Subgroups — C₁₇×#17680 #16875424

Order 4352.

878 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3515	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#2970	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#2923	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#1537	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1535	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1535	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1534	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#1532	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1532	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1531	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1529	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1528	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1528	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#1524	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₇×#330	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₇×#557	C₄	1	1	yes	characteristic
17	C₁₇×#554	C₄	1	1	yes	characteristic
18	C₁₇×#554	C₄	1	1	yes	characteristic
19	C₁₇×#553	C₄	1	1	yes	characteristic
20	C₁₇×#553	C₄	1	1	yes	characteristic
21	C₁₇×#552	—	2	1	no	—
22	C₁₇×#552	—	2	1	no	—
23	C₁₇×#552	—	2	1	no	—
24	C₁₇×#552	C₄	1	1	yes	characteristic
25	C₁₇×#552	C₄	1	1	yes	characteristic
26	C₁₇×#547	—	2	1	no	—
27	C₁₇×#547	C₄	1	1	yes	characteristic
28	C₁₇×#541	—	2	1	no	—
29	C₁₇×#539	—	2	1	no	—
30	C₁₇×#539	—	2	1	no	—
31	C₁₇×#533	C₂²	1	1	yes	characteristic
32	C₁₇×#529	C₂²	1	1	yes	characteristic
33	C₁₇×#529	C₂²	1	1	yes	characteristic
34	C₁₇×#529	C₂²	1	1	yes	characteristic
35	C₂×C₁₇×#125	C₂²	1	1	yes	characteristic
36	C₂×C₁₇×#125	C₂²	1	1	yes	characteristic
37	C₁₇×#520	—	2	1	no	—
38	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
39	C₁₇×#446	—	2	1	no	—
40	C₁₇×#435	—	2	1	no	—
41	C₁₇×#435	—	2	1	no	—
42	C₈×D₄×C₁₇	—	2	1	no	—
43	C₁₇×#433	—	2	1	no	—
44	C₁₇×#433	—	2	1	no	—
45	C₁₇×#432	C₂²	1	1	yes	characteristic
46	C₁₇×#432	C₂²	1	1	yes	characteristic
47	C₁₇×#432	C₂²	1	1	yes	characteristic
48	C₁₇×#432	C₂²	1	1	yes	characteristic
49	C₁₇×#432	C₂²	1	1	yes	characteristic
50	C₁₇×#432	C₂²	1	1	yes	characteristic
51	C₁₇×#432	C₂²	1	1	yes	characteristic
52	C₁₇×#424	—	2	1	no	—
53	C₁₇×#408	—	2	1	no	—
54	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
55	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
56	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
57	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
58	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
59	C₁₇×#330	C₂²	1	1	yes	characteristic
60	C₁₇×#330	C₂²	1	1	yes	characteristic
61	C₁₇×#330	C₂²	1	1	yes	characteristic
62	C₁₇×#330	C₂²	1	1	yes	characteristic
63	C₁₇×#330	C₂²	1	1	yes	characteristic
64	C₁₇×#330	C₂²	1	1	yes	characteristic
65	C₁₇×#330	C₂²	1	1	yes	characteristic
66	C₁₇×#330	C₂²	1	1	yes	characteristic
67	C₁₇×#330	C₂²	1	1	yes	characteristic
68	C₁₇×#330	C₂²	1	1	yes	characteristic
69	C₁₇×#330	C₂²	1	1	yes	characteristic
70	C₁₇×#330	C₂²	1	1	yes	characteristic
71	C₁₇×#329	C₂²	1	1	yes	characteristic
72	C₁₇×#329	C₂²	1	1	yes	characteristic
73	C₁₇×#329	C₂²	1	1	yes	characteristic
74	C₁₇×#329	C₂²	1	1	yes	characteristic
75	C₂×#41×C₁₇	—	2	1	no	—
76	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
77	C₂×M₁₆×C₁₇	—	2	1	no	—
78	C₂×M₁₆×C₁₇	—	2	1	no	—
79	C₂²×C₈×C₁₇	—	2	1	no	—
80	C₂²×C₈×C₁₇	—	2	1	no	—
81	C₂²×C₈×C₁₇	—	2	1	no	—
82	C₁₇×C₄⋊Q₈	—	2	1	no	—
83	C₁₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
84	C₁₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
