Subgroups — #22624566

Order 9344.

930 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989339	C₂	1	2	yes	maximal, complemented
2	#17989332	C₂	1	2	yes	maximal, complemented
3	#17989314	C₂	1	1	yes	maximal, characteristic, complemented
4	#17989307	C₂	1	2	yes	maximal, complemented
5	#17989305	C₂	1	1	yes	maximal, characteristic, complemented
6	#17989301	C₂	1	1	yes	maximal, characteristic, complemented
7	#17989296	C₂	1	1	yes	maximal, characteristic, complemented
8	#17989289	C₂	1	1	yes	maximal, characteristic, complemented
9	#17989277	C₂	1	1	yes	maximal, characteristic, complemented
10	#17989274	C₂	1	2	yes	maximal, complemented
11	#17989272	C₂	1	1	yes	maximal, characteristic, complemented
12	#17989218	C₂	1	1	yes	maximal, characteristic, complemented
13	#17989215	C₂	1	1	yes	maximal, characteristic, complemented
14	#17989205	C₂	1	2	yes	maximal, complemented
15	#17989204	C₂	1	1	yes	maximal, characteristic, complemented
16	#17989204	C₂	1	1	yes	maximal, characteristic, complemented
17	#17989204	C₂	1	2	yes	maximal, complemented
18	#17989194	C₂	1	2	yes	maximal, complemented
19	#17989179	C₂	1	2	yes	maximal, complemented
20	#17989143	C₂	1	1	yes	maximal, characteristic, complemented
21	#17989119	C₂	1	1	yes	maximal, characteristic, complemented
22	#17989119	C₂	1	1	yes	maximal, characteristic, complemented
23	#553×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
24	#14556591	C₂²	1	2	yes	—
25	#14556590	C₂²	1	1	yes	characteristic
26	#14556590	C₂²	1	1	yes	characteristic
27	#14556590	C₂²	1	2	yes	—
28	#14556590	C₂²	1	2	yes	—
29	#14556590	C₂²	1	1	yes	characteristic
30	#14556590	C₂²	1	1	yes	characteristic
31	#14556586	C₂²	1	2	yes	—
32	#14556585	C₂²	1	2	yes	—
33	#14556584	C₂²	1	2	yes	—
34	#14556584	C₂²	1	2	yes	—
35	#14556584	C₂²	1	2	yes	—
36	#14556584	C₂²	1	2	yes	—
37	#14556584	C₂²	1	2	yes	—
38	#14556584	C₂²	1	2	yes	—
39	#14556584	C₂²	1	1	yes	characteristic
40	#14556584	C₂²	1	1	yes	characteristic
41	#14556583	C₂²	1	1	yes	characteristic
42	#14556583	C₂²	1	2	yes	—
43	#14556582	C₂²	1	1	yes	characteristic
44	#14556582	C₂²	1	1	yes	characteristic
45	#14556582	C₂²	1	1	yes	characteristic
46	#14556582	C₂²	1	2	yes	—
47	#14556582	C₂²	1	1	yes	characteristic
48	#14556581	C₂²	1	2	yes	—
49	#14556581	C₂²	1	2	yes	—
50	#14556581	C₂²	1	2	yes	—
51	#14556581	C₂²	1	2	yes	—
52	#14556578	C₂²	1	2	yes	—
53	#14556578	C₂²	1	1	yes	characteristic
54	#14556578	C₂²	1	1	yes	characteristic
55	#14556578	C₂²	1	2	yes	—
56	#14556578	C₂²	1	2	yes	—
57	#14556577	C₂²	1	2	yes	—
58	#14556577	C₂²	1	2	yes	—
59	#14556575	C₂²	1	2	yes	—
60	#14556574	C₂²	1	2	yes	—
61	#14556573	C₂²	1	1	yes	characteristic
62	#14556573	C₂²	1	1	yes	characteristic
63	#14556573	C₂²	1	2	yes	—
64	#14556572	C₂²	1	2	yes	—
