×D₇₃	1	1	yes	characteristic
402	C₄²	C₂²×D₇₃	1	2	yes	—
403	C₂³	—	292	4	no	—
404	C₂³	—	292	4	no	—
405	C₂³	—	292	4	no	—
406	C₂³	—	292	4	no	—
407	C₂³	—	292	4	no	—
408	C₂³	—	73	1	no	—
409	C₂³	—	73	4	no	—
410	C₂³	—	73	2	no	—
411	C₂³	—	146	8	no	—
412	C₂³	C₂³×D₇₃	1	2	yes	—
413	C₂³	C₂³×D₇₃	1	4	yes	—
414	Q₈	—	2	2	no	—
415	Q₈	—	146	2	no	—
416	D₄	—	2	4	no	—
417	D₄	—	2	2	no	—
418	D₄	—	2	4	no	—
419	D₄	—	4	4	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	4	no	—
422	D₄	—	292	2	no	—
423	D₄	—	292	4	no	—
424	D₄	—	292	4	no	—
425	D₄	—	292	4	no	—
426	D₄	—	292	4	no	—
427	D₄	—	292	4	no	—
428	D₄	—	292	4	no	—
429	D₄	—	292	4	no	—
430	D₄	—	146	4	no	—
431	D₄	—	146	4	no	—
432	D₄	—	146	2	no	—
433	D₄	—	146	4	no	—
434	D₄	—	146	4	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	292	4	no	—
438	C₂×C₄	—	292	4	no	—
439	C₂×C₄	—	73	1	no	—
440	C₂×C₄	—	73	1	no	—
441	C₂×C₄	—	73	1	no	—
442	C₂×C₄	—	73	2	no	—
443	C₂×C₄	—	73	2	no	—
444	C₂×C₄	—	73	2	no	—
445	C₂×C₄	—	146	2	no	—
446	C₂×C₄	—	146	2	no	—
447	C₂×C₄	—	146	2	no	—
448	C₂×C₄	—	146	4	no	—
449	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
450	C₂×C₄	C₂³×D₇₃	1	2	yes	—
451	C₂×C₄	C₂³×D₇₃	1	2	yes	—
452	C₂×C₄	C₂³×D₇₃	1	2	yes	—
453	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
454	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
455	C₂²	—	2	4	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	4	no	—
459	C₂²	—	2	4	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	584	8	no	—
462	C₂²	—	584	8	no	—
463	C₂²	—	73	2	no	—
464	C₂²	—	146	4	no	—
465	C₂²	—	146	2	no	—
466	C₂²	—	146	2	no	—
467	C₂²	—	146	4	no	—
468	C₂²	—	146	2	no	—
469	C₂²	—	146	4	no	—
470	C₂²	—	146	1	no	—
471	C₂²	—	146	1	no	—
472	C₂²	C₂⁴×D₇₃	1	1	yes	characteristic
473	C₄	—	2	2	no	—
474	C₄	—	2	1	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	146	2	no	—
478	C₄	—	146	1	no	—
479	C₄	—	146	1	no	—
480	C₄	—	146	2	no	—
481	C₄	—	146	2	no	—
482	C₄	—	146	1	no	—
483	C₄	#14556636	1	2	yes	—
484	C₄	#14556637	1	2	yes	—
485	C₂	—	4	2	no	—
486	C₂	—	4	4	no	—
487	C₂	—	292	2	no	—
488	C₂	—	292	4	no	—
489	C₂	—	146	2	no	—
490	C₂	H(5,𝔽₂)×D₇₃	1	1	yes	characteristic
491	C₂	C₂×#14556636	1	1	yes	characteristic
492	C₂	C₂×#14556637	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₃
commutator, socle	C₂²×C₇₃	C₂⁵
Fitting	#550×C₇₃	C₂
hypercenter	#550	D₇₃
hypocenter	C₇₃	#3543
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #550