85	C₁₇×#126	—	2	1	no	—
86	C₁₇×#126	—	2	1	no	—
87	C₁₇×#126	—	2	1	no	—
88	C₁₇×#126	—	2	1	no	—
89	C₁₇×#126	—	2	1	no	—
90	C₁₇×#126	—	2	1	no	—
91	C₁₇×#126	—	2	1	no	—
92	C₁₇×#125	—	2	1	no	—
93	C₁₇×#125	—	2	1	no	—
94	C₁₇×#125	—	2	1	no	—
95	C₁₇×#125	—	2	1	no	—
96	C₁₇×#125	—	2	1	no	—
97	C₁₇×#125	—	2	1	no	—
98	C₁₇×#125	—	2	1	no	—
99	C₁₇×#125	—	2	1	no	—
100	C₁₇×#125	—	2	1	no	—
101	C₁₇×#125	C₂×C₄	1	1	yes	characteristic
102	C₁₇×#125	C₂×C₄	1	1	yes	characteristic
103	C₁₇×#125	C₂×C₄	1	1	yes	characteristic
104	C₁₇×#125	C₂×C₄	1	1	yes	characteristic
105	C₁₇×#125	C₂³	1	1	yes	characteristic
106	C₁₇×#125	C₂³	1	1	yes	characteristic
107	C₁₇×#125	C₂³	1	1	yes	characteristic
108	C₁₇×#124	C₂³	1	1	yes	characteristic
109	C₁₇×#123	—	2	1	no	—
110	C₁₇×#123	—	2	1	no	—
111	C₁₇×#123	—	2	1	no	—
112	C₁₇×#123	—	2	1	no	—
113	C₁₇×#123	—	2	1	no	—
114	C₁₇×#123	—	2	1	no	—
115	C₁₇×#123	—	2	1	no	—
116	C₁₇×#123	—	2	1	no	—
117	C₁₇×#123	—	2	1	no	—
118	C₁₇×C₂²⋊Q₈	—	2	1	no	—
119	C₁₇×C₂²⋊Q₈	—	2	1	no	—
120	C₁₇×C₂²⋊Q₈	—	2	1	no	—
121	C₁₇×C₂²⋊Q₈	—	2	1	no	—
122	C₁₇×C₂²⋊Q₈	—	2	1	no	—
123	C₁₇×C₂²⋊Q₈	—	2	1	no	—
124	C₁₇×C₂²⋊Q₈	—	2	1	no	—
125	C₁₇×C₂²⋊Q₈	—	2	1	no	—
126	C₁₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
127	C₁₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
128	C₁₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
129	C₁₇×#121	—	2	1	no	—
130	C₁₇×#121	—	2	1	no	—
131	C₁₇×#121	C₂×C₄	1	1	yes	characteristic
132	C₁₇×#121	C₂×C₄	1	1	yes	characteristic
133	C₁₇×#121	C₂×C₄	1	1	yes	characteristic
134	C₄×Q₈×C₁₇	—	2	1	no	—
135	C₄×Q₈×C₁₇	—	2	1	no	—
136	C₄×Q₈×C₁₇	—	2	1	no	—
137	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
138	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
139	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
140	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
141	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
142	C₄×D₄×C₁₇	—	2	1	no	—
143	C₄×D₄×C₁₇	—	2	1	no	—
144	C₄×D₄×C₁₇	—	2	1	no	—
145	C₄×D₄×C₁₇	—	2	1	no	—
146	C₄×D₄×C₁₇	—	2	1	no	—
147	C₄×D₄×C₁₇	—	2	1	no	—
148	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
149	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
150	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
151	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
152	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
153	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
154	C₄×D₄×C₁₇	D₄	1	1	yes	characteristic
155	C₄×D₄×C₁₇	D₄	1	1	yes	characteristic
156	C₄×D₄×C₁₇	D₄	1	1	yes	characteristic
157	C₁₇×#117	—	2	1	no	—
158	C₁₇×#117	—	2	1	no	—
159	C₁₇×#117	—	2	1	no	—
160	C₁₇×#117	—	2	1	no	—
161	C₁₇×#117	—	2	1	no	—
162	C₁₇×#117	C₂×C₄	1	1	yes	characteristic
163	C₁₇×#117	C₂×C₄	1	1	yes	characteristic
164	C₁₇×#117	D₄	1	1	yes	characteristic
165	C₁₇×#117	D₄	1	1	yes	characteristic
166	C₁₇×#117	D₄	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
168	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
169	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
170	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
171	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
172	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
176	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
179	C₁₇×C₄⋊C₈	—	2	1	no	—
180	C₁₇×C₄⋊C₈	—	2	1	no	—
181	C₁₇×C₄⋊C₈	—	2	1	no	—
182	C₁₇×C₄⋊C₈	—	2	1	no	—
183	C₁₇×C₄⋊C₈	—	2	1	no	—
184	C₁₇×C₄⋊C₈	—	2	1	no	—
185	C₁₇×C₄⋊C₈	—	2	1	no	—
186	C₁₇×C₂²⋊C₈	—	2	1	no	—
187	C₁₇×C₂²⋊C₈	—	2	1	no	—
188	C₁₇×C₂²⋊C₈	—	2	1	no	—
189	C₁₇×C₂²⋊C₈	—	2	1	no	—
190	C₁₇×C₂²⋊C₈	—	2	1	no	—