65	#14556572	C₂²	1	2	yes	—
66	#14556572	C₂²	1	2	yes	—
67	#14556571	C₂²	1	1	yes	characteristic
68	#14556571	C₂²	1	1	yes	characteristic
69	#14556570	C₂²	1	2	yes	—
70	#14556570	C₂²	1	1	yes	characteristic
71	#14556570	C₂²	1	1	yes	characteristic
72	#14556570	C₂²	1	2	yes	—
73	#14556570	C₂²	1	2	yes	—
74	#14556569	C₂²	1	2	yes	—
75	#14556569	C₂²	1	2	yes	—
76	#14556568	C₂²	1	2	yes	—
77	#14556568	C₂²	1	2	yes	—
78	#14556568	C₂²	1	2	yes	—
79	#14556568	C₂²	1	2	yes	—
80	#14556568	C₂²	1	2	yes	—
81	#14556568	C₂²	1	2	yes	—
82	#14556563	C₂²	1	2	yes	—
83	#14556563	C₂²	1	2	yes	—
84	#14556562	C₂²	1	1	yes	characteristic
85	#14556562	C₂²	1	1	yes	characteristic
86	C₄×Dic₁₄₆	C₂²	1	2	yes	—
87	C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic
88	C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic
89	#14556556	C₂²	1	2	yes	—
90	#14556556	C₂²	1	2	yes	—
91	#14556556	C₂²	1	1	yes	characteristic
92	#14556556	C₂²	1	1	yes	characteristic
93	#14556556	C₂²	1	2	yes	—
94	D₄×Dic₇₃	C₂²	1	2	yes	—
95	D₄×Dic₇₃	C₂²	1	1	yes	characteristic
96	D₄×Dic₇₃	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊D₇₃	C₂²	1	2	yes	—
98	C₄×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic
100	#14556550	C₂²	1	1	yes	characteristic
101	#14556550	C₂²	1	1	yes	characteristic
102	#14556550	C₂²	1	2	yes	—
103	#14556550	C₂²	1	1	yes	characteristic
104	#14556550	C₂²	1	2	yes	—
105	#14556549	C₂²	1	1	yes	characteristic
106	#14556549	C₂²	1	1	yes	characteristic
107	#14556547	C₂²	1	2	yes	—
108	#14556547	C₂²	1	2	yes	—
109	C₂×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
110	C₂×#11924007	C₂²	1	2	yes	—
111	C₄²×D₇₃	C₂²	1	1	yes	characteristic
112	#126×C₇₃	C₂²	1	2	yes	—
113	#125×C₇₃	C₂²	1	1	yes	characteristic
114	#123×C₇₃	C₂²	1	2	yes	—
115	#121×C₇₃	C₂²	1	1	yes	characteristic
116	#121×C₇₃	C₂²	1	1	yes	characteristic
117	#121×C₇₃	C₂²	1	2	yes	—
118	C₄×D₄×C₇₃	C₂²	1	2	yes	—
119	C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
120	C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
121	#117×C₇₃	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
123	C₂×Dic₁₄₆	C₂³	1	1	yes	characteristic
124	C₂×Dic₁₄₆	C₂³	1	2	yes	—
125	C₂×Dic₁₄₆	C₂³	1	2	yes	—
126	C₂×Dic₁₄₆	C₂³	1	2	yes	—
127	C₂×Dic₁₄₆	C₂³	1	1	yes	characteristic
128	C₂×Dic₁₄₆	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
130	C₂×C₂²⋊D₇₃	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
132	C₂²×Dic₇₃	C₂³	1	2	yes	—
133	C₂²×Dic₇₃	C₂³	1	2	yes	—
134	C₂²×Dic₇₃	C₂³	1	2	yes	—
135	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
136	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
138	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
139	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
140	C₄⋊Dic₇₃	C₂³	1	2	yes	—