Complements

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

N	H ≅ G/N	type
1. #17989325	C₂	semidirect
2. #17989322	C₂	semidirect
3. #17989257	C₂	semidirect
4. #17989232	C₂	semidirect
5. #17989225	C₂	semidirect
6. D₄×D₂₉₂	C₂	semidirect
7. #17989222	C₂	semidirect
8. #17989221	C₂	semidirect
9. #17989190	C₂	semidirect
10. #17989188	C₂	semidirect
11. #17989151	C₂	semidirect
12. #17989150	C₂	semidirect
13. #17989145	C₂	semidirect
14. #127×D₇₃	C₂	semidirect
15. #17989124	C₂	semidirect
16. #17989119	C₂	semidirect
17. #550×C₇₃	C₂	semidirect
18. C₂×#11924027	C₂²	semidirect
19. C₂²×D₂₉₂	C₂²	semidirect
20. C₂×D₄×D₇₃	C₂²	semidirect
21. C₂×D₄×D₇₃	C₂²	semidirect
22. C₂×D₄×D₇₃	C₂²	semidirect
23. C₂×D₄×D₇₃	C₂²	semidirect
24. C₂×D₄×D₇₃	C₂²	semidirect
26. #14556587	C₂²	semidirect
27. #14556587	C₂²	semidirect
28. #14556587	C₂²	semidirect
29. #14556587	C₂²	semidirect
30. #14556586	C₂²	semidirect
31. #14556584	C₂²	semidirect
32. #14556582	C₂²	semidirect
33. #14556582	C₂²	semidirect
34. #14556580	C₂²	semidirect
35. #14556580	C₂²	semidirect
36. #14556579	C₂²	semidirect
37. #14556578	C₂²	semidirect
38. #14556576	C₂²	semidirect
39. #14556576	C₂²	semidirect
40. #14556575	C₂²	semidirect
41. #14556574	C₂²	semidirect
42. #14556573	C₂²	semidirect
43. #14556573	C₂²	semidirect
44. #14556571	C₂²	semidirect
45. #14556567	C₂²	semidirect
47. #14556566	C₂²	semidirect
48. #14556565	C₂²	semidirect
49. #14556565	C₂²	semidirect
50. #14556565	C₂²	semidirect
51. #14556564	C₂²	semidirect
52. #14556563	C₂²	semidirect
53. #14556563	C₂²	semidirect
54. #14556563	C₂²	semidirect
56. #14556562	C₂²	semidirect
57. #14556562	C₂²	semidirect
58. #14556561	C₂²	semidirect
59. #14556561	C₂²	semidirect
60. #14556559	C₂²	semidirect
61. #14556559	C₂²	semidirect
62. #14556559	C₂²	semidirect
63. #14556559	C₂²	semidirect
64. C₄×Dic₁₄₆	C₂²	semidirect
65. C₄×D₂₉₂	C₂²	semidirect
66. C₄×D₂₉₂	C₂²	semidirect
67. C₄×D₂₉₂	C₂²	semidirect
68. D₄×Dic₇₃	C₂²	semidirect
69. #14556553	C₂²	semidirect
70. C₄×C₂²⋊D₇₃	C₂²	semidirect
71. #14556550	C₂²	semidirect
72. #14556548	C₂²	semidirect
73. C₂×#11924005	C₂²	semidirect
74. C₄²×D₇₃	C₂²	semidirect
75. C₂×#41×C₇₃	C₂²	semidirect
76. #127×C₇₃	C₂²	semidirect
77. #127×C₇₃	C₂²	semidirect
78. #121×C₇₃	C₂²	semidirect
79. #121×C₇₃	C₂²	semidirect
80. C₄×Q₈×C₇₃	C₂²	semidirect
81. C₄×D₄×C₇₃	C₂²	semidirect
82. C₄×D₄×C₇₃	C₂²	semidirect
247. C₇₃	#3543	semidirect
251. #550	D₇₃	semidirect
266. C₂×#41	C₂×D₇₃	semidirect
278. #127	C₂×D₇₃	semidirect
279. #127	C₂×D₇₃	semidirect
308. #121	C₂×D₇₃	semidirect
309. #121	C₂×D₇₃	semidirect
317. C₄×Q₈	C₂×D₇₃	semidirect
324. C₄×D₄	C₂×D₇₃	semidirect
325. C₄×D₄	C₂×D₇₃	semidirect