191	C₁₇×C₂²⋊C₈	—	2	1	no	—
192	C₁₇×C₂²⋊C₈	—	2	1	no	—
193	C₁₇×#97	—	2	1	no	—
194	C₁₇×#97	—	2	1	no	—
195	C₁₇×#97	—	2	1	no	—
196	C₁₇×#97	C₂³	1	1	yes	characteristic
197	C₁₇×#97	C₂³	1	1	yes	characteristic
198	C₁₇×#97	C₂³	1	1	yes	characteristic
199	C₁₇×#97	C₂³	1	1	yes	characteristic
200	C₁₇×#97	C₂³	1	1	yes	characteristic
201	C₁₇×#97	C₂³	1	1	yes	characteristic
202	C₁₇×#97	C₂³	1	1	yes	characteristic
203	C₁₇×#97	C₂³	1	1	yes	characteristic
204	C₄×C₈×C₁₇	—	2	1	no	—
205	C₄×C₈×C₁₇	—	2	1	no	—
206	#41×C₁₇	—	4	2	no	—
207	#41×C₁₇	—	4	4	no	—
208	C₂×Q₈×C₁₇	—	2	1	no	—
209	C₂×Q₈×C₁₇	—	2	1	no	—
210	C₂×Q₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
211	C₂×Q₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
212	C₂×D₄×C₁₇	—	2	1	no	—
213	C₂×D₄×C₁₇	—	2	1	no	—
214	C₂×D₄×C₁₇	—	2	1	no	—
215	C₂×D₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
216	C₂×D₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
217	C₂×D₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
218	C₂×D₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
219	C₂²×C₄×C₁₇	—	2	1	no	—
220	C₂²×C₄×C₁₇	—	2	1	no	—
221	C₂²×C₄×C₁₇	—	2	1	no	—
222	C₂²×C₄×C₁₇	—	2	1	no	—
223	C₂²×C₄×C₁₇	—	2	1	no	—
224	C₂²×C₄×C₁₇	—	2	1	no	—
225	C₂²×C₄×C₁₇	—	2	1	no	—
226	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
227	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
228	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
229	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
235	M₁₆×C₁₇	—	4	2	no	—
236	M₁₆×C₁₇	—	4	2	no	—
237	C₂×C₈×C₁₇	—	2	1	no	—
238	C₂×C₈×C₁₇	—	2	1	no	—
239	C₂×C₈×C₁₇	—	2	1	no	—
240	C₂×C₈×C₁₇	—	2	1	no	—
241	C₂×C₈×C₁₇	—	2	1	no	—
242	C₂×C₈×C₁₇	—	2	1	no	—
243	C₂×C₈×C₁₇	—	2	1	no	—
244	C₂×C₈×C₁₇	—	2	1	no	—
245	C₂×C₈×C₁₇	—	4	2	no	—
246	C₂×C₈×C₁₇	—	4	2	no	—
247	C₂×C₈×C₁₇	—	4	2	no	—
248	C₄⋊C₄×C₁₇	—	2	1	no	—
249	C₄⋊C₄×C₁₇	—	2	1	no	—
250	C₄⋊C₄×C₁₇	—	2	1	no	—
251	C₄⋊C₄×C₁₇	—	2	1	no	—
252	C₄⋊C₄×C₁₇	—	2	1	no	—
253	C₄⋊C₄×C₁₇	—	2	1	no	—
254	C₄⋊C₄×C₁₇	—	2	1	no	—
255	C₄⋊C₄×C₁₇	—	2	1	no	—
256	C₄⋊C₄×C₁₇	—	2	1	no	—
257	C₄⋊C₄×C₁₇	—	2	1	no	—
258	C₄⋊C₄×C₁₇	—	2	1	no	—
259	C₄⋊C₄×C₁₇	—	2	1	no	—
260	C₄⋊C₄×C₁₇	—	2	1	no	—
261	C₄⋊C₄×C₁₇	—	2	1	no	—
262	C₄⋊C₄×C₁₇	—	2	1	no	—
263	C₄⋊C₄×C₁₇	—	2	1	no	—
264	C₄⋊C₄×C₁₇	—	2	1	no	—
265	C₄⋊C₄×C₁₇	—	2	1	no	—
266	C₄⋊C₄×C₁₇	—	2	1	no	—
267	C₄⋊C₄×C₁₇	—	2	1	no	—
268	C₄⋊C₄×C₁₇	—	2	1	no	—
269	C₄⋊C₄×C₁₇	—	2	1	no	—
270	C₄⋊C₄×C₁₇	—	2	1	no	—
271	C₄⋊C₄×C₁₇	—	2	1	no	—
272	C₄⋊C₄×C₁₇	—	2	1	no	—
273	C₄⋊C₄×C₁₇	—	2	1	no	—
274	C₄⋊C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
275	C₄⋊C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
276	C₄⋊C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
277	C₄⋊C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
278	C₄⋊C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
279	C₄⋊C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
280	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
281	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
282	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
283	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
284	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
285	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
286	C₂²⋊C₄×C₁₇	—	2	1	no	—
287	C₂²⋊C₄×C₁₇	—	2	1	no	—
288	C₂²⋊C₄×C₁₇	—	2	1	no	—
289	C₂²⋊C₄×C₁₇	—	2	1	no	—
290	C₂²⋊C₄×C₁₇	—	2	1	no	—
291	C₂²⋊C₄×C₁₇	—	2	1	no	—
292	C₂²⋊C₄×C₁₇	—	2	1	no	—
293	C₂²⋊C₄×C₁₇	—	2	1	no	—
294	C₂²⋊C₄×C₁₇	—	2	1	no	—
295	C₂²⋊C₄×C₁₇	—	2	1	no	—
296	C₂²⋊C₄×C₁₇	—	2	1	no	—
297	C₂²⋊C₄×C₁₇	—	2	1	no	—