141	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
142	C₄⋊Dic₇₃	C₂³	1	2	yes	—
143	C₄⋊Dic₇₃	C₂³	1	2	yes	—
144	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
145	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
146	C₄⋊Dic₇₃	C₂³	1	2	yes	—
147	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
149	C₄⋊Dic₇₃	C₂³	1	2	yes	—
150	C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
151	#11924007	C₂³	1	1	yes	characteristic
152	#11924007	C₂³	1	2	yes	—
153	#11924007	C₂³	1	2	yes	—
154	#11924007	C₂³	1	2	yes	—
155	#11924007	C₂³	1	1	yes	characteristic
156	#11924007	C₂³	1	2	yes	—
157	#11924007	C₂³	1	2	yes	—
158	#11924007	C₂³	1	1	yes	characteristic
159	#11924007	C₂³	1	2	yes	—
160	#11924007	C₂³	1	1	yes	characteristic
161	#11924007	C₂³	1	2	yes	—
162	#11924007	C₂³	1	2	yes	—
163	#11924007	C₂³	1	2	yes	—
164	#11924007	C₂³	1	2	yes	—
165	#11924007	C₂³	1	2	yes	—
166	#11924007	C₂³	1	2	yes	—
167	#11924007	C₂³	1	2	yes	—
168	#11924007	C₂³	1	2	yes	—
169	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
170	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
171	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
179	C₂²⋊Dic₇₃	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
181	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
182	C₂²⋊Dic₇₃	C₂³	1	2	yes	—
183	#11924005	C₂³	1	2	yes	—
184	#11924005	C₂³	1	2	yes	—
185	#11924005	C₂³	1	2	yes	—
186	#11924005	C₂³	1	1	yes	characteristic
187	#11924005	C₂³	1	1	yes	characteristic
188	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
189	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
190	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
191	C₄×Dic₇₃	C₂³	1	2	yes	—
192	C₄×Dic₇₃	C₂³	1	2	yes	—
193	C₄×Dic₇₃	C₂³	1	2	yes	—
194	C₄×Dic₇₃	C₂³	1	2	yes	—
195	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
196	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
197	C₄×Dic₇₃	C₂³	1	2	yes	—
198	C₄×Dic₇₃	C₂³	1	2	yes	—
199	C₂×D₄×C₇₃	C₂³	1	1	yes	characteristic
200	C₂×D₄×C₇₃	C₂³	1	1	yes	characteristic
201	C₂×D₄×C₇₃	C₂³	1	2	yes	—
202	C₂×D₄×C₇₃	C₂³	1	2	yes	—
203	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
204	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
205	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
206	C₂²×C₄×C₇₃	C₂³	1	2	yes	—
207	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
208	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
209	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
210	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
212	C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
214	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
215	C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
216	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
