Subgroups — C₁₇×#61443 #16919187

Order 4352.

1848 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3480	C₂	1	2	yes	maximal, complemented
2	C₁₇×#3403	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3390	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#3371	C₂	1	2	yes	maximal, complemented
5	C₁₇×#3355	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#3350	C₂	1	2	yes	maximal, complemented
7	C₁₇×#3326	C₂	1	2	yes	maximal, complemented
8	C₁₇×#3313	C₂	1	2	yes	maximal, complemented
9	C₁₇×#3309	C₂	1	2	yes	maximal, complemented
10	C₁₇×#3277	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#3271	C₂	1	2	yes	maximal, complemented
12	C₁₇×#3171	C₂	1	2	yes	maximal, complemented
13	C₁₇×#3168	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#3108	C₂	1	2	yes	maximal, complemented
15	C₁₇×#3106	C₂	1	2	yes	maximal, complemented
16	C₁₇×#3102	C₂	1	2	yes	maximal, complemented
17	C₁₇×#2965	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₁₇×#137	C₂	1	2	yes	maximal, complemented
19	C₄×C₁₇×#135	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₇×#137	C₂²	1	2	yes	—
21	C₂×C₁₇×#135	C₂²	1	1	yes	characteristic
22	C₁₇×#559	—	2	2	no	—
23	C₁₇×#559	C₂²	1	2	yes	—
24	C₁₇×#557	C₂²	1	2	yes	—
25	C₁₇×#556	—	2	2	no	—
26	C₁₇×#556	C₂²	1	2	yes	—
27	C₁₇×#553	—	2	2	no	—
28	C₁₇×#553	—	2	2	no	—
29	C₁₇×#553	C₂²	1	2	yes	—
30	C₁₇×#553	C₂²	1	2	yes	—
31	C₁₇×#550	C₂²	1	2	yes	—
32	C₁₇×#548	C₂²	1	2	yes	—
33	C₁₇×#548	C₂²	1	2	yes	—
34	C₁₇×#532	—	2	2	no	—
35	C₁₇×#532	C₂²	1	2	yes	—
36	C₁₇×#529	—	2	2	no	—
37	C₁₇×#529	—	2	2	no	—
38	C₁₇×#529	C₂²	1	2	yes	—
39	C₁₇×#529	C₂²	1	2	yes	—
40	C₄×#41×C₁₇	—	2	2	no	—
41	C₄×#41×C₁₇	C₂²	1	2	yes	—
42	C₄×#41×C₁₇	C₂²	1	2	yes	—
43	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₁₇	C₂²	1	2	yes	—
45	C₁₇×#501	C₂²	1	2	yes	—
46	C₁₇×#499	C₂²	1	1	yes	characteristic
47	C₁₇×#496	C₂²	1	2	yes	—
48	C₁₇×#495	C₂²	1	1	yes	characteristic
49	C₁₇×#490	C₂²	1	2	yes	—
50	C₁₇×#489	C₂²	1	2	yes	—
51	C₁₇×#488	C₂²	1	2	yes	—
52	C₁₇×#485	C₂²	1	2	yes	—
53	C₁₇×#483	C₂²	1	2	yes	—
54	C₁₇×#482	C₂²	1	2	yes	—
55	C₁₇×#482	C₂²	1	2	yes	—
56	C₁₇×#482	C₂²	1	2	yes	—
57	C₁₇×#480	C₂²	1	2	yes	—
58	C₁₇×#479	C₂²	1	2	yes	—
59	C₁₇×#479	C₂²	1	2	yes	—
60	C₁₇×#479	C₂²	1	2	yes	—
61	C₁₇×#478	C₂²	1	2	yes	—
62	C₁₇×#477	C₂²	1	2	yes	—
63	C₁₇×#476	C₂²	1	2	yes	—
64	C₁₇×#469	C₂²	1	2	yes	—
65	C₁₇×#469	C₂²	1	2	yes	—
66	C₁₇×#468	C₂²	1	2	yes	—
67	C₁₇×#468	C₂²	1	2	yes	—
68	C₁₇×#467	C₂²	1	1	yes	characteristic
69	C₁₇×#466	C₂²	1	1	yes	characteristic
70	C₁₇×#465	C₂²	1	2	yes	—
71	C₁₇×#464	C₂²	1	2	yes	—
72	C₁₇×#464	C₂²	1	2	yes	—
73	C₁₇×#464	C₂²	1	2	yes	—
74	C₁₇×#463	C₂²	1	2	yes	—
75	C₁₇×#460	C₂²	1	2	yes	—
76	C₁₇×#459	C₂²	1	2	yes	—
77	C₁₇×#452	C₂²	1	2	yes	—
78	C₁₇×#451	C₂²	1	2	yes	—
79	C₁₇×#449	C₂²	1	2	yes	—
80	C₁₇×#449	C₂²	1	2	yes	—
81	C₁₇×#449	C₂²	1	2	yes	—
82	C₁₇×#448	C₂²	1	2	yes	—
83	C₁₇×#446	C₂²	1	1	yes	characteristic
84	C₁₇×#446	C₂²	1	1	yes	characteristic
85	C₁₇×#441	C₂²	1	2	yes	—
86	C₁₇×#441	C₂²	1	2	yes	—
87	C₁₇×#440	C₂²	1	2	yes	—
88	C₁₇×#440	C₂²	1	2	yes	—
89	C₄×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic
90	C₄×Q₁₆×C₁₇	C₂²	1	2	yes	—
91	C₄×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic
92	C₄×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic
93	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	—
94	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	—
95	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	—
96	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	—
97	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	—
98	C₄×D₈×C₁₇	C₂²	1	1	yes	characteristic
99	C₄×D₈×C₁₇	C₂²	1	2	yes	—
100	C₄×D₈×C₁₇	C₂²	1	1	yes	characteristic
101	C₄×D₈×C₁₇	C₂²	1	1	yes	characteristic
102	C₁₇×#436	C₂²	1	1	yes	characteristic
103	C₁₇×#436	C₂²	1	1	yes	characteristic
104	C₁₇×#435	C₂²	1	2	yes	—
105	C₁₇×#435	C₂²	1	2	yes	—