298	C₂²⋊C₄×C₁₇	—	2	1	no	—
299	C₂²⋊C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
300	C₂²⋊C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
301	C₂²⋊C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
302	C₂²⋊C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
303	C₂²⋊C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
304	C₂²⋊C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
305	C₄²×C₁₇	—	2	1	no	—
306	C₄²×C₁₇	—	2	1	no	—
307	C₄²×C₁₇	—	2	1	no	—
308	C₄²×C₁₇	—	2	1	no	—
309	C₄²×C₁₇	—	2	1	no	—
310	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
311	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
312	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
313	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
320	#17680	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
321	C₂³×C₁₇	—	2	1	no	—
322	C₂³×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
323	C₂³×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
324	C₂³×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
325	Q₈×C₁₇	—	4	1	no	—
326	Q₈×C₁₇	—	4	1	no	—
327	Q₈×C₁₇	—	4	2	no	—
328	Q₈×C₁₇	—	8	1	no	—
329	D₄×C₁₇	—	2	2	no	—
330	D₄×C₁₇	—	2	2	no	—
331	D₄×C₁₇	—	4	1	no	—
332	D₄×C₁₇	—	4	1	no	—
333	D₄×C₁₇	—	4	2	no	—
334	D₄×C₁₇	—	4	2	no	—
335	D₄×C₁₇	—	8	1	no	—
336	C₂×C₄×C₁₇	—	2	2	no	—
337	C₂×C₄×C₁₇	—	2	1	no	—
338	C₂×C₄×C₁₇	—	2	1	no	—
339	C₂×C₄×C₁₇	—	2	1	no	—
340	C₂×C₄×C₁₇	—	2	1	no	—
341	C₂×C₄×C₁₇	—	2	1	no	—
342	C₂×C₄×C₁₇	—	2	1	no	—
343	C₂×C₄×C₁₇	—	2	1	no	—
344	C₂×C₄×C₁₇	—	4	1	no	—
345	C₂×C₄×C₁₇	—	4	1	no	—
346	C₂×C₄×C₁₇	—	4	1	no	—
347	C₂×C₄×C₁₇	—	4	1	no	—
348	C₂×C₄×C₁₇	—	4	1	no	—
349	C₂×C₄×C₁₇	—	4	1	no	—
350	C₂×C₄×C₁₇	—	4	1	no	—
351	C₂×C₄×C₁₇	—	4	1	no	—
352	C₂×C₄×C₁₇	—	4	2	no	—
353	C₂×C₄×C₁₇	—	4	2	no	—
354	C₂×C₄×C₁₇	—	4	2	no	—
355	C₂×C₄×C₁₇	—	8	1	no	—
356	C₂×C₄×C₁₇	—	8	1	no	—
357	C₂×C₄×C₁₇	—	8	1	no	—
358	C₂×C₄×C₁₇	—	8	1	no	—
359	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
360	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
361	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
362	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
363	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
364	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
365	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
366	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
367	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
368	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
369	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
371	C₈×C₁₇	—	2	2	no	—
372	C₈×C₁₇	—	4	1	no	—
373	C₈×C₁₇	—	4	1	no	—
374	C₈×C₁₇	—	4	1	no	—
375	C₈×C₁₇	—	4	1	no	—
376	C₈×C₁₇	—	4	1	no	—
377	C₈×C₁₇	—	4	1	no	—
378	C₈×C₁₇	—	4	1	no	—
379	#3515	C₂×C₁₇	1	1	yes	characteristic
380	#2970	C₂×C₁₇	1	1	yes	characteristic, complemented
381	#2923	C₂×C₁₇	1	1	yes	characteristic, complemented
382	#1537	C₂×C₁₇	1	1	yes	characteristic, complemented
383	#1535	C₂×C₁₇	1	1	yes	characteristic, complemented
384	#1535	C₂×C₁₇	1	1	yes	characteristic, complemented
385	#1534	C₂×C₁₇	1	1	yes	characteristic, complemented
386	#1532	C₂×C₁₇	1	1	yes	characteristic, complemented
387	#1532	C₂×C₁₇	1	1	yes	characteristic, complemented
388	#1531	C₂×C₁₇	1	1	yes	characteristic, complemented
389	#1529	C₂×C₁₇	1	1	yes	characteristic, complemented
390	#1528	C₂×C₁₇	1	1	yes	characteristic, complemented
391	#1528	C₂×C₁₇	1	1	yes	characteristic, complemented
392	#1524	C₂×C₁₇	1	1	yes	characteristic, complemented
393	C₂×#330	C₂×C₁₇	1	1	yes	characteristic, complemented
394	C₂²×C₁₇	—	2	1	no	—