219	C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
220	C₄²×C₇₃	C₂³	1	2	yes	—
221	C₄²×C₇₃	C₂³	1	1	yes	characteristic
222	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
223	C₂³×C₇₃	C₂⁴	1	2	yes	—
224	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
225	C₂²×D₇₃	C₂⁴	1	1	yes	characteristic
226	D₄×C₇₃	—	2	2	no	—
227	D₄×C₇₃	—	4	2	no	—
228	D₄×C₇₃	—	4	1	no	—
229	D₄×C₇₃	—	4	2	no	—
230	C₂×C₄×C₇₃	—	2	2	no	—
231	C₂×C₄×C₇₃	—	2	2	no	—
232	C₂×C₄×C₇₃	—	4	2	no	—
233	C₂×C₄×C₇₃	—	4	2	no	—
234	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
235	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
236	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
239	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₇₃	C₂⁴	1	2	yes	—
241	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
242	C₂²⋊D₇₃	—	4	1	no	—
243	C₂²⋊D₇₃	—	4	2	no	—
244	C₂²⋊D₇₃	—	4	1	no	—
245	C₂×Dic₇₃	—	4	2	no	—
246	C₂×Dic₇₃	—	4	2	no	—
247	C₂×Dic₇₃	—	4	2	no	—
248	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₇₃	C₂⁴	1	2	yes	—
250	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₇₃	C₂⁴	1	2	yes	—
253	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₇₃	C₂⁴	1	2	yes	—
256	C₂×Dic₇₃	C₂⁴	1	2	yes	—
257	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
259	C₄×D₇₃	—	2	2	no	—
260	C₄×D₇₃	—	4	1	no	—
261	C₄×D₇₃	—	4	1	no	—
262	Dic₁₄₆	—	2	2	no	—
263	Dic₁₄₆	—	4	1	no	—
264	Dic₁₄₆	—	4	2	no	—
265	Dic₁₄₆	—	4	2	no	—
266	Dic₁₄₆	—	4	2	no	—
267	Dic₁₄₆	—	4	2	no	—
268	C₂²×C₇₃	—	2	1	no	—
269	C₂²×C₇₃	—	2	1	no	—
270	C₂²×C₇₃	—	2	2	no	—
271	C₂²×C₇₃	—	2	1	no	—
272	C₂²×C₇₃	—	2	2	no	—
273	C₂²×C₇₃	—	2	2	no	—
274	C₂²×C₇₃	—	2	1	no	—
275	C₂²×C₇₃	—	2	1	no	—
276	C₂²×C₇₃	—	2	1	no	—
277	C₂²×C₇₃	C₂⁵	1	1	yes	characteristic
278	C₂×D₇₃	—	2	1	no	—
279	C₂×D₇₃	—	2	1	no	—
280	C₂×D₇₃	—	2	1	no	—
281	C₄×C₇₃	—	2	1	no	—
282	C₄×C₇₃	—	2	1	no	—
283	C₄×C₇₃	—	2	2	no	—
284	C₄×C₇₃	—	2	1	no	—
285	C₄×C₇₃	—	2	2	no	—
286	C₄×C₇₃	—	2	2	no	—
287	C₄×C₇₃	—	2	1	no	—
288	C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
289	Dic₇₃	—	2	2	no	—
290	Dic₇₃	—	2	1	no	—
291	Dic₇₃	—	2	1	no	—
292	Dic₇₃	—	2	1	no	—
293	Dic₇₃	—	2	1	no	—
294	Dic₇₃	—	2	2	no	—
295	Dic₇₃	—	2	1	no	—
296	Dic₇₃	—	2	1	no	—
297	Dic₇₃	—	2	2	no	—
298	Dic₇₃	—	2	2	no	—
299	Dic₇₃	—	2	1	no	—
300	C₂×C₇₃	—	4	1	no	—
301	C₂×C₇₃	—	4	1	no	—
302	C₂×C₇₃	—	4	2	no	—
303	C₂×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
304	C₂×C₇₃	#585	1	1	yes	characteristic
305	C₂×C₇₃	#585	1	1	yes	characteristic
306	D₇₃	—	4	1	no	—
307	#3565	—	73	1	no	maximal, Sylow
308	C₇₃	#3565	1	1	yes	characteristic, complemented, Sylow
309	#563	—	73	2	no	—
310	#562	—	73	2	no	—
311	#557	—	73	1	no	—
312	#556	—	73	2	no	—
313	#556	—	73	1	no	—
314	#555	—	73	1	no	—
315	#554	—	73	1	no	—
316	#553	—	73	1	no	—