106	C₁₇×#431	C₂²	1	1	yes	characteristic
107	C₁₇×#431	C₂²	1	2	yes	—
108	C₁₇×#428	C₂²	1	2	yes	—
109	C₁₇×#427	C₂²	1	1	yes	characteristic
110	C₁₇×#419	C₂²	1	2	yes	—
111	C₁₇×#417	C₂²	1	2	yes	—
112	C₁₇×#416	C₂²	1	2	yes	—
113	C₄×M₁₆×C₁₇	C₂²	1	2	yes	—
114	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
115	C₂×#41×C₁₇	—	2	2	no	—
116	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
117	C₂×#41×C₁₇	C₂³	1	2	yes	—
118	C₂×#41×C₁₇	C₂³	1	2	yes	—
119	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
120	C₁₇×#137	—	2	8	no	—
121	C₁₇×#135	—	2	4	no	—
122	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
123	C₂×Q₁₆×C₁₇	C₂³	1	1	yes	characteristic
124	C₂×Q₁₆×C₁₇	C₂³	1	1	yes	characteristic
125	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
129	C₂×D₈×C₁₇	C₂³	1	1	yes	characteristic
130	C₂×D₈×C₁₇	C₂³	1	1	yes	characteristic
131	C₂×D₈×C₁₇	C₂³	1	2	yes	—
132	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
133	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
134	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
135	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
136	C₁₇×C₄⋊Q₈	—	2	2	no	—
137	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₁₇×#127	—	2	2	no	—
139	C₁₇×#127	C₂³	1	2	yes	—
140	C₁₇×#126	—	2	2	no	—
141	C₁₇×#126	—	2	2	no	—
142	C₁₇×#126	—	2	2	no	—
143	C₁₇×#126	—	2	2	no	—
144	C₁₇×#126	—	2	2	no	—
145	C₁₇×#126	—	2	2	no	—
146	C₁₇×#125	—	2	2	no	—
147	C₁₇×#125	—	2	2	no	—
148	C₁₇×#125	C₂³	1	2	yes	—
149	C₁₇×#125	C₂³	1	2	yes	—
150	C₁₇×#124	—	2	2	no	—
151	C₁₇×#124	—	2	2	no	—
152	C₁₇×#124	—	2	2	no	—
153	C₁₇×#124	—	2	2	no	—
154	C₁₇×#124	—	2	2	no	—
155	C₁₇×#124	C₂³	1	2	yes	—
156	C₁₇×#124	C₂³	1	2	yes	—
157	C₁₇×#123	—	2	2	no	—
158	C₁₇×#123	—	2	2	no	—
159	C₁₇×#123	—	2	2	no	—
160	C₁₇×#123	—	2	2	no	—
161	C₁₇×#123	—	2	2	no	—
162	C₁₇×#123	—	2	2	no	—
163	C₁₇×C₂²⋊Q₈	—	2	2	no	—
164	C₁₇×C₂²⋊Q₈	—	2	2	no	—
165	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
166	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
167	C₁₇×#121	—	2	2	no	—
168	C₁₇×#121	—	2	2	no	—
169	C₁₇×#121	—	2	2	no	—
170	C₁₇×#121	—	2	2	no	—
171	C₁₇×#121	—	2	2	no	—
172	C₁₇×#121	—	2	2	no	—
173	C₁₇×#121	—	2	2	no	—
174	C₁₇×#121	C₂³	1	2	yes	—
175	C₁₇×#121	C₂³	1	2	yes	—
176	C₁₇×#121	C₂³	1	2	yes	—
177	C₁₇×#121	C₂³	1	2	yes	—
178	C₄×Q₈×C₁₇	—	2	2	no	—
179	C₄×Q₈×C₁₇	—	2	2	no	—
180	C₄×Q₈×C₁₇	—	2	2	no	—
181	C₄×Q₈×C₁₇	—	2	2	no	—
182	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
183	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
184	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
185	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
186	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
187	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
188	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
189	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₁₇	—	2	2	no	—
191	C₄×D₄×C₁₇	—	2	2	no	—
192	C₄×D₄×C₁₇	—	2	2	no	—
193	C₄×D₄×C₁₇	—	2	2	no	—
194	C₄×D₄×C₁₇	—	2	2	no	—
195	C₄×D₄×C₁₇	—	2	2	no	—
196	C₄×D₄×C₁₇	—	2	2	no	—
197	C₄×D₄×C₁₇	—	2	2	no	—
198	C₄×D₄×C₁₇	—	2	2	no	—
199	C₄×D₄×C₁₇	—	2	2	no	—
200	C₄×D₄×C₁₇	—	2	2	no	—
201	C₄×D₄×C₁₇	—	2	2	no	—
202	C₄×D₄×C₁₇	—	2	2	no	—
203	C₄×D₄×C₁₇	D₄	1	1	yes	characteristic
204	C₄×D₄×C₁₇	D₄	1	2	yes	—
205	C₄×D₄×C₁₇	C₂³	1	2	yes	—
206	C₄×D₄×C₁₇	C₂³	1	2	yes	—
207	C₄×D₄×C₁₇	C₂³	1	2	yes	—
208	C₄×D₄×C₁₇	C₂³	1	2	yes	—
209	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
210	C₄×D₄×C₁₇	C₂³	1	2	yes	—
211	C₁₇×#117	—	2	2	no	—
212	C₁₇×#117	—	2	2	no	—
213	C₁₇×#117	—	2	2	no	—
214	C₁₇×#117	—	2	2	no	—
215	C₁₇×#117	D₄	1	2	yes	—
216	C₁₇×#117	D₄	1	1	yes	characteristic
217	C₁₇×#117	C₂³	1	2	yes	—
218	C₁₇×#117	C₂³	1	2	yes	—
219	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
220	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
221	C₂×C₄²×C₁₇	—	2	2	no	—
222	C₂×C₄²×C₁₇	—	2	2	no	—