395	C₂²×C₁₇	—	2	1	no	—
396	C₂²×C₁₇	—	2	1	no	—
397	C₂²×C₁₇	—	2	1	no	—
398	C₂²×C₁₇	—	2	1	no	—
399	C₂²×C₁₇	—	2	1	no	—
400	C₂²×C₁₇	—	2	1	no	—
401	C₂²×C₁₇	—	2	1	no	—
402	C₂²×C₁₇	—	4	1	no	—
403	C₂²×C₁₇	—	4	1	no	—
404	C₂²×C₁₇	—	4	1	no	—
405	C₂²×C₁₇	#421	1	2	yes	—
406	C₂²×C₁₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
407	C₄×C₁₇	—	2	1	no	—
408	C₄×C₁₇	—	2	1	no	—
409	C₄×C₁₇	—	2	1	no	—
410	C₄×C₁₇	—	2	1	no	—
411	C₄×C₁₇	—	2	1	no	—
412	C₄×C₁₇	—	2	1	no	—
413	C₄×C₁₇	—	2	1	no	—
414	C₄×C₁₇	—	2	1	no	—
415	C₄×C₁₇	—	2	1	no	—
416	C₄×C₁₇	—	2	1	no	—
417	C₄×C₁₇	—	2	1	no	—
418	C₄×C₁₇	—	2	1	no	—
419	C₄×C₁₇	—	4	1	no	—
420	C₄×C₁₇	—	4	1	no	—
421	C₄×C₁₇	—	4	1	no	—
422	C₄×C₁₇	—	4	1	no	—
423	C₄×C₁₇	—	4	1	no	—
424	C₄×C₁₇	—	4	1	no	—
425	C₄×C₁₇	—	4	1	no	—
426	#557	C₄×C₁₇	1	1	yes	characteristic
427	#554	C₄×C₁₇	1	1	yes	characteristic
428	#554	C₄×C₁₇	1	1	yes	characteristic
429	#553	C₄×C₁₇	1	1	yes	characteristic
430	#553	C₄×C₁₇	1	1	yes	characteristic
431	#552	—	2	1	no	—
432	#552	—	2	1	no	—
433	#552	—	2	1	no	—
434	#552	C₄×C₁₇	1	1	yes	characteristic
435	#552	C₄×C₁₇	1	1	yes	characteristic
436	#547	—	2	1	no	—
437	#547	C₄×C₁₇	1	1	yes	characteristic
438	#541	—	2	1	no	—
439	#539	—	2	1	no	—
440	#539	—	2	1	no	—
441	#533	C₂²×C₁₇	1	1	yes	characteristic
442	#529	C₂²×C₁₇	1	1	yes	characteristic
443	#529	C₂²×C₁₇	1	1	yes	characteristic
444	#529	C₂²×C₁₇	1	1	yes	characteristic
445	C₂×#125	C₂²×C₁₇	1	1	yes	characteristic
446	C₂×#125	C₂²×C₁₇	1	1	yes	characteristic
447	#520	—	2	1	no	—
448	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
449	#446	—	2	1	no	—
450	#435	—	2	1	no	—
451	#435	—	2	1	no	—
452	C₈×D₄	—	2	1	no	—
453	#433	—	2	1	no	—
454	#433	—	2	1	no	—
455	#432	C₂²×C₁₇	1	1	yes	characteristic
456	#432	C₂²×C₁₇	1	1	yes	characteristic
457	#432	C₂²×C₁₇	1	1	yes	characteristic
458	#432	C₂²×C₁₇	1	1	yes	characteristic
459	#432	C₂²×C₁₇	1	1	yes	characteristic
460	#432	C₂²×C₁₇	1	1	yes	characteristic
461	#432	C₂²×C₁₇	1	1	yes	characteristic
462	#424	—	2	1	no	—
463	#408	—	2	1	no	—
464	C₄×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
465	C₄×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
466	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
467	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
468	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
469	#330	C₂²×C₁₇	1	1	yes	characteristic
470	#330	C₂²×C₁₇	1	1	yes	characteristic
471	#330	C₂²×C₁₇	1	1	yes	characteristic
472	#330	C₂²×C₁₇	1	1	yes	characteristic
473	#330	C₂²×C₁₇	1	1	yes	characteristic
474	#330	C₂²×C₁₇	1	1	yes	characteristic
475	#330	C₂²×C₁₇	1	1	yes	characteristic
476	#330	C₂²×C₁₇	1	1	yes	characteristic
477	#330	C₂²×C₁₇	1	1	yes	characteristic
478	#330	C₂²×C₁₇	1	1	yes	characteristic
479	#330	C₂²×C₁₇	1	1	yes	characteristic
480	#330	C₂²×C₁₇	1	1	yes	characteristic
481	#329	C₂²×C₁₇	1	1	yes	characteristic
482	#329	C₂²×C₁₇	1	1	yes	characteristic
483	#329	C₂²×C₁₇	1	1	yes	characteristic
484	#329	C₂²×C₁₇	1	1	yes	characteristic
485	C₂×C₁₇	—	2	2	no	—
486	C₂×C₁₇	—	4	1	no	—
487	C₂×C₁₇	—	4	1	no	—
488	C₂×C₁₇	—	8	1	no	—
489	C₂×C₁₇	#2889	1	1	yes	characteristic
490	C₂×C₁₇	C₂×#421	1	1	yes	characteristic
491	C₂×C₁₇	#2901	1	1	yes	characteristic
492	C₂×#41	—	2	1	no	—
493	C₂×#41	D₄×C₁₇	1	1	yes	characteristic
494	C₂×M₁₆	—	2	1	no	—
495	C₂×M₁₆	—	2	1	no	—
496	C₂²×C₈	—	2	1	no	—
497	C₂²×C₈	—	2	1	no	—
498	C₂²×C₈	—	2	1	no	—
499	C₄⋊Q₈	—	2	1	no	—
500	C₄⋊Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
501	C₄⋊Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
502	#126	—	2	1	no	—
503	#126	—	2	1	no	—