317	#553	D₇₃	1	1	yes	characteristic, complemented
318	#552	—	73	2	no	—
319	#552	—	73	1	no	—
320	#552	—	73	1	no	—
321	#544	—	73	1	no	—
322	#544	—	73	1	no	—
323	#542	—	73	2	no	—
324	#542	—	73	1	no	—
325	#542	—	73	1	no	—
326	#542	—	73	2	no	—
327	#541	—	73	2	no	—
328	#539	—	73	2	no	—
329	#533	—	73	1	no	—
330	#529	—	73	1	no	—
331	#529	—	73	1	no	—
332	C₄⋊Q₈	—	73	1	no	—
333	C₄⋊Q₈	—	73	1	no	—
334	C₄⋊Q₈	—	73	2	no	—
335	C₄⋊Q₈	—	73	2	no	—
336	C₄⋊Q₈	—	73	1	no	—
337	C₄⋊Q₈	—	73	1	no	—
338	C₄⋊Q₈	—	73	2	no	—
339	#126	—	73	2	no	—
340	#126	—	73	2	no	—
341	#126	—	73	1	no	—
342	#126	—	73	1	no	—
343	#126	—	73	2	no	—
344	#126	—	73	2	no	—
345	#126	—	73	2	no	—
346	#126	—	73	2	no	—
347	#126	—	73	2	no	—
348	#126	—	73	2	no	—
349	#126	C₂×D₇₃	1	2	yes	—
350	#125	—	73	1	no	—
351	#125	—	73	1	no	—
352	#125	—	73	2	no	—
353	#125	—	73	2	no	—
354	#125	—	73	2	no	—
355	#125	—	73	2	no	—
356	#125	—	73	1	no	—
357	#125	—	73	2	no	—
358	#125	—	73	1	no	—
359	#125	—	73	1	no	—
360	#125	—	73	2	no	—
361	#125	C₂×D₇₃	1	1	yes	characteristic
362	#124	—	73	1	no	—
363	#124	—	73	1	no	—
364	#124	—	73	2	no	—
365	#124	—	73	2	no	—
366	#124	—	73	2	no	—
367	#124	—	73	2	no	—
368	#124	—	73	2	no	—
369	#123	—	73	2	no	—
370	#123	—	73	2	no	—
371	#123	—	73	2	no	—
372	#123	—	73	2	no	—
373	#123	—	73	1	no	—
374	#123	—	73	1	no	—
375	#123	—	73	2	no	—
376	#123	—	73	2	no	—
377	#123	C₂×D₇₃	1	2	yes	—
378	C₂²⋊Q₈	—	73	2	no	—
379	C₂²⋊Q₈	—	73	1	no	—
380	C₂²⋊Q₈	—	73	1	no	—
381	C₂²⋊Q₈	—	73	2	no	—
382	C₂²⋊Q₈	—	73	2	no	—
383	C₂²⋊Q₈	—	73	1	no	—
384	C₂²⋊Q₈	—	73	1	no	—
385	C₂²⋊Q₈	—	73	2	no	—
386	C₂²⋊Q₈	—	73	2	no	—
387	C₂²⋊Q₈	—	73	2	no	—
388	C₂²⋊Q₈	—	73	2	no	—
389	C₂²⋊Q₈	—	73	2	no	—
390	C₂²⋊Q₈	—	73	2	no	—
391	C₂²⋊Q₈	—	73	2	no	—
392	C₂²⋊Q₈	—	73	2	no	—
393	#121	—	73	1	no	—
394	#121	—	73	1	no	—
395	#121	—	73	2	no	—
396	#121	—	73	2	no	—
397	#121	C₂×D₇₃	1	1	yes	characteristic
398	#121	C₂×D₇₃	1	1	yes	characteristic
399	#121	C₂×D₇₃	1	2	yes	—
400	C₄×Q₈	—	73	2	no	—
401	C₄×Q₈	—	73	2	no	—
402	C₄×Q₈	—	73	1	no	—
403	C₄×Q₈	—	73	2	no	—
404	C₄×Q₈	—	73	1	no	—
405	C₄×Q₈	—	73	1	no	—
406	C₄×Q₈	—	73	1	no	—
407	C₄×Q₈	—	73	2	no	—
408	C₄×D₄	—	73	2	no	—
409	C₄×D₄	—	73	1	no	—
410	C₄×D₄	—	73	1	no	—
411	C₄×D₄	—	73	2	no	—
412	C₄×D₄	—	73	1	no	—
413	C₄×D₄	—	73	1	no	—
414	C₄×D₄	C₂×D₇₃	1	1	yes	characteristic
415	C₄×D₄	C₂×D₇₃	1	1	yes	characteristic
416	C₄×D₄	C₂×D₇₃	1	2	yes	—
417	#117	—	73	1	no	—
418	#117	—	73	1	no	—
419	#117	—	73	2	no	—
420	#117	—	73	2	no	—
421	#117	—	73	1	no	—
422	#117	—	73	1	no	—
423	#117	—	73	1	no	—
424	#117	—	73	2	no	—
425	#117	—	73	2	no	—
426	#117	C₂×D₇₃	1	1	yes	characteristic
427	C₂×C₄⋊C₄	—	73	2	no	—
428	C₂×C₄⋊C₄	—	73	1	no	—
429	C₂×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
430	C₂×C₄²	—	73	1	no	—
431	C₂×Q₈	—	73	1	no	—
432	C₂×Q₈	—	73	2	no	—