223	C₂×C₄²×C₁₇	—	2	2	no	—
224	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
225	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
226	C₁₇×#107	C₂³	1	1	yes	characteristic
227	C₁₇×#107	C₂³	1	1	yes	characteristic
228	C₁₇×#107	C₂³	1	1	yes	characteristic
229	C₁₇×#107	C₂³	1	2	yes	—
230	C₁₇×#107	C₂³	1	1	yes	characteristic
231	C₁₇×#107	C₂³	1	2	yes	—
232	C₁₇×#106	C₂³	1	2	yes	—
233	C₁₇×#106	C₂³	1	2	yes	—
234	C₁₇×#106	C₂³	1	2	yes	—
235	C₁₇×#106	C₂³	1	2	yes	—
236	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
237	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
238	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
239	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
240	C₁₇×#103	C₂³	1	2	yes	—
241	C₁₇×#103	C₂³	1	2	yes	—
242	C₁₇×#103	C₂³	1	2	yes	—
243	C₁₇×#103	C₂³	1	2	yes	—
244	C₁₇×#103	C₂³	1	2	yes	—
245	C₁₇×#103	C₂³	1	2	yes	—
246	C₁₇×#103	C₂³	1	2	yes	—
247	C₁₇×#103	C₂³	1	2	yes	—
248	C₁₇×#102	C₂³	1	2	yes	—
249	C₁₇×#102	C₂³	1	2	yes	—
250	C₁₇×#102	C₂³	1	2	yes	—
251	C₁₇×#102	C₂³	1	2	yes	—
252	C₁₇×#102	C₂³	1	2	yes	—
253	C₁₇×#102	C₂³	1	2	yes	—
254	C₁₇×#102	C₂³	1	2	yes	—
255	C₁₇×#102	C₂³	1	2	yes	—
256	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₁₇×#97	C₂³	1	2	yes	—
260	C₁₇×#97	C₂³	1	2	yes	—
261	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
264	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₁₇	C₂³	1	2	yes	—
266	#41×C₁₇	—	2	4	no	—
267	#41×C₁₇	—	2	4	no	—
268	#41×C₁₇	—	4	2	no	—
269	#41×C₁₇	—	4	2	no	—
270	#41×C₁₇	—	4	2	no	—
271	#41×C₁₇	—	4	8	no	—
272	C₂×Q₈×C₁₇	—	2	2	no	—
273	C₂×Q₈×C₁₇	—	2	2	no	—
274	C₂×Q₈×C₁₇	—	2	4	no	—
275	C₂×Q₈×C₁₇	—	4	2	no	—
276	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
277	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
278	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
279	C₂×D₄×C₁₇	—	2	2	no	—
280	C₂×D₄×C₁₇	—	2	2	no	—
281	C₂×D₄×C₁₇	—	2	2	no	—
282	C₂×D₄×C₁₇	—	2	2	no	—
283	C₂×D₄×C₁₇	—	2	2	no	—
284	C₂×D₄×C₁₇	—	2	2	no	—
285	C₂×D₄×C₁₇	—	2	2	no	—
286	C₂×D₄×C₁₇	—	2	2	no	—
287	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
288	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
289	C₂×D₄×C₁₇	C₂⁴	1	2	yes	—
290	C₂×D₄×C₁₇	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₁₇	—	2	2	no	—
292	C₂²×C₄×C₁₇	—	2	2	no	—
293	C₂²×C₄×C₁₇	—	2	2	no	—
294	C₂²×C₄×C₁₇	—	2	2	no	—
295	C₂²×C₄×C₁₇	—	2	2	no	—
296	C₂²×C₄×C₁₇	—	2	2	no	—
297	C₂²×C₄×C₁₇	—	2	2	no	—
298	C₂²×C₄×C₁₇	—	2	2	no	—
299	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
300	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
303	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
305	Q₁₆×C₁₇	—	2	4	no	—
306	Q₁₆×C₁₇	—	4	1	no	—
307	Q₁₆×C₁₇	#41	1	4	yes	complemented
308	SD₁₆×C₁₇	—	2	4	no	—
309	SD₁₆×C₁₇	—	2	4	no	—
310	SD₁₆×C₁₇	—	2	4	no	—
311	SD₁₆×C₁₇	—	4	2	no	—
312	D₈×C₁₇	—	2	2	no	—
313	D₈×C₁₇	—	4	1	no	—
314	D₈×C₁₇	—	4	2	no	—
315	M₁₆×C₁₇	—	2	4	no	—
316	M₁₆×C₁₇	—	4	2	no	—
317	C₂×C₈×C₁₇	—	2	2	no	—
318	C₂×C₈×C₁₇	—	4	1	no	—
319	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
320	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
321	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
322	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
323	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
324	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
325	C₄⋊C₄×C₁₇	—	2	2	no	—
326	C₄⋊C₄×C₁₇	—	2	2	no	—
327	C₄⋊C₄×C₁₇	—	2	2	no	—
328	C₄⋊C₄×C₁₇	—	2	2	no	—
329	C₄⋊C₄×C₁₇	—	2	2	no	—
330	C₄⋊C₄×C₁₇	—	2	2	no	—
331	C₄⋊C₄×C₁₇	—	2	2	no	—
332	C₄⋊C₄×C₁₇	—	2	2	no	—
333	C₄⋊C₄×C₁₇	—	2	2	no	—
334	C₄⋊C₄×C₁₇	—	2	2	no	—
335	C₄⋊C₄×C₁₇	—	2	2	no	—
336	C₄⋊C₄×C₁₇	—	2	2	no	—
337	C₄⋊C₄×C₁₇	—	2	2	no	—
338	C₄⋊C₄×C₁₇	—	2	2	no	—
339	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
340	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
341	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