504	#126	—	2	1	no	—
505	#126	—	2	1	no	—
506	#126	—	2	1	no	—
507	#126	—	2	1	no	—
508	#126	—	2	1	no	—
509	#125	—	2	1	no	—
510	#125	—	2	1	no	—
511	#125	—	2	1	no	—
512	#125	—	2	1	no	—
513	#125	—	2	1	no	—
514	#125	—	2	1	no	—
515	#125	—	2	1	no	—
516	#125	—	2	1	no	—
517	#125	—	2	1	no	—
518	#125	C₂×C₄×C₁₇	1	1	yes	characteristic
519	#125	C₂×C₄×C₁₇	1	1	yes	characteristic
520	#125	C₂×C₄×C₁₇	1	1	yes	characteristic
521	#125	C₂×C₄×C₁₇	1	1	yes	characteristic
522	#125	C₂³×C₁₇	1	1	yes	characteristic
523	#125	C₂³×C₁₇	1	1	yes	characteristic
524	#125	C₂³×C₁₇	1	1	yes	characteristic
525	#124	C₂³×C₁₇	1	1	yes	characteristic
526	#123	—	2	1	no	—
527	#123	—	2	1	no	—
528	#123	—	2	1	no	—
529	#123	—	2	1	no	—
530	#123	—	2	1	no	—
531	#123	—	2	1	no	—
532	#123	—	2	1	no	—
533	#123	—	2	1	no	—
534	#123	—	2	1	no	—
535	C₂²⋊Q₈	—	2	1	no	—
536	C₂²⋊Q₈	—	2	1	no	—
537	C₂²⋊Q₈	—	2	1	no	—
538	C₂²⋊Q₈	—	2	1	no	—
539	C₂²⋊Q₈	—	2	1	no	—
540	C₂²⋊Q₈	—	2	1	no	—
541	C₂²⋊Q₈	—	2	1	no	—
542	C₂²⋊Q₈	—	2	1	no	—
543	C₂²⋊Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
544	C₂²⋊Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
545	C₂²⋊Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
546	#121	—	2	1	no	—
547	#121	—	2	1	no	—
548	#121	C₂×C₄×C₁₇	1	1	yes	characteristic
549	#121	C₂×C₄×C₁₇	1	1	yes	characteristic
550	#121	C₂×C₄×C₁₇	1	1	yes	characteristic
551	C₄×Q₈	—	2	1	no	—
552	C₄×Q₈	—	2	1	no	—
553	C₄×Q₈	—	2	1	no	—
554	C₄×Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
555	C₄×Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
556	C₄×Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
557	C₄×Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
558	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
559	C₄×D₄	—	2	1	no	—
560	C₄×D₄	—	2	1	no	—
561	C₄×D₄	—	2	1	no	—
562	C₄×D₄	—	2	1	no	—
563	C₄×D₄	—	2	1	no	—
564	C₄×D₄	—	2	1	no	—
565	C₄×D₄	C₂×C₄×C₁₇	1	1	yes	characteristic
566	C₄×D₄	C₂×C₄×C₁₇	1	1	yes	characteristic
567	C₄×D₄	C₂×C₄×C₁₇	1	1	yes	characteristic
568	C₄×D₄	C₂×C₄×C₁₇	1	1	yes	characteristic
569	C₄×D₄	C₂×C₄×C₁₇	1	1	yes	characteristic
570	C₄×D₄	C₂×C₄×C₁₇	1	1	yes	characteristic
571	C₄×D₄	D₄×C₁₇	1	1	yes	characteristic
572	C₄×D₄	D₄×C₁₇	1	1	yes	characteristic
573	C₄×D₄	D₄×C₁₇	1	1	yes	characteristic
574	#117	—	2	1	no	—
575	#117	—	2	1	no	—
576	#117	—	2	1	no	—
577	#117	—	2	1	no	—
578	#117	—	2	1	no	—
579	#117	C₂×C₄×C₁₇	1	1	yes	characteristic
580	#117	C₂×C₄×C₁₇	1	1	yes	characteristic
581	#117	D₄×C₁₇	1	1	yes	characteristic
582	#117	D₄×C₁₇	1	1	yes	characteristic
583	#117	D₄×C₁₇	1	1	yes	characteristic
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	1	no	—
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	—	2	1	no	—
589	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
593	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
594	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
595	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
596	C₄⋊C₈	—	2	1	no	—
597	C₄⋊C₈	—	2	1	no	—
598	C₄⋊C₈	—	2	1	no	—
599	C₄⋊C₈	—	2	1	no	—
600	C₄⋊C₈	—	2	1	no	—
601	C₄⋊C₈	—	2	1	no	—
602	C₄⋊C₈	—	2	1	no	—
603	C₂²⋊C₈	—	2	1	no	—
604	C₂²⋊C₈	—	2	1	no	—
605	C₂²⋊C₈	—	2	1	no	—
606	C₂²⋊C₈	—	2	1	no	—
607	C₂²⋊C₈	—	2	1	no	—
608	C₂²⋊C₈	—	2	1	no	—
609	C₂²⋊C₈	—	2	1	no	—
610	#97	—	2	1	no	—
611	#97	—	2	1	no	—
612	#97	—	2	1	no	—
613	#97	C₂³×C₁₇	1	1	yes	characteristic
614	#97	C₂³×C₁₇	1	1	yes	characteristic
615	#97	C₂³×C₁₇	1	1	yes	characteristic
616	#97	C₂³×C₁₇	1	1	yes	characteristic
617	#97	C₂³×C₁₇	1	1	yes	characteristic
618	#97	C₂³×C₁₇	1	1	yes	characteristic
619	#97	C₂³×C₁₇	1	1	yes	characteristic