433	C₂×Q₈	—	73	2	no	—
434	C₂×Q₈	—	73	2	no	—
435	C₂×Q₈	—	73	2	no	—
436	C₂×Q₈	—	73	1	no	—
437	C₂×D₄	—	73	1	no	—
438	C₂×D₄	—	73	2	no	—
439	C₂×D₄	—	73	1	no	—
440	C₂×D₄	C₂²×D₇₃	1	1	yes	characteristic
441	C₂×D₄	C₂²×D₇₃	1	2	yes	—
442	C₂×D₄	C₂²×D₇₃	1	1	yes	characteristic
443	C₂×D₄	C₂²×D₇₃	1	2	yes	—
444	C₂²×C₄	—	73	2	no	—
445	C₂²×C₄	—	73	2	no	—
446	C₂²×C₄	—	73	2	no	—
447	C₂²×C₄	—	73	1	no	—
448	C₂²×C₄	—	73	1	no	—
449	C₂²×C₄	—	73	1	no	—
450	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
451	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
452	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
453	C₂²×C₄	C₂²×D₇₃	1	2	yes	—
454	C₄⋊C₄	—	73	1	no	—
455	C₄⋊C₄	—	73	2	no	—
456	C₄⋊C₄	—	73	2	no	—
457	C₄⋊C₄	—	73	2	no	—
458	C₄⋊C₄	—	73	1	no	—
459	C₄⋊C₄	—	73	2	no	—
460	C₄⋊C₄	—	73	2	no	—
461	C₄⋊C₄	—	73	1	no	—
462	C₄⋊C₄	—	73	2	no	—
463	C₄⋊C₄	—	73	1	no	—
464	C₄⋊C₄	—	73	2	no	—
465	C₄⋊C₄	—	73	2	no	—
466	C₄⋊C₄	—	73	2	no	—
467	C₄⋊C₄	—	73	2	no	—
468	C₄⋊C₄	—	73	2	no	—
469	C₄⋊C₄	—	73	2	no	—
470	C₄⋊C₄	—	73	2	no	—
471	C₄⋊C₄	—	73	2	no	—
472	C₄⋊C₄	—	73	1	no	—
473	C₄⋊C₄	—	73	1	no	—
474	C₄⋊C₄	—	73	2	no	—
475	C₄⋊C₄	—	73	1	no	—
476	C₄⋊C₄	—	73	2	no	—
477	C₄⋊C₄	—	73	1	no	—
478	C₄⋊C₄	—	73	2	no	—
479	C₄⋊C₄	—	73	1	no	—
480	C₄⋊C₄	—	73	2	no	—
481	C₄⋊C₄	—	73	1	no	—
482	C₄⋊C₄	—	73	1	no	—
483	C₄⋊C₄	—	73	2	no	—
484	C₄⋊C₄	—	73	1	no	—
485	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
486	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
487	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
488	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
490	C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
491	C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
492	C₂²⋊C₄	—	73	2	no	—
493	C₂²⋊C₄	—	73	1	no	—
494	C₂²⋊C₄	—	73	1	no	—
495	C₂²⋊C₄	—	73	2	no	—
496	C₂²⋊C₄	—	73	1	no	—
497	C₂²⋊C₄	—	73	1	no	—
498	C₂²⋊C₄	—	73	1	no	—
499	C₂²⋊C₄	—	73	2	no	—
500	C₂²⋊C₄	—	73	2	no	—
501	C₂²⋊C₄	—	73	2	no	—
502	C₂²⋊C₄	—	73	1	no	—
503	C₂²⋊C₄	—	73	2	no	—
504	C₂²⋊C₄	—	73	2	no	—
505	C₂²⋊C₄	—	73	2	no	—
506	C₂²⋊C₄	—	73	2	no	—
507	C₂²⋊C₄	—	73	2	no	—
508	C₂²⋊C₄	—	73	1	no	—
509	C₂²⋊C₄	—	73	2	no	—
510	C₂²⋊C₄	—	73	1	no	—
511	C₂²⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
512	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
513	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
514	C₂²⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
515	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
516	C₂²⋊C₄	C₂²×D₇₃	1	2	yes	—
517	C₄²	—	73	1	no	—
518	C₄²	—	73	1	no	—
519	C₄²	—	73	1	no	—
520	C₄²	—	73	2	no	—
521	C₄²	—	73	2	no	—
522	C₄²	—	73	2	no	—
523	C₄²	—	73	2	no	—
524	C₄²	—	73	1	no	—
525	C₄²	—	73	1	no	—
526	C₄²	—	73	2	no	—
527	C₄²	—	73	2	no	—
528	C₄²	C₂²×D₇₃	1	1	yes	characteristic