342	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
343	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
344	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
345	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
346	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
347	C₂²⋊C₄×C₁₇	—	2	2	no	—
348	C₂²⋊C₄×C₁₇	—	2	2	no	—
349	C₂²⋊C₄×C₁₇	—	2	2	no	—
350	C₂²⋊C₄×C₁₇	—	2	2	no	—
351	C₂²⋊C₄×C₁₇	—	2	2	no	—
352	C₂²⋊C₄×C₁₇	—	2	2	no	—
353	C₂²⋊C₄×C₁₇	—	2	2	no	—
354	C₂²⋊C₄×C₁₇	—	2	2	no	—
355	C₂²⋊C₄×C₁₇	—	2	2	no	—
356	C₂²⋊C₄×C₁₇	—	2	2	no	—
357	C₂²⋊C₄×C₁₇	—	2	2	no	—
358	C₂²⋊C₄×C₁₇	—	2	2	no	—
359	C₂²⋊C₄×C₁₇	—	2	2	no	—
360	C₂²⋊C₄×C₁₇	—	2	2	no	—
361	C₂²⋊C₄×C₁₇	—	2	2	no	—
362	C₂²⋊C₄×C₁₇	—	2	2	no	—
363	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
364	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
365	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
366	C₄²×C₁₇	—	2	2	no	—
367	C₄²×C₁₇	—	2	2	no	—
368	C₄²×C₁₇	—	2	2	no	—
369	C₄²×C₁₇	—	2	2	no	—
370	C₄²×C₁₇	—	2	2	no	—
371	C₄²×C₁₇	—	2	2	no	—
372	C₄²×C₁₇	—	2	2	no	—
373	C₄²×C₁₇	—	2	2	no	—
374	C₄²×C₁₇	C₂×D₄	1	2	yes	—
375	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
376	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
377	C₄²×C₁₇	C₂×D₄	1	2	yes	—
378	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
379	C₄²×C₁₇	C₂⁴	1	2	yes	—
380	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
381	#61443	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
382	C₂³×C₁₇	—	2	2	no	—
383	C₂³×C₁₇	—	2	2	no	—
384	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
385	C₂³×C₁₇	C₂²×D₄	1	2	yes	—
386	Q₈×C₁₇	—	2	2	no	—
387	Q₈×C₁₇	—	2	2	no	—
388	Q₈×C₁₇	—	2	2	no	—
389	Q₈×C₁₇	—	4	1	no	—
390	Q₈×C₁₇	—	4	4	no	—
391	Q₈×C₁₇	—	4	4	no	—
392	Q₈×C₁₇	C₂×#41	1	4	yes	—
393	D₄×C₁₇	—	2	2	no	—
394	D₄×C₁₇	—	2	2	no	—
395	D₄×C₁₇	—	2	2	no	—
396	D₄×C₁₇	—	2	2	no	—
397	D₄×C₁₇	—	4	2	no	—
398	D₄×C₁₇	—	4	1	no	—
399	D₄×C₁₇	—	4	4	no	—
400	D₄×C₁₇	—	4	4	no	—
401	D₄×C₁₇	—	4	4	no	—
402	D₄×C₁₇	—	4	4	no	—
403	D₄×C₁₇	—	4	4	no	—
404	D₄×C₁₇	—	8	2	no	—
405	D₄×C₁₇	—	8	2	no	—
406	D₄×C₁₇	—	8	2	no	—
407	C₂×C₄×C₁₇	—	2	2	no	—
408	C₂×C₄×C₁₇	—	2	2	no	—
409	C₂×C₄×C₁₇	—	2	4	no	—
410	C₂×C₄×C₁₇	—	2	1	no	—
411	C₂×C₄×C₁₇	—	2	2	no	—
412	C₂×C₄×C₁₇	—	2	1	no	—
413	C₂×C₄×C₁₇	—	2	2	no	—
414	C₂×C₄×C₁₇	—	2	2	no	—
415	C₂×C₄×C₁₇	—	2	2	no	—
416	C₂×C₄×C₁₇	—	2	2	no	—
417	C₂×C₄×C₁₇	—	2	2	no	—
418	C₂×C₄×C₁₇	—	2	2	no	—
419	C₂×C₄×C₁₇	—	4	1	no	—
420	C₂×C₄×C₁₇	—	4	2	no	—
421	C₂×C₄×C₁₇	—	4	4	no	—
422	C₂×C₄×C₁₇	—	4	4	no	—
423	C₂×C₄×C₁₇	—	4	4	no	—
424	C₂×C₄×C₁₇	—	4	4	no	—
425	C₂×C₄×C₁₇	—	4	4	no	—
426	C₂×C₄×C₁₇	—	8	2	no	—
427	C₂×C₄×C₁₇	—	8	2	no	—
428	C₂×C₄×C₁₇	—	8	2	no	—
429	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
433	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
434	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
436	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
438	C₈×C₁₇	—	2	1	no	—
439	C₈×C₁₇	—	2	2	no	—
440	C₈×C₁₇	—	2	1	no	—
441	C₈×C₁₇	—	2	1	no	—
442	C₈×C₁₇	—	2	2	no	—
443	C₈×C₁₇	C₂×#41	1	2	yes	—
444	#3480	C₂×C₁₇	1	2	yes	complemented
445	#3403	C₂×C₁₇	1	1	yes	characteristic, complemented
446	#3390	C₂×C₁₇	1	1	yes	characteristic, complemented
447	#3371	C₂×C₁₇	1	2	yes	complemented
448	#3355	C₂×C₁₇	1	1	yes	characteristic, complemented
449	#3350	C₂×C₁₇	1	2	yes	complemented
450	#3326	C₂×C₁₇	1	2	yes	complemented
451	#3313	C₂×C₁₇	1	2	yes	complemented
452	#3309	C₂×C₁₇	1	2	yes	complemented
453	#3277	C₂×C₁₇	1	1	yes	characteristic, complemented
454	#3271	C₂×C₁₇	1	2	yes	complemented
455	#3171	C₂×C₁₇	1	2	yes	complemented
456	#3168	C₂×C₁₇	1	1	yes	characteristic, complemented
457	#3108	C₂×C₁₇	1	2	yes	complemented
458	#3106	C₂×C₁₇	1	2	yes	complemented
459	#3102	C₂×C₁₇	1	2	yes	complemented
460	#2965	C₂×C₁₇	1	1	yes	characteristic, complemented
461	C₄×#137	C₂×C₁₇	1	2	yes	complemented