620	#97	C₂³×C₁₇	1	1	yes	characteristic
621	C₄×C₈	—	2	1	no	—
622	C₄×C₈	—	2	1	no	—
623	C₁₇	#17680	1	1	yes	characteristic, direct product factor, Sylow
624	#41	—	4	2	no	—
625	#41	—	4	4	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
629	C₂×Q₈	C₂²×C₄×C₁₇	1	1	yes	characteristic
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
634	C₂×D₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
635	C₂×D₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
636	C₂×D₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
645	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
646	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
647	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
648	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
649	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
650	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
651	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
652	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
653	M₁₆	—	4	2	no	—
654	M₁₆	—	4	2	no	—
655	C₂×C₈	—	2	1	no	—
656	C₂×C₈	—	2	1	no	—
657	C₂×C₈	—	2	1	no	—
658	C₂×C₈	—	2	1	no	—
659	C₂×C₈	—	2	1	no	—
660	C₂×C₈	—	2	1	no	—
661	C₂×C₈	—	2	1	no	—
662	C₂×C₈	—	2	1	no	—
663	C₂×C₈	—	4	2	no	—
664	C₂×C₈	—	4	2	no	—
665	C₂×C₈	—	4	2	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	1	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
693	C₄⋊C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
694	C₄⋊C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
695	C₄⋊C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
696	C₄⋊C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
697	C₄⋊C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
698	C₄⋊C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
699	C₄⋊C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
700	C₄⋊C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
701	C₄⋊C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
702	C₄⋊C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
703	C₄⋊C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
704	C₂²⋊C₄	—	2	1	no	—
705	C₂²⋊C₄	—	2	1	no	—
706	C₂²⋊C₄	—	2	1	no	—
707	C₂²⋊C₄	—	2	1	no	—
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	1	no	—
710	C₂²⋊C₄	—	2	1	no	—
711	C₂²⋊C₄	—	2	1	no	—
712	C₂²⋊C₄	—	2	1	no	—
713	C₂²⋊C₄	—	2	1	no	—
714	C₂²⋊C₄	—	2	1	no	—
715	C₂²⋊C₄	—	2	1	no	—
716	C₂²⋊C₄	—	2	1	no	—
717	C₂²⋊C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
718	C₂²⋊C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
719	C₂²⋊C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
720	C₂²⋊C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
721	C₂²⋊C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
722	C₂²⋊C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
723	C₄²	—	2	1	no	—
724	C₄²	—	2	1	no	—
725	C₄²	—	2	1	no	—
726	C₄²	—	2	1	no	—
727	C₄²	—	2	1	no	—
728	C₄²	C₂²×C₄×C₁₇	1	1	yes	characteristic
729	C₄²	C₂²×C₄×C₁₇	1	1	yes	characteristic
730	C₄²	C₂²×C₄×C₁₇	1	1	yes	characteristic
731	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
732	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
733	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
734	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
735	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
736	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
737	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
738	C₂³	—	2	1	no	—
739	C₂³	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
740	C₂³	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