529	C₄²	C₂²×D₇₃	1	2	yes	—
530	C₂³	—	73	1	no	—
531	C₂³	C₂³×D₇₃	1	1	yes	characteristic
532	C₂³	C₂³×D₇₃	1	1	yes	characteristic
533	C₂³	C₂³×D₇₃	1	2	yes	—
534	Q₈	—	292	2	no	—
535	Q₈	—	292	2	no	—
536	Q₈	—	292	1	no	—
537	Q₈	—	292	2	no	—
538	Q₈	—	292	2	no	—
539	Q₈	—	146	2	no	—
540	D₄	—	2	2	no	—
541	D₄	—	4	2	no	—
542	D₄	—	4	1	no	—
543	D₄	—	4	2	no	—
544	D₄	—	292	1	no	—
545	D₄	—	292	1	no	—
546	D₄	—	292	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	292	1	no	—
552	C₂×C₄	—	292	1	no	—
553	C₂×C₄	—	292	2	no	—
554	C₂×C₄	—	292	2	no	—
555	C₂×C₄	—	292	2	no	—
556	C₂×C₄	—	73	1	no	—
557	C₂×C₄	—	73	2	no	—
558	C₂×C₄	—	73	1	no	—
559	C₂×C₄	—	73	1	no	—
560	C₂×C₄	—	73	1	no	—
561	C₂×C₄	—	73	2	no	—
562	C₂×C₄	—	73	1	no	—
563	C₂×C₄	—	73	2	no	—
564	C₂×C₄	—	73	2	no	—
565	C₂×C₄	—	73	1	no	—
566	C₂×C₄	—	73	1	no	—
567	C₂×C₄	—	146	2	no	—
568	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
569	C₂×C₄	C₂³×D₇₃	1	2	yes	—
570	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₇₃	1	2	yes	—
572	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
573	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
574	C₂×C₄	C₂³×D₇₃	1	2	yes	—
575	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	2	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	146	1	no	—
586	C₂²	—	146	1	no	—
587	C₂²	—	146	1	no	—
588	C₂²	C₂⁴×D₇₃	1	1	yes	characteristic
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	2	no	—
596	C₄	—	146	1	no	—
597	C₄	—	146	2	no	—
598	C₄	—	146	1	no	—
599	C₄	—	146	1	no	—
600	C₄	—	146	2	no	—
601	C₄	—	146	1	no	—
602	C₄	—	146	1	no	—
603	C₄	—	146	2	no	—
604	C₄	—	146	2	no	—
605	C₄	—	146	1	no	—
606	C₄	—	146	1	no	—
607	C₄	#14556638	1	2	yes	—
608	C₂	—	4	1	no	—
609	C₂	—	4	1	no	—
610	C₂	—	4	2	no	—
611	C₂	—	292	1	no	—
612	C₂	C₂×#14556638	1	1	yes	characteristic
613	C₂	#17989422	1	1	yes	characteristic
614	C₂	#17989423	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₃
commutator, socle	C₂²×C₇₃	C₂⁵
Fitting	#553×C₇₃	C₂
hypercenter	#553	D₇₃
hypocenter	C₇₃	#3565
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #17989339	C₂	semidirect
2. #17989332	C₂	semidirect
3. #17989314	C₂	semidirect
4. #17989307	C₂	semidirect
5. #17989305	C₂	semidirect
6. #17989301	C₂	semidirect
7. #17989296	C₂	semidirect
8. #17989289	C₂	semidirect
9. #17989277	C₂	semidirect
10. #17989274	C₂	semidirect
11. #17989272	C₂	semidirect
12. #17989218	C₂	semidirect
13. #17989215	C₂	semidirect
14. #17989205	C₂	semidirect
15. #17989204	C₂	semidirect
16. #17989204	C₂	semidirect
17. #17989204	C₂	semidirect
18. #17989194	C₂	semidirect
19. #17989179	C₂	semidirect
20. #17989143	C₂	semidirect
21. #17989119	C₂	semidirect
22. #17989119	C₂	semidirect
23. #553×C₇₃	C₂	semidirect
308. C₇₃	#3565	semidirect
317. #553	D₇₃	semidirect