462	C₄×#135	C₂×C₁₇	1	1	yes	characteristic, complemented
463	C₂²×C₁₇	—	2	2	no	—
464	C₂²×C₁₇	—	2	1	no	—
465	C₂²×C₁₇	—	2	2	no	—
466	C₂²×C₁₇	—	2	1	no	—
467	C₂²×C₁₇	—	2	2	no	—
468	C₂²×C₁₇	—	2	1	no	—
469	C₂²×C₁₇	—	4	2	no	—
470	C₂²×C₁₇	—	4	2	no	—
471	C₂²×C₁₇	—	4	2	no	—
472	C₂²×C₁₇	—	4	2	no	—
473	C₂²×C₁₇	—	4	2	no	—
474	C₂²×C₁₇	—	4	2	no	—
475	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
476	C₄×C₁₇	—	2	1	no	—
477	C₄×C₁₇	—	2	1	no	—
478	C₄×C₁₇	—	2	2	no	—
479	C₄×C₁₇	—	2	1	no	—
480	C₄×C₁₇	—	2	2	no	—
481	C₄×C₁₇	—	2	4	no	—
482	C₄×C₁₇	—	2	2	no	—
483	C₄×C₁₇	—	2	1	no	—
484	C₄×C₁₇	—	4	2	no	—
485	C₄×C₁₇	—	4	2	no	—
486	C₄×C₁₇	—	4	2	no	—
487	C₄×C₁₇	—	4	2	no	—
488	C₄×C₁₇	—	4	2	no	—
489	C₄×C₁₇	#575	1	2	yes	—
490	C₄×C₁₇	C₂²×#41	1	1	yes	characteristic
491	C₄×C₁₇	#585	1	1	yes	characteristic
492	C₂×#137	C₂²×C₁₇	1	2	yes	—
493	C₂×#135	C₂²×C₁₇	1	1	yes	characteristic
494	#559	—	2	2	no	—
495	#559	C₂²×C₁₇	1	2	yes	—
496	#557	C₂²×C₁₇	1	2	yes	—
497	#556	—	2	2	no	—
498	#556	C₂²×C₁₇	1	2	yes	—
499	#553	—	2	2	no	—
500	#553	—	2	2	no	—
501	#553	C₂²×C₁₇	1	2	yes	—
502	#553	C₂²×C₁₇	1	2	yes	—
503	#550	C₂²×C₁₇	1	2	yes	—
504	#548	C₂²×C₁₇	1	2	yes	—
505	#548	C₂²×C₁₇	1	2	yes	—
506	#532	—	2	2	no	—
507	#532	C₂²×C₁₇	1	2	yes	—
508	#529	—	2	2	no	—
509	#529	—	2	2	no	—
510	#529	C₂²×C₁₇	1	2	yes	—
511	#529	C₂²×C₁₇	1	2	yes	—
512	C₄×#41	—	2	2	no	—
513	C₄×#41	C₂²×C₁₇	1	2	yes	—
514	C₄×#41	C₂²×C₁₇	1	2	yes	—
515	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
516	C₂×C₄×Q₈	C₂²×C₁₇	1	2	yes	—
517	#501	C₂²×C₁₇	1	2	yes	—
518	#499	C₂²×C₁₇	1	1	yes	characteristic
519	#496	C₂²×C₁₇	1	2	yes	—
520	#495	C₂²×C₁₇	1	1	yes	characteristic
521	#490	C₂²×C₁₇	1	2	yes	—
522	#489	C₂²×C₁₇	1	2	yes	—
523	#488	C₂²×C₁₇	1	2	yes	—
524	#485	C₂²×C₁₇	1	2	yes	—
525	#483	C₂²×C₁₇	1	2	yes	—
526	#482	C₂²×C₁₇	1	2	yes	—
527	#482	C₂²×C₁₇	1	2	yes	—
528	#482	C₂²×C₁₇	1	2	yes	—
529	#480	C₂²×C₁₇	1	2	yes	—
530	#479	C₂²×C₁₇	1	2	yes	—
531	#479	C₂²×C₁₇	1	2	yes	—
532	#479	C₂²×C₁₇	1	2	yes	—
533	#478	C₂²×C₁₇	1	2	yes	—
534	#477	C₂²×C₁₇	1	2	yes	—
535	#476	C₂²×C₁₇	1	2	yes	—
536	#469	C₂²×C₁₇	1	2	yes	—
537	#469	C₂²×C₁₇	1	2	yes	—
538	#468	C₂²×C₁₇	1	2	yes	—
539	#468	C₂²×C₁₇	1	2	yes	—
540	#467	C₂²×C₁₇	1	1	yes	characteristic
541	#466	C₂²×C₁₇	1	1	yes	characteristic
542	#465	C₂²×C₁₇	1	2	yes	—
543	#464	C₂²×C₁₇	1	2	yes	—
544	#464	C₂²×C₁₇	1	2	yes	—
545	#464	C₂²×C₁₇	1	2	yes	—
546	#463	C₂²×C₁₇	1	2	yes	—
547	#460	C₂²×C₁₇	1	2	yes	—
548	#459	C₂²×C₁₇	1	2	yes	—
549	#452	C₂²×C₁₇	1	2	yes	—
550	#451	C₂²×C₁₇	1	2	yes	—
551	#449	C₂²×C₁₇	1	2	yes	—
552	#449	C₂²×C₁₇	1	2	yes	—
553	#449	C₂²×C₁₇	1	2	yes	—
554	#448	C₂²×C₁₇	1	2	yes	—
555	#446	C₂²×C₁₇	1	1	yes	characteristic
556	#446	C₂²×C₁₇	1	1	yes	characteristic
557	#441	C₂²×C₁₇	1	2	yes	—
558	#441	C₂²×C₁₇	1	2	yes	—
559	#440	C₂²×C₁₇	1	2	yes	—
560	#440	C₂²×C₁₇	1	2	yes	—
561	C₄×Q₁₆	C₂²×C₁₇	1	2	yes	—
562	C₄×Q₁₆	C₂²×C₁₇	1	1	yes	characteristic
563	C₄×Q₁₆	C₂²×C₁₇	1	1	yes	characteristic
564	C₄×Q₁₆	C₂²×C₁₇	1	1	yes	characteristic
565	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	—
566	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	—
567	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	—
568	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	—
569	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	—
570	C₄×D₈	C₂²×C₁₇	1	1	yes	characteristic
571	C₄×D₈	C₂²×C₁₇	1	2	yes	—
572	C₄×D₈	C₂²×C₁₇	1	1	yes	characteristic
573	C₄×D₈	C₂²×C₁₇	1	1	yes	characteristic
574	#436	C₂²×C₁₇	1	1	yes	characteristic
575	#436	C₂²×C₁₇	1	1	yes	characteristic
576	#435	C₂²×C₁₇	1	2	yes	—
577	#435	C₂²×C₁₇	1	2	yes	—
578	#431	C₂²×C₁₇	1	1	yes	characteristic
579	#431	C₂²×C₁₇	1	2	yes	—
580	#428	C₂²×C₁₇	1	2	yes	—
581	#427	C₂²×C₁₇	1	1	yes	characteristic
582	#419	C₂²×C₁₇	1	2	yes	—
583	#417	C₂²×C₁₇	1	2	yes	—
584	#416	C₂²×C₁₇	1	2	yes	—
585	C₄×M₁₆	C₂²×C₁₇	1	2	yes	—
586	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