741	C₂³	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
742	Q₈	—	4	1	no	—
743	Q₈	—	4	1	no	—
744	Q₈	—	4	2	no	—
745	Q₈	—	8	1	no	—
746	D₄	—	2	2	no	—
747	D₄	—	2	2	no	—
748	D₄	—	4	1	no	—
749	D₄	—	4	1	no	—
750	D₄	—	4	2	no	—
751	D₄	—	4	2	no	—
752	D₄	—	8	1	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	2	no	—
770	C₂×C₄	—	4	2	no	—
771	C₂×C₄	—	4	2	no	—
772	C₂×C₄	—	8	1	no	—
773	C₂×C₄	—	8	1	no	—
774	C₂×C₄	—	8	1	no	—
775	C₂×C₄	—	8	1	no	—
776	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
777	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
778	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
779	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
780	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
781	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
782	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
783	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
784	C₂×C₄	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
785	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
786	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
787	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
788	C₈	—	2	2	no	—
789	C₈	—	4	1	no	—
790	C₈	—	4	1	no	—
791	C₈	—	4	1	no	—
792	C₈	—	4	1	no	—
793	C₈	—	4	1	no	—
794	C₈	—	4	1	no	—
795	C₈	—	4	1	no	—
796	C₂²	—	2	1	no	—
797	C₂²	—	2	1	no	—
798	C₂²	—	2	1	no	—
799	C₂²	—	2	1	no	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	4	1	no	—
807	C₂²	C₁₇×#421	1	2	yes	—
808	C₂²	C₂²×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
809	C₄	—	2	1	no	—
810	C₄	—	2	1	no	—
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	1	no	—
814	C₄	—	2	1	no	—
815	C₄	—	2	1	no	—
816	C₄	—	2	1	no	—
817	C₄	—	2	1	no	—
818	C₄	—	2	1	no	—
819	C₄	—	2	1	no	—
820	C₄	—	2	1	no	—
821	C₄	—	4	1	no	—
822	C₄	—	4	1	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	1	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	1	no	—
827	C₄	—	4	1	no	—
828	C₂	—	2	2	no	—
829	C₂	—	4	1	no	—
830	C₂	—	4	1	no	—
831	C₂	—	8	1	no	—
832	C₂	C₁₇×#2889	1	1	yes	characteristic
833	C₂	C₂×C₁₇×#421	1	1	yes	characteristic
834	C₂	C₁₇×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₇
Frattini, cosocle	C₄²	C₂⁴×C₁₇
prime radical	C₁₇×#3515	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄×#41×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₇×#2970	C₂	semidirect
3. C₁₇×#2923	C₂	semidirect
4. C₁₇×#1537	C₂	semidirect
5. C₁₇×#1535	C₂	semidirect
6. C₁₇×#1535	C₂	semidirect
7. C₁₇×#1534	C₂	semidirect
8. C₁₇×#1532	C₂	semidirect
9. C₁₇×#1532	C₂	semidirect
10. C₁₇×#1531	C₂	semidirect
11. C₁₇×#1529	C₂	semidirect
12. C₁₇×#1528	C₂	semidirect
13. C₁₇×#1528	C₂	semidirect
14. C₁₇×#1524	C₂	semidirect
15. C₂×C₁₇×#330	C₂	semidirect
320. #17680	C₁₇	direct (N × H)
380. #2970	C₂×C₁₇	semidirect
381. #2923	C₂×C₁₇	semidirect
382. #1537	C₂×C₁₇	semidirect
383. #1535	C₂×C₁₇	semidirect
384. #1535	C₂×C₁₇	semidirect
385. #1534	C₂×C₁₇	semidirect
386. #1532	C₂×C₁₇	semidirect
387. #1532	C₂×C₁₇	semidirect
388. #1531	C₂×C₁₇	semidirect
389. #1529	C₂×C₁₇	semidirect
390. #1528	C₂×C₁₇	semidirect
391. #1528	C₂×C₁₇	semidirect
392. #1524	C₂×C₁₇	semidirect
393. C₂×#330	C₂×C₁₇	semidirect
623. C₁₇	#17680	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×#3515	2
C₁₇×#2970	2
C₁₇×#2923	2
C₁₇×#1537	2
C₁₇×#1535	2
C₁₇×#1534	2
C₁₇×#1532	2
C₁₇×#1531	2
C₁₇×#1529	2
C₁₇×#1528	2
C₁₇×#1524	2
C₂×C₁₇×#330	2
#17680	17

Subgroups — C17×#17680 #16875424

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#17680 #16875424