587	C₂×C₁₇	—	4	2	no	—
588	C₂×C₁₇	—	4	1	no	—
589	C₂×C₁₇	—	8	2	no	—
590	C₂×C₁₇	—	8	2	no	—
591	C₂×C₁₇	D₄×#41	1	1	yes	characteristic
592	C₂×C₁₇	C₂×#575	1	1	yes	characteristic
593	C₂×C₁₇	#3584	1	1	yes	characteristic
594	C₂×#41	—	2	2	no	—
595	C₂×#41	D₄×C₁₇	1	1	yes	characteristic
596	C₂×#41	C₂³×C₁₇	1	2	yes	—
597	C₂×#41	C₂³×C₁₇	1	2	yes	—
598	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
599	#137	—	2	8	no	—
600	#135	—	2	4	no	—
601	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
602	C₂×Q₁₆	C₂³×C₁₇	1	1	yes	characteristic
603	C₂×Q₁₆	C₂³×C₁₇	1	1	yes	characteristic
604	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
605	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
606	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
607	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
608	C₂×D₈	C₂³×C₁₇	1	1	yes	characteristic
609	C₂×D₈	C₂³×C₁₇	1	1	yes	characteristic
610	C₂×D₈	C₂³×C₁₇	1	2	yes	—
611	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
612	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
613	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
614	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
615	C₄⋊Q₈	—	2	2	no	—
616	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
617	#127	—	2	2	no	—
618	#127	C₂³×C₁₇	1	2	yes	—
619	#126	—	2	2	no	—
620	#126	—	2	2	no	—
621	#126	—	2	2	no	—
622	#126	—	2	2	no	—
623	#126	—	2	2	no	—
624	#126	—	2	2	no	—
625	#125	—	2	2	no	—
626	#125	—	2	2	no	—
627	#125	C₂³×C₁₇	1	2	yes	—
628	#125	C₂³×C₁₇	1	2	yes	—
629	#124	—	2	2	no	—
630	#124	—	2	2	no	—
631	#124	—	2	2	no	—
632	#124	—	2	2	no	—
633	#124	—	2	2	no	—
634	#124	C₂³×C₁₇	1	2	yes	—
635	#124	C₂³×C₁₇	1	2	yes	—
636	#123	—	2	2	no	—
637	#123	—	2	2	no	—
638	#123	—	2	2	no	—
639	#123	—	2	2	no	—
640	#123	—	2	2	no	—
641	#123	—	2	2	no	—
642	C₂²⋊Q₈	—	2	2	no	—
643	C₂²⋊Q₈	—	2	2	no	—
644	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
645	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
646	#121	—	2	2	no	—
647	#121	—	2	2	no	—
648	#121	—	2	2	no	—
649	#121	—	2	2	no	—
650	#121	—	2	2	no	—
651	#121	—	2	2	no	—
652	#121	—	2	2	no	—
653	#121	C₂³×C₁₇	1	2	yes	—
654	#121	C₂³×C₁₇	1	2	yes	—
655	#121	C₂³×C₁₇	1	2	yes	—
656	#121	C₂³×C₁₇	1	2	yes	—
657	C₄×Q₈	—	2	2	no	—
658	C₄×Q₈	—	2	2	no	—
659	C₄×Q₈	—	2	2	no	—
660	C₄×Q₈	—	2	2	no	—
661	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
662	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
663	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
664	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
665	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
666	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
667	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
668	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	—	2	2	no	—
678	C₄×D₄	—	2	2	no	—
679	C₄×D₄	—	2	2	no	—
680	C₄×D₄	—	2	2	no	—
681	C₄×D₄	—	2	2	no	—
682	C₄×D₄	D₄×C₁₇	1	1	yes	characteristic
683	C₄×D₄	D₄×C₁₇	1	2	yes	—
684	C₄×D₄	C₂³×C₁₇	1	2	yes	—
685	C₄×D₄	C₂³×C₁₇	1	2	yes	—
686	C₄×D₄	C₂³×C₁₇	1	2	yes	—
687	C₄×D₄	C₂³×C₁₇	1	2	yes	—
688	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
689	C₄×D₄	C₂³×C₁₇	1	2	yes	—
690	#117	—	2	2	no	—
691	#117	—	2	2	no	—
692	#117	—	2	2	no	—
693	#117	—	2	2	no	—
694	#117	D₄×C₁₇	1	2	yes	—
695	#117	D₄×C₁₇	1	1	yes	characteristic
696	#117	C₂³×C₁₇	1	2	yes	—
697	#117	C₂³×C₁₇	1	2	yes	—
698	C₂×C₄⋊C₄	—	2	2	no	—
699	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
700	C₂×C₄²	—	2	2	no	—
701	C₂×C₄²	—	2	2	no	—
702	C₂×C₄²	—	2	2	no	—
703	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
704	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
705	#107	C₂³×C₁₇	1	1	yes	characteristic
706	#107	C₂³×C₁₇	1	1	yes	characteristic
707	#107	C₂³×C₁₇	1	2	yes	—
708	#107	C₂³×C₁₇	1	1	yes	characteristic
709	#107	C₂³×C₁₇	1	2	yes	—
710	#107	C₂³×C₁₇	1	1	yes	characteristic
711	#106	C₂³×C₁₇	1	2	yes	—
712	#106	C₂³×C₁₇	1	2	yes	—
713	#106	C₂³×C₁₇	1	2	yes	—
714	#106	C₂³×C₁₇	1	2	yes	—
715	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
716	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
717	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
718	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
719	#103	C₂³×C₁₇	1	2	yes	—
720	#103	C₂³×C₁₇	1	2	yes	—
721	#103	C₂³×C₁₇	1	2	yes	—
722	#103	C₂³×C₁₇	1	2	yes	—
723	#103	C₂³×C₁₇	1	2	yes	—
724	#103	C₂³×C₁₇	1	2	yes	—
725	#103	C₂³×C₁₇	1	2	yes	—
726	#103	C₂³×C₁₇	1	2	yes	—
727	#102	C₂³×C₁₇	1	2	yes	—
728	#102	C₂³×C₁₇	1	2	yes	—
729	#102	C₂³×C₁₇	1	2	yes	—
730	#102	C₂³×C₁₇	1	2	yes	—
731	#102	C₂³×C₁₇	1	2	yes	—
732	#102	C₂³×C₁₇	1	2	yes	—
733	#102	C₂³×C₁₇	1	2	yes	—
734	#102	C₂³×C₁₇	1	2	yes	—
735	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
736	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
737	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
738	#97	C₂³×C₁₇	1	2	yes	—
739	#97	C₂³×C₁₇	1	2	yes	—
740	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
741	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
742	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
743	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
744	C₄×C₈	C₂³×C₁₇	1	2	yes	—
745	C₁₇	#61443	1	1	yes	characteristic, direct product factor, Sylow
746	#41	—	2	4	no	—
747	#41	—	2	4	no	—
748	#41	—	4	2	no	—
749	#41	—	4	2	no	—
750	#41	—	4	2	no	—
751	#41	—	4	8	no	—
752	C₂×Q₈	—	2	2	no	—
753	C₂×Q₈	—	2	2	no	—
754	C₂×Q₈	—	2	4	no	—
755	C₂×Q₈	—	4	2	no	—
756	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
757	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
758	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
768	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
769	C₂×D₄	C₂⁴×C₁₇	1	2	yes	—
770	C₂×D₄	C₂⁴×C₁₇	1	2	yes	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
780	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
781	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
782	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
785	Q₁₆	—	2	4	no	—
786	Q₁₆	—	4	1	no	—
787	Q₁₆	#41×C₁₇	1	4	yes	complemented
788	SD₁₆	—	2	4	no	—
789	SD₁₆	—	2	4	no	—
790	SD₁₆	—	2	4	no	—
791	SD₁₆	—	4	2	no	—
792	D₈	—	2	2	no	—
793	D₈	—	4	1	no	—
794	D₈	—	4	2	no	—
795	M₁₆	—	2	4	no	—
796	M₁₆	—	4	2	no	—
797	C₂×C₈	—	2	2	no	—
798	C₂×C₈	—	4	1	no	—
799	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
800	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
801	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
802	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
803	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
804	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
820	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
821	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
822	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
823	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
824	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
825	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
826	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
844	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
845	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
846	C₄²	—	2	2	no	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	2	no	—
851	C₄²	—	2	2	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	2	no	—
854	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
855	C₄²	C₂×D₄×C₁₇	1	2	yes	—
856	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
857	C₄²	C₂×D₄×C₁₇	1	2	yes	—
858	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
859	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
860	C₄²	C₂⁴×C₁₇	1	2	yes	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	2	no	—
863	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
864	C₂³	C₂²×D₄×C₁₇	1	2	yes	—
865	Q₈	—	2	2	no	—
866	Q₈	—	2	2	no	—
867	Q₈	—	2	2	no	—
868	Q₈	—	4	1	no	—
869	Q₈	—	4	4	no	—
870	Q₈	—	4	4	no	—
871	Q₈	C₂×#41×C₁₇	1	4	yes	—
872	D₄	—	2	2	no	—
873	D₄	—	2	2	no	—
874	D₄	—	2	2	no	—
875	D₄	—	2	2	no	—
876	D₄	—	4	2	no	—
877	D₄	—	4	1	no	—
878	D₄	—	4	4	no	—
879	D₄	—	4	4	no	—
880	D₄	—	4	4	no	—
881	D₄	—	4	4	no	—
882	D₄	—	4	4	no	—
883	D₄	—	8	2	no	—
884	D₄	—	8	2	no	—
885	D₄	—	8	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	4	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	4	1	no	—
899	C₂×C₄	—	4	2	no	—
900	C₂×C₄	—	4	4	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	4	4	no	—
903	C₂×C₄	—	4	4	no	—
904	C₂×C₄	—	4	4	no	—
905	C₂×C₄	—	8	2	no	—
906	C₂×C₄	—	8	2	no	—
907	C₂×C₄	—	8	2	no	—
908	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
909	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
910	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
911	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
912	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
913	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
914	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
915	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
916	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
917	C₈	—	2	1	no	—
918	C₈	—	2	2	no	—
919	C₈	—	2	1	no	—
920	C₈	—	2	1	no	—
921	C₈	—	2	2	no	—
922	C₈	C₂×#41×C₁₇	1	2	yes	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	4	2	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
936	C₄	—	2	1	no	—
937	C₄	—	2	2	no	—
938	C₄	—	2	4	no	—
939	C₄	—	2	2	no	—
940	C₄	—	2	1	no	—
941	C₄	—	2	1	no	—
942	C₄	—	2	1	no	—
943	C₄	—	2	2	no	—
944	C₄	—	4	2	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	C₁₇×#575	1	2	yes	—
950	C₄	C₂²×#41×C₁₇	1	1	yes	characteristic
951	C₄	C₁₇×#585	1	1	yes	characteristic
952	C₂	—	4	2	no	—
953	C₂	—	4	1	no	—
954	C₂	—	8	2	no	—
955	C₂	—	8	2	no	—
956	C₂	D₄×#41×C₁₇	1	1	yes	characteristic
957	C₂	C₂×C₁₇×#575	1	1	yes	characteristic
958	C₂	C₁₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
socle	C₂²×C₁₇	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₄×#41×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3480	C₂	semidirect
2. C₁₇×#3403	C₂	semidirect
3. C₁₇×#3390	C₂	semidirect
4. C₁₇×#3371	C₂	semidirect
5. C₁₇×#3355	C₂	semidirect
6. C₁₇×#3350	C₂	semidirect
7. C₁₇×#3326	C₂	semidirect
8. C₁₇×#3313	C₂	semidirect
9. C₁₇×#3309	C₂	semidirect
10. C₁₇×#3277	C₂	semidirect
11. C₁₇×#3271	C₂	semidirect
12. C₁₇×#3171	C₂	semidirect
13. C₁₇×#3168	C₂	semidirect
14. C₁₇×#3108	C₂	semidirect
15. C₁₇×#3106	C₂	semidirect
16. C₁₇×#3102	C₂	semidirect
17. C₁₇×#2965	C₂	semidirect
18. C₄×C₁₇×#137	C₂	semidirect
19. C₄×C₁₇×#135	C₂	semidirect
307. Q₁₆×C₁₇	#41	semidirect
381. #61443	C₁₇	direct (N × H)
444. #3480	C₂×C₁₇	semidirect
445. #3403	C₂×C₁₇	semidirect
446. #3390	C₂×C₁₇	semidirect
447. #3371	C₂×C₁₇	semidirect
448. #3355	C₂×C₁₇	semidirect
449. #3350	C₂×C₁₇	semidirect
450. #3326	C₂×C₁₇	semidirect
451. #3313	C₂×C₁₇	semidirect
452. #3309	C₂×C₁₇	semidirect
453. #3277	C₂×C₁₇	semidirect
454. #3271	C₂×C₁₇	semidirect
455. #3171	C₂×C₁₇	semidirect
456. #3168	C₂×C₁₇	semidirect
457. #3108	C₂×C₁₇	semidirect
458. #3106	C₂×C₁₇	semidirect
459. #3102	C₂×C₁₇	semidirect
460. #2965	C₂×C₁₇	semidirect
461. C₄×#137	C₂×C₁₇	semidirect
462. C₄×#135	C₂×C₁₇	semidirect
745. C₁₇	#61443	direct (N × H)
787. Q₁₆	#41×C₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×#3480	2
C₁₇×#3403	2
C₁₇×#3390	2
C₁₇×#3371	2
C₁₇×#3355	2
C₁₇×#3350	2
C₁₇×#3326	2
C₁₇×#3313	2
C₁₇×#3309	2
C₁₇×#3277	2
C₁₇×#3271	2
C₁₇×#3171	2
C₁₇×#3168	2
C₁₇×#3108	2
C₁₇×#3106	2
C₁₇×#3102	2
C₁₇×#2965	2
C₄×C₁₇×#137	2
C₄×C₁₇×#135	2
#61443	17

Subgroups — C17×#61443 #16919187

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61443 #16919187